proposition: Lemma tightapSet_dec {X : tightapSet} : LEM -> ∏ x y : X, (x != y <-> x ≠ y).
proof: Proof. intros Hdec x y. destruct (Hdec (x ≠ y)) as [ Hneq | Heq ]. - split. + intros _ ; apply Hneq. + intros _ Heq. rewrite <- Heq in Hneq. revert Hneq. now apply isirrefltightapSet. - split. + intros Hneq. apply fromempty, Hneq. now apply istighttightapSet. + intros Hneq. exact (fromempty (Heq Hneq)). Qed.
imports: UniMath.Algebra.BinaryOperations UniMath.Foundations.Propositions UniMath.MoreFoundations.Sets UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.DecidablePropositions