policy|kernel3=Classical.choice,Quot.sound,propext|apexExtra=|specPrefix=Proofs.
cert|ScalarProofs.L_val|cone=Classical.choice,Quot.sound,propext|type=@Eq.{1} Nat (ScalarProofs.scVal curve25519.backend.serial.u64.constants.L) ScalarProofs.Ell
cert|ScalarProofs.sub_loop_spec|cone=Classical.choice,Quot.sound,propext|type=∀ (a b : ScalarProofs.Sc) (mask a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 : Aeneas.Std.U64) (ha : @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 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))))))) (hb : @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))) b) (@List.cons.{0} Aeneas.Std.U64 b0 (@List.cons.{0} Aeneas.Std.U64 b1 (@List.cons.{0} Aeneas.Std.U64 b2 (@List.cons.{0} Aeneas.Std.U64 b3 (@List.cons.{0} Aeneas.Std.U64 b4 (@List.nil.{0} Aeneas.Std.U64))))))) (hmask : @Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 mask) (@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 52) (instOfNatNat (nat_lit 52)))) (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))) (hbnd : And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a0) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a1) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a2) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a3) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a4) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b0) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 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 52) (instOfNatNat (nat_lit 52))))) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 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 52) (instOfNatNat (nat_lit 52))))) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 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 52) (instOfNatNat (nat_lit 52))))) (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 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 52) (instOfNatNat (nat_lit 52)))))))))))))), @Aeneas.Std.WP.spec.{0} (Prod.{0, 0} curve25519.backend.serial.u64.scalar.Scalar52 Aeneas.Std.U64) (curve25519.backend.serial.u64.scalar.Scalar52.sub_loop (@Aeneas.Std.core.ops.range.Range.mk.{0} Aeneas.Std.Usize (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)))) (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))))) a b curve25519.backend.serial.u64.scalar.Scalar52.ZERO mask (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))))) fun (dw : Prod.{0, 0} ScalarProofs.Sc Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (d0 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (d1 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (d2 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (d3 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (d4 : Aeneas.Std.U64) => @Exists.{1} Nat fun (β1 : Nat) => @Exists.{1} Nat fun (β2 : Nat) => @Exists.{1} Nat fun (β3 : Nat) => @Exists.{1} Nat fun (β4 : Nat) => @Exists.{1} Nat fun (β5 : Nat) => 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 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))) (@Prod.fst.{0, 0} ScalarProofs.Sc Aeneas.Std.U64 dw)) (@List.cons.{0} Aeneas.Std.U64 d0 (@List.cons.{0} Aeneas.Std.U64 d1 (@List.cons.{0} Aeneas.Std.U64 d2 (@List.cons.{0} Aeneas.Std.U64 d3 (@List.cons.{0} Aeneas.Std.U64 d4 (@List.nil.{0} Aeneas.Std.U64))))))) (And (@LE.le.{0} Nat instLENat β1 (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) (And (@LE.le.{0} Nat instLENat β2 (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) (And (@LE.le.{0} Nat instLENat β3 (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) (And (@LE.le.{0} Nat instLENat β4 (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) (And (@LE.le.{0} Nat instLENat β5 (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 d0) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 d1) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 d2) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 d3) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 d4) (@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} Nat (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 d0) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b0)) (@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 52) (instOfNatNat (nat_lit 52)))) β1))) (And (@Eq.{1} Nat (@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 d1) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b1)) β1) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@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 52) (instOfNatNat (nat_lit 52)))) β2))) (And (@Eq.{1} Nat (@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 d2) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b2)) β2) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@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 52) (instOfNatNat (nat_lit 52)))) β3))) (And (@Eq.{1} Nat (@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 d3) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b3)) β3) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@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 52) (instOfNatNat (nat_lit 52)))) β4))) (And (@Eq.{1} Nat (@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 d4) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b4)) β4) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a4) (@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 52) (instOfNatNat (nat_lit 52)))) β5))) (@Eq.{1} Nat (@HShiftRight.hShiftRight.{0, 0, 0} Nat Nat Nat (@instHShiftRightOfShiftRight.{0} Nat Nat.instShiftRight) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 (@Prod.snd.{0, 0} ScalarProofs.Sc Aeneas.Std.U64 dw)) (@OfNat.ofNat.{0} Nat (nat_lit 63) (instOfNatNat (nat_lit 63)))) β5))))))))))))))))
cert|ScalarProofs.cond_add_l_one_spec|cone=Classical.choice,Quot.sound,propext|type=∀ (s : ScalarProofs.Sc) (c : subtle.Choice) (s0 s1 s2 s3 s4 : Aeneas.Std.U64) (hs : @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))) s) (@List.cons.{0} Aeneas.Std.U64 s0 (@List.cons.{0} Aeneas.Std.U64 s1 (@List.cons.{0} Aeneas.Std.U64 s2 (@List.cons.{0} Aeneas.Std.U64 s3 (@List.cons.{0} Aeneas.Std.U64 s4 (@List.nil.{0} Aeneas.Std.U64))))))) (hc : @Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 c) (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) (hbnd : And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s0) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s1) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s2) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s3) (@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))))) (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s4) (@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))))))))), @Aeneas.Std.WP.spec.{0} (Prod.{0, 0} Aeneas.Std.U64 curve25519.backend.serial.u64.scalar.Scalar52) (curve25519.backend.serial.u64.scalar.Scalar52.conditional_add_l s c) fun (cw : Prod.{0, 0} Aeneas.Std.U64 ScalarProofs.Sc) => @Exists.{1} Aeneas.Std.U64 fun (r0 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (r1 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (r2 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (r3 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (r4 : Aeneas.Std.U64) => @Exists.{1} Nat fun (γ1 : Nat) => @Exists.{1} Nat fun (γ2 : Nat) => @Exists.{1} Nat fun (γ3 : Nat) => @Exists.{1} Nat fun (γ4 : Nat) => @Exists.{1} Nat fun (γ5 : Nat) => 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 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))) (@Prod.snd.{0, 0} Aeneas.Std.U64 ScalarProofs.Sc cw)) (@List.cons.{0} Aeneas.Std.U64 r0 (@List.cons.{0} Aeneas.Std.U64 r1 (@List.cons.{0} Aeneas.Std.U64 r2 (@List.cons.{0} Aeneas.Std.U64 r3 (@List.cons.{0} Aeneas.Std.U64 r4 (@List.nil.{0} Aeneas.Std.U64))))))) (And (@LE.le.{0} Nat instLENat γ1 (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) (And (@LE.le.{0} Nat instLENat γ2 (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) (And (@LE.le.{0} Nat instLENat γ3 (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) (And (@LE.le.{0} Nat instLENat γ4 (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) (And (@LE.le.{0} Nat instLENat γ5 (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 r0) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 r1) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 r2) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 r3) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 r4) (@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} Nat (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 r0) (@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 52) (instOfNatNat (nat_lit 52)))) γ1)) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s0) (@OfNat.ofNat.{0} Nat (nat_lit 671914833335277) (instOfNatNat (nat_lit 671914833335277))))) (And (@Eq.{1} Nat (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 r1) (@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 52) (instOfNatNat (nat_lit 52)))) γ2)) (@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 s1) (@OfNat.ofNat.{0} Nat (nat_lit 3916664325105025) (instOfNatNat (nat_lit 3916664325105025)))) γ1)) (And (@Eq.{1} Nat (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 r2) (@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 52) (instOfNatNat (nat_lit 52)))) γ3)) (@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 s2) (@OfNat.ofNat.{0} Nat (nat_lit 1367801) (instOfNatNat (nat_lit 1367801)))) γ2)) (And (@Eq.{1} Nat (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 r3) (@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 52) (instOfNatNat (nat_lit 52)))) γ4)) (@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 s3) (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0)))) γ3)) (@Eq.{1} Nat (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 r4) (@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 52) (instOfNatNat (nat_lit 52)))) γ5)) (@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 s4) (@OfNat.ofNat.{0} Nat (nat_lit 17592186044416) (instOfNatNat (nat_lit 17592186044416)))) γ4))))))))))))))))
cert|ScalarProofs.sub_val_spec|cone=Classical.choice,Quot.sound,propext|type=∀ (a b : ScalarProofs.Sc) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 : Aeneas.Std.U64) (ha : @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 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))))))) (hb : @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))) b) (@List.cons.{0} Aeneas.Std.U64 b0 (@List.cons.{0} Aeneas.Std.U64 b1 (@List.cons.{0} Aeneas.Std.U64 b2 (@List.cons.{0} Aeneas.Std.U64 b3 (@List.cons.{0} Aeneas.Std.U64 b4 (@List.nil.{0} Aeneas.Std.U64))))))) (hab : And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a0) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a1) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a2) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a3) (@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))))) (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a4) (@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))))))))) (hbb : And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b0) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 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 52) (instOfNatNat (nat_lit 52))))) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 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 52) (instOfNatNat (nat_lit 52))))) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 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 52) (instOfNatNat (nat_lit 52))))) (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 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 52) (instOfNatNat (nat_lit 52))))))))) (hcb : @LE.le.{0} Nat instLENat (ScalarProofs.scVal b) ScalarProofs.Ell), @Aeneas.Std.WP.spec.{0} curve25519.backend.serial.u64.scalar.Scalar52 (curve25519.backend.serial.u64.scalar.Scalar52.sub a b) fun (r : curve25519.backend.serial.u64.scalar.Scalar52) => And (@Exists.{1} Aeneas.Std.U64 fun (s0 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (s1 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (s2 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (s3 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (s4 : 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 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))) r) (@List.cons.{0} Aeneas.Std.U64 s0 (@List.cons.{0} Aeneas.Std.U64 s1 (@List.cons.{0} Aeneas.Std.U64 s2 (@List.cons.{0} Aeneas.Std.U64 s3 (@List.cons.{0} Aeneas.Std.U64 s4 (@List.nil.{0} Aeneas.Std.U64))))))) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s0) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s1) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s2) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s3) (@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))))) (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s4) (@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 (@Exists.{1} Nat fun (β : Nat) => And (@LE.le.{0} Nat instLENat β (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))) (And (@Eq.{1} Nat (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (ScalarProofs.scVal r) (ScalarProofs.scVal b)) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (ScalarProofs.scVal a) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) ScalarProofs.Ell β))) (@Eq.{1} Nat β (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))) → @LT.lt.{0} Nat instLTNat (ScalarProofs.scVal a) (ScalarProofs.scVal b)))) (@Eq.{1} (ZMod ScalarProofs.Ell) (ScalarProofs.scDenote r) (@HSub.hSub.{0, 0, 0} (ZMod ScalarProofs.Ell) (ZMod ScalarProofs.Ell) (ZMod ScalarProofs.Ell) (@instHSub.{0} (ZMod ScalarProofs.Ell) (@SubNegMonoid.toSub.{0} (ZMod ScalarProofs.Ell) (@AddGroup.toSubNegMonoid.{0} (ZMod ScalarProofs.Ell) (@AddGroupWithOne.toAddGroup.{0} (ZMod ScalarProofs.Ell) (@Ring.toAddGroupWithOne.{0} (ZMod ScalarProofs.Ell) (@CommRing.toRing.{0} (ZMod ScalarProofs.Ell) (ZMod.commRing ScalarProofs.Ell))))))) (ScalarProofs.scDenote a) (ScalarProofs.scDenote b))))
cert|ScalarProofs.add_val_spec|cone=Classical.choice,Quot.sound,propext|type=∀ (a b : ScalarProofs.Sc) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 : Aeneas.Std.U64) (ha : @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 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))))))) (hb : @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))) b) (@List.cons.{0} Aeneas.Std.U64 b0 (@List.cons.{0} Aeneas.Std.U64 b1 (@List.cons.{0} Aeneas.Std.U64 b2 (@List.cons.{0} Aeneas.Std.U64 b3 (@List.cons.{0} Aeneas.Std.U64 b4 (@List.nil.{0} Aeneas.Std.U64))))))) (hab : And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a0) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a1) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a2) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a3) (@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))))) (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a4) (@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))))))))) (hbb : And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b0) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 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 52) (instOfNatNat (nat_lit 52))))) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 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 52) (instOfNatNat (nat_lit 52))))) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 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 52) (instOfNatNat (nat_lit 52))))) (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 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 52) (instOfNatNat (nat_lit 52))))))))) (hca : @LT.lt.{0} Nat instLTNat (ScalarProofs.scVal a) ScalarProofs.Ell) (hcb : @LT.lt.{0} Nat instLTNat (ScalarProofs.scVal b) ScalarProofs.Ell), @Aeneas.Std.WP.spec.{0} curve25519.backend.serial.u64.scalar.Scalar52 (curve25519.backend.serial.u64.scalar.Scalar52.add a b) fun (r : curve25519.backend.serial.u64.scalar.Scalar52) => And (@Exists.{1} Aeneas.Std.U64 fun (s0 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (s1 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (s2 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (s3 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (s4 : 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 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))) r) (@List.cons.{0} Aeneas.Std.U64 s0 (@List.cons.{0} Aeneas.Std.U64 s1 (@List.cons.{0} Aeneas.Std.U64 s2 (@List.cons.{0} Aeneas.Std.U64 s3 (@List.cons.{0} Aeneas.Std.U64 s4 (@List.nil.{0} Aeneas.Std.U64))))))) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s0) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s1) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s2) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s3) (@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))))) (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s4) (@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 (@LT.lt.{0} Nat instLTNat (ScalarProofs.scVal r) ScalarProofs.Ell) (@Eq.{1} (ZMod ScalarProofs.Ell) (ScalarProofs.scDenote r) (@HAdd.hAdd.{0, 0, 0} (ZMod ScalarProofs.Ell) (ZMod ScalarProofs.Ell) (ZMod ScalarProofs.Ell) (@instHAdd.{0} (ZMod ScalarProofs.Ell) (@Distrib.toAdd.{0} (ZMod ScalarProofs.Ell) (@NonUnitalNonAssocSemiring.toDistrib.{0} (ZMod ScalarProofs.Ell) (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} (ZMod ScalarProofs.Ell) (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} (ZMod ScalarProofs.Ell) (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} (ZMod ScalarProofs.Ell) (@CommRing.toNonUnitalCommRing.{0} (ZMod ScalarProofs.Ell) (ZMod.commRing ScalarProofs.Ell)))))))) (ScalarProofs.scDenote a) (ScalarProofs.scDenote b))))
cert|ScalarProofs.mul_internal_spec|cone=Classical.choice,Quot.sound,propext|type=∀ (a b : ScalarProofs.Sc) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 : Aeneas.Std.U64) (ha : @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 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))))))) (hb : @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))) b) (@List.cons.{0} Aeneas.Std.U64 b0 (@List.cons.{0} Aeneas.Std.U64 b1 (@List.cons.{0} Aeneas.Std.U64 b2 (@List.cons.{0} Aeneas.Std.U64 b3 (@List.cons.{0} Aeneas.Std.U64 b4 (@List.nil.{0} Aeneas.Std.U64))))))) (hbnd : And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a0) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a1) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a2) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a3) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a4) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b0) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 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 52) (instOfNatNat (nat_lit 52))))) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 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 52) (instOfNatNat (nat_lit 52))))) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 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 52) (instOfNatNat (nat_lit 52))))) (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 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 52) (instOfNatNat (nat_lit 52)))))))))))))), @Aeneas.Std.WP.spec.{0} (Aeneas.Std.Array.{0} Aeneas.Std.U128 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 9) (instOfNatNat (nat_lit 9))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 9) (instOfNatNat (nat_lit 9))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 9) (instOfNatNat (nat_lit 9))) (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 9) (instOfNatNat (nat_lit 9))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 9) (instOfNatNat (nat_lit 9))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) (curve25519.backend.serial.u64.scalar.Scalar52.mul_internal a b) fun (zz : Aeneas.Std.Array.{0} Aeneas.Std.U128 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 9) (instOfNatNat (nat_lit 9))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 9) (instOfNatNat (nat_lit 9))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 9) (instOfNatNat (nat_lit 9))) (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 9) (instOfNatNat (nat_lit 9))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 9) (instOfNatNat (nat_lit 9))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) => @Exists.{1} Aeneas.Std.U128 fun (z0 : Aeneas.Std.U128) => @Exists.{1} Aeneas.Std.U128 fun (z1 : Aeneas.Std.U128) => @Exists.{1} Aeneas.Std.U128 fun (z2 : Aeneas.Std.U128) => @Exists.{1} Aeneas.Std.U128 fun (z3 : Aeneas.Std.U128) => @Exists.{1} Aeneas.Std.U128 fun (z4 : Aeneas.Std.U128) => @Exists.{1} Aeneas.Std.U128 fun (z5 : Aeneas.Std.U128) => @Exists.{1} Aeneas.Std.U128 fun (z6 : Aeneas.Std.U128) => @Exists.{1} Aeneas.Std.U128 fun (z7 : Aeneas.Std.U128) => @Exists.{1} Aeneas.Std.U128 fun (z8 : Aeneas.Std.U128) => And (@Eq.{1} (List.{0} Aeneas.Std.U128) (@Subtype.val.{1} (List.{0} Aeneas.Std.U128) (fun (l : List.{0} Aeneas.Std.U128) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U128 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 9) (instOfNatNat (nat_lit 9))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 9) (instOfNatNat (nat_lit 9))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 9) (instOfNatNat (nat_lit 9))) (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 9) (instOfNatNat (nat_lit 9))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 9) (instOfNatNat (nat_lit 9))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true)))))) zz) (@List.cons.{0} Aeneas.Std.U128 z0 (@List.cons.{0} Aeneas.Std.U128 z1 (@List.cons.{0} Aeneas.Std.U128 z2 (@List.cons.{0} Aeneas.Std.U128 z3 (@List.cons.{0} Aeneas.Std.U128 z4 (@List.cons.{0} Aeneas.Std.U128 z5 (@List.cons.{0} Aeneas.Std.U128 z6 (@List.cons.{0} Aeneas.Std.U128 z7 (@List.cons.{0} Aeneas.Std.U128 z8 (@List.nil.{0} Aeneas.Std.U128))))))))))) (And (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U128 z0) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a0) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b0))) (And (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U128 z1) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a0) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b1)) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a1) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b0)))) (And (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U128 z2) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a0) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b2)) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a1) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b1))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a2) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b0)))) (And (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U128 z3) (@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) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a0) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b3)) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a1) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b2))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a2) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b1))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a3) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b0)))) (And (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U128 z4) (@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) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a0) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b4)) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a1) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b3))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a2) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b2))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a3) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b1))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a4) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b0)))) (And (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U128 z5) (@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) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a1) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b4)) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a2) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b3))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a3) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b2))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a4) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b1)))) (And (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U128 z6) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a2) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b4)) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a3) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b3))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a4) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b2)))) (And (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U128 z7) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a3) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b4)) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a4) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b3)))) (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U128 z8) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a4) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b4)))))))))))
cert|ScalarProofs.part1_spec|cone=Classical.choice,Quot.sound,propext|type=∀ (sum : Aeneas.Std.U128) (hs : @LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U128 sum) (@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 124) (instOfNatNat (nat_lit 124))))), @Aeneas.Std.WP.spec.{0} (Prod.{0, 0} Aeneas.Std.U128 Aeneas.Std.U64) (curve25519.backend.serial.u64.scalar.Scalar52.montgomery_reduce.part1 sum) fun (cw : Prod.{0, 0} Aeneas.Std.U128 Aeneas.Std.U64) => And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 (@Prod.snd.{0, 0} Aeneas.Std.U128 Aeneas.Std.U64 cw)) (@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} Nat (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U128 (@Prod.fst.{0, 0} Aeneas.Std.U128 Aeneas.Std.U64 cw)) (@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))))) (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U128 sum) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 (@Prod.snd.{0, 0} Aeneas.Std.U128 Aeneas.Std.U64 cw)) (@OfNat.ofNat.{0} Nat (nat_lit 671914833335277) (instOfNatNat (nat_lit 671914833335277))))))
cert|ScalarProofs.montgomery_reduce_spec|cone=Classical.choice,Quot.sound,propext|type=∀ (limbs : Aeneas.Std.Array.{0} Aeneas.Std.U128 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 9) (instOfNatNat (nat_lit 9))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 9) (instOfNatNat (nat_lit 9))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 9) (instOfNatNat (nat_lit 9))) (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 9) (instOfNatNat (nat_lit 9))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 9) (instOfNatNat (nat_lit 9))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) (z0 z1 z2 z3 z4 z5 z6 z7 z8 : Aeneas.Std.U128) (hl : @Eq.{1} (List.{0} Aeneas.Std.U128) (@Subtype.val.{1} (List.{0} Aeneas.Std.U128) (fun (l : List.{0} Aeneas.Std.U128) => @Eq.{1} Nat (@List.length.{0} Aeneas.Std.U128 l) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 9) (instOfNatNat (nat_lit 9))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 9) (instOfNatNat (nat_lit 9))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 9) (instOfNatNat (nat_lit 9))) (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 9) (instOfNatNat (nat_lit 9))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 9) (instOfNatNat (nat_lit 9))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true)))))) limbs) (@List.cons.{0} Aeneas.Std.U128 z0 (@List.cons.{0} Aeneas.Std.U128 z1 (@List.cons.{0} Aeneas.Std.U128 z2 (@List.cons.{0} Aeneas.Std.U128 z3 (@List.cons.{0} Aeneas.Std.U128 z4 (@List.cons.{0} Aeneas.Std.U128 z5 (@List.cons.{0} Aeneas.Std.U128 z6 (@List.cons.{0} Aeneas.Std.U128 z7 (@List.cons.{0} Aeneas.Std.U128 z8 (@List.nil.{0} Aeneas.Std.U128))))))))))) (hzb : And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U128 z0) (@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 107) (instOfNatNat (nat_lit 107))))) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U128 z1) (@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 107) (instOfNatNat (nat_lit 107))))) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U128 z2) (@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 107) (instOfNatNat (nat_lit 107))))) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U128 z3) (@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 107) (instOfNatNat (nat_lit 107))))) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U128 z4) (@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 107) (instOfNatNat (nat_lit 107))))) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U128 z5) (@HPow.hPow.{0, 0, 0} Nat Nat Nat (@instHPow.{0, 0} Nat Nat (@Monoid.toPow.{0} Nat 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(instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 107) (instOfNatNat (nat_lit 107))))))))))))) (hZ : @LT.lt.{0} Nat instLTNat (@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) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U128 z0) (@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 52) (instOfNatNat (nat_lit 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(@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} (ZMod ScalarProofs.Ell) (@CommRing.toNonUnitalCommRing.{0} (ZMod ScalarProofs.Ell) (ZMod.commRing ScalarProofs.Ell)))))))) (ScalarProofs.scDenote r) (@HPow.hPow.{0, 0, 0} (ZMod ScalarProofs.Ell) Nat (ZMod ScalarProofs.Ell) (@instHPow.{0, 0} (ZMod ScalarProofs.Ell) Nat (@Monoid.toPow.{0} (ZMod ScalarProofs.Ell) (@MonoidWithZero.toMonoid.{0} (ZMod ScalarProofs.Ell) (@Semiring.toMonoidWithZero.{0} (ZMod ScalarProofs.Ell) (@CommSemiring.toSemiring.{0} (ZMod ScalarProofs.Ell) (@CommRing.toCommSemiring.{0} (ZMod ScalarProofs.Ell) (ZMod.commRing ScalarProofs.Ell))))))) (@OfNat.ofNat.{0} (ZMod ScalarProofs.Ell) (nat_lit 2) (@instOfNatAtLeastTwo.{0} (ZMod ScalarProofs.Ell) (nat_lit 2) (@AddMonoidWithOne.toNatCast.{0} (ZMod ScalarProofs.Ell) (@AddGroupWithOne.toAddMonoidWithOne.{0} (ZMod ScalarProofs.Ell) (@Ring.toAddGroupWithOne.{0} (ZMod ScalarProofs.Ell) (@CommRing.toRing.{0} (ZMod ScalarProofs.Ell) (ZMod.commRing ScalarProofs.Ell))))) 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cert|ScalarProofs.mul_spec|cone=Classical.choice,Quot.sound,propext|type=∀ (a b : ScalarProofs.Sc) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 : Aeneas.Std.U64) (ha : @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 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))))))) (hb : @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 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Aeneas.Std.UScalarTy.U64 a2) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a3) (@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))))) (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a4) (@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))))))))) (hbb : And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b0) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 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 52) (instOfNatNat (nat_lit 52))))) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 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 52) (instOfNatNat (nat_lit 52))))) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 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 52) (instOfNatNat (nat_lit 52))))) (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 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 52) (instOfNatNat (nat_lit 52))))))))) (hcab : @LT.lt.{0} Nat instLTNat (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (ScalarProofs.scVal a) (ScalarProofs.scVal b)) (@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 260) (instOfNatNat (nat_lit 260)))) ScalarProofs.Ell)), @Aeneas.Std.WP.spec.{0} curve25519.backend.serial.u64.scalar.Scalar52 (curve25519.backend.serial.u64.scalar.Scalar52.mul a b) fun (r : curve25519.backend.serial.u64.scalar.Scalar52) => And (@Exists.{1} Aeneas.Std.U64 fun (s0 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (s1 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (s2 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (s3 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (s4 : 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 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))) r) (@List.cons.{0} Aeneas.Std.U64 s0 (@List.cons.{0} Aeneas.Std.U64 s1 (@List.cons.{0} Aeneas.Std.U64 s2 (@List.cons.{0} Aeneas.Std.U64 s3 (@List.cons.{0} Aeneas.Std.U64 s4 (@List.nil.{0} Aeneas.Std.U64))))))) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s0) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s1) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s2) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s3) (@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))))) (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s4) (@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 (@LT.lt.{0} Nat instLTNat (ScalarProofs.scVal r) ScalarProofs.Ell) (@Eq.{1} (ZMod ScalarProofs.Ell) (ScalarProofs.scDenote r) (@HMul.hMul.{0, 0, 0} (ZMod ScalarProofs.Ell) (ZMod ScalarProofs.Ell) (ZMod ScalarProofs.Ell) (@instHMul.{0} (ZMod ScalarProofs.Ell) (@Distrib.toMul.{0} (ZMod ScalarProofs.Ell) (@NonUnitalNonAssocSemiring.toDistrib.{0} (ZMod ScalarProofs.Ell) (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} (ZMod ScalarProofs.Ell) (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} (ZMod ScalarProofs.Ell) (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} (ZMod ScalarProofs.Ell) (@CommRing.toNonUnitalCommRing.{0} (ZMod ScalarProofs.Ell) (ZMod.commRing ScalarProofs.Ell)))))))) (ScalarProofs.scDenote a) (ScalarProofs.scDenote b))))
cert|ScalarProofs.scalarImplementation|cone=Classical.choice,Quot.sound,propext|type=And (∀ (a b : ScalarProofs.Sc), ScalarProofs.ScBnd a → ScalarProofs.ScBnd b → @LT.lt.{0} Nat instLTNat (ScalarProofs.scVal a) ScalarProofs.Ell → @LT.lt.{0} Nat instLTNat (ScalarProofs.scVal b) ScalarProofs.Ell → @Aeneas.Std.WP.spec.{0} curve25519.backend.serial.u64.scalar.Scalar52 (curve25519.backend.serial.u64.scalar.Scalar52.add a b) fun (r : curve25519.backend.serial.u64.scalar.Scalar52) => And (ScalarProofs.ScBnd r) (And (@LT.lt.{0} Nat instLTNat (ScalarProofs.scVal r) ScalarProofs.Ell) (@Eq.{1} (ZMod ScalarProofs.Ell) (ScalarProofs.scDenote r) (@HAdd.hAdd.{0, 0, 0} (ZMod ScalarProofs.Ell) (ZMod ScalarProofs.Ell) (ZMod ScalarProofs.Ell) (@instHAdd.{0} (ZMod ScalarProofs.Ell) (@Distrib.toAdd.{0} (ZMod ScalarProofs.Ell) (@NonUnitalNonAssocSemiring.toDistrib.{0} (ZMod ScalarProofs.Ell) (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} (ZMod ScalarProofs.Ell) (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} (ZMod ScalarProofs.Ell) (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} (ZMod ScalarProofs.Ell) (@CommRing.toNonUnitalCommRing.{0} (ZMod ScalarProofs.Ell) (ZMod.commRing ScalarProofs.Ell)))))))) (ScalarProofs.scDenote a) (ScalarProofs.scDenote b))))) (And (∀ (a b : ScalarProofs.Sc), ScalarProofs.ScBnd a → ScalarProofs.ScBnd b → @LT.lt.{0} Nat instLTNat (ScalarProofs.scVal a) ScalarProofs.Ell → @LE.le.{0} Nat instLENat (ScalarProofs.scVal b) ScalarProofs.Ell → @Aeneas.Std.WP.spec.{0} curve25519.backend.serial.u64.scalar.Scalar52 (curve25519.backend.serial.u64.scalar.Scalar52.sub a b) fun (r : curve25519.backend.serial.u64.scalar.Scalar52) => And (ScalarProofs.ScBnd r) (And (@LT.lt.{0} Nat instLTNat (ScalarProofs.scVal r) ScalarProofs.Ell) (@Eq.{1} (ZMod ScalarProofs.Ell) (ScalarProofs.scDenote r) (@HSub.hSub.{0, 0, 0} (ZMod ScalarProofs.Ell) (ZMod ScalarProofs.Ell) (ZMod ScalarProofs.Ell) (@instHSub.{0} (ZMod ScalarProofs.Ell) (@SubNegMonoid.toSub.{0} (ZMod ScalarProofs.Ell) (@AddGroup.toSubNegMonoid.{0} (ZMod ScalarProofs.Ell) (@AddGroupWithOne.toAddGroup.{0} (ZMod ScalarProofs.Ell) (@Ring.toAddGroupWithOne.{0} (ZMod ScalarProofs.Ell) (@CommRing.toRing.{0} (ZMod ScalarProofs.Ell) (ZMod.commRing ScalarProofs.Ell))))))) (ScalarProofs.scDenote a) (ScalarProofs.scDenote b))))) (∀ (a b : ScalarProofs.Sc), ScalarProofs.ScBnd a → ScalarProofs.ScBnd b → @LT.lt.{0} Nat instLTNat (ScalarProofs.scVal a) ScalarProofs.Ell → @LT.lt.{0} Nat instLTNat (ScalarProofs.scVal b) ScalarProofs.Ell → @Aeneas.Std.WP.spec.{0} curve25519.backend.serial.u64.scalar.Scalar52 (curve25519.backend.serial.u64.scalar.Scalar52.mul a b) fun (r : curve25519.backend.serial.u64.scalar.Scalar52) => And (ScalarProofs.ScBnd r) (And (@LT.lt.{0} Nat instLTNat (ScalarProofs.scVal r) ScalarProofs.Ell) (@Eq.{1} (ZMod ScalarProofs.Ell) (ScalarProofs.scDenote r) (@HMul.hMul.{0, 0, 0} (ZMod ScalarProofs.Ell) (ZMod ScalarProofs.Ell) (ZMod ScalarProofs.Ell) (@instHMul.{0} (ZMod ScalarProofs.Ell) (@Distrib.toMul.{0} (ZMod ScalarProofs.Ell) (@NonUnitalNonAssocSemiring.toDistrib.{0} (ZMod ScalarProofs.Ell) (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} (ZMod ScalarProofs.Ell) (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} (ZMod ScalarProofs.Ell) (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} (ZMod ScalarProofs.Ell) (@CommRing.toNonUnitalCommRing.{0} (ZMod ScalarProofs.Ell) (ZMod.commRing ScalarProofs.Ell)))))))) (ScalarProofs.scDenote a) (ScalarProofs.scDenote b))))))
cert|ScalarProofs.montgomery_mul_spec|cone=Classical.choice,Quot.sound,propext|type=∀ (a b : ScalarProofs.Sc) (a0 a1 a2 a3 a4 b0 b1 b2 b3 b4 : Aeneas.Std.U64) (ha : @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 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))))))) (hb : @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))) b) (@List.cons.{0} Aeneas.Std.U64 b0 (@List.cons.{0} Aeneas.Std.U64 b1 (@List.cons.{0} Aeneas.Std.U64 b2 (@List.cons.{0} Aeneas.Std.U64 b3 (@List.cons.{0} Aeneas.Std.U64 b4 (@List.nil.{0} Aeneas.Std.U64))))))) (hab : And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a0) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a1) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a2) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a3) (@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))))) (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a4) (@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))))))))) (hbb : And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 b0) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 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 52) (instOfNatNat (nat_lit 52))))) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 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 52) (instOfNatNat (nat_lit 52))))) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 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 52) (instOfNatNat (nat_lit 52))))) (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 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 52) (instOfNatNat (nat_lit 52))))))))) (hcab : @LT.lt.{0} Nat instLTNat (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (ScalarProofs.scVal a) (ScalarProofs.scVal b)) (@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 260) (instOfNatNat (nat_lit 260)))) ScalarProofs.Ell)), @Aeneas.Std.WP.spec.{0} curve25519.backend.serial.u64.scalar.Scalar52 (curve25519.backend.serial.u64.scalar.Scalar52.montgomery_mul a b) fun (r : curve25519.backend.serial.u64.scalar.Scalar52) => And (@Exists.{1} Aeneas.Std.U64 fun (s0 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (s1 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (s2 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (s3 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (s4 : 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 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))) r) (@List.cons.{0} Aeneas.Std.U64 s0 (@List.cons.{0} Aeneas.Std.U64 s1 (@List.cons.{0} Aeneas.Std.U64 s2 (@List.cons.{0} Aeneas.Std.U64 s3 (@List.cons.{0} Aeneas.Std.U64 s4 (@List.nil.{0} Aeneas.Std.U64))))))) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s0) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s1) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s2) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s3) (@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))))) (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s4) (@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 (@LT.lt.{0} Nat instLTNat (ScalarProofs.scVal r) ScalarProofs.Ell) (@Eq.{1} (ZMod ScalarProofs.Ell) (@HMul.hMul.{0, 0, 0} (ZMod ScalarProofs.Ell) (ZMod ScalarProofs.Ell) (ZMod ScalarProofs.Ell) (@instHMul.{0} (ZMod ScalarProofs.Ell) (@Distrib.toMul.{0} (ZMod ScalarProofs.Ell) (@NonUnitalNonAssocSemiring.toDistrib.{0} (ZMod ScalarProofs.Ell) (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} (ZMod ScalarProofs.Ell) (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} (ZMod ScalarProofs.Ell) (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} (ZMod ScalarProofs.Ell) (@CommRing.toNonUnitalCommRing.{0} (ZMod ScalarProofs.Ell) (ZMod.commRing ScalarProofs.Ell)))))))) (ScalarProofs.scDenote r) (@HPow.hPow.{0, 0, 0} (ZMod ScalarProofs.Ell) Nat (ZMod ScalarProofs.Ell) (@instHPow.{0, 0} (ZMod ScalarProofs.Ell) Nat (@Monoid.toPow.{0} (ZMod ScalarProofs.Ell) (@MonoidWithZero.toMonoid.{0} (ZMod ScalarProofs.Ell) (@Semiring.toMonoidWithZero.{0} (ZMod ScalarProofs.Ell) (@CommSemiring.toSemiring.{0} (ZMod ScalarProofs.Ell) (@CommRing.toCommSemiring.{0} (ZMod ScalarProofs.Ell) (ZMod.commRing ScalarProofs.Ell))))))) (@OfNat.ofNat.{0} (ZMod ScalarProofs.Ell) (nat_lit 2) (@instOfNatAtLeastTwo.{0} (ZMod ScalarProofs.Ell) (nat_lit 2) (@AddMonoidWithOne.toNatCast.{0} (ZMod ScalarProofs.Ell) (@AddGroupWithOne.toAddMonoidWithOne.{0} (ZMod ScalarProofs.Ell) (@Ring.toAddGroupWithOne.{0} (ZMod ScalarProofs.Ell) (@CommRing.toRing.{0} (ZMod ScalarProofs.Ell) (ZMod.commRing ScalarProofs.Ell))))) (@Nat.instAtLeastTwoHAddOfNat (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))) (@Nat.instNeZeroSucc (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0))))))) (@OfNat.ofNat.{0} Nat (nat_lit 260) (instOfNatNat (nat_lit 260))))) (@HMul.hMul.{0, 0, 0} (ZMod ScalarProofs.Ell) (ZMod ScalarProofs.Ell) (ZMod ScalarProofs.Ell) (@instHMul.{0} (ZMod ScalarProofs.Ell) (@Distrib.toMul.{0} (ZMod ScalarProofs.Ell) (@NonUnitalNonAssocSemiring.toDistrib.{0} (ZMod ScalarProofs.Ell) (@NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} (ZMod ScalarProofs.Ell) (@NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{0} (ZMod ScalarProofs.Ell) (@NonUnitalCommRing.toNonUnitalNonAssocCommRing.{0} (ZMod ScalarProofs.Ell) (@CommRing.toNonUnitalCommRing.{0} (ZMod ScalarProofs.Ell) (ZMod.commRing ScalarProofs.Ell)))))))) (ScalarProofs.scDenote a) (ScalarProofs.scDenote b))))
cert|ScalarProofs.bytes_unpack_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 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))))) (words : Aeneas.Std.Array.{0} Aeneas.Std.U64 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 8) (instOfNatNat (nat_lit 8))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 8) (instOfNatNat (nat_lit 8))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 8) (instOfNatNat (nat_lit 8))) (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 8) (instOfNatNat (nat_lit 8))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 8) (instOfNatNat (nat_lit 8))) (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) (w0 w1 w2 w3 w4 w5 w6 w7 : Aeneas.Std.U64) (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)))))) bytes) (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))))) (hw : @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 8) (instOfNatNat (nat_lit 8))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 8) (instOfNatNat (nat_lit 8))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 8) (instOfNatNat (nat_lit 8))) (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 8) (instOfNatNat (nat_lit 8))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 8) (instOfNatNat (nat_lit 8))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true)))))) words) (@List.cons.{0} Aeneas.Std.U64 w0 (@List.cons.{0} Aeneas.Std.U64 w1 (@List.cons.{0} Aeneas.Std.U64 w2 (@List.cons.{0} Aeneas.Std.U64 w3 (@List.cons.{0} Aeneas.Std.U64 w4 (@List.cons.{0} Aeneas.Std.U64 w5 (@List.cons.{0} Aeneas.Std.U64 w6 (@List.cons.{0} Aeneas.Std.U64 w7 (@List.nil.{0} Aeneas.Std.U64)))))))))) (hz : And (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 w0) (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0)))) (And (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 w1) (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0)))) (And (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 w2) (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0)))) (And (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 w3) (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0)))) (And (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 w4) (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0)))) (And (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 w5) (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0)))) (And (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 w6) (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0)))) (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 w7) (@OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0))))))))))), @Aeneas.Std.WP.spec.{0} (Aeneas.Std.Array.{0} Aeneas.Std.U64 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 8) (instOfNatNat (nat_lit 8))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 8) (instOfNatNat (nat_lit 8))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 8) (instOfNatNat (nat_lit 8))) (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 8) (instOfNatNat (nat_lit 8))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 8) (instOfNatNat (nat_lit 8))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) (curve25519.backend.serial.u64.scalar.Scalar52.from_bytes_wide_parts_loop0 (@Aeneas.Std.core.ops.range.Range.mk.{0} Aeneas.Std.Usize (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)))) (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 8) (instOfNatNat (nat_lit 8))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 8) (instOfNatNat (nat_lit 8))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 8) (instOfNatNat (nat_lit 8))) (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 8) (instOfNatNat (nat_lit 8))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 8) (instOfNatNat (nat_lit 8))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true))))) bytes words) fun (ws : Aeneas.Std.Array.{0} Aeneas.Std.U64 (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 8) (instOfNatNat (nat_lit 8))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 8) (instOfNatNat (nat_lit 8))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 8) (instOfNatNat (nat_lit 8))) (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 8) (instOfNatNat (nat_lit 8))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 8) (instOfNatNat (nat_lit 8))) (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) => @Exists.{1} Aeneas.Std.U64 fun (v4 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (v5 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (v6 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (v7 : 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 Aeneas.Std.UScalarTy.Usize (Aeneas.Std.Usize.ofNat (@OfNat.ofNat.{0} Nat (nat_lit 8) (instOfNatNat (nat_lit 8))) (@of_decide_eq_true (@LE.le.{0} Nat instLENat (@OfNat.ofNat.{0} Nat (nat_lit 8) (instOfNatNat (nat_lit 8))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 8) (instOfNatNat (nat_lit 8))) (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 8) (instOfNatNat (nat_lit 8))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize)) (Nat.decLe (@OfNat.ofNat.{0} Nat (nat_lit 8) (instOfNatNat (nat_lit 8))) (Aeneas.Std.UScalar.cMax Aeneas.Std.UScalarTy.Usize))) Bool.true) (@Eq.refl.{1} Bool Bool.true)))))) ws) (@List.cons.{0} Aeneas.Std.U64 v0 (@List.cons.{0} Aeneas.Std.U64 v1 (@List.cons.{0} Aeneas.Std.U64 v2 (@List.cons.{0} Aeneas.Std.U64 v3 (@List.cons.{0} Aeneas.Std.U64 v4 (@List.cons.{0} Aeneas.Std.U64 v5 (@List.cons.{0} Aeneas.Std.U64 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(@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 56) (instOfNatNat (nat_lit 56))))))) (And (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 v5) (@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) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b40) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b41) (@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 b42) (@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 b43) (@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 b44) (@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 b45) (@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 (nat_lit 40)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b46) (@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 48) (instOfNatNat (nat_lit 48)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b47) (@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 56) (instOfNatNat (nat_lit 56))))))) (And (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 v6) (@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) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b48) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b49) (@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 b50) (@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 b51) (@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 b52) (@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 b53) (@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 (nat_lit 40)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b54) (@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 48) (instOfNatNat (nat_lit 48)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b55) (@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 56) (instOfNatNat (nat_lit 56))))))) (@Eq.{1} Nat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 v7) (@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) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b56) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b57) (@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 b58) (@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 b59) (@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 b60) (@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 b61) (@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 (nat_lit 40)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b62) (@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 48) (instOfNatNat (nat_lit 48)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b63) (@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 56) (instOfNatNat (nat_lit 56))))))))))))))
cert|ScalarProofs.from_bytes_wide_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 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)))))) bytes) (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 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) (@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 (nat_lit 40)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b6) (@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 48) (instOfNatNat (nat_lit 48)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b7) (@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 56) (instOfNatNat (nat_lit 56)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b8) (@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 64) (instOfNatNat (nat_lit 64)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b9) (@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 72) (instOfNatNat (nat_lit 72)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b10) (@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 80) (instOfNatNat (nat_lit 80)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b11) (@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 88) (instOfNatNat (nat_lit 88)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b12) (@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 96) (instOfNatNat (nat_lit 96)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b13) (@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 104) (instOfNatNat (nat_lit 104)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b14) (@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 112) (instOfNatNat (nat_lit 112)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b15) (@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 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 Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat (nat_lit 144) (instOfNatNat (nat_lit 144)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b19) (@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 152) (instOfNatNat (nat_lit 152)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b20) (@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 160) (instOfNatNat (nat_lit 160)))))) (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U8 b21) (@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 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 Aeneas.Std.UScalarTy.U8 b24) (@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 b25) (@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 b26) 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(@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 504) (instOfNatNat (nat_lit 504))))))), @Aeneas.Std.WP.spec.{0} curve25519.backend.serial.u64.scalar.Scalar52 (curve25519.backend.serial.u64.scalar.Scalar52.from_bytes_wide bytes) fun (r : curve25519.backend.serial.u64.scalar.Scalar52) => And (@Exists.{1} Aeneas.Std.U64 fun (s0 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (s1 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (s2 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (s3 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (s4 : 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 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))) r) (@List.cons.{0} Aeneas.Std.U64 s0 (@List.cons.{0} Aeneas.Std.U64 s1 (@List.cons.{0} Aeneas.Std.U64 s2 (@List.cons.{0} Aeneas.Std.U64 s3 (@List.cons.{0} Aeneas.Std.U64 s4 (@List.nil.{0} Aeneas.Std.U64))))))) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s0) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 s1) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val 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(ScalarProofs.scDenote r) (@Nat.cast.{0} (ZMod ScalarProofs.Ell) (@AddMonoidWithOne.toNatCast.{0} (ZMod ScalarProofs.Ell) (@AddGroupWithOne.toAddMonoidWithOne.{0} (ZMod ScalarProofs.Ell) (@Ring.toAddGroupWithOne.{0} (ZMod ScalarProofs.Ell) (@CommRing.toRing.{0} (ZMod ScalarProofs.Ell) (ZMod.commRing ScalarProofs.Ell))))) T)))
spec|ScalarProofs.Ell|def|value=@OfNat.ofNat.{0} Nat (nat_lit 7237005577332262213973186563042994240857116359379907606001950938285454250989) (instOfNatNat (nat_lit 7237005577332262213973186563042994240857116359379907606001950938285454250989))
spec|ScalarProofs.Sc|def|value=curve25519.backend.serial.u64.scalar.Scalar52
spec|ScalarProofs.ScBnd|def|value=fun (a : ScalarProofs.Sc) => @Exists.{1} Aeneas.Std.U64 fun (a0 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (a1 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (a2 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (a3 : Aeneas.Std.U64) => @Exists.{1} Aeneas.Std.U64 fun (a4 : 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 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 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))))))) (And (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a0) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a1) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a2) (@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 (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a3) (@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))))) (@LT.lt.{0} Nat instLTNat (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a4) (@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)))))))))
spec|ScalarProofs.scDenote|def|value=fun (a : ScalarProofs.Sc) => @Nat.cast.{0} (ZMod ScalarProofs.Ell) (@AddMonoidWithOne.toNatCast.{0} (ZMod ScalarProofs.Ell) (@AddGroupWithOne.toAddMonoidWithOne.{0} (ZMod ScalarProofs.Ell) (@Ring.toAddGroupWithOne.{0} (ZMod ScalarProofs.Ell) (@CommRing.toRing.{0} (ZMod ScalarProofs.Ell) (ZMod.commRing ScalarProofs.Ell))))) (ScalarProofs.scVal a)
spec|ScalarProofs.scLimbs|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 52) (instOfNatNat (nat_lit 52)))) (@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 104) (instOfNatNat (nat_lit 104)))) (@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 156) (instOfNatNat (nat_lit 156)))) (@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 208) (instOfNatNat (nat_lit 208)))) (@Aeneas.Std.UScalar.val Aeneas.Std.UScalarTy.U64 a4))
spec|ScalarProofs.scVal|def|value=fun (a : ScalarProofs.Sc) => ScalarProofs.scVal.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) => ScalarProofs.scLimbs a0 a1 a2 a3 a4) fun (x : List.{0} Aeneas.Std.U64) => @OfNat.ofNat.{0} Nat (nat_lit 0) (instOfNatNat (nat_lit 0))
spec|ScalarProofs.scVal._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|ScalarProofs.scVal._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|ScalarProofs.scVal.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) => @ScalarProofs.scVal._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) => @ScalarProofs.scVal._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) => @ScalarProofs.scVal._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) => @ScalarProofs.scVal._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) => @ScalarProofs.scVal._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) => @ScalarProofs.scVal._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