policy|kernel3=Classical.choice,Quot.sound,propext|apexExtra=ed25519.Signature,ed25519.Signature.r_bytes,ed25519.Signature.s_bytes,ed_sigs.sha512_hash3|specPrefix=Proofs.
cert|CurveFieldProofs.fieldImplementation|cone=Classical.choice,Quot.sound,propext|type=CurveFieldProofs.IsFieldImplementation
cert|CurveFieldProofs.edwardsImplementation|cone=Classical.choice,Quot.sound,propext|type=CurveFieldProofs.IsEdwardsImplementation
cert|CurveFieldProofs.naf_table_spec|cone=Classical.choice,Quot.sound,propext|type=∀ (A : CurveFieldProofs.EdPoint) (hA : CurveFieldProofs.ExtValid A) (hcA : CurveFieldProofs.OnCurveExt A), @Aeneas.Std.WP.spec.{0} (curve25519.window.NafLookupTable5 curve25519.backend.serial.curve_models.ProjectiveNielsPoint) (curve25519.window.NafLookupTable5ProjectiveNielsPoint.Insts.CoreConvertFromSharedAEdwardsPoint.from A) fun (tbl : curve25519.window.NafLookupTable5 curve25519.backend.serial.curve_models.ProjectiveNielsPoint) => @Exists.{1} curve25519.backend.serial.curve_models.ProjectiveNielsPoint fun (e0 : curve25519.backend.serial.curve_models.ProjectiveNielsPoint) => @Exists.{1} curve25519.backend.serial.curve_models.ProjectiveNielsPoint fun (e1 : curve25519.backend.serial.curve_models.ProjectiveNielsPoint) => @Exists.{1} curve25519.backend.serial.curve_models.ProjectiveNielsPoint fun (e2 : curve25519.backend.serial.curve_models.ProjectiveNielsPoint) => @Exists.{1} curve25519.backend.serial.curve_models.ProjectiveNielsPoint fun (e3 : curve25519.backend.serial.curve_models.ProjectiveNielsPoint) => @Exists.{1} curve25519.backend.serial.curve_models.ProjectiveNielsPoint fun (e4 : curve25519.backend.serial.curve_models.ProjectiveNielsPoint) => @Exists.{1} curve25519.backend.serial.curve_models.ProjectiveNielsPoint fun (e5 : curve25519.backend.serial.curve_models.ProjectiveNielsPoint) => @Exists.{1} curve25519.backend.serial.curve_models.ProjectiveNielsPoint fun (e6 : curve25519.backend.serial.curve_models.ProjectiveNielsPoint) => @Exists.{1} curve25519.backend.serial.curve_models.ProjectiveNielsPoint fun (e7 : curve25519.backend.serial.curve_models.ProjectiveNielsPoint) => And (@Eq.{1} (List.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint) (CurveFieldProofs.tblEntries tbl) (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e0 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e1 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e2 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e3 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e4 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e5 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e6 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e7 (@List.nil.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint)))))))))) (And (CurveFieldProofs.NafEntryOf e0 A (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0)))) (And (CurveFieldProofs.NafEntryOf e1 A (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) (And (CurveFieldProofs.NafEntryOf e2 A (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2)))) (And (CurveFieldProofs.NafEntryOf e3 A (@OfNat.ofNat.{0} Nat (nat_lit 3) (instOfNatNat (nat_lit 3)))) (And (CurveFieldProofs.NafEntryOf e4 A (@OfNat.ofNat.{0} Nat (nat_lit 4) (instOfNatNat (nat_lit 4)))) (And (CurveFieldProofs.NafEntryOf e5 A (@OfNat.ofNat.{0} Nat (nat_lit 5) (instOfNatNat (nat_lit 5)))) (And (CurveFieldProofs.NafEntryOf e6 A (@OfNat.ofNat.{0} Nat (nat_lit 6) (instOfNatNat (nat_lit 6)))) (CurveFieldProofs.NafEntryOf e7 A (@OfNat.ofNat.{0} Nat (nat_lit 7) (instOfNatNat (nat_lit 7)))))))))))
cert|CurveFieldProofs.naf_select_spec|cone=Classical.choice,Quot.sound,propext|type=∀ (tbl : curve25519.window.NafLookupTable5 curve25519.backend.serial.curve_models.ProjectiveNielsPoint) (x : Aeneas.Std.Usize) (e0 e1 e2 e3 e4 e5 e6 e7 : curve25519.backend.serial.curve_models.ProjectiveNielsPoint) (hl : @Eq.{1} (List.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint) (CurveFieldProofs.tblEntries tbl) (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e0 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e1 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e2 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e3 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e4 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e5 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e6 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e7 (@List.nil.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint)))))))))) (hodd : @Eq.{1} Nat (@HMod.hMod.{0, 0, 0} Nat Nat Nat (@instHMod.{0} Nat Nat.instMod) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize x) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2)))) (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) (hlt : @LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize x) (@OfNat.ofNat.{0} Nat (nat_lit 16) (instOfNatNat (nat_lit 16)))), @Aeneas.Std.WP.spec.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint (@curve25519.window.NafLookupTable5.select curve25519.backend.serial.curve_models.ProjectiveNielsPoint curve25519.backend.serial.curve_models.ProjectiveNielsPoint.Insts.CoreMarkerCopy tbl x) fun (r : curve25519.backend.serial.curve_models.ProjectiveNielsPoint) => And (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize x) (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))) → @Eq.{1} curve25519.backend.serial.curve_models.ProjectiveNielsPoint r e0) (And (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize x) (@OfNat.ofNat.{0} Nat (nat_lit 3) (instOfNatNat (nat_lit 3))) → @Eq.{1} curve25519.backend.serial.curve_models.ProjectiveNielsPoint r e1) (And (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize x) (@OfNat.ofNat.{0} Nat (nat_lit 5) (instOfNatNat (nat_lit 5))) → @Eq.{1} curve25519.backend.serial.curve_models.ProjectiveNielsPoint r e2) (And (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize x) (@OfNat.ofNat.{0} Nat (nat_lit 7) (instOfNatNat (nat_lit 7))) → @Eq.{1} curve25519.backend.serial.curve_models.ProjectiveNielsPoint r e3) (And (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize x) (@OfNat.ofNat.{0} Nat (nat_lit 9) (instOfNatNat (nat_lit 9))) → @Eq.{1} curve25519.backend.serial.curve_models.ProjectiveNielsPoint r e4) (And (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize x) (@OfNat.ofNat.{0} Nat (nat_lit 11) (instOfNatNat (nat_lit 11))) → @Eq.{1} curve25519.backend.serial.curve_models.ProjectiveNielsPoint r e5) (And (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize x) (@OfNat.ofNat.{0} Nat (nat_lit 13) (instOfNatNat (nat_lit 13))) → @Eq.{1} curve25519.backend.serial.curve_models.ProjectiveNielsPoint r e6) (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize x) (@OfNat.ofNat.{0} Nat (nat_lit 15) (instOfNatNat (nat_lit 15))) → @Eq.{1} curve25519.backend.serial.curve_models.ProjectiveNielsPoint r e7)))))))
cert|CurveFieldProofs.proj_double_law|cone=Classical.choice,Quot.sound,propext|type=∀ (p : CurveFieldProofs.ProjPoint) (hp : CurveFieldProofs.ProjValid p) (hcp : CurveFieldProofs.OnCurve (CurveFieldProofs.projX p) (CurveFieldProofs.projY p)), @Aeneas.Std.WP.spec.{0} curve25519.backend.serial.curve_models.CompletedPoint (curve25519.backend.serial.curve_models.ProjectivePoint.double p) fun (t : curve25519.backend.serial.curve_models.CompletedPoint) => And (CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.CompletedPoint.X t) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 54) (instOfNatNat (nat_lit 54))))) (And (CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.CompletedPoint.Y t) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 54) (instOfNatNat (nat_lit 54))))) (And (CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.CompletedPoint.Z t) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 54) (instOfNatNat (nat_lit 54))))) (And (CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.CompletedPoint.T t) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 54) (instOfNatNat (nat_lit 54))))) (And (@Ne.{1} CurveFieldProofs.Fp (CurveFieldProofs.denote (curve25519.backend.serial.curve_models.CompletedPoint.Z t)) (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 0) (@Zero.toOfNat0.{0} CurveFieldProofs.Fp (@MulZeroClass.toZero.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toMulZeroClass.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))))) (And (@Ne.{1} CurveFieldProofs.Fp (CurveFieldProofs.denote (curve25519.backend.serial.curve_models.CompletedPoint.T t)) (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 0) (@Zero.toOfNat0.{0} CurveFieldProofs.Fp (@MulZeroClass.toZero.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toMulZeroClass.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))))) (And (@Eq.{1} CurveFieldProofs.Fp (CurveFieldProofs.complX t) (@Prod.fst.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp (CurveFieldProofs.edAdd (@Prod.mk.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp (CurveFieldProofs.projX p) (CurveFieldProofs.projY p)) (@Prod.mk.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp (CurveFieldProofs.projX p) (CurveFieldProofs.projY p))))) (@Eq.{1} CurveFieldProofs.Fp (CurveFieldProofs.complY t) (@Prod.snd.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp (CurveFieldProofs.edAdd (@Prod.mk.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp (CurveFieldProofs.projX p) (CurveFieldProofs.projY p)) (@Prod.mk.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp (CurveFieldProofs.projX p) (CurveFieldProofs.projY p)))))))))))
cert|CurveFieldProofs.compl_as_projective_law|cone=Classical.choice,Quot.sound,propext|type=∀ (p : CurveFieldProofs.ComplPoint) (hbX : CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.CompletedPoint.X p) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 54) (instOfNatNat (nat_lit 54))))) (hbY : CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.CompletedPoint.Y p) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 54) (instOfNatNat (nat_lit 54))))) (hbZ : CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.CompletedPoint.Z p) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 54) (instOfNatNat (nat_lit 54))))) (hbT : CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.CompletedPoint.T p) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 54) (instOfNatNat (nat_lit 54))))) (hZ0 : @Ne.{1} CurveFieldProofs.Fp (CurveFieldProofs.denote (curve25519.backend.serial.curve_models.CompletedPoint.Z p)) (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 0) (@Zero.toOfNat0.{0} CurveFieldProofs.Fp (@MulZeroClass.toZero.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toMulZeroClass.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))))) (hT0 : @Ne.{1} CurveFieldProofs.Fp (CurveFieldProofs.denote (curve25519.backend.serial.curve_models.CompletedPoint.T p)) (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 0) (@Zero.toOfNat0.{0} CurveFieldProofs.Fp (@MulZeroClass.toZero.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toMulZeroClass.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))))), @Aeneas.Std.WP.spec.{0} curve25519.backend.serial.curve_models.ProjectivePoint (curve25519.backend.serial.curve_models.CompletedPoint.as_projective p) fun (r : curve25519.backend.serial.curve_models.ProjectivePoint) => And (CurveFieldProofs.ProjValid r) (And (@Eq.{1} CurveFieldProofs.Fp (CurveFieldProofs.projX r) (CurveFieldProofs.complX p)) (@Eq.{1} CurveFieldProofs.Fp (CurveFieldProofs.projY r) (CurveFieldProofs.complY p)))
cert|CurveFieldProofs.dsm_step_p_law|cone=Classical.choice,Quot.sound,propext|type=∀ (t : CurveFieldProofs.ComplPoint) (tbl : curve25519.window.NafLookupTable5 curve25519.backend.serial.curve_models.ProjectiveNielsPoint) (d : Aeneas.Std.I8) (A : CurveFieldProofs.EdPoint) (e0 e1 e2 e3 e4 e5 e6 e7 : curve25519.backend.serial.curve_models.ProjectiveNielsPoint) (hl : @Eq.{1} (List.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint) (CurveFieldProofs.tblEntries tbl) (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e0 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e1 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e2 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e3 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e4 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e5 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e6 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e7 (@List.nil.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint)))))))))) (h0 : CurveFieldProofs.NafEntryOf e0 A (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0)))) (h1 : CurveFieldProofs.NafEntryOf e1 A (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) (h2 : CurveFieldProofs.NafEntryOf e2 A (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2)))) (h3 : CurveFieldProofs.NafEntryOf e3 A (@OfNat.ofNat.{0} Nat (nat_lit 3) (instOfNatNat (nat_lit 3)))) (h4 : CurveFieldProofs.NafEntryOf e4 A (@OfNat.ofNat.{0} Nat (nat_lit 4) (instOfNatNat (nat_lit 4)))) (h5 : CurveFieldProofs.NafEntryOf e5 A (@OfNat.ofNat.{0} Nat (nat_lit 5) (instOfNatNat (nat_lit 5)))) (h6 : CurveFieldProofs.NafEntryOf e6 A (@OfNat.ofNat.{0} Nat (nat_lit 6) (instOfNatNat (nat_lit 6)))) (h7 : CurveFieldProofs.NafEntryOf e7 A (@OfNat.ofNat.{0} Nat (nat_lit 7) (instOfNatNat (nat_lit 7)))) (hbX : CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.CompletedPoint.X t) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 54) (instOfNatNat (nat_lit 54))))) (hbY : CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.CompletedPoint.Y t) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 54) (instOfNatNat (nat_lit 54))))) (hbZ : CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.CompletedPoint.Z t) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 54) (instOfNatNat (nat_lit 54))))) (hbT : CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.CompletedPoint.T t) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 54) (instOfNatNat (nat_lit 54))))) (hZ0 : @Ne.{1} CurveFieldProofs.Fp (CurveFieldProofs.denote (curve25519.backend.serial.curve_models.CompletedPoint.Z t)) (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 0) (@Zero.toOfNat0.{0} CurveFieldProofs.Fp (@MulZeroClass.toZero.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toMulZeroClass.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))))) (hT0 : @Ne.{1} CurveFieldProofs.Fp (CurveFieldProofs.denote (curve25519.backend.serial.curve_models.CompletedPoint.T t)) (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 0) (@Zero.toOfNat0.{0} CurveFieldProofs.Fp (@MulZeroClass.toZero.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toMulZeroClass.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))))) (hct : CurveFieldProofs.OnCurve (CurveFieldProofs.complX t) (CurveFieldProofs.complY t)) (hd : Or (@Eq.{1} Int (@Aeneas.Std.IScalar.val Aeneas.Std.IScalarTy.I8 d) (@OfNat.ofNat.{0} Int (nat_lit 0) (@instOfNat (nat_lit 0)))) (@Eq.{1} Int (@HMod.hMod.{0, 0, 0} Int Int Int (@instHMod.{0} Int Int.instMod) (@Aeneas.Std.IScalar.val Aeneas.Std.IScalarTy.I8 d) (@OfNat.ofNat.{0} Int (nat_lit 2) (@instOfNat (nat_lit 2)))) (@OfNat.ofNat.{0} Int (nat_lit 1) (@instOfNat (nat_lit 1))))) (hdlo : @LT.lt.{0} Int Int.instLTInt (@Neg.neg.{0} Int Int.instNegInt (@OfNat.ofNat.{0} Int (nat_lit 16) (@instOfNat (nat_lit 16)))) (@Aeneas.Std.IScalar.val Aeneas.Std.IScalarTy.I8 d)) (hdhi : @LT.lt.{0} Int Int.instLTInt (@Aeneas.Std.IScalar.val Aeneas.Std.IScalarTy.I8 d) (@OfNat.ofNat.{0} Int (nat_lit 16) (@instOfNat (nat_lit 16)))), @Aeneas.Std.WP.spec.{0} curve25519.backend.serial.curve_models.CompletedPoint (curve25519.backend.serial.scalar_mul.vartime_double_base.dsm_step_p t tbl d) fun (r : curve25519.backend.serial.curve_models.CompletedPoint) => And (CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.CompletedPoint.X r) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 54) (instOfNatNat (nat_lit 54))))) (And (CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.CompletedPoint.Y r) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 54) (instOfNatNat (nat_lit 54))))) (And (CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.CompletedPoint.Z r) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 54) (instOfNatNat (nat_lit 54))))) (And (CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.CompletedPoint.T r) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 54) (instOfNatNat (nat_lit 54))))) (And (@Ne.{1} CurveFieldProofs.Fp (CurveFieldProofs.denote (curve25519.backend.serial.curve_models.CompletedPoint.Z r)) (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 0) (@Zero.toOfNat0.{0} CurveFieldProofs.Fp (@MulZeroClass.toZero.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toMulZeroClass.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))))) (And (@Ne.{1} CurveFieldProofs.Fp (CurveFieldProofs.denote (curve25519.backend.serial.curve_models.CompletedPoint.T r)) (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 0) (@Zero.toOfNat0.{0} CurveFieldProofs.Fp (@MulZeroClass.toZero.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toMulZeroClass.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))))) (And (CurveFieldProofs.OnCurve (CurveFieldProofs.complX r) (CurveFieldProofs.complY r)) (@Eq.{1} (Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) (@Prod.mk.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp (CurveFieldProofs.complX r) (CurveFieldProofs.complY r)) (CurveFieldProofs.edDigit (CurveFieldProofs.edPt A) (@Aeneas.Std.IScalar.val Aeneas.Std.IScalarTy.I8 d) (@Prod.mk.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp (CurveFieldProofs.complX t) (CurveFieldProofs.complY t))))))))))
cert|CurveFieldProofs.dsm_step_b_law|cone=Classical.choice,Quot.sound,propext|type=∀ (t : CurveFieldProofs.ComplPoint) (tbl : curve25519.window.NafLookupTable5 curve25519.backend.serial.curve_models.ProjectiveNielsPoint) (d : Aeneas.Std.I8) (A : CurveFieldProofs.EdPoint) (e0 e1 e2 e3 e4 e5 e6 e7 : curve25519.backend.serial.curve_models.ProjectiveNielsPoint) (hl : @Eq.{1} (List.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint) (CurveFieldProofs.tblEntries tbl) (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e0 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e1 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e2 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e3 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e4 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e5 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e6 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e7 (@List.nil.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint)))))))))) (h0 : CurveFieldProofs.NafEntryOf e0 A (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0)))) (h1 : CurveFieldProofs.NafEntryOf e1 A (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) (h2 : CurveFieldProofs.NafEntryOf e2 A (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2)))) (h3 : CurveFieldProofs.NafEntryOf e3 A (@OfNat.ofNat.{0} Nat (nat_lit 3) (instOfNatNat (nat_lit 3)))) (h4 : CurveFieldProofs.NafEntryOf e4 A (@OfNat.ofNat.{0} Nat (nat_lit 4) (instOfNatNat (nat_lit 4)))) (h5 : CurveFieldProofs.NafEntryOf e5 A (@OfNat.ofNat.{0} Nat (nat_lit 5) (instOfNatNat (nat_lit 5)))) (h6 : CurveFieldProofs.NafEntryOf e6 A (@OfNat.ofNat.{0} Nat (nat_lit 6) (instOfNatNat (nat_lit 6)))) (h7 : CurveFieldProofs.NafEntryOf e7 A (@OfNat.ofNat.{0} Nat (nat_lit 7) (instOfNatNat (nat_lit 7)))) (hbX : CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.CompletedPoint.X t) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 54) (instOfNatNat (nat_lit 54))))) (hbY : CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.CompletedPoint.Y t) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 54) (instOfNatNat (nat_lit 54))))) (hbZ : CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.CompletedPoint.Z t) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 54) (instOfNatNat (nat_lit 54))))) (hbT : CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.CompletedPoint.T t) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 54) (instOfNatNat (nat_lit 54))))) (hZ0 : @Ne.{1} CurveFieldProofs.Fp (CurveFieldProofs.denote (curve25519.backend.serial.curve_models.CompletedPoint.Z t)) (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 0) (@Zero.toOfNat0.{0} CurveFieldProofs.Fp (@MulZeroClass.toZero.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toMulZeroClass.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))))) (hT0 : @Ne.{1} CurveFieldProofs.Fp (CurveFieldProofs.denote (curve25519.backend.serial.curve_models.CompletedPoint.T t)) (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 0) (@Zero.toOfNat0.{0} CurveFieldProofs.Fp (@MulZeroClass.toZero.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toMulZeroClass.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))))) (hct : CurveFieldProofs.OnCurve (CurveFieldProofs.complX t) (CurveFieldProofs.complY t)) (hd : Or (@Eq.{1} Int (@Aeneas.Std.IScalar.val Aeneas.Std.IScalarTy.I8 d) (@OfNat.ofNat.{0} Int (nat_lit 0) (@instOfNat (nat_lit 0)))) (@Eq.{1} Int (@HMod.hMod.{0, 0, 0} Int Int Int (@instHMod.{0} Int Int.instMod) (@Aeneas.Std.IScalar.val Aeneas.Std.IScalarTy.I8 d) (@OfNat.ofNat.{0} Int (nat_lit 2) (@instOfNat (nat_lit 2)))) (@OfNat.ofNat.{0} Int (nat_lit 1) (@instOfNat (nat_lit 1))))) (hdlo : @LT.lt.{0} Int Int.instLTInt (@Neg.neg.{0} Int Int.instNegInt (@OfNat.ofNat.{0} Int (nat_lit 16) (@instOfNat (nat_lit 16)))) (@Aeneas.Std.IScalar.val Aeneas.Std.IScalarTy.I8 d)) (hdhi : @LT.lt.{0} Int Int.instLTInt (@Aeneas.Std.IScalar.val Aeneas.Std.IScalarTy.I8 d) (@OfNat.ofNat.{0} Int (nat_lit 16) (@instOfNat (nat_lit 16)))), @Aeneas.Std.WP.spec.{0} curve25519.backend.serial.curve_models.CompletedPoint (curve25519.backend.serial.scalar_mul.vartime_double_base.dsm_step_b t tbl d) fun (r : curve25519.backend.serial.curve_models.CompletedPoint) => And (CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.CompletedPoint.X r) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 54) (instOfNatNat (nat_lit 54))))) (And (CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.CompletedPoint.Y r) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 54) (instOfNatNat (nat_lit 54))))) (And (CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.CompletedPoint.Z r) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 54) (instOfNatNat (nat_lit 54))))) (And (CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.CompletedPoint.T r) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 54) (instOfNatNat (nat_lit 54))))) (And (@Ne.{1} CurveFieldProofs.Fp (CurveFieldProofs.denote (curve25519.backend.serial.curve_models.CompletedPoint.Z r)) (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 0) (@Zero.toOfNat0.{0} CurveFieldProofs.Fp (@MulZeroClass.toZero.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toMulZeroClass.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))))) (And (@Ne.{1} CurveFieldProofs.Fp (CurveFieldProofs.denote (curve25519.backend.serial.curve_models.CompletedPoint.T r)) (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 0) (@Zero.toOfNat0.{0} CurveFieldProofs.Fp (@MulZeroClass.toZero.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toMulZeroClass.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))))) (And (CurveFieldProofs.OnCurve (CurveFieldProofs.complX r) (CurveFieldProofs.complY r)) (@Eq.{1} (Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) (@Prod.mk.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp (CurveFieldProofs.complX r) (CurveFieldProofs.complY r)) (CurveFieldProofs.edDigit (CurveFieldProofs.edPt A) (@Aeneas.Std.IScalar.val Aeneas.Std.IScalarTy.I8 d) (@Prod.mk.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp (CurveFieldProofs.complX t) (CurveFieldProofs.complY t))))))))))
cert|CurveFieldProofs.dsm_loop_spec|cone=Classical.choice,Quot.sound,propext|type=∀ (i : Aeneas.Std.Usize) (hi : @Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize i) (@OfNat.ofNat.{0} Nat (nat_lit 255) (instOfNatNat (nat_lit 255)))) (a_naf b_naf : Aeneas.Std.Array.{0} Aeneas.Std.I8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) (ta tb : curve25519.window.NafLookupTable5 curve25519.backend.serial.curve_models.ProjectiveNielsPoint) (A B : CurveFieldProofs.EdPoint) (hta : CurveFieldProofs.NafTableOf ta A) (htb : CurveFieldProofs.NafTableOf tb B) (hda : CurveFieldProofs.NafDigits a_naf) (hdb : CurveFieldProofs.NafDigits b_naf), @Aeneas.Std.WP.spec.{0} curve25519.backend.serial.curve_models.ProjectivePoint (curve25519.backend.serial.scalar_mul.vartime_double_base.dsm_loop i a_naf b_naf ta tb) fun (res : curve25519.backend.serial.curve_models.ProjectivePoint) => And (CurveFieldProofs.ProjValid res) (And (CurveFieldProofs.OnCurve (CurveFieldProofs.projX res) (CurveFieldProofs.projY res)) (@Eq.{1} (Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) (@Prod.mk.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp (CurveFieldProofs.projX res) (CurveFieldProofs.projY res)) (CurveFieldProofs.dsmFold (CurveFieldProofs.nafDigit a_naf) (CurveFieldProofs.nafDigit b_naf) (CurveFieldProofs.edPt A) (CurveFieldProofs.edPt B) CurveFieldProofs.edId (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))))))
cert|CurveFieldProofs.naf_load_spec|cone=Classical.choice,Quot.sound,propext|type=∀ (self : curve25519.scalar.Scalar) (x_u64 : Aeneas.Std.Array.{0} Aeneas.Std.U64 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 5) (instOfNatNat (nat_lit 5))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 5) (instOfNatNat (nat_lit 5))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 5) (instOfNatNat (nat_lit 5))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 5) (instOfNatNat (nat_lit 5))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 5) (instOfNatNat (nat_lit 5))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) (b0 b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12 b13 b14 b15 b16 b17 b18 b19 b20 b21 b22 b23 b24 b25 b26 b27 b28 b29 b30 b31 : Aeneas.Std.U8) (hb : @Eq.{1} (List.{0} Aeneas.Std.U8) (@Subtype.val.{1} (List.{0} Aeneas.Std.U8) (fun (l : List.{0} Aeneas.Std.U8) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U8 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true)))))) (curve25519.scalar.Scalar.bytes self)) (@List.cons.{0} Aeneas.Std.U8 b0 (@List.cons.{0} Aeneas.Std.U8 b1 (@List.cons.{0} Aeneas.Std.U8 b2 (@List.cons.{0} Aeneas.Std.U8 b3 (@List.cons.{0} Aeneas.Std.U8 b4 (@List.cons.{0} Aeneas.Std.U8 b5 (@List.cons.{0} Aeneas.Std.U8 b6 (@List.cons.{0} Aeneas.Std.U8 b7 (@List.cons.{0} Aeneas.Std.U8 b8 (@List.cons.{0} Aeneas.Std.U8 b9 (@List.cons.{0} Aeneas.Std.U8 b10 (@List.cons.{0} Aeneas.Std.U8 b11 (@List.cons.{0} Aeneas.Std.U8 b12 (@List.cons.{0} Aeneas.Std.U8 b13 (@List.cons.{0} Aeneas.Std.U8 b14 (@List.cons.{0} Aeneas.Std.U8 b15 (@List.cons.{0} Aeneas.Std.U8 b16 (@List.cons.{0} Aeneas.Std.U8 b17 (@List.cons.{0} Aeneas.Std.U8 b18 (@List.cons.{0} Aeneas.Std.U8 b19 (@List.cons.{0} Aeneas.Std.U8 b20 (@List.cons.{0} Aeneas.Std.U8 b21 (@List.cons.{0} Aeneas.Std.U8 b22 (@List.cons.{0} Aeneas.Std.U8 b23 (@List.cons.{0} Aeneas.Std.U8 b24 (@List.cons.{0} Aeneas.Std.U8 b25 (@List.cons.{0} Aeneas.Std.U8 b26 (@List.cons.{0} Aeneas.Std.U8 b27 (@List.cons.{0} 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(nat_lit 5) (instOfNatNat (nat_lit 5))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true)))))) x_u64) (@List.cons.{0} (Aeneas.Std.UScalar Aeneas.Std.UScalarTy.U64) (Aeneas.Std.U64.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.U64)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.U64)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.U64)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.U64))) Bool.true) (@Eq.refl.{1} Bool Bool.true)))) (@List.cons.{0} (Aeneas.Std.UScalar Aeneas.Std.UScalarTy.U64) 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(curve25519.scalar.Scalar.non_adjacent_form_loop0 self x_u64 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) fun (ws : Aeneas.Std.Array.{0} Aeneas.Std.U64 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 5) (instOfNatNat (nat_lit 5))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 5) (instOfNatNat (nat_lit 5))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 5) (instOfNatNat (nat_lit 5))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 5) (instOfNatNat (nat_lit 5))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 5) (instOfNatNat (nat_lit 5))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) => @Exists.{1} Aeneas.Std.U64 fun (v0 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (v1 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (v2 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (v3 : Aeneas.Std.U64) => And (@Eq.{1} (List.{0} Aeneas.Std.U64) (@Subtype.val.{1} (List.{0} Aeneas.Std.U64) (fun (l : List.{0} Aeneas.Std.U64) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U64 l) (@Aeneas.Std.UScalar.val 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(@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b0) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b1) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 8) (instOfNatNat (nat_lit 8)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b2) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 16) (instOfNatNat (nat_lit 16)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b3) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 24) (instOfNatNat (nat_lit 24)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b4) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b5) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 40) (instOfNatNat 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cert|CurveFieldProofs.naf_exit|cone=Classical.choice,Quot.sound,propext|type=∀ (V pos carry : Nat) (S : Int) (hV : @LT.lt.{0} Nat instLTNat V (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 253) (instOfNatNat (nat_lit 253))))) (hpos : @LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) pos) (hc : @LE.le.{0} Nat instLENat carry (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) (hcp : @Eq.{1} Nat carry (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))) → @LE.le.{0} Nat instLENat pos (@OfNat.ofNat.{0} Nat (nat_lit 254) (instOfNatNat (nat_lit 254)))) (hinv : @Eq.{1} Int (@HAdd.hAdd.{0, 0, 0} Int Int Int (@instHAdd.{0} Int Int.instAdd) S (@HMul.hMul.{0, 0, 0} Int Int Int (@instHMul.{0} Int Int.instMul) (@Nat.cast.{0} Int instNatCastInt carry) (@HPow.hPow.{0, 0, 0} Int Nat Int (@instHPow.{0, 0} Int Nat (@Monoid.toPow.{0} Int Int.instMonoid)) (@OfNat.ofNat.{0} Int (nat_lit 2) (@instOfNat (nat_lit 2))) pos))) (@Nat.cast.{0} Int instNatCastInt (@HMod.hMod.{0, 0, 0} Nat Nat Nat (@instHMod.{0} Nat Nat.instMod) V (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) pos)))), @Eq.{1} Int S (@Nat.cast.{0} Int instNatCastInt V)
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(instOfNatNat (nat_lit 1))) → (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 carry) (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))) → @LE.le.{0} Nat instLENat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize pos) (@OfNat.ofNat.{0} Nat (nat_lit 254) (instOfNatNat (nat_lit 254)))) → (∀ (k : Nat), @LE.le.{0} Nat instLENat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize pos) k → @LT.lt.{0} Nat instLTNat k (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) → @Eq.{1} Int (CurveFieldProofs.nafDigit naf k) (@OfNat.ofNat.{0} Int (nat_lit 0) (@instOfNat (nat_lit 0)))) → (∀ (k : Nat), @LT.lt.{0} Nat instLTNat k (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) → And (Or (@Eq.{1} Int (CurveFieldProofs.nafDigit naf k) (@OfNat.ofNat.{0} Int (nat_lit 0) (@instOfNat (nat_lit 0)))) (@Eq.{1} Int (@HMod.hMod.{0, 0, 0} Int Int Int (@instHMod.{0} Int Int.instMod) (CurveFieldProofs.nafDigit naf k) (@OfNat.ofNat.{0} Int (nat_lit 2) (@instOfNat (nat_lit 2)))) (@OfNat.ofNat.{0} Int (nat_lit 1) (@instOfNat (nat_lit 1))))) (And (@LT.lt.{0} Int Int.instLTInt (@Neg.neg.{0} Int Int.instNegInt (@OfNat.ofNat.{0} Int (nat_lit 16) (@instOfNat (nat_lit 16)))) (CurveFieldProofs.nafDigit naf k)) (@LT.lt.{0} Int Int.instLTInt (CurveFieldProofs.nafDigit naf k) (@OfNat.ofNat.{0} Int (nat_lit 16) (@instOfNat (nat_lit 16)))))) → @Eq.{1} Int (@HAdd.hAdd.{0, 0, 0} Int Int Int (@instHAdd.{0} Int Int.instAdd) (CurveFieldProofs.nafSum naf (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256)))) (@HMul.hMul.{0, 0, 0} Int Int Int (@instHMul.{0} Int Int.instMul) (@Nat.cast.{0} Int instNatCastInt (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 carry)) (@HPow.hPow.{0, 0, 0} Int Nat Int (@instHPow.{0, 0} Int Nat (@Monoid.toPow.{0} Int Int.instMonoid)) (@OfNat.ofNat.{0} Int (nat_lit 2) (@instOfNat (nat_lit 2))) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize pos)))) (@Nat.cast.{0} Int instNatCastInt (@HMod.hMod.{0, 0, 0} Nat Nat Nat (@instHMod.{0} Nat Nat.instMod) V (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize pos)))) → @Aeneas.Std.WP.spec.{0} (Aeneas.Std.Array.{0} Aeneas.Std.I8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) (curve25519.scalar.Scalar.non_adjacent_form_loop1 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 5) (instOfNatNat (nat_lit 5))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 5) (instOfNatNat (nat_lit 5))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 5) (instOfNatNat (nat_lit 5))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 5) (instOfNatNat (nat_lit 5))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 5) (instOfNatNat (nat_lit 5))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true)))) naf x_u64 (Aeneas.Std.U64.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.U64)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.U64)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.U64)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.U64))) Bool.true) (@Eq.refl.{1} Bool Bool.true)))) (Aeneas.Std.U64.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 31) (instOfNatNat (nat_lit 31))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 31) (instOfNatNat (nat_lit 31))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.U64)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 31) (instOfNatNat (nat_lit 31))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.U64)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 31) (instOfNatNat (nat_lit 31))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.U64)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 31) (instOfNatNat (nat_lit 31))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.U64))) Bool.true) (@Eq.refl.{1} Bool Bool.true)))) pos carry) fun (res : Aeneas.Std.Array.{0} Aeneas.Std.I8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe 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cert|CurveFieldProofs.non_adjacent_form_spec|cone=Classical.choice,Quot.sound,propext|type=∀ (self : curve25519.scalar.Scalar) (b0 b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12 b13 b14 b15 b16 b17 b18 b19 b20 b21 b22 b23 b24 b25 b26 b27 b28 b29 b30 b31 : Aeneas.Std.U8) (hb : @Eq.{1} (List.{0} Aeneas.Std.U8) (@Subtype.val.{1} (List.{0} Aeneas.Std.U8) (fun (l : List.{0} Aeneas.Std.U8) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U8 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) 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cert|CurveFieldProofs.run_basepoint|cone=Classical.choice,Quot.sound,propext|type=@Exists.{1} CurveFieldProofs.EdPoint fun (B : CurveFieldProofs.EdPoint) => And (@Eq.{1} (Aeneas.Std.Result.{0} curve25519.edwards.EdwardsPoint) curve25519.backend.serial.u64.constants.ED25519_BASEPOINT_POINT (@Aeneas.Std.Result.ok.{0} CurveFieldProofs.EdPoint B)) (And (CurveFieldProofs.ExtValid B) (And (CurveFieldProofs.OnCurveExt B) (@Eq.{1} (Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) (CurveFieldProofs.edPt B) CurveFieldProofs.edBasePt)))
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@LT.lt.{0} Nat instLTNat Vb (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 253) (instOfNatNat (nat_lit 253))))) (hAv : CurveFieldProofs.ExtValid A) (hAc : CurveFieldProofs.OnCurveExt A), @Aeneas.Std.WP.spec.{0} curve25519.edwards.EdwardsPoint (curve25519.backend.serial.scalar_mul.vartime_double_base.mul a A b) fun (R : curve25519.edwards.EdwardsPoint) => And (CurveFieldProofs.ExtValid R) (And (CurveFieldProofs.OnCurveExt R) (@Exists.{1} (Aeneas.Std.Array.{0} Aeneas.Std.I8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax 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Bool.true))))) fun (nb : Aeneas.Std.Array.{0} Aeneas.Std.I8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) => And (CurveFieldProofs.NafDigits na) (And (CurveFieldProofs.NafDigits nb) (And (@Eq.{1} Int (CurveFieldProofs.nafSum na (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256)))) (@Nat.cast.{0} Int instNatCastInt Va)) (And (@Eq.{1} Int (CurveFieldProofs.nafSum nb (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256)))) (@Nat.cast.{0} Int instNatCastInt Vb)) (@Eq.{1} (Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) (CurveFieldProofs.edPt R) (CurveFieldProofs.dsmFold (CurveFieldProofs.nafDigit na) (CurveFieldProofs.nafDigit nb) (CurveFieldProofs.edPt A) CurveFieldProofs.edBasePt CurveFieldProofs.edId (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))))))))))
cert|CurveFieldProofs.verify_loop_full|cone=Classical.choice,Quot.sound,propext|type=∀ (e r : Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))), @Aeneas.Std.WP.spec.{0} Bool (curve25519.ed_sigs.verification_key.VerificationKey.verify_sha512_loop r e Bool.true (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) fun (res : Bool) => @Eq.{1} Bool res (@Decidable.decide (CurveFieldProofs.rangeEq e r (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0)))) (CurveFieldProofs.instDecidableRangeEq e r (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0)))))
cert|CurveFieldProofs.to_bytes_spec|cone=Classical.choice,Quot.sound,propext|type=∀ (a : CurveFieldProofs.Fe) (l0 l1 l2 l3 l4 : Aeneas.Std.U64) (hl : @Eq.{1} (List.{0} Aeneas.Std.U64) (@Subtype.val.{1} (List.{0} Aeneas.Std.U64) (fun (l : List.{0} Aeneas.Std.U64) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U64 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 5) (instOfNatNat (nat_lit 5))) curve25519.backend.serial.u64.field.FieldElement51._proof_1))) a) (@List.cons.{0} Aeneas.Std.U64 l0 (@List.cons.{0} Aeneas.Std.U64 l1 (@List.cons.{0} Aeneas.Std.U64 l2 (@List.cons.{0} Aeneas.Std.U64 l3 (@List.cons.{0} Aeneas.Std.U64 l4 (@List.nil.{0} Aeneas.Std.U64))))))), @Aeneas.Std.WP.spec.{0} (Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) (CurveFieldProofs.fe_to_bytes a) fun (s : Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) => @Eq.{1} Nat (CurveFieldProofs.bytesVal s) (@HMod.hMod.{0, 0, 0} Nat Nat Nat (@instHMod.{0} Nat Nat.instMod) (CurveFieldProofs.feVal a) CurveFieldProofs.P)
cert|CurveFieldProofs.ed_compress_spec|cone=Classical.choice,Quot.sound,propext|type=∀ (Pt : CurveFieldProofs.EdPoint) (hv : CurveFieldProofs.ExtValid Pt), @Aeneas.Std.WP.spec.{0} curve25519.edwards.CompressedEdwardsY (curve25519.edwards.EdwardsPoint.compress Pt) fun (s : curve25519.edwards.CompressedEdwardsY) => @Eq.{1} Nat (CurveFieldProofs.bytesVal s) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@ZMod.val CurveFieldProofs.P (CurveFieldProofs.edY Pt)) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@HMod.hMod.{0, 0, 0} Nat Nat Nat (@instHMod.{0} Nat Nat.instMod) (@ZMod.val CurveFieldProofs.P (CurveFieldProofs.edX Pt)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2)))) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 255) (instOfNatNat (nat_lit 255))))))
cert|ScalarProofs.from_bytes_mod_order_wide_spec|cone=Classical.choice,Quot.sound,propext|type=∀ (input : Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 64) (instOfNatNat (nat_lit 64))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 64) (instOfNatNat (nat_lit 64))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 64) (instOfNatNat (nat_lit 64))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 64) (instOfNatNat (nat_lit 64))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 64) (instOfNatNat (nat_lit 64))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) (b0 b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12 b13 b14 b15 b16 b17 b18 b19 b20 b21 b22 b23 b24 b25 b26 b27 b28 b29 b30 b31 b32 b33 b34 b35 b36 b37 b38 b39 b40 b41 b42 b43 b44 b45 b46 b47 b48 b49 b50 b51 b52 b53 b54 b55 b56 b57 b58 b59 b60 b61 b62 b63 : Aeneas.Std.U8) (hb : @Eq.{1} (List.{0} Aeneas.Std.U8) (@Subtype.val.{1} (List.{0} Aeneas.Std.U8) (fun (l : List.{0} Aeneas.Std.U8) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U8 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 64) (instOfNatNat (nat_lit 64))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 64) (instOfNatNat (nat_lit 64))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 64) (instOfNatNat (nat_lit 64))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 64) (instOfNatNat (nat_lit 64))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 64) (instOfNatNat (nat_lit 64))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true)))))) input) (have y : List.{0} Aeneas.Std.U8 := have y : List.{0} Aeneas.Std.U8 := have y : List.{0} Aeneas.Std.U8 := have y : List.{0} Aeneas.Std.U8 := @List.cons.{0} Aeneas.Std.U8 b60 (@List.cons.{0} Aeneas.Std.U8 b61 (@List.cons.{0} Aeneas.Std.U8 b62 (@List.cons.{0} Aeneas.Std.U8 b63 (@List.nil.{0} Aeneas.Std.U8)))); @List.cons.{0} Aeneas.Std.U8 b56 (@List.cons.{0} Aeneas.Std.U8 b57 (@List.cons.{0} Aeneas.Std.U8 b58 (@List.cons.{0} Aeneas.Std.U8 b59 y))); have y : List.{0} Aeneas.Std.U8 := @List.cons.{0} Aeneas.Std.U8 b52 (@List.cons.{0} Aeneas.Std.U8 b53 (@List.cons.{0} Aeneas.Std.U8 b54 (@List.cons.{0} Aeneas.Std.U8 b55 y))); @List.cons.{0} Aeneas.Std.U8 b48 (@List.cons.{0} Aeneas.Std.U8 b49 (@List.cons.{0} Aeneas.Std.U8 b50 (@List.cons.{0} Aeneas.Std.U8 b51 y))); have y : List.{0} Aeneas.Std.U8 := have y : List.{0} Aeneas.Std.U8 := @List.cons.{0} Aeneas.Std.U8 b44 (@List.cons.{0} Aeneas.Std.U8 b45 (@List.cons.{0} Aeneas.Std.U8 b46 (@List.cons.{0} Aeneas.Std.U8 b47 y))); @List.cons.{0} Aeneas.Std.U8 b40 (@List.cons.{0} Aeneas.Std.U8 b41 (@List.cons.{0} Aeneas.Std.U8 b42 (@List.cons.{0} Aeneas.Std.U8 b43 y))); have y : List.{0} Aeneas.Std.U8 := @List.cons.{0} Aeneas.Std.U8 b36 (@List.cons.{0} Aeneas.Std.U8 b37 (@List.cons.{0} Aeneas.Std.U8 b38 (@List.cons.{0} Aeneas.Std.U8 b39 y))); @List.cons.{0} Aeneas.Std.U8 b32 (@List.cons.{0} Aeneas.Std.U8 b33 (@List.cons.{0} Aeneas.Std.U8 b34 (@List.cons.{0} Aeneas.Std.U8 b35 y))); have y : List.{0} Aeneas.Std.U8 := have y : List.{0} Aeneas.Std.U8 := have y : List.{0} Aeneas.Std.U8 := @List.cons.{0} Aeneas.Std.U8 b28 (@List.cons.{0} Aeneas.Std.U8 b29 (@List.cons.{0} Aeneas.Std.U8 b30 (@List.cons.{0} Aeneas.Std.U8 b31 y))); @List.cons.{0} Aeneas.Std.U8 b24 (@List.cons.{0} Aeneas.Std.U8 b25 (@List.cons.{0} Aeneas.Std.U8 b26 (@List.cons.{0} Aeneas.Std.U8 b27 y))); have y : List.{0} Aeneas.Std.U8 := @List.cons.{0} Aeneas.Std.U8 b20 (@List.cons.{0} Aeneas.Std.U8 b21 (@List.cons.{0} Aeneas.Std.U8 b22 (@List.cons.{0} Aeneas.Std.U8 b23 y))); @List.cons.{0} Aeneas.Std.U8 b16 (@List.cons.{0} Aeneas.Std.U8 b17 (@List.cons.{0} Aeneas.Std.U8 b18 (@List.cons.{0} Aeneas.Std.U8 b19 y))); have y : List.{0} Aeneas.Std.U8 := have y : List.{0} Aeneas.Std.U8 := @List.cons.{0} Aeneas.Std.U8 b12 (@List.cons.{0} Aeneas.Std.U8 b13 (@List.cons.{0} Aeneas.Std.U8 b14 (@List.cons.{0} Aeneas.Std.U8 b15 y))); @List.cons.{0} Aeneas.Std.U8 b8 (@List.cons.{0} Aeneas.Std.U8 b9 (@List.cons.{0} Aeneas.Std.U8 b10 (@List.cons.{0} Aeneas.Std.U8 b11 y))); have y : List.{0} Aeneas.Std.U8 := @List.cons.{0} Aeneas.Std.U8 b4 (@List.cons.{0} Aeneas.Std.U8 b5 (@List.cons.{0} Aeneas.Std.U8 b6 (@List.cons.{0} Aeneas.Std.U8 b7 y))); @List.cons.{0} Aeneas.Std.U8 b0 (@List.cons.{0} Aeneas.Std.U8 b1 (@List.cons.{0} Aeneas.Std.U8 b2 (@List.cons.{0} Aeneas.Std.U8 b3 y))))) (T : Nat) (hT : @Eq.{1} Nat T (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat 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cert|CurveFieldProofs.vartime_dsm_basepoint_spec|cone=Classical.choice,Quot.sound,propext|type=∀ (a b : curve25519.scalar.Scalar) (A : CurveFieldProofs.EdPoint) (a0 a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a11 a12 a13 a14 a15 a16 a17 a18 a19 a20 a21 a22 a23 a24 a25 a26 a27 a28 a29 a30 a31 b0 b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12 b13 b14 b15 b16 b17 b18 b19 b20 b21 b22 b23 b24 b25 b26 b27 b28 b29 b30 b31 : Aeneas.Std.U8) (hab : @Eq.{1} (List.{0} Aeneas.Std.U8) (@Subtype.val.{1} (List.{0} Aeneas.Std.U8) (fun (l : List.{0} Aeneas.Std.U8) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U8 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax 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@LT.lt.{0} Nat instLTNat Vb (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 253) (instOfNatNat (nat_lit 253))))) (hAv : CurveFieldProofs.ExtValid A) (hAc : CurveFieldProofs.OnCurveExt A), @Aeneas.Std.WP.spec.{0} curve25519.edwards.EdwardsPoint (curve25519.edwards.EdwardsPoint.vartime_double_scalar_mul_basepoint a A b) fun (R : curve25519.edwards.EdwardsPoint) => And (CurveFieldProofs.ExtValid R) (And (CurveFieldProofs.OnCurveExt R) (@Exists.{1} (Aeneas.Std.Array.{0} Aeneas.Std.I8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax 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Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) => @Exists.{1} (Aeneas.Std.Array.{0} Aeneas.Std.I8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) fun (nb : Aeneas.Std.Array.{0} Aeneas.Std.I8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) => And (CurveFieldProofs.NafDigits na) (And (CurveFieldProofs.NafDigits nb) (And (@Eq.{1} Int (CurveFieldProofs.nafSum na (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256)))) (@Nat.cast.{0} Int instNatCastInt Va)) (And (@Eq.{1} Int (CurveFieldProofs.nafSum nb (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256)))) (@Nat.cast.{0} Int instNatCastInt Vb)) (@Eq.{1} (Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) (CurveFieldProofs.edPt R) (CurveFieldProofs.dsmFold (CurveFieldProofs.nafDigit na) (CurveFieldProofs.nafDigit nb) (CurveFieldProofs.edPt A) CurveFieldProofs.edBasePt CurveFieldProofs.edId (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))))))))))
cert|CurveFieldProofs.enc_point_inj|cone=Classical.choice,Quot.sound,propext|type=∀ (Pt Q : CurveFieldProofs.EdPoint) (hPv : CurveFieldProofs.ExtValid Pt) (hPc : CurveFieldProofs.OnCurveExt Pt) (hQv : CurveFieldProofs.ExtValid Q) (hQc : CurveFieldProofs.OnCurveExt Q) (h : @Eq.{1} Nat (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@ZMod.val CurveFieldProofs.P (CurveFieldProofs.edY Pt)) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@HMod.hMod.{0, 0, 0} Nat Nat Nat (@instHMod.{0} Nat Nat.instMod) (@ZMod.val CurveFieldProofs.P (CurveFieldProofs.edX Pt)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2)))) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 255) (instOfNatNat (nat_lit 255)))))) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@ZMod.val CurveFieldProofs.P (CurveFieldProofs.edY Q)) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@HMod.hMod.{0, 0, 0} Nat Nat Nat (@instHMod.{0} Nat Nat.instMod) (@ZMod.val CurveFieldProofs.P (CurveFieldProofs.edX Q)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2)))) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 255) (instOfNatNat (nat_lit 255))))))), @Eq.{1} (Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) (CurveFieldProofs.edPt Pt) (CurveFieldProofs.edPt Q)
cert|CurveFieldProofs.pow_p58_spec|cone=Classical.choice,Quot.sound,propext|type=∀ (a : CurveFieldProofs.Fe) (hba : CurveFieldProofs.Bnd a (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 54) (instOfNatNat (nat_lit 54))))), @Aeneas.Std.WP.spec.{0} curve25519.backend.serial.u64.field.FieldElement51 (curve25519.field.FieldElement51.pow_p58 a) fun (r : curve25519.backend.serial.u64.field.FieldElement51) => And (CurveFieldProofs.Bnd r (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 52) (instOfNatNat (nat_lit 52))))) (@Eq.{1} CurveFieldProofs.Fp (CurveFieldProofs.denote r) (@HPow.hPow.{0, 0, 0} CurveFieldProofs.Fp Nat CurveFieldProofs.Fp (@instHPow.{0, 0} CurveFieldProofs.Fp Nat (@Monoid.toPow.{0} CurveFieldProofs.Fp (@MonoidWithZero.toMonoid.{0} CurveFieldProofs.Fp (@Semiring.toMonoidWithZero.{0} CurveFieldProofs.Fp (@DivisionSemiring.toSemiring.{0} CurveFieldProofs.Fp (@Semifield.toDivisionSemiring.{0} CurveFieldProofs.Fp (@Field.toSemifield.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP)))))))) (CurveFieldProofs.denote a) (@HSub.hSub.{0, 0, 0} Nat Nat Nat (@instHSub.{0} Nat instSubNat) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 252) (instOfNatNat (nat_lit 252)))) (@OfNat.ofNat.{0} Nat (nat_lit 3) (instOfNatNat (nat_lit 3))))))
cert|CurveFieldProofs.fe_ct_eq_spec|cone=Classical.choice,Quot.sound,propext|type=∀ (a b : CurveFieldProofs.Fe), @Aeneas.Std.WP.spec.{0} subtle.Choice (curve25519.backend.serial.u64.field.FieldElement51.Insts.SubtleConstantTimeEq.ct_eq a b) fun (c : subtle.Choice) => And (Or (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 c) (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0)))) (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 c) (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) (Iff (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 c) (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) (@Eq.{1} CurveFieldProofs.Fp (CurveFieldProofs.denote a) (CurveFieldProofs.denote b)))
cert|CurveFieldProofs.sqrt_core|cone=Classical.choice,Quot.sound,propext|type=∀ (u v x : CurveFieldProofs.Fp) (hv : @Ne.{1} CurveFieldProofs.Fp v (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 0) (@Zero.toOfNat0.{0} CurveFieldProofs.Fp (@MulZeroClass.toZero.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toMulZeroClass.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))))) (hx : @Eq.{1} CurveFieldProofs.Fp (@HMul.hMul.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHMul.{0} CurveFieldProofs.Fp (@Distrib.toMul.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) (@HPow.hPow.{0, 0, 0} CurveFieldProofs.Fp Nat CurveFieldProofs.Fp (@instHPow.{0, 0} CurveFieldProofs.Fp Nat (@Monoid.toPow.{0} CurveFieldProofs.Fp (@MonoidWithZero.toMonoid.{0} CurveFieldProofs.Fp (@Semiring.toMonoidWithZero.{0} CurveFieldProofs.Fp (@DivisionSemiring.toSemiring.{0} CurveFieldProofs.Fp (@Semifield.toDivisionSemiring.{0} CurveFieldProofs.Fp (@Field.toSemifield.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP)))))))) x (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2)))) v) u), Or (@Eq.{1} CurveFieldProofs.Fp (@HMul.hMul.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHMul.{0} CurveFieldProofs.Fp (@Distrib.toMul.{0} CurveFieldProofs.Fp 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CurveFieldProofs.Fp (@instHPow.{0, 0} CurveFieldProofs.Fp Nat (@Monoid.toPow.{0} CurveFieldProofs.Fp (@MonoidWithZero.toMonoid.{0} CurveFieldProofs.Fp (@Semiring.toMonoidWithZero.{0} CurveFieldProofs.Fp (@DivisionSemiring.toSemiring.{0} CurveFieldProofs.Fp (@Semifield.toDivisionSemiring.{0} CurveFieldProofs.Fp (@Field.toSemifield.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP)))))))) v (@OfNat.ofNat.{0} Nat (nat_lit 3) (instOfNatNat (nat_lit 3))))) (@HPow.hPow.{0, 0, 0} CurveFieldProofs.Fp Nat CurveFieldProofs.Fp (@instHPow.{0, 0} CurveFieldProofs.Fp Nat (@Monoid.toPow.{0} CurveFieldProofs.Fp (@MonoidWithZero.toMonoid.{0} CurveFieldProofs.Fp (@Semiring.toMonoidWithZero.{0} CurveFieldProofs.Fp (@DivisionSemiring.toSemiring.{0} CurveFieldProofs.Fp (@Semifield.toDivisionSemiring.{0} CurveFieldProofs.Fp (@Field.toSemifield.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP)))))))) (@HMul.hMul.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHMul.{0} CurveFieldProofs.Fp (@Distrib.toMul.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) u (@HPow.hPow.{0, 0, 0} CurveFieldProofs.Fp Nat CurveFieldProofs.Fp (@instHPow.{0, 0} CurveFieldProofs.Fp Nat (@Monoid.toPow.{0} CurveFieldProofs.Fp (@MonoidWithZero.toMonoid.{0} CurveFieldProofs.Fp (@Semiring.toMonoidWithZero.{0} CurveFieldProofs.Fp (@DivisionSemiring.toSemiring.{0} CurveFieldProofs.Fp (@Semifield.toDivisionSemiring.{0} CurveFieldProofs.Fp (@Field.toSemifield.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP)))))))) v (@OfNat.ofNat.{0} Nat (nat_lit 7) (instOfNatNat (nat_lit 7))))) (@HSub.hSub.{0, 0, 0} Nat Nat Nat (@instHSub.{0} Nat instSubNat) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 252) (instOfNatNat (nat_lit 252)))) (@OfNat.ofNat.{0} Nat (nat_lit 3) (instOfNatNat (nat_lit 3)))))) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))))) u) (@Eq.{1} CurveFieldProofs.Fp (@HMul.hMul.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHMul.{0} CurveFieldProofs.Fp (@Distrib.toMul.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) v (@HPow.hPow.{0, 0, 0} CurveFieldProofs.Fp Nat CurveFieldProofs.Fp (@instHPow.{0, 0} CurveFieldProofs.Fp Nat (@Monoid.toPow.{0} CurveFieldProofs.Fp (@MonoidWithZero.toMonoid.{0} CurveFieldProofs.Fp (@Semiring.toMonoidWithZero.{0} CurveFieldProofs.Fp (@DivisionSemiring.toSemiring.{0} CurveFieldProofs.Fp (@Semifield.toDivisionSemiring.{0} CurveFieldProofs.Fp (@Field.toSemifield.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP)))))))) (@HMul.hMul.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHMul.{0} CurveFieldProofs.Fp (@Distrib.toMul.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp 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(@Field.toSemifield.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP)))))))) v (@OfNat.ofNat.{0} Nat (nat_lit 3) (instOfNatNat (nat_lit 3))))) (@HPow.hPow.{0, 0, 0} CurveFieldProofs.Fp Nat CurveFieldProofs.Fp (@instHPow.{0, 0} CurveFieldProofs.Fp Nat (@Monoid.toPow.{0} CurveFieldProofs.Fp (@MonoidWithZero.toMonoid.{0} CurveFieldProofs.Fp (@Semiring.toMonoidWithZero.{0} CurveFieldProofs.Fp (@DivisionSemiring.toSemiring.{0} CurveFieldProofs.Fp (@Semifield.toDivisionSemiring.{0} CurveFieldProofs.Fp (@Field.toSemifield.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP)))))))) (@HMul.hMul.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHMul.{0} CurveFieldProofs.Fp (@Distrib.toMul.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) u (@HPow.hPow.{0, 0, 0} CurveFieldProofs.Fp Nat CurveFieldProofs.Fp (@instHPow.{0, 0} CurveFieldProofs.Fp Nat (@Monoid.toPow.{0} CurveFieldProofs.Fp (@MonoidWithZero.toMonoid.{0} CurveFieldProofs.Fp (@Semiring.toMonoidWithZero.{0} CurveFieldProofs.Fp (@DivisionSemiring.toSemiring.{0} CurveFieldProofs.Fp (@Semifield.toDivisionSemiring.{0} CurveFieldProofs.Fp (@Field.toSemifield.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP)))))))) v (@OfNat.ofNat.{0} Nat (nat_lit 7) (instOfNatNat (nat_lit 7))))) (@HSub.hSub.{0, 0, 0} Nat Nat Nat (@instHSub.{0} Nat instSubNat) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 252) (instOfNatNat (nat_lit 252)))) (@OfNat.ofNat.{0} Nat (nat_lit 3) (instOfNatNat (nat_lit 3)))))) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))))) (@Neg.neg.{0} CurveFieldProofs.Fp (@NegZeroClass.toNeg.{0} CurveFieldProofs.Fp (@SubNegZeroMonoid.toNegZeroClass.{0} CurveFieldProofs.Fp (@SubtractionMonoid.toSubNegZeroMonoid.{0} CurveFieldProofs.Fp (@SubtractionCommMonoid.toSubtractionMonoid.{0} CurveFieldProofs.Fp (@AddCommGroup.toDivisionAddCommMonoid.{0} CurveFieldProofs.Fp (@Ring.toAddCommGroup.{0} CurveFieldProofs.Fp (@DivisionRing.toRing.{0} CurveFieldProofs.Fp (@Field.toDivisionRing.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP))))))))) u))
cert|CurveFieldProofs.sqrt_ratio_i_sq_spec|cone=Classical.choice,Quot.sound,propext|type=∀ (u v : CurveFieldProofs.Fe) (hbu : CurveFieldProofs.Bnd u (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 54) (instOfNatNat (nat_lit 54))))) (hbv : CurveFieldProofs.Bnd v (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 54) (instOfNatNat (nat_lit 54))))) (hvne : @Ne.{1} CurveFieldProofs.Fp (CurveFieldProofs.denote v) (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 0) (@Zero.toOfNat0.{0} CurveFieldProofs.Fp (@MulZeroClass.toZero.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toMulZeroClass.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))))) (x : CurveFieldProofs.Fp) (hx : @Eq.{1} CurveFieldProofs.Fp (@HMul.hMul.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHMul.{0} CurveFieldProofs.Fp (@Distrib.toMul.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) (@HPow.hPow.{0, 0, 0} CurveFieldProofs.Fp Nat CurveFieldProofs.Fp (@instHPow.{0, 0} CurveFieldProofs.Fp Nat (@Monoid.toPow.{0} CurveFieldProofs.Fp (@MonoidWithZero.toMonoid.{0} CurveFieldProofs.Fp (@Semiring.toMonoidWithZero.{0} CurveFieldProofs.Fp (@DivisionSemiring.toSemiring.{0} CurveFieldProofs.Fp (@Semifield.toDivisionSemiring.{0} CurveFieldProofs.Fp (@Field.toSemifield.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP)))))))) x (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2)))) (CurveFieldProofs.denote v)) (CurveFieldProofs.denote u)), @Aeneas.Std.WP.spec.{0} (Prod.{0, 0} subtle.Choice curve25519.backend.serial.u64.field.FieldElement51) (curve25519.field.FieldElement51.sqrt_ratio_i u v) fun (cr : Prod.{0, 0} subtle.Choice curve25519.backend.serial.u64.field.FieldElement51) => And (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 (@Prod.fst.{0, 0} subtle.Choice curve25519.backend.serial.u64.field.FieldElement51 cr)) (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) (And (CurveFieldProofs.Bnd (@Prod.snd.{0, 0} subtle.Choice curve25519.backend.serial.u64.field.FieldElement51 cr) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 52) (instOfNatNat (nat_lit 52))))) (And (@Eq.{1} CurveFieldProofs.Fp (@HMul.hMul.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHMul.{0} CurveFieldProofs.Fp (@Distrib.toMul.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) (@HPow.hPow.{0, 0, 0} CurveFieldProofs.Fp Nat CurveFieldProofs.Fp (@instHPow.{0, 0} CurveFieldProofs.Fp Nat (@Monoid.toPow.{0} CurveFieldProofs.Fp (@MonoidWithZero.toMonoid.{0} CurveFieldProofs.Fp (@Semiring.toMonoidWithZero.{0} CurveFieldProofs.Fp (@DivisionSemiring.toSemiring.{0} CurveFieldProofs.Fp (@Semifield.toDivisionSemiring.{0} CurveFieldProofs.Fp (@Field.toSemifield.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP)))))))) (CurveFieldProofs.denote (@Prod.snd.{0, 0} subtle.Choice curve25519.backend.serial.u64.field.FieldElement51 cr)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2)))) (CurveFieldProofs.denote v)) (CurveFieldProofs.denote u)) (@Eq.{1} Nat (@HMod.hMod.{0, 0, 0} Nat Nat Nat (@instHMod.{0} Nat Nat.instMod) (@ZMod.val CurveFieldProofs.P (CurveFieldProofs.denote (@Prod.snd.{0, 0} subtle.Choice curve25519.backend.serial.u64.field.FieldElement51 cr))) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2)))) (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0))))))
cert|CurveFieldProofs.from_bytes_spec|cone=Classical.choice,Quot.sound,propext|type=∀ (bytes : Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) (b0 b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12 b13 b14 b15 b16 b17 b18 b19 b20 b21 b22 b23 b24 b25 b26 b27 b28 b29 b30 b31 : Aeneas.Std.U8) (hbl : @Eq.{1} (List.{0} Aeneas.Std.U8) (@Subtype.val.{1} (List.{0} Aeneas.Std.U8) (fun (l : List.{0} Aeneas.Std.U8) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U8 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true)))))) bytes) (@List.cons.{0} Aeneas.Std.U8 b0 (@List.cons.{0} Aeneas.Std.U8 b1 (@List.cons.{0} Aeneas.Std.U8 b2 (@List.cons.{0} Aeneas.Std.U8 b3 (@List.cons.{0} Aeneas.Std.U8 b4 (@List.cons.{0} Aeneas.Std.U8 b5 (@List.cons.{0} Aeneas.Std.U8 b6 (@List.cons.{0} Aeneas.Std.U8 b7 (@List.cons.{0} Aeneas.Std.U8 b8 (@List.cons.{0} Aeneas.Std.U8 b9 (@List.cons.{0} Aeneas.Std.U8 b10 (@List.cons.{0} Aeneas.Std.U8 b11 (@List.cons.{0} Aeneas.Std.U8 b12 (@List.cons.{0} Aeneas.Std.U8 b13 (@List.cons.{0} Aeneas.Std.U8 b14 (@List.cons.{0} Aeneas.Std.U8 b15 (@List.cons.{0} Aeneas.Std.U8 b16 (@List.cons.{0} Aeneas.Std.U8 b17 (@List.cons.{0} Aeneas.Std.U8 b18 (@List.cons.{0} Aeneas.Std.U8 b19 (@List.cons.{0} Aeneas.Std.U8 b20 (@List.cons.{0} Aeneas.Std.U8 b21 (@List.cons.{0} Aeneas.Std.U8 b22 (@List.cons.{0} Aeneas.Std.U8 b23 (@List.cons.{0} Aeneas.Std.U8 b24 (@List.cons.{0} Aeneas.Std.U8 b25 (@List.cons.{0} Aeneas.Std.U8 b26 (@List.cons.{0} Aeneas.Std.U8 b27 (@List.cons.{0} Aeneas.Std.U8 b28 (@List.cons.{0} Aeneas.Std.U8 b29 (@List.cons.{0} Aeneas.Std.U8 b30 (@List.cons.{0} Aeneas.Std.U8 b31 (@List.nil.{0} Aeneas.Std.U8)))))))))))))))))))))))))))))))))), @Aeneas.Std.WP.spec.{0} curve25519.backend.serial.u64.field.FieldElement51 (curve25519.backend.serial.u64.field.FieldElement51.from_bytes bytes) fun (r : curve25519.backend.serial.u64.field.FieldElement51) => And (CurveFieldProofs.Bnd r (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 51) (instOfNatNat (nat_lit 51))))) (@Eq.{1} Nat (CurveFieldProofs.feVal r) (@HMod.hMod.{0, 0, 0} Nat Nat Nat (@instHMod.{0} Nat Nat.instMod) (CurveFieldProofs.bytesVal bytes) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 255) (instOfNatNat (nat_lit 255))))))
cert|CurveFieldProofs.decompress_of_canonical|cone=Classical.choice,Quot.sound,propext|type=∀ (Q : CurveFieldProofs.EdPoint) (hQv : CurveFieldProofs.ExtValid Q) (hQc : CurveFieldProofs.OnCurveExt Q) (rb : Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) (b0 b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12 b13 b14 b15 b16 b17 b18 b19 b20 b21 b22 b23 b24 b25 b26 b27 b28 b29 b30 b31 : Aeneas.Std.U8) (hbl : @Eq.{1} (List.{0} Aeneas.Std.U8) (@Subtype.val.{1} (List.{0} Aeneas.Std.U8) (fun (l : List.{0} Aeneas.Std.U8) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U8 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true)))))) rb) (@List.cons.{0} Aeneas.Std.U8 b0 (@List.cons.{0} Aeneas.Std.U8 b1 (@List.cons.{0} Aeneas.Std.U8 b2 (@List.cons.{0} Aeneas.Std.U8 b3 (@List.cons.{0} Aeneas.Std.U8 b4 (@List.cons.{0} Aeneas.Std.U8 b5 (@List.cons.{0} Aeneas.Std.U8 b6 (@List.cons.{0} Aeneas.Std.U8 b7 (@List.cons.{0} Aeneas.Std.U8 b8 (@List.cons.{0} Aeneas.Std.U8 b9 (@List.cons.{0} Aeneas.Std.U8 b10 (@List.cons.{0} Aeneas.Std.U8 b11 (@List.cons.{0} Aeneas.Std.U8 b12 (@List.cons.{0} Aeneas.Std.U8 b13 (@List.cons.{0} Aeneas.Std.U8 b14 (@List.cons.{0} Aeneas.Std.U8 b15 (@List.cons.{0} Aeneas.Std.U8 b16 (@List.cons.{0} Aeneas.Std.U8 b17 (@List.cons.{0} Aeneas.Std.U8 b18 (@List.cons.{0} Aeneas.Std.U8 b19 (@List.cons.{0} Aeneas.Std.U8 b20 (@List.cons.{0} Aeneas.Std.U8 b21 (@List.cons.{0} Aeneas.Std.U8 b22 (@List.cons.{0} Aeneas.Std.U8 b23 (@List.cons.{0} Aeneas.Std.U8 b24 (@List.cons.{0} Aeneas.Std.U8 b25 (@List.cons.{0} Aeneas.Std.U8 b26 (@List.cons.{0} Aeneas.Std.U8 b27 (@List.cons.{0} Aeneas.Std.U8 b28 (@List.cons.{0} Aeneas.Std.U8 b29 (@List.cons.{0} Aeneas.Std.U8 b30 (@List.cons.{0} Aeneas.Std.U8 b31 (@List.nil.{0} Aeneas.Std.U8)))))))))))))))))))))))))))))))))) (henc : @Eq.{1} Nat (CurveFieldProofs.bytesVal rb) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@ZMod.val CurveFieldProofs.P (CurveFieldProofs.edY Q)) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@HMod.hMod.{0, 0, 0} Nat Nat Nat (@instHMod.{0} Nat Nat.instMod) (@ZMod.val CurveFieldProofs.P (CurveFieldProofs.edX Q)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2)))) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 255) (instOfNatNat (nat_lit 255))))))), @Aeneas.Std.WP.spec.{0} (Option.{0} curve25519.edwards.EdwardsPoint) (curve25519.edwards.CompressedEdwardsY.decompress rb) fun (o : Option.{0} curve25519.edwards.EdwardsPoint) => @Exists.{1} CurveFieldProofs.EdPoint fun (Pt : CurveFieldProofs.EdPoint) => And (@Eq.{1} (Option.{0} curve25519.edwards.EdwardsPoint) o (@Option.some.{0} CurveFieldProofs.EdPoint Pt)) (And (CurveFieldProofs.ExtValid Pt) (And (CurveFieldProofs.OnCurveExt Pt) (@Eq.{1} (Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) (CurveFieldProofs.edPt Pt) (CurveFieldProofs.edPt Q))))
cert|CurveFieldProofs.verify_accepts_iff|cone=Classical.choice,Quot.sound,ed25519.Signature,ed25519.Signature.r_bytes,ed25519.Signature.s_bytes,ed_sigs.sha512_hash3,propext|type=∀ (self : curve25519.ed_sigs.verification_key.VerificationKey) (sig : ed25519.Signature) (msg : Aeneas.Std.Slice.{0} Aeneas.Std.U8) (rb sb : Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) (s : curve25519.scalar.Scalar) (er : curve25519.edwards.CompressedEdwardsY) (e : Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) (hrb : @Eq.{1} (Aeneas.Std.Result.{0} (Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true)))))) (ed25519.Signature.r_bytes sig) (@Aeneas.Std.Result.ok.{0} (Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) rb)) (hsb : @Eq.{1} (Aeneas.Std.Result.{0} (Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true)))))) (ed25519.Signature.s_bytes sig) (@Aeneas.Std.Result.ok.{0} (Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) sb)) (hA : @Eq.{1} (Aeneas.Std.Result.{0} Bool) (curve25519.ed_sigs.verification_key.VerificationKey.a_bytes_nonzero self) (@Aeneas.Std.Result.ok.{0} Bool Bool.true)) (hleg : @Eq.{1} (Aeneas.Std.Result.{0} Bool) (curve25519.ed_sigs.verification_key.is_legacy_excluded_r rb) (@Aeneas.Std.Result.ok.{0} Bool Bool.false)) (hs : @Eq.{1} (Aeneas.Std.Result.{0} (Aeneas.Std.core.result.Result.{0, 0} curve25519.scalar.Scalar curve25519.ed_sigs.error.Error)) (curve25519.ed_sigs.verification_key.check_scalar_canonical sb) (@Aeneas.Std.Result.ok.{0} (Aeneas.Std.core.result.Result.{0, 0} curve25519.scalar.Scalar curve25519.ed_sigs.error.Error) (@Aeneas.Std.core.result.Result.Ok.{0, 0} curve25519.scalar.Scalar curve25519.ed_sigs.error.Error s))) (hrec : @Eq.{1} (Aeneas.Std.Result.{0} curve25519.edwards.CompressedEdwardsY) (curve25519.ed_sigs.verification_key.VerificationKey.recompute_r_sha512 self rb s msg) (@Aeneas.Std.Result.ok.{0} curve25519.edwards.CompressedEdwardsY er)) (he : @Eq.{1} (Aeneas.Std.Result.{0} (Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true)))))) (curve25519.edwards.CompressedEdwardsY.as_bytes er) (@Aeneas.Std.Result.ok.{0} (Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) e)), Iff (@Eq.{1} (Aeneas.Std.Result.{0} (Aeneas.Std.core.result.Result.{0, 0} Unit curve25519.ed_sigs.error.Error)) (curve25519.ed_sigs.verification_key.VerificationKey.verify_sha512 self sig msg) (@Aeneas.Std.Result.ok.{0} (Aeneas.Std.core.result.Result.{0, 0} Unit curve25519.ed_sigs.error.Error) (@Aeneas.Std.core.result.Result.Ok.{0, 0} Unit curve25519.ed_sigs.error.Error Unit.unit))) (CurveFieldProofs.rangeEq e rb (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0))))
cert|CurveFieldProofs.verify_accepts_iff_point|cone=Classical.choice,Quot.sound,ed25519.Signature,ed25519.Signature.r_bytes,ed25519.Signature.s_bytes,ed_sigs.sha512_hash3,propext|type=∀ (self : curve25519.ed_sigs.verification_key.VerificationKey) (sig : ed25519.Signature) (msg : Aeneas.Std.Slice.{0} Aeneas.Std.U8) (rb sb : Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) (s : curve25519.scalar.Scalar) (er : curve25519.edwards.CompressedEdwardsY) (e : Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) (hrb : @Eq.{1} (Aeneas.Std.Result.{0} (Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true)))))) (ed25519.Signature.r_bytes sig) (@Aeneas.Std.Result.ok.{0} (Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) rb)) (hsb : @Eq.{1} (Aeneas.Std.Result.{0} (Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true)))))) (ed25519.Signature.s_bytes sig) (@Aeneas.Std.Result.ok.{0} (Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide 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curve25519.scalar.Scalar curve25519.ed_sigs.error.Error s))) (hrec : @Eq.{1} (Aeneas.Std.Result.{0} curve25519.edwards.CompressedEdwardsY) (curve25519.ed_sigs.verification_key.VerificationKey.recompute_r_sha512 self rb s msg) (@Aeneas.Std.Result.ok.{0} curve25519.edwards.CompressedEdwardsY er)) (he : @Eq.{1} (Aeneas.Std.Result.{0} (Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true)))))) (curve25519.edwards.CompressedEdwardsY.as_bytes er) (@Aeneas.Std.Result.ok.{0} (Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) e)) (hkv : 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cert|CurveFieldProofs.verify_accepts_iff_point_eq|cone=Classical.choice,Quot.sound,ed25519.Signature,ed25519.Signature.r_bytes,ed25519.Signature.s_bytes,ed_sigs.sha512_hash3,propext|type=∀ (self : curve25519.ed_sigs.verification_key.VerificationKey) (sig : ed25519.Signature) (msg : Aeneas.Std.Slice.{0} Aeneas.Std.U8) (rb sb : Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 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cert|CurveFieldProofs.verify_accepts_iff_decompress|cone=Classical.choice,Quot.sound,ed25519.Signature,ed25519.Signature.r_bytes,ed25519.Signature.s_bytes,ed_sigs.sha512_hash3,propext|type=∀ (self : curve25519.ed_sigs.verification_key.VerificationKey) (sig : ed25519.Signature) (msg : Aeneas.Std.Slice.{0} Aeneas.Std.U8) (rb sb : Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 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(@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 t22) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 176) (instOfNatNat (nat_lit 176)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 t23) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 184) (instOfNatNat (nat_lit 184)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 t24) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 192) (instOfNatNat (nat_lit 192)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 t25) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 200) (instOfNatNat (nat_lit 200)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 t26) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 208) (instOfNatNat (nat_lit 208)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 t27) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 216) (instOfNatNat (nat_lit 216)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 t28) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 224) (instOfNatNat (nat_lit 224)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 t29) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 232) (instOfNatNat (nat_lit 232)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 t30) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 240) (instOfNatNat (nat_lit 240)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 t31) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 248) (instOfNatNat (nat_lit 248))))))) (hVslt : @LT.lt.{0} Nat instLTNat Vs (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 253) (instOfNatNat (nat_lit 253))))) (Q : CurveFieldProofs.EdPoint) (hQv : CurveFieldProofs.ExtValid Q) (hQc : CurveFieldProofs.OnCurveExt Q) (b0 b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12 b13 b14 b15 b16 b17 b18 b19 b20 b21 b22 b23 b24 b25 b26 b27 b28 b29 b30 b31 : Aeneas.Std.U8) (hbl : @Eq.{1} (List.{0} Aeneas.Std.U8) (@Subtype.val.{1} (List.{0} Aeneas.Std.U8) (fun (l : List.{0} Aeneas.Std.U8) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U8 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true)))))) rb) (@List.cons.{0} Aeneas.Std.U8 b0 (@List.cons.{0} Aeneas.Std.U8 b1 (@List.cons.{0} Aeneas.Std.U8 b2 (@List.cons.{0} Aeneas.Std.U8 b3 (@List.cons.{0} Aeneas.Std.U8 b4 (@List.cons.{0} Aeneas.Std.U8 b5 (@List.cons.{0} Aeneas.Std.U8 b6 (@List.cons.{0} Aeneas.Std.U8 b7 (@List.cons.{0} Aeneas.Std.U8 b8 (@List.cons.{0} Aeneas.Std.U8 b9 (@List.cons.{0} Aeneas.Std.U8 b10 (@List.cons.{0} Aeneas.Std.U8 b11 (@List.cons.{0} Aeneas.Std.U8 b12 (@List.cons.{0} Aeneas.Std.U8 b13 (@List.cons.{0} Aeneas.Std.U8 b14 (@List.cons.{0} Aeneas.Std.U8 b15 (@List.cons.{0} Aeneas.Std.U8 b16 (@List.cons.{0} Aeneas.Std.U8 b17 (@List.cons.{0} Aeneas.Std.U8 b18 (@List.cons.{0} Aeneas.Std.U8 b19 (@List.cons.{0} Aeneas.Std.U8 b20 (@List.cons.{0} Aeneas.Std.U8 b21 (@List.cons.{0} Aeneas.Std.U8 b22 (@List.cons.{0} Aeneas.Std.U8 b23 (@List.cons.{0} Aeneas.Std.U8 b24 (@List.cons.{0} Aeneas.Std.U8 b25 (@List.cons.{0} Aeneas.Std.U8 b26 (@List.cons.{0} Aeneas.Std.U8 b27 (@List.cons.{0} Aeneas.Std.U8 b28 (@List.cons.{0} Aeneas.Std.U8 b29 (@List.cons.{0} Aeneas.Std.U8 b30 (@List.cons.{0} Aeneas.Std.U8 b31 (@List.nil.{0} Aeneas.Std.U8)))))))))))))))))))))))))))))))))) (henc : @Eq.{1} Nat (CurveFieldProofs.bytesVal rb) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@ZMod.val CurveFieldProofs.P (CurveFieldProofs.edY Q)) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@HMod.hMod.{0, 0, 0} Nat Nat Nat (@instHMod.{0} Nat Nat.instMod) (@ZMod.val CurveFieldProofs.P (CurveFieldProofs.edX Q)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2)))) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 255) (instOfNatNat (nat_lit 255))))))), @Exists.{1} CurveFieldProofs.EdPoint fun (R' : CurveFieldProofs.EdPoint) => @Exists.{1} CurveFieldProofs.EdPoint fun (Pt : CurveFieldProofs.EdPoint) => And (CurveFieldProofs.ExtValid R') (And (CurveFieldProofs.OnCurveExt R') (And (@Eq.{1} (Aeneas.Std.Result.{0} (Option.{0} curve25519.edwards.EdwardsPoint)) (curve25519.edwards.CompressedEdwardsY.decompress rb) (@Aeneas.Std.Result.ok.{0} (Option.{0} CurveFieldProofs.EdPoint) (@Option.some.{0} CurveFieldProofs.EdPoint Pt))) (And (CurveFieldProofs.ExtValid Pt) (And (CurveFieldProofs.OnCurveExt Pt) (Iff (@Eq.{1} (Aeneas.Std.Result.{0} (Aeneas.Std.core.result.Result.{0, 0} Unit curve25519.ed_sigs.error.Error)) (curve25519.ed_sigs.verification_key.VerificationKey.verify_sha512 self sig msg) (@Aeneas.Std.Result.ok.{0} (Aeneas.Std.core.result.Result.{0, 0} Unit curve25519.ed_sigs.error.Error) (@Aeneas.Std.core.result.Result.Ok.{0, 0} Unit curve25519.ed_sigs.error.Error Unit.unit))) (@Eq.{1} (Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) (CurveFieldProofs.edPt Pt) (CurveFieldProofs.edPt R')))))))
spec|CurveFieldProofs.Bnd|def|value=fun (a : CurveFieldProofs.Fe) (c : Nat) => CurveFieldProofs.feVal.match_1.{1} (fun (x : List.{0} Aeneas.Std.U64) => Prop) (@Subtype.val.{1} (List.{0} Aeneas.Std.U64) (fun (l : List.{0} Aeneas.Std.U64) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U64 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 5) (instOfNatNat (nat_lit 5))) curve25519.backend.serial.u64.field.FieldElement51._proof_1))) a) (fun (a0 a1 a2 a3 a4 : Aeneas.Std.U64) => And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a0) c) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a1) c) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a2) c) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a3) c) (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a4) c))))) fun (x : List.{0} Aeneas.Std.U64) => False
spec|CurveFieldProofs.ComplPoint|def|value=curve25519.backend.serial.curve_models.CompletedPoint
spec|CurveFieldProofs.EdPoint|def|value=curve25519.edwards.EdwardsPoint
spec|CurveFieldProofs.ExtValid|def|value=fun (Pt : CurveFieldProofs.EdPoint) => And (CurveFieldProofs.Bnd (curve25519.edwards.EdwardsPoint.X Pt) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 52) (instOfNatNat (nat_lit 52))))) (And (CurveFieldProofs.Bnd (curve25519.edwards.EdwardsPoint.Y Pt) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 52) (instOfNatNat (nat_lit 52))))) (And (CurveFieldProofs.Bnd (curve25519.edwards.EdwardsPoint.Z Pt) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 52) (instOfNatNat (nat_lit 52))))) (And (CurveFieldProofs.Bnd (curve25519.edwards.EdwardsPoint.T Pt) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 52) (instOfNatNat (nat_lit 52))))) (And (@Ne.{1} CurveFieldProofs.Fp (CurveFieldProofs.denote (curve25519.edwards.EdwardsPoint.Z Pt)) (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 0) (@Zero.toOfNat0.{0} CurveFieldProofs.Fp (@MulZeroClass.toZero.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toMulZeroClass.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))))) (@Eq.{1} CurveFieldProofs.Fp (@HMul.hMul.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHMul.{0} CurveFieldProofs.Fp (@Distrib.toMul.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) (CurveFieldProofs.denote (curve25519.edwards.EdwardsPoint.X Pt)) (CurveFieldProofs.denote (curve25519.edwards.EdwardsPoint.Y Pt))) (@HMul.hMul.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHMul.{0} CurveFieldProofs.Fp (@Distrib.toMul.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) (CurveFieldProofs.denote (curve25519.edwards.EdwardsPoint.Z Pt)) (CurveFieldProofs.denote (curve25519.edwards.EdwardsPoint.T Pt))))))))
spec|CurveFieldProofs.Fe|def|value=curve25519.backend.serial.u64.field.FieldElement51
spec|CurveFieldProofs.Fp|def|value=ZMod CurveFieldProofs.P
spec|CurveFieldProofs.IsEdwardsImplementation|other|type=Prop
spec|CurveFieldProofs.IsFieldImplementation|other|type=Prop
spec|CurveFieldProofs.IsNielsOf|def|value=fun (N : CurveFieldProofs.ProjNiels) (Pt : CurveFieldProofs.EdPoint) => And (@Eq.{1} CurveFieldProofs.Fp (CurveFieldProofs.denote (curve25519.backend.serial.curve_models.ProjectiveNielsPoint.Y_plus_X N)) (@HAdd.hAdd.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHAdd.{0} CurveFieldProofs.Fp (@Distrib.toAdd.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) (CurveFieldProofs.denote (curve25519.edwards.EdwardsPoint.Y Pt)) (CurveFieldProofs.denote (curve25519.edwards.EdwardsPoint.X Pt)))) (And (@Eq.{1} CurveFieldProofs.Fp (CurveFieldProofs.denote (curve25519.backend.serial.curve_models.ProjectiveNielsPoint.Y_minus_X N)) (@HSub.hSub.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHSub.{0} CurveFieldProofs.Fp (@SubNegMonoid.toSub.{0} CurveFieldProofs.Fp (@AddGroup.toSubNegMonoid.{0} CurveFieldProofs.Fp (@AddGroupWithOne.toAddGroup.{0} CurveFieldProofs.Fp (@Ring.toAddGroupWithOne.{0} CurveFieldProofs.Fp (@DivisionRing.toRing.{0} CurveFieldProofs.Fp (@Field.toDivisionRing.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP)))))))) (CurveFieldProofs.denote (curve25519.edwards.EdwardsPoint.Y Pt)) (CurveFieldProofs.denote (curve25519.edwards.EdwardsPoint.X Pt)))) (And (@Eq.{1} CurveFieldProofs.Fp (CurveFieldProofs.denote (curve25519.backend.serial.curve_models.ProjectiveNielsPoint.Z N)) (CurveFieldProofs.denote (curve25519.edwards.EdwardsPoint.Z Pt))) (@Eq.{1} CurveFieldProofs.Fp (@HMul.hMul.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHMul.{0} CurveFieldProofs.Fp (@Distrib.toMul.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 121666) (@instOfNatAtLeastTwo.{0} CurveFieldProofs.Fp (nat_lit 121666) (@AddMonoidWithOne.toNatCast.{0} CurveFieldProofs.Fp (@AddGroupWithOne.toAddMonoidWithOne.{0} CurveFieldProofs.Fp (@Ring.toAddGroupWithOne.{0} CurveFieldProofs.Fp (@DivisionRing.toRing.{0} CurveFieldProofs.Fp (@Field.toDivisionRing.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP)))))) CurveFieldProofs.IsNielsOf._proof_1)) (CurveFieldProofs.denote (curve25519.backend.serial.curve_models.ProjectiveNielsPoint.T2d N))) (@HMul.hMul.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHMul.{0} CurveFieldProofs.Fp (@Distrib.toMul.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) (@Neg.neg.{0} CurveFieldProofs.Fp (@NegZeroClass.toNeg.{0} CurveFieldProofs.Fp (@SubNegZeroMonoid.toNegZeroClass.{0} CurveFieldProofs.Fp (@SubtractionMonoid.toSubNegZeroMonoid.{0} CurveFieldProofs.Fp (@SubtractionCommMonoid.toSubtractionMonoid.{0} CurveFieldProofs.Fp (@AddCommGroup.toDivisionAddCommMonoid.{0} CurveFieldProofs.Fp (@Ring.toAddCommGroup.{0} CurveFieldProofs.Fp (@DivisionRing.toRing.{0} CurveFieldProofs.Fp (@Field.toDivisionRing.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP))))))))) (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 243330) (@instOfNatAtLeastTwo.{0} CurveFieldProofs.Fp (nat_lit 243330) (@AddMonoidWithOne.toNatCast.{0} CurveFieldProofs.Fp (@AddGroupWithOne.toAddMonoidWithOne.{0} CurveFieldProofs.Fp (@Ring.toAddGroupWithOne.{0} CurveFieldProofs.Fp (@DivisionRing.toRing.{0} CurveFieldProofs.Fp (@Field.toDivisionRing.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP)))))) CurveFieldProofs.IsNielsOf._proof_2))) (CurveFieldProofs.denote (curve25519.edwards.EdwardsPoint.T Pt))))))
spec|CurveFieldProofs.IsNielsOf._proof_1|prop|type=Nat.AtLeastTwo (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@OfNat.ofNat.{0} Nat (nat_lit 121665) (instOfNatNat (nat_lit 121665))) (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))
spec|CurveFieldProofs.IsNielsOf._proof_2|prop|type=Nat.AtLeastTwo (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@OfNat.ofNat.{0} Nat (nat_lit 243329) (instOfNatNat (nat_lit 243329))) (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))
spec|CurveFieldProofs.NafDigits|def|value=fun (a : Aeneas.Std.Array.{0} Aeneas.Std.I8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) CurveFieldProofs.nafDigit._proof_1)) => ∀ (k : Nat), @LT.lt.{0} Nat instLTNat k (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) → And (Or (@Eq.{1} Int (CurveFieldProofs.nafDigit a k) (@OfNat.ofNat.{0} Int (nat_lit 0) (@instOfNat (nat_lit 0)))) (@Eq.{1} Int (@HMod.hMod.{0, 0, 0} Int Int Int (@instHMod.{0} Int Int.instMod) (CurveFieldProofs.nafDigit a k) (@OfNat.ofNat.{0} Int (nat_lit 2) (@instOfNat (nat_lit 2)))) (@OfNat.ofNat.{0} Int (nat_lit 1) (@instOfNat (nat_lit 1))))) (And (@LT.lt.{0} Int Int.instLTInt (@Neg.neg.{0} Int Int.instNegInt (@OfNat.ofNat.{0} Int (nat_lit 16) (@instOfNat (nat_lit 16)))) (CurveFieldProofs.nafDigit a k)) (@LT.lt.{0} Int Int.instLTInt (CurveFieldProofs.nafDigit a k) (@OfNat.ofNat.{0} Int (nat_lit 16) (@instOfNat (nat_lit 16)))))
spec|CurveFieldProofs.NafEntryOf|def|value=fun (e : curve25519.backend.serial.curve_models.ProjectiveNielsPoint) (A : CurveFieldProofs.EdPoint) (k : Nat) => And (CurveFieldProofs.ProjNielsValid e) (@Exists.{1} CurveFieldProofs.EdPoint fun (Q : CurveFieldProofs.EdPoint) => And (CurveFieldProofs.IsNielsOf e Q) (And (CurveFieldProofs.ExtValid Q) (And (CurveFieldProofs.OnCurveExt Q) (@Eq.{1} (Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) (CurveFieldProofs.edPt Q) (CurveFieldProofs.edOdd k (CurveFieldProofs.edPt A))))))
spec|CurveFieldProofs.NafTableOf|def|value=fun (tbl : curve25519.window.NafLookupTable5 curve25519.backend.serial.curve_models.ProjectiveNielsPoint) (A : CurveFieldProofs.EdPoint) => @Exists.{1} curve25519.backend.serial.curve_models.ProjectiveNielsPoint fun (e0 : curve25519.backend.serial.curve_models.ProjectiveNielsPoint) => @Exists.{1} curve25519.backend.serial.curve_models.ProjectiveNielsPoint fun (e1 : curve25519.backend.serial.curve_models.ProjectiveNielsPoint) => @Exists.{1} curve25519.backend.serial.curve_models.ProjectiveNielsPoint fun (e2 : curve25519.backend.serial.curve_models.ProjectiveNielsPoint) => @Exists.{1} curve25519.backend.serial.curve_models.ProjectiveNielsPoint fun (e3 : curve25519.backend.serial.curve_models.ProjectiveNielsPoint) => @Exists.{1} curve25519.backend.serial.curve_models.ProjectiveNielsPoint fun (e4 : curve25519.backend.serial.curve_models.ProjectiveNielsPoint) => @Exists.{1} curve25519.backend.serial.curve_models.ProjectiveNielsPoint fun (e5 : curve25519.backend.serial.curve_models.ProjectiveNielsPoint) => @Exists.{1} curve25519.backend.serial.curve_models.ProjectiveNielsPoint fun (e6 : curve25519.backend.serial.curve_models.ProjectiveNielsPoint) => @Exists.{1} curve25519.backend.serial.curve_models.ProjectiveNielsPoint fun (e7 : curve25519.backend.serial.curve_models.ProjectiveNielsPoint) => And (@Eq.{1} (List.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint) (CurveFieldProofs.tblEntries tbl) (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e0 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e1 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e2 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e3 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e4 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e5 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e6 (@List.cons.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint e7 (@List.nil.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint)))))))))) (And (CurveFieldProofs.NafEntryOf e0 A (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0)))) (And (CurveFieldProofs.NafEntryOf e1 A (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) (And (CurveFieldProofs.NafEntryOf e2 A (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2)))) (And (CurveFieldProofs.NafEntryOf e3 A (@OfNat.ofNat.{0} Nat (nat_lit 3) (instOfNatNat (nat_lit 3)))) (And (CurveFieldProofs.NafEntryOf e4 A (@OfNat.ofNat.{0} Nat (nat_lit 4) (instOfNatNat (nat_lit 4)))) (And (CurveFieldProofs.NafEntryOf e5 A (@OfNat.ofNat.{0} Nat (nat_lit 5) (instOfNatNat (nat_lit 5)))) (And (CurveFieldProofs.NafEntryOf e6 A (@OfNat.ofNat.{0} Nat (nat_lit 6) (instOfNatNat (nat_lit 6)))) (CurveFieldProofs.NafEntryOf e7 A (@OfNat.ofNat.{0} Nat (nat_lit 7) (instOfNatNat (nat_lit 7)))))))))))
spec|CurveFieldProofs.OnCurve|def|value=fun (x y : CurveFieldProofs.Fp) => @Eq.{1} CurveFieldProofs.Fp (@HAdd.hAdd.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHAdd.{0} CurveFieldProofs.Fp (@Distrib.toAdd.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) (@Neg.neg.{0} CurveFieldProofs.Fp (@NegZeroClass.toNeg.{0} CurveFieldProofs.Fp (@SubNegZeroMonoid.toNegZeroClass.{0} CurveFieldProofs.Fp (@SubtractionMonoid.toSubNegZeroMonoid.{0} CurveFieldProofs.Fp (@SubtractionCommMonoid.toSubtractionMonoid.{0} CurveFieldProofs.Fp (@AddCommGroup.toDivisionAddCommMonoid.{0} CurveFieldProofs.Fp (@Ring.toAddCommGroup.{0} CurveFieldProofs.Fp (@DivisionRing.toRing.{0} CurveFieldProofs.Fp (@Field.toDivisionRing.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP))))))))) (@HPow.hPow.{0, 0, 0} CurveFieldProofs.Fp Nat CurveFieldProofs.Fp (@instHPow.{0, 0} CurveFieldProofs.Fp Nat (@Monoid.toPow.{0} CurveFieldProofs.Fp (@MonoidWithZero.toMonoid.{0} CurveFieldProofs.Fp (@Semiring.toMonoidWithZero.{0} CurveFieldProofs.Fp (@DivisionSemiring.toSemiring.{0} CurveFieldProofs.Fp (@Semifield.toDivisionSemiring.{0} CurveFieldProofs.Fp (@Field.toSemifield.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP)))))))) x (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))))) (@HPow.hPow.{0, 0, 0} CurveFieldProofs.Fp Nat CurveFieldProofs.Fp (@instHPow.{0, 0} CurveFieldProofs.Fp Nat (@Monoid.toPow.{0} CurveFieldProofs.Fp (@MonoidWithZero.toMonoid.{0} CurveFieldProofs.Fp (@Semiring.toMonoidWithZero.{0} CurveFieldProofs.Fp (@DivisionSemiring.toSemiring.{0} CurveFieldProofs.Fp (@Semifield.toDivisionSemiring.{0} CurveFieldProofs.Fp (@Field.toSemifield.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP)))))))) y (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))))) (@HAdd.hAdd.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHAdd.{0} CurveFieldProofs.Fp (@Distrib.toAdd.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 1) (@One.toOfNat1.{0} CurveFieldProofs.Fp (@AddMonoidWithOne.toOne.{0} CurveFieldProofs.Fp (@AddGroupWithOne.toAddMonoidWithOne.{0} CurveFieldProofs.Fp (@Ring.toAddGroupWithOne.{0} CurveFieldProofs.Fp (@DivisionRing.toRing.{0} CurveFieldProofs.Fp (@Field.toDivisionRing.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP)))))))) (@HMul.hMul.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHMul.{0} CurveFieldProofs.Fp (@Distrib.toMul.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) (@HMul.hMul.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHMul.{0} CurveFieldProofs.Fp (@Distrib.toMul.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) CurveFieldProofs.edD (@HPow.hPow.{0, 0, 0} CurveFieldProofs.Fp Nat CurveFieldProofs.Fp (@instHPow.{0, 0} CurveFieldProofs.Fp Nat (@Monoid.toPow.{0} CurveFieldProofs.Fp (@MonoidWithZero.toMonoid.{0} CurveFieldProofs.Fp (@Semiring.toMonoidWithZero.{0} CurveFieldProofs.Fp (@DivisionSemiring.toSemiring.{0} CurveFieldProofs.Fp (@Semifield.toDivisionSemiring.{0} CurveFieldProofs.Fp (@Field.toSemifield.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP)))))))) x (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))))) (@HPow.hPow.{0, 0, 0} CurveFieldProofs.Fp Nat CurveFieldProofs.Fp (@instHPow.{0, 0} CurveFieldProofs.Fp Nat (@Monoid.toPow.{0} CurveFieldProofs.Fp (@MonoidWithZero.toMonoid.{0} CurveFieldProofs.Fp (@Semiring.toMonoidWithZero.{0} CurveFieldProofs.Fp (@DivisionSemiring.toSemiring.{0} CurveFieldProofs.Fp (@Semifield.toDivisionSemiring.{0} CurveFieldProofs.Fp (@Field.toSemifield.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP)))))))) y (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))))))
spec|CurveFieldProofs.OnCurveExt|def|value=fun (P : CurveFieldProofs.EdPoint) => CurveFieldProofs.OnCurve (CurveFieldProofs.edX P) (CurveFieldProofs.edY P)
spec|CurveFieldProofs.P|def|value=@HSub.hSub.{0, 0, 0} Nat Nat Nat (@instHSub.{0} Nat instSubNat) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 255) (instOfNatNat (nat_lit 255)))) (@OfNat.ofNat.{0} Nat (nat_lit 19) (instOfNatNat (nat_lit 19)))
spec|CurveFieldProofs.ProjNiels|def|value=curve25519.backend.serial.curve_models.ProjectiveNielsPoint
spec|CurveFieldProofs.ProjNielsValid|def|value=fun (N : CurveFieldProofs.ProjNiels) => And (CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.ProjectiveNielsPoint.Y_plus_X N) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 53) (instOfNatNat (nat_lit 53))))) (And (CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.ProjectiveNielsPoint.Y_minus_X N) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 53) (instOfNatNat (nat_lit 53))))) (And (CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.ProjectiveNielsPoint.Z N) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 52) (instOfNatNat (nat_lit 52))))) (And (CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.ProjectiveNielsPoint.T2d N) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 52) (instOfNatNat (nat_lit 52))))) (@Ne.{1} CurveFieldProofs.Fp (CurveFieldProofs.denote (curve25519.backend.serial.curve_models.ProjectiveNielsPoint.Z N)) (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 0) (@Zero.toOfNat0.{0} CurveFieldProofs.Fp (@MulZeroClass.toZero.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toMulZeroClass.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))))))))
spec|CurveFieldProofs.ProjPoint|def|value=curve25519.backend.serial.curve_models.ProjectivePoint
spec|CurveFieldProofs.ProjValid|def|value=fun (Pt : CurveFieldProofs.ProjPoint) => And (CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.ProjectivePoint.X Pt) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 52) (instOfNatNat (nat_lit 52))))) (And (CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.ProjectivePoint.Y Pt) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 52) (instOfNatNat (nat_lit 52))))) (And (CurveFieldProofs.Bnd (curve25519.backend.serial.curve_models.ProjectivePoint.Z Pt) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 52) (instOfNatNat (nat_lit 52))))) (@Ne.{1} CurveFieldProofs.Fp (CurveFieldProofs.denote (curve25519.backend.serial.curve_models.ProjectivePoint.Z Pt)) (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 0) (@Zero.toOfNat0.{0} CurveFieldProofs.Fp (@MulZeroClass.toZero.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toMulZeroClass.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P))))))))))))
spec|CurveFieldProofs.bytesVal|def|value=fun (s : Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) CurveFieldProofs.bytesVal._proof_1)) => CurveFieldProofs.bytesVal.match_1.{1} (fun (x : List.{0} Aeneas.Std.U8) => Nat) (@Subtype.val.{1} (List.{0} Aeneas.Std.U8) (fun (l : List.{0} Aeneas.Std.U8) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U8 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) CurveFieldProofs.bytesVal._proof_1))) s) (fun (b0 b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12 b13 b14 b15 b16 b17 b18 b19 b20 b21 b22 b23 b24 b25 b26 b27 b28 b29 b30 b31 : Aeneas.Std.U8) => @HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat 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(nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 120) (instOfNatNat (nat_lit 120)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b16) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 128) (instOfNatNat (nat_lit 128)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b17) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 136) (instOfNatNat (nat_lit 136)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b18) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat 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(@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 168) (instOfNatNat (nat_lit 168)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b22) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 176) (instOfNatNat (nat_lit 176)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b23) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 184) (instOfNatNat (nat_lit 184)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val 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spec|CurveFieldProofs.bytesVal._proof_1|prop|type=@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)
spec|CurveFieldProofs.bytesVal._sparseCasesOn_1|def|value=fun {α : Type u} {motive : (t : List.{u} α) → Sort u_1} (t : List.{u} α) (cons : (head : α) → (tail : List.{u} α) → motive (@List.cons.{u} α head tail)) => @List.rec.{u_1, u} α (fun (t : List.{u} α) => ((h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{u} α t)) → motive t) → motive t) (fun («else» : (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{u} α (@List.nil.{u} α))) → motive (@List.nil.{u} α)) => «else» (@Nat.ne_of_beq_eq_false (Nat.land (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))) (Nat.shiftRight (nat_lit 2) (nat_lit 0))) (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))) (@Eq.refl.{1} Bool Bool.false))) (fun (head : α) (tail : List.{u} α) (tail_ih : ((h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{u} α tail)) → motive tail) → motive tail) («else» : (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{u} α (@List.cons.{u} α head tail))) → motive (@List.cons.{u} α head tail)) => cons head tail) t
spec|CurveFieldProofs.bytesVal._sparseCasesOn_2|def|value=fun {α : Type u} {motive : (t : List.{u} α) → Sort u_1} (t : List.{u} α) (nil : motive (@List.nil.{u} α)) => @List.rec.{u_1, u} α (fun (t : List.{u} α) => ((h : Nat.hasNotBit (nat_lit 1) (@List.ctorIdx.{u} α t)) → motive t) → motive t) (fun («else» : (h : Nat.hasNotBit (nat_lit 1) (@List.ctorIdx.{u} α (@List.nil.{u} α))) → motive (@List.nil.{u} α)) => nil) (fun (head : α) (tail : List.{u} α) (tail_ih : ((h : Nat.hasNotBit (nat_lit 1) (@List.ctorIdx.{u} α tail)) → motive tail) → motive tail) («else» : (h : Nat.hasNotBit (nat_lit 1) (@List.ctorIdx.{u} α (@List.cons.{u} α head tail))) → motive (@List.cons.{u} α head tail)) => «else» (@Nat.ne_of_beq_eq_false (Nat.land (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))) (Nat.shiftRight (nat_lit 1) (nat_lit 1))) (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))) (@Eq.refl.{1} Bool Bool.false))) t
spec|CurveFieldProofs.bytesVal.match_1|def|value=fun (motive : List.{0} Aeneas.Std.U8 → Sort u_1) (x : List.{0} Aeneas.Std.U8) (h_1 : (b0 b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12 b13 b14 b15 b16 b17 b18 b19 b20 b21 b22 b23 b24 b25 b26 b27 b28 b29 b30 b31 : Aeneas.Std.U8) → motive (@List.cons.{0} Aeneas.Std.U8 b0 (@List.cons.{0} Aeneas.Std.U8 b1 (@List.cons.{0} Aeneas.Std.U8 b2 (@List.cons.{0} Aeneas.Std.U8 b3 (@List.cons.{0} Aeneas.Std.U8 b4 (@List.cons.{0} Aeneas.Std.U8 b5 (@List.cons.{0} Aeneas.Std.U8 b6 (@List.cons.{0} Aeneas.Std.U8 b7 (@List.cons.{0} Aeneas.Std.U8 b8 (@List.cons.{0} Aeneas.Std.U8 b9 (@List.cons.{0} Aeneas.Std.U8 b10 (@List.cons.{0} Aeneas.Std.U8 b11 (@List.cons.{0} Aeneas.Std.U8 b12 (@List.cons.{0} Aeneas.Std.U8 b13 (@List.cons.{0} Aeneas.Std.U8 b14 (@List.cons.{0} Aeneas.Std.U8 b15 (@List.cons.{0} Aeneas.Std.U8 b16 (@List.cons.{0} Aeneas.Std.U8 b17 (@List.cons.{0} Aeneas.Std.U8 b18 (@List.cons.{0} Aeneas.Std.U8 b19 (@List.cons.{0} Aeneas.Std.U8 b20 (@List.cons.{0} Aeneas.Std.U8 b21 (@List.cons.{0} Aeneas.Std.U8 b22 (@List.cons.{0} Aeneas.Std.U8 b23 (@List.cons.{0} Aeneas.Std.U8 b24 (@List.cons.{0} Aeneas.Std.U8 b25 (@List.cons.{0} Aeneas.Std.U8 b26 (@List.cons.{0} Aeneas.Std.U8 b27 (@List.cons.{0} Aeneas.Std.U8 b28 (@List.cons.{0} Aeneas.Std.U8 b29 (@List.cons.{0} Aeneas.Std.U8 b30 (@List.cons.{0} Aeneas.Std.U8 b31 (@List.nil.{0} Aeneas.Std.U8)))))))))))))))))))))))))))))))))) (h_2 : (x : List.{0} Aeneas.Std.U8) → motive x) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive x) x (fun (head : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head x)) tail (fun (head_1 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 x))) tail (fun (head_2 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 x)))) tail (fun (head_3 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 x))))) tail (fun (head_4 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 x)))))) tail (fun (head_5 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 x))))))) tail (fun (head_6 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 x)))))))) tail (fun (head_7 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 x))))))))) tail (fun (head_8 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 x)))))))))) tail (fun (head_9 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 x))))))))))) tail (fun (head_10 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 x)))))))))))) tail (fun (head_11 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 x))))))))))))) tail (fun (head_12 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 x)))))))))))))) tail (fun (head_13 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 x))))))))))))))) tail (fun (head_14 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 x)))))))))))))))) tail (fun (head_15 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 x))))))))))))))))) tail (fun (head_16 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 x)))))))))))))))))) tail (fun (head_17 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 x))))))))))))))))))) tail (fun (head_18 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 x)))))))))))))))))))) tail (fun (head_19 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 (@List.cons.{0} Aeneas.Std.U8 head_19 x))))))))))))))))))))) tail (fun (head_20 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 (@List.cons.{0} Aeneas.Std.U8 head_19 (@List.cons.{0} Aeneas.Std.U8 head_20 x)))))))))))))))))))))) tail (fun (head_21 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 (@List.cons.{0} Aeneas.Std.U8 head_19 (@List.cons.{0} Aeneas.Std.U8 head_20 (@List.cons.{0} Aeneas.Std.U8 head_21 x))))))))))))))))))))))) tail (fun (head_22 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 (@List.cons.{0} Aeneas.Std.U8 head_19 (@List.cons.{0} Aeneas.Std.U8 head_20 (@List.cons.{0} Aeneas.Std.U8 head_21 (@List.cons.{0} Aeneas.Std.U8 head_22 x)))))))))))))))))))))))) tail (fun (head_23 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 (@List.cons.{0} Aeneas.Std.U8 head_19 (@List.cons.{0} Aeneas.Std.U8 head_20 (@List.cons.{0} Aeneas.Std.U8 head_21 (@List.cons.{0} Aeneas.Std.U8 head_22 (@List.cons.{0} Aeneas.Std.U8 head_23 x))))))))))))))))))))))))) tail (fun (head_24 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 (@List.cons.{0} Aeneas.Std.U8 head_19 (@List.cons.{0} Aeneas.Std.U8 head_20 (@List.cons.{0} Aeneas.Std.U8 head_21 (@List.cons.{0} Aeneas.Std.U8 head_22 (@List.cons.{0} Aeneas.Std.U8 head_23 (@List.cons.{0} Aeneas.Std.U8 head_24 x)))))))))))))))))))))))))) tail (fun (head_25 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 (@List.cons.{0} Aeneas.Std.U8 head_19 (@List.cons.{0} Aeneas.Std.U8 head_20 (@List.cons.{0} Aeneas.Std.U8 head_21 (@List.cons.{0} Aeneas.Std.U8 head_22 (@List.cons.{0} Aeneas.Std.U8 head_23 (@List.cons.{0} Aeneas.Std.U8 head_24 (@List.cons.{0} Aeneas.Std.U8 head_25 x))))))))))))))))))))))))))) tail (fun (head_26 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 (@List.cons.{0} Aeneas.Std.U8 head_19 (@List.cons.{0} Aeneas.Std.U8 head_20 (@List.cons.{0} Aeneas.Std.U8 head_21 (@List.cons.{0} Aeneas.Std.U8 head_22 (@List.cons.{0} Aeneas.Std.U8 head_23 (@List.cons.{0} Aeneas.Std.U8 head_24 (@List.cons.{0} Aeneas.Std.U8 head_25 (@List.cons.{0} Aeneas.Std.U8 head_26 x)))))))))))))))))))))))))))) tail (fun (head_27 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 (@List.cons.{0} Aeneas.Std.U8 head_19 (@List.cons.{0} Aeneas.Std.U8 head_20 (@List.cons.{0} Aeneas.Std.U8 head_21 (@List.cons.{0} Aeneas.Std.U8 head_22 (@List.cons.{0} Aeneas.Std.U8 head_23 (@List.cons.{0} Aeneas.Std.U8 head_24 (@List.cons.{0} Aeneas.Std.U8 head_25 (@List.cons.{0} Aeneas.Std.U8 head_26 (@List.cons.{0} Aeneas.Std.U8 head_27 x))))))))))))))))))))))))))))) tail (fun (head_28 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 (@List.cons.{0} Aeneas.Std.U8 head_19 (@List.cons.{0} Aeneas.Std.U8 head_20 (@List.cons.{0} Aeneas.Std.U8 head_21 (@List.cons.{0} Aeneas.Std.U8 head_22 (@List.cons.{0} Aeneas.Std.U8 head_23 (@List.cons.{0} Aeneas.Std.U8 head_24 (@List.cons.{0} Aeneas.Std.U8 head_25 (@List.cons.{0} Aeneas.Std.U8 head_26 (@List.cons.{0} Aeneas.Std.U8 head_27 (@List.cons.{0} Aeneas.Std.U8 head_28 x)))))))))))))))))))))))))))))) tail (fun (head_29 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 (@List.cons.{0} Aeneas.Std.U8 head_19 (@List.cons.{0} Aeneas.Std.U8 head_20 (@List.cons.{0} Aeneas.Std.U8 head_21 (@List.cons.{0} Aeneas.Std.U8 head_22 (@List.cons.{0} Aeneas.Std.U8 head_23 (@List.cons.{0} Aeneas.Std.U8 head_24 (@List.cons.{0} Aeneas.Std.U8 head_25 (@List.cons.{0} Aeneas.Std.U8 head_26 (@List.cons.{0} Aeneas.Std.U8 head_27 (@List.cons.{0} Aeneas.Std.U8 head_28 (@List.cons.{0} Aeneas.Std.U8 head_29 x))))))))))))))))))))))))))))))) tail (fun (head_30 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 (@List.cons.{0} Aeneas.Std.U8 head_19 (@List.cons.{0} Aeneas.Std.U8 head_20 (@List.cons.{0} Aeneas.Std.U8 head_21 (@List.cons.{0} Aeneas.Std.U8 head_22 (@List.cons.{0} Aeneas.Std.U8 head_23 (@List.cons.{0} Aeneas.Std.U8 head_24 (@List.cons.{0} Aeneas.Std.U8 head_25 (@List.cons.{0} Aeneas.Std.U8 head_26 (@List.cons.{0} Aeneas.Std.U8 head_27 (@List.cons.{0} Aeneas.Std.U8 head_28 (@List.cons.{0} Aeneas.Std.U8 head_29 (@List.cons.{0} Aeneas.Std.U8 head_30 x)))))))))))))))))))))))))))))))) tail (fun (head_31 : Aeneas.Std.U8) (tail : List.{0} Aeneas.Std.U8) => @CurveFieldProofs.bytesVal._sparseCasesOn_2.{u_1, 0} Aeneas.Std.U8 (fun (x : List.{0} Aeneas.Std.U8) => motive (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 (@List.cons.{0} Aeneas.Std.U8 head_19 (@List.cons.{0} Aeneas.Std.U8 head_20 (@List.cons.{0} Aeneas.Std.U8 head_21 (@List.cons.{0} Aeneas.Std.U8 head_22 (@List.cons.{0} Aeneas.Std.U8 head_23 (@List.cons.{0} Aeneas.Std.U8 head_24 (@List.cons.{0} Aeneas.Std.U8 head_25 (@List.cons.{0} Aeneas.Std.U8 head_26 (@List.cons.{0} Aeneas.Std.U8 head_27 (@List.cons.{0} Aeneas.Std.U8 head_28 (@List.cons.{0} Aeneas.Std.U8 head_29 (@List.cons.{0} Aeneas.Std.U8 head_30 (@List.cons.{0} Aeneas.Std.U8 head_31 x))))))))))))))))))))))))))))))))) tail (h_1 head head_1 head_2 head_3 head_4 head_5 head_6 head_7 head_8 head_9 head_10 head_11 head_12 head_13 head_14 head_15 head_16 head_17 head_18 head_19 head_20 head_21 head_22 head_23 head_24 head_25 head_26 head_27 head_28 head_29 head_30 head_31) fun (h : Nat.hasNotBit (nat_lit 1) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 (@List.cons.{0} Aeneas.Std.U8 head_19 (@List.cons.{0} Aeneas.Std.U8 head_20 (@List.cons.{0} Aeneas.Std.U8 head_21 (@List.cons.{0} Aeneas.Std.U8 head_22 (@List.cons.{0} Aeneas.Std.U8 head_23 (@List.cons.{0} Aeneas.Std.U8 head_24 (@List.cons.{0} Aeneas.Std.U8 head_25 (@List.cons.{0} Aeneas.Std.U8 head_26 (@List.cons.{0} Aeneas.Std.U8 head_27 (@List.cons.{0} Aeneas.Std.U8 head_28 (@List.cons.{0} Aeneas.Std.U8 head_29 (@List.cons.{0} Aeneas.Std.U8 head_30 (@List.cons.{0} Aeneas.Std.U8 head_31 tail))))))))))))))))))))))))))))))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 (@List.cons.{0} Aeneas.Std.U8 head_19 (@List.cons.{0} Aeneas.Std.U8 head_20 (@List.cons.{0} Aeneas.Std.U8 head_21 (@List.cons.{0} Aeneas.Std.U8 head_22 (@List.cons.{0} Aeneas.Std.U8 head_23 (@List.cons.{0} Aeneas.Std.U8 head_24 (@List.cons.{0} Aeneas.Std.U8 head_25 (@List.cons.{0} Aeneas.Std.U8 head_26 (@List.cons.{0} Aeneas.Std.U8 head_27 (@List.cons.{0} Aeneas.Std.U8 head_28 (@List.cons.{0} Aeneas.Std.U8 head_29 (@List.cons.{0} Aeneas.Std.U8 head_30 tail)))))))))))))))))))))))))))))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 (@List.cons.{0} Aeneas.Std.U8 head_19 (@List.cons.{0} Aeneas.Std.U8 head_20 (@List.cons.{0} Aeneas.Std.U8 head_21 (@List.cons.{0} Aeneas.Std.U8 head_22 (@List.cons.{0} Aeneas.Std.U8 head_23 (@List.cons.{0} Aeneas.Std.U8 head_24 (@List.cons.{0} Aeneas.Std.U8 head_25 (@List.cons.{0} Aeneas.Std.U8 head_26 (@List.cons.{0} Aeneas.Std.U8 head_27 (@List.cons.{0} Aeneas.Std.U8 head_28 (@List.cons.{0} Aeneas.Std.U8 head_29 tail))))))))))))))))))))))))))))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 (@List.cons.{0} Aeneas.Std.U8 head_19 (@List.cons.{0} Aeneas.Std.U8 head_20 (@List.cons.{0} Aeneas.Std.U8 head_21 (@List.cons.{0} Aeneas.Std.U8 head_22 (@List.cons.{0} Aeneas.Std.U8 head_23 (@List.cons.{0} Aeneas.Std.U8 head_24 (@List.cons.{0} Aeneas.Std.U8 head_25 (@List.cons.{0} Aeneas.Std.U8 head_26 (@List.cons.{0} Aeneas.Std.U8 head_27 (@List.cons.{0} Aeneas.Std.U8 head_28 tail)))))))))))))))))))))))))))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 (@List.cons.{0} Aeneas.Std.U8 head_19 (@List.cons.{0} Aeneas.Std.U8 head_20 (@List.cons.{0} Aeneas.Std.U8 head_21 (@List.cons.{0} Aeneas.Std.U8 head_22 (@List.cons.{0} Aeneas.Std.U8 head_23 (@List.cons.{0} Aeneas.Std.U8 head_24 (@List.cons.{0} Aeneas.Std.U8 head_25 (@List.cons.{0} Aeneas.Std.U8 head_26 (@List.cons.{0} Aeneas.Std.U8 head_27 tail))))))))))))))))))))))))))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 (@List.cons.{0} Aeneas.Std.U8 head_19 (@List.cons.{0} Aeneas.Std.U8 head_20 (@List.cons.{0} Aeneas.Std.U8 head_21 (@List.cons.{0} Aeneas.Std.U8 head_22 (@List.cons.{0} Aeneas.Std.U8 head_23 (@List.cons.{0} Aeneas.Std.U8 head_24 (@List.cons.{0} Aeneas.Std.U8 head_25 (@List.cons.{0} Aeneas.Std.U8 head_26 tail)))))))))))))))))))))))))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 (@List.cons.{0} Aeneas.Std.U8 head_19 (@List.cons.{0} Aeneas.Std.U8 head_20 (@List.cons.{0} Aeneas.Std.U8 head_21 (@List.cons.{0} Aeneas.Std.U8 head_22 (@List.cons.{0} Aeneas.Std.U8 head_23 (@List.cons.{0} Aeneas.Std.U8 head_24 (@List.cons.{0} Aeneas.Std.U8 head_25 tail))))))))))))))))))))))))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 (@List.cons.{0} Aeneas.Std.U8 head_19 (@List.cons.{0} Aeneas.Std.U8 head_20 (@List.cons.{0} Aeneas.Std.U8 head_21 (@List.cons.{0} Aeneas.Std.U8 head_22 (@List.cons.{0} Aeneas.Std.U8 head_23 (@List.cons.{0} Aeneas.Std.U8 head_24 tail)))))))))))))))))))))))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 (@List.cons.{0} Aeneas.Std.U8 head_19 (@List.cons.{0} Aeneas.Std.U8 head_20 (@List.cons.{0} Aeneas.Std.U8 head_21 (@List.cons.{0} Aeneas.Std.U8 head_22 (@List.cons.{0} Aeneas.Std.U8 head_23 tail))))))))))))))))))))))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 (@List.cons.{0} Aeneas.Std.U8 head_19 (@List.cons.{0} Aeneas.Std.U8 head_20 (@List.cons.{0} Aeneas.Std.U8 head_21 (@List.cons.{0} Aeneas.Std.U8 head_22 tail)))))))))))))))))))))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 (@List.cons.{0} Aeneas.Std.U8 head_19 (@List.cons.{0} Aeneas.Std.U8 head_20 (@List.cons.{0} Aeneas.Std.U8 head_21 tail))))))))))))))))))))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 (@List.cons.{0} Aeneas.Std.U8 head_19 (@List.cons.{0} Aeneas.Std.U8 head_20 tail)))))))))))))))))))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 (@List.cons.{0} Aeneas.Std.U8 head_19 tail))))))))))))))))))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 (@List.cons.{0} Aeneas.Std.U8 head_18 tail)))))))))))))))))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 (@List.cons.{0} Aeneas.Std.U8 head_17 tail))))))))))))))))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 (@List.cons.{0} Aeneas.Std.U8 head_16 tail)))))))))))))))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 (@List.cons.{0} Aeneas.Std.U8 head_15 tail))))))))))))))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 (@List.cons.{0} Aeneas.Std.U8 head_14 tail)))))))))))))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 (@List.cons.{0} Aeneas.Std.U8 head_13 tail))))))))))))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 (@List.cons.{0} Aeneas.Std.U8 head_12 tail)))))))))))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 (@List.cons.{0} Aeneas.Std.U8 head_11 tail))))))))))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 (@List.cons.{0} Aeneas.Std.U8 head_10 tail)))))))))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 (@List.cons.{0} Aeneas.Std.U8 head_9 tail))))))))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 (@List.cons.{0} Aeneas.Std.U8 head_8 tail)))))))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 (@List.cons.{0} Aeneas.Std.U8 head_7 tail))))))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 (@List.cons.{0} Aeneas.Std.U8 head_6 tail)))))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 (@List.cons.{0} Aeneas.Std.U8 head_5 tail))))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 (@List.cons.{0} Aeneas.Std.U8 head_4 tail)))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 (@List.cons.{0} Aeneas.Std.U8 head_3 tail))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 (@List.cons.{0} Aeneas.Std.U8 head_2 tail)))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head (@List.cons.{0} Aeneas.Std.U8 head_1 tail))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U8 head tail)) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U8 x)) => h_2 x
spec|CurveFieldProofs.complX|def|value=fun (Pt : CurveFieldProofs.ComplPoint) => @HDiv.hDiv.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHDiv.{0} CurveFieldProofs.Fp (@DivInvMonoid.toDiv.{0} CurveFieldProofs.Fp (@DivisionRing.toDivInvMonoid.{0} CurveFieldProofs.Fp (@Field.toDivisionRing.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP))))) (CurveFieldProofs.denote (curve25519.backend.serial.curve_models.CompletedPoint.X Pt)) (CurveFieldProofs.denote (curve25519.backend.serial.curve_models.CompletedPoint.Z Pt))
spec|CurveFieldProofs.complY|def|value=fun (Pt : CurveFieldProofs.ComplPoint) => @HDiv.hDiv.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHDiv.{0} CurveFieldProofs.Fp (@DivInvMonoid.toDiv.{0} CurveFieldProofs.Fp (@DivisionRing.toDivInvMonoid.{0} CurveFieldProofs.Fp (@Field.toDivisionRing.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP))))) (CurveFieldProofs.denote (curve25519.backend.serial.curve_models.CompletedPoint.Y Pt)) (CurveFieldProofs.denote (curve25519.backend.serial.curve_models.CompletedPoint.T Pt))
spec|CurveFieldProofs.denote|def|value=fun (a : CurveFieldProofs.Fe) => @Nat.cast.{0} CurveFieldProofs.Fp (@AddMonoidWithOne.toNatCast.{0} CurveFieldProofs.Fp (@AddGroupWithOne.toAddMonoidWithOne.{0} CurveFieldProofs.Fp (@Ring.toAddGroupWithOne.{0} CurveFieldProofs.Fp (@CommRing.toRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P))))) (CurveFieldProofs.feVal a)
spec|CurveFieldProofs.dsmFold|def|value=fun (aD bD : Nat → Int) (pA pB x : Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) (x_1 : Nat) => @Nat.brecOn.{1} (fun (x : Nat) => Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp → Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) x_1 (CurveFieldProofs.dsmFold._f aD bD pA pB) x
spec|CurveFieldProofs.dsmFold._f|def|value=fun (aD bD : Nat → Int) (pA pB : Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) (x : Nat) (f : @Nat.below.{1} (fun (x : Nat) => Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp → Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) x) (x_1 : Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) => CurveFieldProofs.dsmFold.match_1.{1} (fun (x : Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) (x_2 : Nat) => @Nat.below.{1} (fun (x : Nat) => Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp → Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) x_2 → Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) x_1 x (fun (P : Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) (x : @Nat.below.{1} (fun (x : Nat) => Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp → Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0)))) => P) (fun (P : Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) (j : Nat) (x : @Nat.below.{1} (fun (x : Nat) => Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp → Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) (Nat.succ j)) => x.1 (CurveFieldProofs.edDigit pB (bD j) (CurveFieldProofs.edDigit pA (aD j) (CurveFieldProofs.edAdd P P)))) f
spec|CurveFieldProofs.dsmFold.match_1|def|value=fun (motive : Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp → Nat → Sort u_1) (x : Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) (x_1 : Nat) (h_1 : (P : Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) → motive P (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0)))) (h_2 : (P : Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) → (j : Nat) → motive P (Nat.succ j)) => @Nat.casesOn.{u_1} (fun (x_2 : Nat) => motive x x_2) x_1 (h_1 x) fun (n : Nat) => h_2 x n
spec|CurveFieldProofs.edAdd|def|value=fun (p q : Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) => @Prod.mk.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp (@HDiv.hDiv.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHDiv.{0} CurveFieldProofs.Fp (@DivInvMonoid.toDiv.{0} CurveFieldProofs.Fp (@DivisionRing.toDivInvMonoid.{0} CurveFieldProofs.Fp (@Field.toDivisionRing.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP))))) (@HAdd.hAdd.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHAdd.{0} CurveFieldProofs.Fp (@Distrib.toAdd.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) (@HMul.hMul.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHMul.{0} CurveFieldProofs.Fp (@Distrib.toMul.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) (@Prod.fst.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp p) (@Prod.snd.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp q)) (@HMul.hMul.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHMul.{0} CurveFieldProofs.Fp (@Distrib.toMul.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) (@Prod.fst.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp q) (@Prod.snd.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp p))) (@HAdd.hAdd.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHAdd.{0} CurveFieldProofs.Fp (@Distrib.toAdd.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 1) (@One.toOfNat1.{0} CurveFieldProofs.Fp (@AddMonoidWithOne.toOne.{0} CurveFieldProofs.Fp (@AddGroupWithOne.toAddMonoidWithOne.{0} CurveFieldProofs.Fp (@Ring.toAddGroupWithOne.{0} CurveFieldProofs.Fp (@DivisionRing.toRing.{0} CurveFieldProofs.Fp (@Field.toDivisionRing.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP)))))))) (@HMul.hMul.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHMul.{0} CurveFieldProofs.Fp (@Distrib.toMul.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) (@HMul.hMul.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHMul.{0} CurveFieldProofs.Fp (@Distrib.toMul.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) (@HMul.hMul.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHMul.{0} CurveFieldProofs.Fp (@Distrib.toMul.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) (@HMul.hMul.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHMul.{0} CurveFieldProofs.Fp (@Distrib.toMul.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) CurveFieldProofs.edD (@Prod.fst.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp p)) (@Prod.fst.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp q)) (@Prod.snd.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp p)) (@Prod.snd.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp q)))) (@HDiv.hDiv.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHDiv.{0} CurveFieldProofs.Fp (@DivInvMonoid.toDiv.{0} CurveFieldProofs.Fp (@DivisionRing.toDivInvMonoid.{0} CurveFieldProofs.Fp (@Field.toDivisionRing.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP))))) (@HAdd.hAdd.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHAdd.{0} CurveFieldProofs.Fp (@Distrib.toAdd.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) (@HMul.hMul.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHMul.{0} CurveFieldProofs.Fp (@Distrib.toMul.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) (@Prod.snd.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp p) (@Prod.snd.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp q)) (@HMul.hMul.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHMul.{0} CurveFieldProofs.Fp (@Distrib.toMul.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) (@Prod.fst.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp p) (@Prod.fst.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp q))) (@HSub.hSub.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHSub.{0} CurveFieldProofs.Fp (@SubNegMonoid.toSub.{0} CurveFieldProofs.Fp (@AddGroup.toSubNegMonoid.{0} CurveFieldProofs.Fp (@AddGroupWithOne.toAddGroup.{0} CurveFieldProofs.Fp (@Ring.toAddGroupWithOne.{0} CurveFieldProofs.Fp (@DivisionRing.toRing.{0} CurveFieldProofs.Fp (@Field.toDivisionRing.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP)))))))) (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 1) (@One.toOfNat1.{0} CurveFieldProofs.Fp (@AddMonoidWithOne.toOne.{0} CurveFieldProofs.Fp (@AddGroupWithOne.toAddMonoidWithOne.{0} CurveFieldProofs.Fp (@Ring.toAddGroupWithOne.{0} CurveFieldProofs.Fp (@DivisionRing.toRing.{0} CurveFieldProofs.Fp (@Field.toDivisionRing.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP)))))))) (@HMul.hMul.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHMul.{0} CurveFieldProofs.Fp (@Distrib.toMul.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) (@HMul.hMul.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHMul.{0} CurveFieldProofs.Fp (@Distrib.toMul.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) (@HMul.hMul.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHMul.{0} CurveFieldProofs.Fp (@Distrib.toMul.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) (@HMul.hMul.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHMul.{0} CurveFieldProofs.Fp (@Distrib.toMul.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toDistrib.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P)))))))) CurveFieldProofs.edD (@Prod.fst.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp p)) (@Prod.fst.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp q)) (@Prod.snd.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp p)) (@Prod.snd.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp q))))
spec|CurveFieldProofs.edBasePt|def|value=@Prod.mk.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 15112221349535400772501151409588531511454012693041857206046113283949847762202) (@instOfNatAtLeastTwo.{0} CurveFieldProofs.Fp (nat_lit 15112221349535400772501151409588531511454012693041857206046113283949847762202) (@AddMonoidWithOne.toNatCast.{0} CurveFieldProofs.Fp (@AddGroupWithOne.toAddMonoidWithOne.{0} CurveFieldProofs.Fp (@Ring.toAddGroupWithOne.{0} CurveFieldProofs.Fp (@DivisionRing.toRing.{0} CurveFieldProofs.Fp (@Field.toDivisionRing.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP)))))) CurveFieldProofs.edBasePt._proof_1)) (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 46316835694926478169428394003475163141307993866256225615783033603165251855960) (@instOfNatAtLeastTwo.{0} CurveFieldProofs.Fp (nat_lit 46316835694926478169428394003475163141307993866256225615783033603165251855960) (@AddMonoidWithOne.toNatCast.{0} CurveFieldProofs.Fp (@AddGroupWithOne.toAddMonoidWithOne.{0} CurveFieldProofs.Fp (@Ring.toAddGroupWithOne.{0} CurveFieldProofs.Fp (@DivisionRing.toRing.{0} CurveFieldProofs.Fp (@Field.toDivisionRing.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP)))))) CurveFieldProofs.edBasePt._proof_2))
spec|CurveFieldProofs.edBasePt._proof_1|prop|type=Nat.AtLeastTwo (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@OfNat.ofNat.{0} Nat (nat_lit 15112221349535400772501151409588531511454012693041857206046113283949847762201) (instOfNatNat (nat_lit 15112221349535400772501151409588531511454012693041857206046113283949847762201))) (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))
spec|CurveFieldProofs.edBasePt._proof_2|prop|type=Nat.AtLeastTwo (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@OfNat.ofNat.{0} Nat (nat_lit 46316835694926478169428394003475163141307993866256225615783033603165251855959) (instOfNatNat (nat_lit 46316835694926478169428394003475163141307993866256225615783033603165251855959))) (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))
spec|CurveFieldProofs.edD|def|value=@HDiv.hDiv.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHDiv.{0} CurveFieldProofs.Fp (@DivInvMonoid.toDiv.{0} CurveFieldProofs.Fp (@DivisionRing.toDivInvMonoid.{0} CurveFieldProofs.Fp (@Field.toDivisionRing.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP))))) (@Neg.neg.{0} CurveFieldProofs.Fp (@NegZeroClass.toNeg.{0} CurveFieldProofs.Fp (@SubNegZeroMonoid.toNegZeroClass.{0} CurveFieldProofs.Fp (@SubtractionMonoid.toSubNegZeroMonoid.{0} CurveFieldProofs.Fp (@SubtractionCommMonoid.toSubtractionMonoid.{0} CurveFieldProofs.Fp (@AddCommGroup.toDivisionAddCommMonoid.{0} CurveFieldProofs.Fp (@Ring.toAddCommGroup.{0} CurveFieldProofs.Fp (@DivisionRing.toRing.{0} CurveFieldProofs.Fp (@Field.toDivisionRing.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP))))))))) (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 121665) (@instOfNatAtLeastTwo.{0} CurveFieldProofs.Fp (nat_lit 121665) (@AddMonoidWithOne.toNatCast.{0} CurveFieldProofs.Fp (@AddGroupWithOne.toAddMonoidWithOne.{0} CurveFieldProofs.Fp (@Ring.toAddGroupWithOne.{0} CurveFieldProofs.Fp (@DivisionRing.toRing.{0} CurveFieldProofs.Fp (@Field.toDivisionRing.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP)))))) CurveFieldProofs.edD._proof_1))) (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 121666) (@instOfNatAtLeastTwo.{0} CurveFieldProofs.Fp (nat_lit 121666) (@AddMonoidWithOne.toNatCast.{0} CurveFieldProofs.Fp (@AddGroupWithOne.toAddMonoidWithOne.{0} CurveFieldProofs.Fp (@Ring.toAddGroupWithOne.{0} CurveFieldProofs.Fp (@DivisionRing.toRing.{0} CurveFieldProofs.Fp (@Field.toDivisionRing.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP)))))) CurveFieldProofs.edD._proof_2))
spec|CurveFieldProofs.edD._proof_1|prop|type=Nat.AtLeastTwo (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@OfNat.ofNat.{0} Nat (nat_lit 121664) (instOfNatNat (nat_lit 121664))) (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))
spec|CurveFieldProofs.edD._proof_2|prop|type=Nat.AtLeastTwo (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@OfNat.ofNat.{0} Nat (nat_lit 121665) (instOfNatNat (nat_lit 121665))) (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))
spec|CurveFieldProofs.edDigit|def|value=fun (aPt : Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) (d : Int) (P : Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) => @ite.{1} (Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) (@LT.lt.{0} Int Int.instLTInt (@OfNat.ofNat.{0} Int (nat_lit 0) (@instOfNat (nat_lit 0))) d) (Int.decLt (@OfNat.ofNat.{0} Int (nat_lit 0) (@instOfNat (nat_lit 0))) d) (CurveFieldProofs.edAdd P (CurveFieldProofs.edOdd (@HDiv.hDiv.{0, 0, 0} Nat Nat Nat (@instHDiv.{0} Nat Nat.instDiv) (@HSub.hSub.{0, 0, 0} Nat Nat Nat (@instHSub.{0} Nat instSubNat) (Int.toNat d) (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2)))) aPt)) (@ite.{1} (Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) (@LT.lt.{0} Int Int.instLTInt d (@OfNat.ofNat.{0} Int (nat_lit 0) (@instOfNat (nat_lit 0)))) (Int.decLt d (@OfNat.ofNat.{0} Int (nat_lit 0) (@instOfNat (nat_lit 0)))) (CurveFieldProofs.edAdd P (CurveFieldProofs.edNeg (CurveFieldProofs.edOdd (@HDiv.hDiv.{0, 0, 0} Nat Nat Nat (@instHDiv.{0} Nat Nat.instDiv) (@HSub.hSub.{0, 0, 0} Nat Nat Nat (@instHSub.{0} Nat instSubNat) (Int.toNat (@Neg.neg.{0} Int Int.instNegInt d)) (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2)))) aPt))) P)
spec|CurveFieldProofs.edId|def|value=@Prod.mk.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 0) (@Zero.toOfNat0.{0} CurveFieldProofs.Fp (@MulZeroClass.toZero.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocSemiring.toMulZeroClass.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} CurveFieldProofs.Fp (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} CurveFieldProofs.Fp (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} CurveFieldProofs.Fp (@CommRing.toNonUnitalCommRing.{0} CurveFieldProofs.Fp (ZMod.commRing CurveFieldProofs.P))))))))) (@OfNat.ofNat.{0} CurveFieldProofs.Fp (nat_lit 1) (@One.toOfNat1.{0} CurveFieldProofs.Fp (@AddMonoidWithOne.toOne.{0} CurveFieldProofs.Fp (@AddGroupWithOne.toAddMonoidWithOne.{0} CurveFieldProofs.Fp (@Ring.toAddGroupWithOne.{0} CurveFieldProofs.Fp (@DivisionRing.toRing.{0} CurveFieldProofs.Fp (@Field.toDivisionRing.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP))))))))
spec|CurveFieldProofs.edNeg|def|value=fun (p : Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) => @Prod.mk.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp (@Neg.neg.{0} CurveFieldProofs.Fp (@NegZeroClass.toNeg.{0} CurveFieldProofs.Fp (@SubNegZeroMonoid.toNegZeroClass.{0} CurveFieldProofs.Fp (@SubtractionMonoid.toSubNegZeroMonoid.{0} CurveFieldProofs.Fp (@SubtractionCommMonoid.toSubtractionMonoid.{0} CurveFieldProofs.Fp (@AddCommGroup.toDivisionAddCommMonoid.{0} CurveFieldProofs.Fp (@Ring.toAddCommGroup.{0} CurveFieldProofs.Fp (@DivisionRing.toRing.{0} CurveFieldProofs.Fp (@Field.toDivisionRing.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP))))))))) (@Prod.fst.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp p)) (@Prod.snd.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp p)
spec|CurveFieldProofs.edOdd|def|value=fun (x : Nat) (x_1 : Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) => @Nat.brecOn.{1} (fun (x : Nat) => Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp → Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) x CurveFieldProofs.edOdd._f x_1
spec|CurveFieldProofs.edOdd._f|def|value=fun (x : Nat) (f : @Nat.below.{1} (fun (x : Nat) => Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp → Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) x) (x_1 : Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) => CurveFieldProofs.edOdd.match_1.{1} (fun (x : Nat) (x_2 : Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) => @Nat.below.{1} (fun (x : Nat) => Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp → Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) x → Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) x x_1 (fun (p : Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) (x : @Nat.below.{1} (fun (x : Nat) => Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp → Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0)))) => p) (fun (k : Nat) (p : Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) (x : @Nat.below.{1} (fun (x : Nat) => Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp → Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) (Nat.succ k)) => CurveFieldProofs.edAdd (CurveFieldProofs.edAdd p p) (x.1 p)) f
spec|CurveFieldProofs.edOdd.match_1|def|value=fun (motive : Nat → Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp → Sort u_1) (x : Nat) (x_1 : Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) (h_1 : (p : Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) → motive (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0))) p) (h_2 : (k : Nat) → (p : Prod.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp) → motive (Nat.succ k) p) => @Nat.casesOn.{u_1} (fun (x : Nat) => motive x x_1) x (h_1 x_1) fun (n : Nat) => h_2 n x_1
spec|CurveFieldProofs.edPt|def|value=fun (P : CurveFieldProofs.EdPoint) => @Prod.mk.{0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp (CurveFieldProofs.edX P) (CurveFieldProofs.edY P)
spec|CurveFieldProofs.edX|def|value=fun (Pt : CurveFieldProofs.EdPoint) => @HDiv.hDiv.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHDiv.{0} CurveFieldProofs.Fp (@DivInvMonoid.toDiv.{0} CurveFieldProofs.Fp (@DivisionRing.toDivInvMonoid.{0} CurveFieldProofs.Fp (@Field.toDivisionRing.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP))))) (CurveFieldProofs.denote (curve25519.edwards.EdwardsPoint.X Pt)) (CurveFieldProofs.denote (curve25519.edwards.EdwardsPoint.Z Pt))
spec|CurveFieldProofs.edY|def|value=fun (Pt : CurveFieldProofs.EdPoint) => @HDiv.hDiv.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHDiv.{0} CurveFieldProofs.Fp (@DivInvMonoid.toDiv.{0} CurveFieldProofs.Fp (@DivisionRing.toDivInvMonoid.{0} CurveFieldProofs.Fp (@Field.toDivisionRing.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP))))) (CurveFieldProofs.denote (curve25519.edwards.EdwardsPoint.Y Pt)) (CurveFieldProofs.denote (curve25519.edwards.EdwardsPoint.Z Pt))
spec|CurveFieldProofs.feVal|def|value=fun (a : CurveFieldProofs.Fe) => CurveFieldProofs.feVal.match_1.{1} (fun (x : List.{0} Aeneas.Std.U64) => Nat) (@Subtype.val.{1} (List.{0} Aeneas.Std.U64) (fun (l : List.{0} Aeneas.Std.U64) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U64 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 5) (instOfNatNat (nat_lit 5))) curve25519.backend.serial.u64.field.FieldElement51._proof_1))) a) (fun (a0 a1 a2 a3 a4 : Aeneas.Std.U64) => CurveFieldProofs.limbsVal a0 a1 a2 a3 a4) fun (x : List.{0} Aeneas.Std.U64) => @OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0))
spec|CurveFieldProofs.feVal._sparseCasesOn_1|def|value=fun {α : Type u} {motive : (t : List.{u} α) → Sort u_1} (t : List.{u} α) (cons : (head : α) → (tail : List.{u} α) → motive (@List.cons.{u} α head tail)) => @List.rec.{u_1, u} α (fun (t : List.{u} α) => ((h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{u} α t)) → motive t) → motive t) (fun («else» : (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{u} α (@List.nil.{u} α))) → motive (@List.nil.{u} α)) => «else» (@Nat.ne_of_beq_eq_false (Nat.land (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))) (Nat.shiftRight (nat_lit 2) (nat_lit 0))) (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))) (@Eq.refl.{1} Bool Bool.false))) (fun (head : α) (tail : List.{u} α) (tail_ih : ((h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{u} α tail)) → motive tail) → motive tail) («else» : (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{u} α (@List.cons.{u} α head tail))) → motive (@List.cons.{u} α head tail)) => cons head tail) t
spec|CurveFieldProofs.feVal._sparseCasesOn_2|def|value=fun {α : Type u} {motive : (t : List.{u} α) → Sort u_1} (t : List.{u} α) (nil : motive (@List.nil.{u} α)) => @List.rec.{u_1, u} α (fun (t : List.{u} α) => ((h : Nat.hasNotBit (nat_lit 1) (@List.ctorIdx.{u} α t)) → motive t) → motive t) (fun («else» : (h : Nat.hasNotBit (nat_lit 1) (@List.ctorIdx.{u} α (@List.nil.{u} α))) → motive (@List.nil.{u} α)) => nil) (fun (head : α) (tail : List.{u} α) (tail_ih : ((h : Nat.hasNotBit (nat_lit 1) (@List.ctorIdx.{u} α tail)) → motive tail) → motive tail) («else» : (h : Nat.hasNotBit (nat_lit 1) (@List.ctorIdx.{u} α (@List.cons.{u} α head tail))) → motive (@List.cons.{u} α head tail)) => «else» (@Nat.ne_of_beq_eq_false (Nat.land (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))) (Nat.shiftRight (nat_lit 1) (nat_lit 1))) (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))) (@Eq.refl.{1} Bool Bool.false))) t
spec|CurveFieldProofs.feVal.match_1|def|value=fun (motive : List.{0} Aeneas.Std.U64 → Sort u_1) (x : List.{0} Aeneas.Std.U64) (h_1 : (a0 a1 a2 a3 a4 : Aeneas.Std.U64) → motive (@List.cons.{0} Aeneas.Std.U64 a0 (@List.cons.{0} Aeneas.Std.U64 a1 (@List.cons.{0} Aeneas.Std.U64 a2 (@List.cons.{0} Aeneas.Std.U64 a3 (@List.cons.{0} Aeneas.Std.U64 a4 (@List.nil.{0} Aeneas.Std.U64))))))) (h_2 : (x : List.{0} Aeneas.Std.U64) → motive x) => @CurveFieldProofs.feVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U64 (fun (x : List.{0} Aeneas.Std.U64) => motive x) x (fun (head : Aeneas.Std.U64) (tail : List.{0} Aeneas.Std.U64) => @CurveFieldProofs.feVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U64 (fun (x : List.{0} Aeneas.Std.U64) => motive (@List.cons.{0} Aeneas.Std.U64 head x)) tail (fun (head_1 : Aeneas.Std.U64) (tail : List.{0} Aeneas.Std.U64) => @CurveFieldProofs.feVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U64 (fun (x : List.{0} Aeneas.Std.U64) => motive (@List.cons.{0} Aeneas.Std.U64 head (@List.cons.{0} Aeneas.Std.U64 head_1 x))) tail (fun (head_2 : Aeneas.Std.U64) (tail : List.{0} Aeneas.Std.U64) => @CurveFieldProofs.feVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U64 (fun (x : List.{0} Aeneas.Std.U64) => motive (@List.cons.{0} Aeneas.Std.U64 head (@List.cons.{0} Aeneas.Std.U64 head_1 (@List.cons.{0} Aeneas.Std.U64 head_2 x)))) tail (fun (head_3 : Aeneas.Std.U64) (tail : List.{0} Aeneas.Std.U64) => @CurveFieldProofs.feVal._sparseCasesOn_1.{u_1, 0} Aeneas.Std.U64 (fun (x : List.{0} Aeneas.Std.U64) => motive (@List.cons.{0} Aeneas.Std.U64 head (@List.cons.{0} Aeneas.Std.U64 head_1 (@List.cons.{0} Aeneas.Std.U64 head_2 (@List.cons.{0} Aeneas.Std.U64 head_3 x))))) tail (fun (head_4 : Aeneas.Std.U64) (tail : List.{0} Aeneas.Std.U64) => @CurveFieldProofs.feVal._sparseCasesOn_2.{u_1, 0} Aeneas.Std.U64 (fun (x : List.{0} Aeneas.Std.U64) => motive (@List.cons.{0} Aeneas.Std.U64 head (@List.cons.{0} Aeneas.Std.U64 head_1 (@List.cons.{0} Aeneas.Std.U64 head_2 (@List.cons.{0} Aeneas.Std.U64 head_3 (@List.cons.{0} Aeneas.Std.U64 head_4 x)))))) tail (h_1 head head_1 head_2 head_3 head_4) fun (h : Nat.hasNotBit (nat_lit 1) (@List.ctorIdx.{0} Aeneas.Std.U64 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U64 head (@List.cons.{0} Aeneas.Std.U64 head_1 (@List.cons.{0} Aeneas.Std.U64 head_2 (@List.cons.{0} Aeneas.Std.U64 head_3 (@List.cons.{0} Aeneas.Std.U64 head_4 tail)))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U64 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U64 head (@List.cons.{0} Aeneas.Std.U64 head_1 (@List.cons.{0} Aeneas.Std.U64 head_2 (@List.cons.{0} Aeneas.Std.U64 head_3 tail))))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U64 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U64 head (@List.cons.{0} Aeneas.Std.U64 head_1 (@List.cons.{0} Aeneas.Std.U64 head_2 tail)))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U64 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U64 head (@List.cons.{0} Aeneas.Std.U64 head_1 tail))) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U64 tail)) => h_2 (@List.cons.{0} Aeneas.Std.U64 head tail)) fun (h : Nat.hasNotBit (nat_lit 2) (@List.ctorIdx.{0} Aeneas.Std.U64 x)) => h_2 x
spec|CurveFieldProofs.fe_to_bytes|def|value=curve25519.backend.serial.u64.field.FieldElement51.to_bytes
spec|CurveFieldProofs.instDecidableRangeEq|def|value=fun (e r : Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) CurveFieldProofs.rangeEq._proof_1)) (n : Nat) => have this : Iff (CurveFieldProofs.rangeEq e r n) (∀ (j : Nat), @LT.lt.{0} Nat instLTNat j (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) → @LE.le.{0} Nat instLENat n j → @Eq.{1} Aeneas.Std.U8 (@GetElem?.getElem!.{0, 0, 0} (List.{0} Aeneas.Std.U8) Nat Aeneas.Std.U8 (fun («as» : List.{0} Aeneas.Std.U8) (i : Nat) => @LT.lt.{0} Nat instLTNat i (@List.length.{0} Aeneas.Std.U8 «as»)) (@List.instGetElem?NatLtLength.{0} Aeneas.Std.U8) (Aeneas.Std.instInhabitedUScalar Aeneas.Std.UScalarTy.U8) (@Subtype.val.{1} (List.{0} Aeneas.Std.U8) (fun (l : List.{0} Aeneas.Std.U8) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U8 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) CurveFieldProofs.rangeEq._proof_1))) e) j) (@GetElem?.getElem!.{0, 0, 0} (List.{0} Aeneas.Std.U8) Nat Aeneas.Std.U8 (fun («as» : List.{0} Aeneas.Std.U8) (i : Nat) => @LT.lt.{0} Nat instLTNat i (@List.length.{0} Aeneas.Std.U8 «as»)) (@List.instGetElem?NatLtLength.{0} Aeneas.Std.U8) (Aeneas.Std.instInhabitedUScalar Aeneas.Std.UScalarTy.U8) (@Subtype.val.{1} (List.{0} Aeneas.Std.U8) (fun (l : List.{0} Aeneas.Std.U8) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U8 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) CurveFieldProofs.rangeEq._proof_1))) r) j)) := CurveFieldProofs.instDecidableRangeEq._proof_1 e r n; @decidable_of_iff (CurveFieldProofs.rangeEq e r n) (∀ (j : Nat), @LT.lt.{0} Nat instLTNat j (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) → @LE.le.{0} Nat instLENat n j → @Eq.{1} Aeneas.Std.U8 (@GetElem?.getElem!.{0, 0, 0} (List.{0} Aeneas.Std.U8) Nat Aeneas.Std.U8 (fun («as» : List.{0} Aeneas.Std.U8) (i : Nat) => @LT.lt.{0} Nat instLTNat i (@List.length.{0} Aeneas.Std.U8 «as»)) (@List.instGetElem?NatLtLength.{0} Aeneas.Std.U8) (Aeneas.Std.instInhabitedUScalar Aeneas.Std.UScalarTy.U8) (@Subtype.val.{1} (List.{0} Aeneas.Std.U8) (fun (l : List.{0} Aeneas.Std.U8) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U8 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) CurveFieldProofs.rangeEq._proof_1))) e) j) (@GetElem?.getElem!.{0, 0, 0} (List.{0} Aeneas.Std.U8) Nat Aeneas.Std.U8 (fun («as» : List.{0} Aeneas.Std.U8) (i : Nat) => @LT.lt.{0} Nat instLTNat i (@List.length.{0} Aeneas.Std.U8 «as»)) (@List.instGetElem?NatLtLength.{0} Aeneas.Std.U8) (Aeneas.Std.instInhabitedUScalar Aeneas.Std.UScalarTy.U8) (@Subtype.val.{1} (List.{0} Aeneas.Std.U8) (fun (l : List.{0} Aeneas.Std.U8) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U8 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) CurveFieldProofs.rangeEq._proof_1))) r) j)) (CurveFieldProofs.instDecidableRangeEq._proof_2 e r n this) (@Nat.decidableBallLT (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (fun (j : Nat) (a : @LT.lt.{0} Nat instLTNat j (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32)))) => @LE.le.{0} Nat instLENat n j → @Eq.{1} Aeneas.Std.U8 (@GetElem?.getElem!.{0, 0, 0} (List.{0} Aeneas.Std.U8) Nat Aeneas.Std.U8 (fun («as» : List.{0} Aeneas.Std.U8) (i : Nat) => @LT.lt.{0} Nat instLTNat i (@List.length.{0} Aeneas.Std.U8 «as»)) (@List.instGetElem?NatLtLength.{0} Aeneas.Std.U8) (Aeneas.Std.instInhabitedUScalar Aeneas.Std.UScalarTy.U8) (@Subtype.val.{1} (List.{0} Aeneas.Std.U8) (fun (l : List.{0} Aeneas.Std.U8) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U8 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) CurveFieldProofs.rangeEq._proof_1))) e) j) (@GetElem?.getElem!.{0, 0, 0} (List.{0} Aeneas.Std.U8) Nat Aeneas.Std.U8 (fun («as» : List.{0} Aeneas.Std.U8) (i : Nat) => @LT.lt.{0} Nat instLTNat i (@List.length.{0} Aeneas.Std.U8 «as»)) (@List.instGetElem?NatLtLength.{0} Aeneas.Std.U8) (Aeneas.Std.instInhabitedUScalar Aeneas.Std.UScalarTy.U8) (@Subtype.val.{1} (List.{0} Aeneas.Std.U8) (fun (l : List.{0} Aeneas.Std.U8) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U8 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) CurveFieldProofs.rangeEq._proof_1))) r) j)) fun (n_1 : Nat) (h : @LT.lt.{0} Nat instLTNat n_1 (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32)))) => (fun (n_2 : Nat) => @forall_prop_decidable (@LE.le.{0} Nat instLENat n n_2) (fun (a : @LE.le.{0} Nat instLENat n n_2) => @Eq.{1} Aeneas.Std.U8 (@GetElem?.getElem!.{0, 0, 0} (List.{0} Aeneas.Std.U8) Nat Aeneas.Std.U8 (fun («as» : List.{0} Aeneas.Std.U8) (i : Nat) => @LT.lt.{0} Nat instLTNat i (@List.length.{0} Aeneas.Std.U8 «as»)) (@List.instGetElem?NatLtLength.{0} Aeneas.Std.U8) (Aeneas.Std.instInhabitedUScalar Aeneas.Std.UScalarTy.U8) (@Subtype.val.{1} (List.{0} Aeneas.Std.U8) (fun (l : List.{0} Aeneas.Std.U8) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U8 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) CurveFieldProofs.rangeEq._proof_1))) e) n_2) (@GetElem?.getElem!.{0, 0, 0} (List.{0} Aeneas.Std.U8) Nat Aeneas.Std.U8 (fun («as» : List.{0} Aeneas.Std.U8) (i : Nat) => @LT.lt.{0} Nat instLTNat i (@List.length.{0} Aeneas.Std.U8 «as»)) (@List.instGetElem?NatLtLength.{0} Aeneas.Std.U8) (Aeneas.Std.instInhabitedUScalar Aeneas.Std.UScalarTy.U8) (@Subtype.val.{1} (List.{0} Aeneas.Std.U8) (fun (l : List.{0} Aeneas.Std.U8) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U8 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) CurveFieldProofs.rangeEq._proof_1))) r) n_2)) (Nat.decLe n n_2) fun (h : @LE.le.{0} Nat instLENat n n_2) => (fun (n : Nat) => Aeneas.Std.instDecidableEqUScalar_1 Aeneas.Std.UScalarTy.U8 (@GetElem?.getElem!.{0, 0, 0} (List.{0} Aeneas.Std.U8) Nat Aeneas.Std.U8 (fun («as» : List.{0} Aeneas.Std.U8) (i : Nat) => @LT.lt.{0} Nat instLTNat i (@List.length.{0} Aeneas.Std.U8 «as»)) (@List.instGetElem?NatLtLength.{0} Aeneas.Std.U8) (Aeneas.Std.instInhabitedUScalar Aeneas.Std.UScalarTy.U8) (@Subtype.val.{1} (List.{0} Aeneas.Std.U8) (fun (l : List.{0} Aeneas.Std.U8) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U8 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) CurveFieldProofs.rangeEq._proof_1))) e) n) (@GetElem?.getElem!.{0, 0, 0} (List.{0} Aeneas.Std.U8) Nat Aeneas.Std.U8 (fun («as» : List.{0} Aeneas.Std.U8) (i : Nat) => @LT.lt.{0} Nat instLTNat i (@List.length.{0} Aeneas.Std.U8 «as»)) (@List.instGetElem?NatLtLength.{0} Aeneas.Std.U8) (Aeneas.Std.instInhabitedUScalar Aeneas.Std.UScalarTy.U8) (@Subtype.val.{1} (List.{0} Aeneas.Std.U8) (fun (l : List.{0} Aeneas.Std.U8) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U8 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) CurveFieldProofs.rangeEq._proof_1))) r) n)) n_2) n_1)
spec|CurveFieldProofs.instDecidableRangeEq._proof_1|prop|type=∀ (e r : Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (@id.{0} (@Eq.{1} Bool (@Decidable.decide (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) (n : Nat), Iff (CurveFieldProofs.rangeEq e r n) (∀ (j : Nat), @LT.lt.{0} Nat instLTNat j (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) → @LE.le.{0} Nat instLENat n j → @Eq.{1} Aeneas.Std.U8 (@GetElem?.getElem!.{0, 0, 0} (List.{0} Aeneas.Std.U8) Nat Aeneas.Std.U8 (fun («as» : List.{0} Aeneas.Std.U8) (i : Nat) => @LT.lt.{0} Nat instLTNat i (@List.length.{0} Aeneas.Std.U8 «as»)) (@List.instGetElem?NatLtLength.{0} Aeneas.Std.U8) (Aeneas.Std.instInhabitedUScalar Aeneas.Std.UScalarTy.U8) (@Subtype.val.{1} (List.{0} Aeneas.Std.U8) (fun (l : List.{0} Aeneas.Std.U8) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U8 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) CurveFieldProofs.rangeEq._proof_1))) e) j) (@GetElem?.getElem!.{0, 0, 0} (List.{0} Aeneas.Std.U8) Nat Aeneas.Std.U8 (fun («as» : List.{0} Aeneas.Std.U8) (i : Nat) => @LT.lt.{0} Nat instLTNat i (@List.length.{0} Aeneas.Std.U8 «as»)) (@List.instGetElem?NatLtLength.{0} Aeneas.Std.U8) (Aeneas.Std.instInhabitedUScalar Aeneas.Std.UScalarTy.U8) (@Subtype.val.{1} (List.{0} Aeneas.Std.U8) (fun (l : List.{0} Aeneas.Std.U8) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U8 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) CurveFieldProofs.rangeEq._proof_1))) r) j))
spec|CurveFieldProofs.instDecidableRangeEq._proof_2|prop|type=∀ (e r : Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) CurveFieldProofs.rangeEq._proof_1)) (n : Nat) (this : Iff (CurveFieldProofs.rangeEq e r n) (∀ (j : Nat), @LT.lt.{0} Nat instLTNat j (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) → @LE.le.{0} Nat instLENat n j → @Eq.{1} Aeneas.Std.U8 (@GetElem?.getElem!.{0, 0, 0} (List.{0} Aeneas.Std.U8) Nat Aeneas.Std.U8 (fun («as» : List.{0} Aeneas.Std.U8) (i : Nat) => @LT.lt.{0} Nat instLTNat i (@List.length.{0} Aeneas.Std.U8 «as»)) (@List.instGetElem?NatLtLength.{0} Aeneas.Std.U8) (Aeneas.Std.instInhabitedUScalar Aeneas.Std.UScalarTy.U8) (@Subtype.val.{1} (List.{0} Aeneas.Std.U8) (fun (l : List.{0} Aeneas.Std.U8) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U8 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) CurveFieldProofs.rangeEq._proof_1))) e) j) (@GetElem?.getElem!.{0, 0, 0} (List.{0} Aeneas.Std.U8) Nat Aeneas.Std.U8 (fun («as» : List.{0} Aeneas.Std.U8) (i : Nat) => @LT.lt.{0} Nat instLTNat i (@List.length.{0} Aeneas.Std.U8 «as»)) (@List.instGetElem?NatLtLength.{0} Aeneas.Std.U8) (Aeneas.Std.instInhabitedUScalar Aeneas.Std.UScalarTy.U8) (@Subtype.val.{1} (List.{0} Aeneas.Std.U8) (fun (l : List.{0} Aeneas.Std.U8) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U8 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) CurveFieldProofs.rangeEq._proof_1))) r) j))), Iff (∀ (j : Nat), @LT.lt.{0} Nat instLTNat j (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) → @LE.le.{0} Nat instLENat n j → @Eq.{1} Aeneas.Std.U8 (@GetElem?.getElem!.{0, 0, 0} (List.{0} Aeneas.Std.U8) Nat Aeneas.Std.U8 (fun («as» : List.{0} Aeneas.Std.U8) (i : Nat) => @LT.lt.{0} Nat instLTNat i (@List.length.{0} Aeneas.Std.U8 «as»)) (@List.instGetElem?NatLtLength.{0} Aeneas.Std.U8) (Aeneas.Std.instInhabitedUScalar Aeneas.Std.UScalarTy.U8) (@Subtype.val.{1} (List.{0} Aeneas.Std.U8) (fun (l : List.{0} Aeneas.Std.U8) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U8 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) CurveFieldProofs.rangeEq._proof_1))) e) j) (@GetElem?.getElem!.{0, 0, 0} (List.{0} Aeneas.Std.U8) Nat Aeneas.Std.U8 (fun («as» : List.{0} Aeneas.Std.U8) (i : Nat) => @LT.lt.{0} Nat instLTNat i (@List.length.{0} Aeneas.Std.U8 «as»)) (@List.instGetElem?NatLtLength.{0} Aeneas.Std.U8) (Aeneas.Std.instInhabitedUScalar Aeneas.Std.UScalarTy.U8) (@Subtype.val.{1} (List.{0} Aeneas.Std.U8) (fun (l : List.{0} Aeneas.Std.U8) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U8 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) CurveFieldProofs.rangeEq._proof_1))) r) j)) (CurveFieldProofs.rangeEq e r n)
spec|CurveFieldProofs.instFactPrimeP|prop|type=Fact (Nat.Prime CurveFieldProofs.P)
spec|CurveFieldProofs.limbsVal|def|value=fun (a0 a1 a2 a3 a4 : Aeneas.Std.U64) => @HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a0) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 51) (instOfNatNat (nat_lit 51)))) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a1))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 102) (instOfNatNat (nat_lit 102)))) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a2))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 153) (instOfNatNat (nat_lit 153)))) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a3))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 204) (instOfNatNat (nat_lit 204)))) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a4))
spec|CurveFieldProofs.nafDigit|def|value=fun (a : Aeneas.Std.Array.{0} Aeneas.Std.I8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) CurveFieldProofs.nafDigit._proof_1)) (k : Nat) => @Aeneas.Std.IScalar.val Aeneas.Std.IScalarTy.I8 (@GetElem?.getElem!.{0, 0, 0} (List.{0} Aeneas.Std.I8) Nat Aeneas.Std.I8 (fun («as» : List.{0} Aeneas.Std.I8) (i : Nat) => @LT.lt.{0} Nat instLTNat i (@List.length.{0} Aeneas.Std.I8 «as»)) (@List.instGetElem?NatLtLength.{0} Aeneas.Std.I8) (Aeneas.Std.instInhabitedIScalar Aeneas.Std.IScalarTy.I8) (@Subtype.val.{1} (List.{0} Aeneas.Std.I8) (fun (l : List.{0} Aeneas.Std.I8) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.I8 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) CurveFieldProofs.nafDigit._proof_1))) a) k)
spec|CurveFieldProofs.nafDigit._proof_1|prop|type=@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)
spec|CurveFieldProofs.nafSum|def|value=fun (naf : Aeneas.Std.Array.{0} Aeneas.Std.I8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) CurveFieldProofs.nafSum._proof_1)) (m : Nat) => @Finset.sum.{0, 0} Nat Int Int.instAddCommMonoid (Finset.range m) fun (k : Nat) => @HMul.hMul.{0, 0, 0} Int Int Int (@instHMul.{0} Int Int.instMul) (CurveFieldProofs.nafDigit naf k) (@HPow.hPow.{0, 0, 0} Int Nat Int (@instHPow.{0, 0} Int Nat (@Monoid.toPow.{0} Int Int.instMonoid)) (@OfNat.ofNat.{0} Int (nat_lit 2) (@instOfNat (nat_lit 2))) k)
spec|CurveFieldProofs.nafSum._proof_1|prop|type=@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 256) (instOfNatNat (nat_lit 256))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)
spec|CurveFieldProofs.projX|def|value=fun (Pt : CurveFieldProofs.ProjPoint) => @HDiv.hDiv.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHDiv.{0} CurveFieldProofs.Fp (@DivInvMonoid.toDiv.{0} CurveFieldProofs.Fp (@DivisionRing.toDivInvMonoid.{0} CurveFieldProofs.Fp (@Field.toDivisionRing.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP))))) (CurveFieldProofs.denote (curve25519.backend.serial.curve_models.ProjectivePoint.X Pt)) (CurveFieldProofs.denote (curve25519.backend.serial.curve_models.ProjectivePoint.Z Pt))
spec|CurveFieldProofs.projY|def|value=fun (Pt : CurveFieldProofs.ProjPoint) => @HDiv.hDiv.{0, 0, 0} CurveFieldProofs.Fp CurveFieldProofs.Fp CurveFieldProofs.Fp (@instHDiv.{0} CurveFieldProofs.Fp (@DivInvMonoid.toDiv.{0} CurveFieldProofs.Fp (@DivisionRing.toDivInvMonoid.{0} CurveFieldProofs.Fp (@Field.toDivisionRing.{0} CurveFieldProofs.Fp (@ZMod.instField CurveFieldProofs.P CurveFieldProofs.instFactPrimeP))))) (CurveFieldProofs.denote (curve25519.backend.serial.curve_models.ProjectivePoint.Y Pt)) (CurveFieldProofs.denote (curve25519.backend.serial.curve_models.ProjectivePoint.Z Pt))
spec|CurveFieldProofs.rangeEq|def|value=fun (e r : Aeneas.Std.Array.{0} Aeneas.Std.U8 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) CurveFieldProofs.rangeEq._proof_1)) (n : Nat) => ∀ (j : Nat), @LE.le.{0} Nat instLENat n j → @LT.lt.{0} Nat instLTNat j (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) → @Eq.{1} Aeneas.Std.U8 (@GetElem?.getElem!.{0, 0, 0} (List.{0} Aeneas.Std.U8) Nat Aeneas.Std.U8 (fun («as» : List.{0} Aeneas.Std.U8) (i : Nat) => @LT.lt.{0} Nat instLTNat i (@List.length.{0} Aeneas.Std.U8 «as»)) (@List.instGetElem?NatLtLength.{0} Aeneas.Std.U8) (Aeneas.Std.instInhabitedUScalar Aeneas.Std.UScalarTy.U8) (@Subtype.val.{1} (List.{0} Aeneas.Std.U8) (fun (l : List.{0} Aeneas.Std.U8) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U8 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) CurveFieldProofs.rangeEq._proof_1))) e) j) (@GetElem?.getElem!.{0, 0, 0} (List.{0} Aeneas.Std.U8) Nat Aeneas.Std.U8 (fun («as» : List.{0} Aeneas.Std.U8) (i : Nat) => @LT.lt.{0} Nat instLTNat i (@List.length.{0} Aeneas.Std.U8 «as»)) (@List.instGetElem?NatLtLength.{0} Aeneas.Std.U8) (Aeneas.Std.instInhabitedUScalar Aeneas.Std.UScalarTy.U8) (@Subtype.val.{1} (List.{0} Aeneas.Std.U8) (fun (l : List.{0} Aeneas.Std.U8) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U8 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) CurveFieldProofs.rangeEq._proof_1))) r) j)
spec|CurveFieldProofs.rangeEq._proof_1|prop|type=@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 32) (instOfNatNat (nat_lit 32))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)
spec|CurveFieldProofs.tblEntries|def|value=fun (tbl : curve25519.window.NafLookupTable5 curve25519.backend.serial.curve_models.ProjectiveNielsPoint) => @Subtype.val.{1} (List.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint) (fun (l : List.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint) => @Eq.{1} Nat (@List.length.{0} curve25519.backend.serial.curve_models.ProjectiveNielsPoint l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 8) (instOfNatNat (nat_lit 8))) curve25519.window.NafLookupTable5._proof_1))) tbl
spec|ScalarProofs.Ell|def|value=@OfNat.ofNat.{0} Nat (nat_lit 7237005577332262213973186563042994240857116359379907606001950938285454250989) (instOfNatNat (nat_lit 7237005577332262213973186563042994240857116359379907606001950938285454250989))