def cancel_pos

bend-collections-laws-math@1.0.0.0 · proofs/math/natural/lcm.bend:184

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend as R

184def cancel_pos(+x: Nat, +y: Nat, +g: Nat, +hg: {Nat.is_lt(0n, g) == True{} : Bool}, +e: {Nat.mul(x, g) == Nat.mul(y, g) : Nat}) -> {x == y : Nat}:
185  match g:
186    case 0n:
187      Empty.absurd({x == y : Nat}, L.false_true(hg))
188    case 1n+ +gp:
189      R.mul_cancel(x, y, gp, e)