def mul0

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/fieldops.bend:180

import Base
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/lib/word.bend as WD
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32.bend as U
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend as LM

180def mul0(+one: Nat, +h1: {one == 1n : Nat}, +x: U32) -> {U32.mul(x, 0) == 0 : U32}:
181  +b = L.subst(Nat, z => {Nat.is_lt(z, WD.sc(32n, one)) == True{} : Bool}, 0n, Nat.mul(v(x), 0n), Equal.sym(Nat, Nat.mul(v(x), 0n), 0n, NA.mul_zero(v(x))), LM.sc_pos1(32n, one, h1))
182  U.injective(U32.mul(x, 0), 0, Equal.trans(Nat, v(U32.mul(x, 0)), Nat.mul(v(x), 0n), 0n, LM.mul_v(one, h1, x, 0, b), NA.mul_zero(v(x))))