--- /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/cofreestar_3.ma".
+include "basic_2/substitution/cpys.ma".
+
+(* CONTEXT-SENSITIVE EXCLUSION FROM FREE VARIABLES **************************)
+
+definition cofrees: relation3 nat lenv term ≝
+ λd,L,U1. ∀U2. ⦃⋆, L⦄ ⊢ U1 ▶*[d, ∞] U2 → ∃T2. ⇧[d, 1] T2 ≡ U2.
+
+interpretation
+ "context-sensitive exclusion from free variables (term)"
+ 'CoFreeStar d L T = (cofrees d L T).
+
+(* Basic forward lemmas *****************************************************)
+
+lemma cofrees_fwd_lift: ∀L,U,d. d ~ϵ 𝐅*⦃L, U⦄ → ∃T. ⇧[d, 1] T ≡ U.
+/2 width=1 by/ qed-.
+
+lemma nlift_frees: ∀L,U,d. (∀T. ⇧[d, 1] T ≡ U → ⊥) → (d ~ϵ 𝐅*⦃L, U⦄ → ⊥).
+#L #U #d #HnTU #H elim (cofrees_fwd_lift … H) -H /2 width=2 by/
+qed-.