def pow_one_one

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/pow.bend:139

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/lemmas/proofs/nat_algebra.bend as NA

139# a^one * 1 == a
140def pow_one_one(+one: Nat, +h1: {one == 1n : Nat}, +a: Nat) -> {Nat.mul(Nat.pow(a, one), 1n) == a : Nat}:
141  +e = L.subst(Nat, o => {Nat.pow(a, o) == a : Nat}, 1n, one, Equal.sym(Nat, one, 1n, h1), NA.mul_one(a))
142  Equal.trans(Nat, Nat.mul(Nat.pow(a, one), 1n), Nat.pow(a, one), a, NA.mul_one(Nat.pow(a, one)), e)