PROOF.gt_flip: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 226-231 of bend-kit-collections@0.1.4.1/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&start_line=226&end_line=231

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

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

Uses (5):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Cmp
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/LAWS.bend&name=flip
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=Flip