def parity_val

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/canon.bend:196

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/field.bend as FS
import bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/field.bend as F
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend as WD
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/num.bend as M
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend as LM

196def parity_val(+one: Nat, +h1: {one == 1n : Nat}, +pp: Nat, +hP: {Nat.add(1n+pp, 19n) == WD.sc(255n, one) : Nat}, +x: List<&2, U32>, +hx: {LM.okb(32n, x, 255n) == True{} : Bool}) -> {v(F.parity(x)) == Nat.mod(Nat.mod(FS.value(x), 1n+pp), 2n) : Nat}:
197  +y = F.freeze(x)
198  Equal.trans(Nat, v(F.low_bit(y)), Nat.mod(FS.value(y), 2n), Nat.mod(Nat.mod(FS.value(x), 1n+pp), 2n), low_bit_val(one, h1, y, freeze_okb(one, h1, pp, hP, x, hx)), M.cong_mod(2n, FS.value(y), Nat.mod(FS.value(x), 1n+pp), freeze_val(one, h1, pp, hP, x, hx)))