- theory of llor now includes (long awaited) non-recursive alternative definition

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc / llor / lleq_llor.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/llor/lleq_llor.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/llor/lleq_llor.etc
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2/etc/llor/lleq_llor.etc
@@ -0,0 +1,35 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/llor.ma".
+include "basic_2/substitution/lleq_alt.ma".
+
+(* LAZY EQUIVALENCE FOR LOCAL ENVIRONMENTS **********************************)
+
+(* Properties on poinwise union for local environments **********************)
+
+lemma llor_lleq_O: ∀T,L1,L2,L. L1 ⩖[T] L2 ≡ L → |L1| ≤ |L2| → |L2| = |L| → L2 ⋕[T, yinj 0] L.
+#T #L1 @(f2_ind … rfw … L1 T) -L1 -T
+#n #IH #L1 #T #Hn #L2 #L #H #HL12 #HL2 elim (llor_inv_alt … H) // destruct
+#HL1 #IHT @lleq_intro_alt //
+#I2 #I #K2 #K #V2 #V #i #_ #HnT #HLK2 #HLK lapply (ldrop_fwd_length_lt2 … HLK)
+#Hi elim (ldrop_O1_lt L1 i) //
+#I1 #K1 #V1 #HLK1 elim (IHT … HLK1 HLK) >HL1 >HL2 <minus_n_n -IHT -HLK1 -HLK
+[
+| * #I0 #K0 #V0 #_ #HLK0 lapply (ldrop_mono … HLK0 … HLK2) -HLK0 -HLK2
+  #H1 #H2 #H3 #_ destruct
+    
+
+
+