def two_mul

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/natlight.bend:34

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA

34def two_mul(+S: Nat) -> {Nat.mul(S, 2n) == Nat.add(S, S) : Nat}:
35  Equal.trans(Nat, Nat.mul(S, 2n), Nat.mul(2n, S), Nat.add(S, S), NA.mul_comm(S, 2n), Equal.cong(Nat, Nat, z => Nat.add(S, z), Nat.mul(1n, S), S, mul1(S)))