update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / lsubv_drops.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubv_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubv_drops.ma
new file mode 100644 (file)
index 0000000..90b59cb
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubv_drops.ma
@@ -0,0 +1,70 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/relocation/drops.ma".
+include "basic_2/dynamic/lsubv.ma".
+
+(* LOCAL ENVIRONMENT REFINEMENT FOR NATIVE VALIDITY *************************)
+
+(* Properties with generic slicing for local environments *******************)
+
+(* Note: the premise 𝐔⦃f⦄ cannot be removed *)
+(* Basic_2A1: includes: lsubsv_drop_O1_conf *)
+lemma lsubv_drops_conf_isuni (a) (h) (G):
+                             ∀L1,L2. G ⊢ L1 ⫃![a,h] L2 →
+                             ∀b,f,K1. 𝐔⦃f⦄ → ⬇*[b,f] L1 ≘ K1 →
+                             ∃∃K2. G ⊢ K1 ⫃![a,h] K2 & ⬇*[b,f] L2 ≘ K2.
+#a #h #G #L1 #L2 #H elim H -L1 -L2
+[ /2 width=3 by ex2_intro/
+| #I #L1 #L2 #HL12 #IH #b #f #K1 #Hf #H
+  elim (drops_inv_bind1_isuni … Hf H) -Hf -H *
+  [ #Hf #H destruct -IH
+    /3 width=3 by lsubv_bind, drops_refl, ex2_intro/
+  | #g #Hg #HLK1 #H destruct -HL12
+    elim (IH … Hg HLK1) -L1 -Hg /3 width=3 by drops_drop, ex2_intro/
+  ]
+| #L1 #L2 #W #V #HVW #HW #HL12 #IH #b #f #K1 #Hf #H
+  elim (drops_inv_bind1_isuni … Hf H) -Hf -H *
+  [ #Hf #H destruct -IH
+    /3 width=3 by drops_refl, lsubv_beta, ex2_intro/
+  | #g #Hg #HLK1 #H destruct -HL12
+    elim (IH … Hg HLK1) -L1 -Hg /3 width=3 by drops_drop, ex2_intro/
+  ]
+]
+qed-.
+
+(* Note: the premise 𝐔⦃f⦄ cannot be removed *)
+(* Basic_2A1: includes: lsubsv_drop_O1_trans *)
+lemma lsubv_drops_trans_isuni (a) (h) (G):
+                              ∀L1,L2. G ⊢ L1 ⫃![a,h] L2 →
+                              ∀b,f,K2. 𝐔⦃f⦄ → ⬇*[b,f] L2 ≘ K2 →
+                              ∃∃K1. G ⊢ K1 ⫃![a,h] K2 & ⬇*[b,f] L1 ≘ K1.
+#a #h #G #L1 #L2 #H elim H -L1 -L2
+[ /2 width=3 by ex2_intro/
+| #I #L1 #L2 #HL12 #IH #b #f #K2 #Hf #H
+  elim (drops_inv_bind1_isuni … Hf H) -Hf -H *
+  [ #Hf #H destruct -IH
+    /3 width=3 by lsubv_bind, drops_refl, ex2_intro/
+  | #g #Hg #HLK2 #H destruct -HL12
+    elim (IH … Hg HLK2) -L2 -Hg /3 width=3 by drops_drop, ex2_intro/
+  ]
+| #L1 #L2 #W #V #HWV #HW #HL12 #IH #b #f #K2 #Hf #H
+  elim (drops_inv_bind1_isuni … Hf H) -Hf -H *
+  [ #Hf #H destruct -IH
+    /3 width=3 by drops_refl, lsubv_beta, ex2_intro/
+  | #g #Hg #HLK2 #H destruct -HL12
+    elim (IH … Hg HLK2) -L2 -Hg /3 width=3 by drops_drop, ex2_intro/
+  ]
+]
+qed-.