Lemma isapbinop_op : ∏ x x' y y' : X, op x y ≠ op x' y' → x ≠ x' ∨ y ≠ y'. 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.
Require Import UniMath.Foundations.Propositions. Require Import UniMath.MoreFoundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.DecidablePropositions.