def gt_flip

bend-kit-collections@0.1.4.1 · PROOF.bend:226

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

226def gt_flip(
227  ~K: Data, ~cmp: K -> K -> Cmp, ~flip: Flip(~K, ~cmp), +x: K, +y: K,
228  e: {cmp(x, y) == GT{} : Cmp}
229) -> {cmp(y, x) == LT{} : Cmp}:
230  Equal.trans(Cmp, cmp(y, x), Laws.flip(cmp(x, y)), LT{}, flip(x, y),
231    Equal.cong(Cmp, Cmp, c => Laws.flip(c), cmp(x, y), GT{}, e))