def gcd_pos

bend-collections-laws-crypto@1.0.0.0 · proofs/math/natural/lcm.bend:104

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

104# a == la g with a > 0 makes g positive
105def gcd_pos(+ap: Nat, +l: Nat, +g: Nat, +e: {1n+ap == Nat.mul(l, g) : Nat}) -> {Nat.is_lt(0n, g) == True{} : Bool}:
106  match g:
107    case 0n:
108      Empty.absurd({Nat.is_lt(0n, 0n) == True{} : Bool}, N.succ_zero(ap, Equal.trans(Nat, 1n+ap, Nat.mul(l, 0n), 0n, e, A.mul_zero(l))))
109    case 1n+gp:
110      {==}