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diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/frees_frees.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/frees_frees.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/relocation/frees.ma".
+
+(* CONTEXT-SENSITIVE FREE VARIABLES *****************************************)
+
+(* Main inversion lemmas ****************************************************)
+
+theorem frees_mono: ∀L,T,f1. L ⊢ 𝐅*⦃T⦄ ≡ f1 → ∀f2. L ⊢ 𝐅*⦃T⦄ ≡ f2 → f1 ≗ f2.
+#L #T #f1 #H elim H -L -T -f1
+[ /3 width=2 by frees_inv_atom, isid_inv_eq_repl/
+| /4 width=5 by frees_inv_sort, eq_push_inv_isid, isid_inv_eq_repl, eq_trans/
+| #I #L #V #f1 #_ #IH #x #H elim (frees_inv_zero … H) -H *
+  [ #H destruct
+  | #Z #Y #X #f2 #Hf2 #H1 #H2 destruct /3 width=5 by eq_next/
+  ]
+| #I #L #V #i #f1 #_ #IH #x #H elim (frees_inv_lref … H) -H *
+  [ #H destruct
+  | #Z #Y #X #f2 #Hf2 #H1 #H2 destruct /3 width=5 by eq_push/
+  ]
+| /4 width=5 by frees_inv_gref, eq_push_inv_isid, isid_inv_eq_repl, eq_trans/
+| #I #L #V #T #p #f1 #f2 #f #_ #_ #Hf #IHV #IHT #g #H elim (frees_inv_bind … H) -H
+  #g1 #g2 #HV #HT #Hg @(sor_mono … Hf) -Hf
+  /5 width=3 by sor_eq_repl_fwd2, sor_eq_repl_fwd1, tl_eq_repl/ (**) (* full auto too slow *)
+| #I #L #V #T #f1 #f2 #f #_ #_ #Hf #IHV #IHT #g #H elim (frees_inv_flat … H) -H
+  #g1 #g2 #HV #HT #Hg @(sor_mono … Hf) -Hf
+  /4 width=3 by sor_eq_repl_fwd2, sor_eq_repl_fwd1/ (**) (* full auto too slow *)
+]
+qed-.