proposition: Lemma isapbinop_op : ∏ x x' y y' : X, op x y ≠ op x' y' -> x ≠ x' ∨ y ≠ y'.
proof: Proof. intros x x' y y' Hop. apply (iscotranstightapSet _ (op x' y)) in Hop. revert Hop ; apply hinhfun ; intros [Hop | Hop]. - left ; revert Hop. now apply islapbinop_op. - right ; revert Hop. now apply israpbinop_op. Qed.
imports: UniMath.Algebra.BinaryOperations UniMath.Foundations.Propositions UniMath.MoreFoundations.Sets UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.DecidablePropositions