qed.
lemma simple_inv_bind: ∀a,I,V,T. 𝐒⦃ⓑ{a,I} V. T⦄ → ⊥.
-/2 width=7/ qed-.
+/2 width=7 by simple_inv_bind_aux/ qed-.
lemma simple_inv_pair: ∀I,V,T. 𝐒⦃②{I}V.T⦄ → ∃J. I = Flat2 J.
-* /2 width=2/ #a #I #V #T #H
+* /2 width=2 by ex_intro/ #a #I #V #T #H
elim (simple_inv_bind … H)
qed-.