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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm_teqx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm_teqx.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 "static_2/syntax/teqx.ma".
+include "basic_2/rt_transition/cpm_drops.ma".
+
+(* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS ***************)
+
+(* Inversion lemmas with sort-irrelevant equivalence for terms **************)
+
+lemma cpm_teqx_inv_lref_sn (n) (h) (G) (L) (i):
+                           ∀X.  ⦃G,L⦄ ⊢ #i ➡[n,h] X → #i ≛ X →
+                           ∧∧ X = #i & n = 0.
+#n #h #G #L #i #X #H1 #H2
+lapply (teqx_inv_lref1 … H2) -H2 #H destruct
+elim (cpm_inv_lref1_drops … H1) -H1 // * [| #m ]
+#K #V1 #V2 #_ #_ #H -V1
+elim (lifts_inv_lref2_uni_lt … H) -H //
+qed-.
+
+lemma cpm_teqx_inv_atom_sn (n) (h) (I) (G) (L):
+                           ∀X. ⦃G,L⦄ ⊢ ⓪{I} ➡[n,h] X → ⓪{I} ≛ X →
+                           ∨∨ ∧∧ X = ⓪{I} & n = 0
+                            | ∃∃s. X = ⋆(⫯[h]s) & I = Sort s & n = 1.
+#n #h * #s #G #L #X #H1 #H2
+[ elim (cpm_inv_sort1 … H1) -H1
+  cases n -n [| #n ] #H #Hn destruct -H2
+  [ /3 width=1 by or_introl, conj/
+  | <(le_n_O_to_eq n) [| /2 width=3 by le_S_S_to_le/ ] -n
+    /3 width=3 by ex3_intro, or_intror/
+  ]
+| elim (cpm_teqx_inv_lref_sn … H1 H2) -H1 -H2 /3 width=1 by or_introl, conj/
+| elim (cpm_inv_gref1 … H1) -H1 -H2 /3 width=1 by or_introl, conj/
+]
+qed-.