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def eq_flip

bend-kit-collections@0.1.4.1 · PROOF.bend:967

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

967def eq_flip(
968  ~K: Data, ~cmp: K -> K -> Cmp, ~flip: Flip(~K, ~cmp), +x: K, +y: K,
969  e: {cmp(x, y) == EQ{} : Cmp}
970) -> {cmp(y, x) == EQ{} : Cmp}:
971  Equal.trans(Cmp, cmp(y, x), Laws.flip(cmp(x, y)), EQ{}, flip(x, y),
972    Equal.cong(Cmp, Cmp, c => Laws.flip(c), cmp(x, y), EQ{}, e))

Uses (5)

Used by (1)