proposition: Lemma equiv_unit A (x : A) : inj (@eq_refl A x = eq_refl) <~> inj unit.
proof: Proof. refine {| equiv x := tt |}. unshelve refine {| equiv_inv x := eq_refl |}. red; intros. destruct x0. reflexivity. red; intros. revert x0. set (foo:=@eq_refl A x). clearbody foo. intros x0. apply axiom_triangle. apply axiom_triangle. Defined.
imports: Equations Utf8 DepElimDec EqDecInstances