def bitlen_okb

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/ed25519/bytes.bend:92

import Base
import bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/x25519.bend as X
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend as LM

92def bitlen_okb(+n: Nat, +xs: List<&2, U32>, +b: Nat, +e: {LM.okb(n, xs, b) == True{} : Bool}) -> {X.bitlen(xs) == e8(n) : Nat}:
93  match n xs:
94    case 0n Nil{}:
95      {==}
96    case 0n Con{x, xt}:
97      Empty.absurd({X.bitlen(Con{x, xt}) == 0n : Nat}, L.true_false(Equal.sym(Bool, False{}, True{}, e)))
98    case 1n+k Nil{}:
99      Empty.absurd({0n == e8(1n+k) : Nat}, L.true_false(Equal.sym(Bool, False{}, True{}, e)))
100    case 1n+ +k Con{+x, +xt}:
101      Equal.cong(Nat, Nat, z => Nat.add(8n, z), X.bitlen(xt), e8(k), bitlen_okb(k, xt, b, L.and_right(Nat.is_le(v(x), b), LM.okb(k, xt, b), e)))