def gt_of_lt

bend-kit-collections@0.1.4.1 · PROOF.bend:568

import Base
import bend-kit-collections@0.1.4.1/LAWS.bend as Laws

568def gt_of_lt(
569  ~K: Data, ~cmp: K -> K -> Cmp, ~flip: Flip(~K, ~cmp), +x: K, +y: K,
570  e: {cmp(x, y) == LT{} : Cmp}
571) -> {cmp(y, x) == GT{} : Cmp}:
572  Equal.trans(Cmp, cmp(y, x), Laws.flip(cmp(x, y)), GT{}, flip(x, y),
573    Equal.cong(Cmp, Cmp, c => Laws.flip(c), cmp(x, y), LT{}, e))