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[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / cpr_drops.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpr_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpr_drops.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/rt_transition/cpm_drops.ma".
+
+(* CONTEXT-SENSITIVE PARALLEL R-TRANSITION FOR TERMS ************************)
+
+(* Advanced inversion lemmas ************************************************)
+
+(* Basic_2A1: includes: cpr_inv_atom1 *)
+lemma cpr_inv_atom1_drops: ∀h,I,G,L,T2. ⦃G, L⦄ ⊢ ⓪{I} ➡[h] T2 →
+                           T2 = ⓪{I} ∨
+                           ∃∃K,V,V2,i. ⬇*[i] L ≡ K.ⓓV & ⦃G, K⦄ ⊢ V ➡[h] V2 &
+                                       ⬆*[⫯i] V2 ≡ T2 & I = LRef i.
+#h #I #G #L #T2 #H elim (cpm_inv_atom1_drops … H) -H *
+[ /2 width=1 by or_introl/
+| #s #_ #_ #H destruct
+| /3 width=8 by ex4_4_intro, or_intror/
+| #m #K #V1 #V2 #i #_ #_ #_ #_ #H destruct
+]
+qed-.
+
+(* Basic_1: includes: pr0_gen_lref pr2_gen_lref *)
+(* Basic_2A1: includes: cpr_inv_lref1 *)
+lemma cpr_inv_lref1_drops: ∀h,G,L,T2,i. ⦃G, L⦄ ⊢ #i ➡[h] T2 →
+                           T2 = #i ∨
+                           ∃∃K,V,V2. ⬇*[i] L ≡ K. ⓓV & ⦃G, K⦄ ⊢ V ➡[h] V2 &
+                                     ⬆*[⫯i] V2 ≡ T2.
+#h #G #L #T2 #i #H elim (cpm_inv_lref1_drops … H) -H *
+[ /2 width=1 by or_introl/
+| /3 width=6 by ex3_3_intro, or_intror/
+| #m #K #V1 #V2 #_ #_ #_ #H destruct
+]
+qed-.