def pass_mod

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/fold.bend:151

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/math/natural/arith.bend as NR
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend as LM

151def pass_mod(+one: Nat, +h1: {one == 1n : Nat}, +pp: Nat, +hP: {Nat.add(1n+pp, 19n) == WD.sc(255n, one) : Nat}, +xs: List<&2, U32>, +hx: {LM.okb(32n, xs, WD.sc(28n, one)) == True{} : Bool}) -> {Nat.mod(FS.value(F.pass(xs)), 1n+pp) == Nat.mod(FS.value(xs), 1n+pp) : Nat}:
152  +c = v(LM.cc(F.carry(xs, 0)))
153  %Equal.sym(Nat, FS.value(xs), Nat.add(Nat.mul(Nat.add(c, c), 1n+pp), FS.value(F.pass(xs))), pass_fold(one, h1, pp, hP, xs, hx)) : {Nat.mod(FS.value(F.pass(xs)), 1n+pp) == Nat.mod(_, 1n+pp) : Nat}
154  Equal.sym(Nat, Nat.mod(Nat.add(Nat.mul(Nat.add(c, c), 1n+pp), FS.value(F.pass(xs))), 1n+pp), Nat.mod(FS.value(F.pass(xs)), 1n+pp), NR.absorb(pp, Nat.add(c, c), FS.value(F.pass(xs))))