update in ground_2 and models

[helm.git] / matita / matita / contribs / lambdadelta / apps_2 / models / veq_vdrop.ma

diff --git a/matita/matita/contribs/lambdadelta/apps_2/models/veq_vdrop.ma b/matita/matita/contribs/lambdadelta/apps_2/models/veq_vdrop.ma
new file mode 100644 (file)
index 0000000..ae31753
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/apps_2/models/veq_vdrop.ma
@@ -0,0 +1,42 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "apps_2/models/vdrop_vlift.ma".
+include "apps_2/models/veq.ma".
+
+(* EVALUATION EQUIVALENCE  **************************************************)
+
+(* Properties with evaluation drop ******************************************)
+
+lemma vdrop_comp (M): ∀i. compatible_2 … (vdrop M i) (veq M) (veq M).
+#M #i #lv1 #lv2 #Hlv12 #j elim (lt_or_ge j i) #Hji
+[ >vdrop_lt // >vdrop_lt //
+| >vdrop_ge // >vdrop_ge //
+]
+qed.
+
+(* Advanced inversion lemmas with evaluation evaluation lift ****************)
+
+lemma veq_inv_vlift_sn (M): ∀lv1,y2,d1,i. ⫯[i←d1]lv1 ≗{M} y2 →
+                            ∃∃lv2,d2. lv1 ≗ lv2 & d1 ≗ d2 & ⫯[i←d2]lv2 ≐ y2.
+#M #lv1 #y2 #d1 #i #H
+@(ex3_2_intro)
+[5: @exteq_sym @vlift_vdrop_eq |1,2: skip
+| #j elim (lt_or_ge j i) #Hji
+  [ lapply (H j) -H >vlift_lt // >vdrop_lt //
+  | lapply (H (↑j)) -H >vlift_gt /2 width=1 by monotonic_le_plus_l/ >vdrop_ge //
+  ]
+| lapply (H i) >vlift_eq //
+]
+qed-.