--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "basic_2/notation/relations/simple_1.ma".
+include "basic_2/syntax/term.ma".
+
+(* SIMPLE (NEUTRAL) TERMS ***************************************************)
+
+inductive simple: predicate term ≝
+ | simple_atom: ∀I. simple (⓪{I})
+ | simple_flat: ∀I,V,T. simple (ⓕ{I} V. T)
+.
+
+interpretation "simple (term)" 'Simple T = (simple T).
+
+(* Basic inversion lemmas ***************************************************)
+
+fact simple_inv_bind_aux: ∀T. 𝐒⦃T⦄ → ∀p,J,W,U. T = ⓑ{p,J}W.U → ⊥.
+#T * -T
+[ #I #p #J #W #U #H destruct
+| #I #V #T #a #J #W #U #H destruct
+]
+qed-.
+
+lemma simple_inv_bind: ∀p,I,V,T. 𝐒⦃ⓑ{p,I} V. T⦄ → ⊥.
+/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 by ex_intro/
+#p #I #V #T #H elim (simple_inv_bind … H)
+qed-.