reaxiomatized lleq fixes a bug in it and allows to park substitution in etc

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / substitution / fqup_lleq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/fqup_lleq.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/fqup_lleq.ma
new file mode 100644 (file)
index 0000000..c0bfa41
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/fqup_lleq.ma
@@ -0,0 +1,32 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/fqu_lleq.ma".
+include "basic_2/substitution/fqup.ma".
+
+(* PLUS-ITERATED SUPCLOSURE *************************************************)
+
+(* Properties on lazy equivalence for local environments ********************)
+
+lemma lleq_fqup_trans: ∀G1,G2,L2,K2,T,U. ⦃G1, L2, T⦄ ⊃+ ⦃G2, K2, U⦄ →
+                       ∀L1. L1 ⋕[T, 0] L2 →
+                       ∃∃K1. ⦃G1, L1, T⦄ ⊃+ ⦃G2, K1, U⦄ & K1 ⋕[U, 0] K2.
+#G1 #G2 #L2 #K2 #T #U #H @(fqup_ind … H) -G2 -K2 -U
+[ #G2 #K2 #U #HTU #L1 #HL12 elim (lleq_fqu_trans … HTU … HL12) -L2
+  /3 width=3 by fqu_fqup, ex2_intro/
+| #G #G2 #K #K2 #U #U2 #_ #HU2 #IHTU #L1 #HL12 elim (IHTU … HL12) -L2
+  #K1 #HTU #HK1 elim (lleq_fqu_trans … HU2 … HK1) -K
+  /3 width=5 by fqup_strap1, ex2_intro/
+]
+qed-.