def mul1

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/fieldops.bend:176

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/u32div.bend as UD
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

176def mul1(+one: Nat, +h1: {one == 1n : Nat}, +x: U32) -> {U32.mul(x, 1) == x : U32}:
177  +b = L.subst(Nat, z => {Nat.is_lt(z, WD.sc(32n, one)) == True{} : Bool}, v(x), Nat.mul(v(x), 1n), Equal.sym(Nat, Nat.mul(v(x), 1n), v(x), NA.mul_one(v(x))), UD.vb(one, h1, x))
178  U.injective(U32.mul(x, 1), x, Equal.trans(Nat, v(U32.mul(x, 1)), Nat.mul(v(x), 1n), v(x), LM.mul_v(one, h1, x, 1, b), NA.mul_one(v(x))))