def two_mul

bend-collections-laws-crypto@1.0.0.0 · proofs/math/natural/roots.bend:68

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as A

68# x 2 == x + x
69def two_mul(+x: Nat) -> {Nat.mul(x, 2n) == Nat.add(x, x) : Nat}:
70  Equal.trans(Nat, Nat.mul(x, 2n), Nat.mul(2n, x), Nat.add(x, x), A.mul_comm(x, 2n), Equal.cong(Nat, Nat, z => Nat.add(x, z), Nat.add(x, 0n), x, A.add_zero(x)))