- equivalence between lfpxs and lpxs + lfeq proved

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / relocation / lex_tc.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lex_tc.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lex_tc.ma
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lex_tc.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/syntax/ext2_tc.ma".
+include "basic_2/relocation/lexs_tc.ma".
+include "basic_2/relocation/lex.ma".
+
+(* GENERIC EXTENSION OF A CONTEXT-SENSITIVE REALTION FOR TERMS **************)
+
+(* Inversion lemmas with transitive closure *********************************)
+
+lemma s_rs_transitive_lex_inv_isid: ∀R. s_rs_transitive … R (λ_.lex R) →
+                                    s_rs_transitive_isid cfull (cext2 R).
+#R #HR #f #Hf #L2 #T1 #T2 #H #L1 #HL12
+elim (ext2_tc … H) -H
+[ /3 width=1 by ext2_inv_tc, ext2_unit/
+| #I #V1 #V2 #HV12
+  @ext2_inv_tc @ext2_pair
+  @(HR … HV12) -HV12 /2 width=3 by ex2_intro/ (**) (* auto fails *)
+]
+qed-.