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dalek-ed25519-verified/verification/SCALAR-AUDIT-MANIFEST.txt

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audit: bind the scalar statements, and make the accounting identity mean audit Closes four round-7/8 findings. Certified by the round-12 sweep: five repositories, both buttons and every self-test, 48/48 GREEN. ── `scalar-statements-unbound` (gpt, round 7, CRITICAL) ──────────────────── The main button bound its 31 certificates' elaborated statements and reachable specification bodies. This button bound NONE of its thirteen, while TRUSTED-BASE item 8 said the audit covers "every certificate" — false across the 44-certificate surface. The finding was raised in round 7, lost from the round-8 work list by an F-number collision between two reviewers, and re-raised in round 8. Proofs/ScalarAudit.lean is generated from each fork's OWN Audit.lean, so the canonicalisation is provably the same code: pp.all rendering, whitespace normalisation, transitive specification closure. check-scalar.sh Phase 3c pins the block's digest, requires the committed copy to match byte-for-byte so a mismatch can be DIFFED, and cross-checks the auditor's certificate set against the button's CERTS array. dalek ecf3a3f8 · anza 0d942e47 · risc0 4b550a61 · betrusted 4b550a61 risc0 and betrusted share a digest and that is correct, not a collision: their ScalarSubSpec.lean differs only in doc prose and in `black_box` entries inside `simp only [...]` lists AFTER `:= by`. Proof scripts. They bind the same statements over the same specifications, which is the documented scope. selftest-scalar-statements.sh ships the two attacks the reviewer asked for: ok gutted statement caught (cone unchanged) ok rewritten specification body caught (name and cone unchanged) The second rewrites a reachable reference body to `id (…)` — DEFINITIONALLY EQUAL, so the corpus compiles and every proof typechecks and the cone is byte-identical. Every earlier phase is blind to it. ── `drv-surface-no-cones` + `accounting-certifies-enumeration` (claude) ──── The round-7 accounting identity proved every kernel constant was ENUMERATED. The reviewer showed enumeration is not audit: their planted claim WAS enumerated, as DRV|LTLAccAudit.bait.smuggled|theorem with a real cone, and nothing examined it — rows had no cone, no allowlist covered them, the statement digest does not reach instruments, and Phase 2b gates DECLARED AXIOMS, a different question. "Progress of one step, not two." DRV rows now carry their axiom cone and are pinned in driver-allowlist.txt by inventory_gate.sh with a DRV tag — the same implementation that pins the corpus, in both directions, because a second copy of a coverage gate is a second thing to drift. The axiom policy is per-surface and enforced per surface: the corpus admits exactly the sanctioned boundary, the instruments admit none, and an instrument axiom fails EVEN WHEN ALLOWLISTED. Verified with the reviewer's own payload, both placements: before the walk -> UNCLASSIFIED: DRV|…|bait.smuggled|theorem|Classical.choice,Quot.sound,propext after the walk -> ACCOUNTING FAILED names it (kernel-side) ── `drv-naming-heuristic` (claude, round 7) ──────────────────────────────── Retired as load-bearing rather than patched. The rule admits a theorem whose name extends a constant declared alongside it, and "breaks in one line" — declare `def bait`, then `theorem bait.smuggled` walks through. It stays as a fast readable first check; membership in a committed allowlist is what now carries the weight, and a new row fails closed whatever it is called. ── what round 11 caught, which was mine ─────────────────────────────────── DRV rows first shipped WITHOUT their originating driver. dalek and anza run two drivers, each declaring its own `corpus`; keyed on name alone those two distinct declarations produced one byte-identical row, `sort -u` collapsed them, and the trailers summed to 37 against 36. The estate had already learned this on the corpus walk — INV rows carry their module because two modules both declare CurveFieldProofs.zero_spec — and I rebuilt the record without it. Rows now carry their driver, and the gate FAILS CLOSED ON DUPLICATE RECORDS naming the collision: two declarations sharing one entry means one is covered by the other's, which is exactly how a real declaration hides. The trailer now checks what the drivers EMITTED, not what survives de-duplication — conflating "the run was truncated" with "two rows were identical" is what let a record-format defect present itself as an arithmetic complaint. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
2026-08-03 10:15:26 +00:00
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_dalek.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_dalek.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_dalek.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.
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_dalek.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_dalek.backend.serial.u64.scalar.Scalar52) (curve25519_dalek.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_dalek.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
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_dalek.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_dalek.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))) (@OfN
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_dalek.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_dalek.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))) (@OfN
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_dalek.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_dalek.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))) (@Of
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_dalek.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 Nat.instMonoid)) (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))) (@OfNat.ofNat.{0} Nat
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_dalek.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_dalek.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.o
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_dalek.backend.serial.u64.scalar.Scalar52 (curve25519_dalek.backend.serial.u64.scalar.Scalar52.add a b) fun (r : curve25519_dalek.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_dalek.backend.serial.u64.scalar.Scalar52 (curve25519_dalek.backend.serial.u64.scalar.Scalar52.sub a b) fun (r : curve25519_dalek.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_dalek.backend.serial.u64.scalar.Scalar52 (curve25519_dalek.backend.serial.u64.scalar.Scalar52.mul a b) fun (r : curve25519_dalek.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_dalek.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_dalek.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))
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} A
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.U
spec|ScalarProofs.Ell|def|value=@OfNat.ofNat.{0} Nat (nat_lit 7237005577332262213973186563042994240857116359379907606001950938285454250989) (instOfNatNat (nat_lit 7237005577332262213973186563042994240857116359379907606001950938285454250989))
spec|ScalarProofs.Sc|def|value=curve25519_dalek.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_dalek.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_dalek.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
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