--- /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 "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-.