def base

bend-collections-laws-math@1.0.0.0 · proofs/math/number/egcd.bend:64

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

64# the base case: a * 1 == a + b * 0
65def base(+a: Nat, +b: Nat) -> {Nat.mul(a, 1n) == Nat.add(a, Nat.mul(b, 0n)) : Nat}:
66  %Equal.sym(Nat, Nat.mul(a, 1n), a, A.mul_one(a)) : {_ == Nat.add(a, Nat.mul(b, 0n)) : Nat}
67  %Equal.sym(Nat, Nat.mul(b, 0n), 0n, A.mul_zero(b)) : {a == Nat.add(a, _) : Nat}
68  Equal.sym(Nat, Nat.add(a, 0n), a, A.add_zero(a))