update in lambdadelta

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / substitution / gget_gget.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/substitution/gget_gget.ma b/matita/matita/contribs/lambdadelta/basic_2A/substitution/gget_gget.ma
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2A/substitution/gget_gget.ma
@@ -0,0 +1,40 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_2A/substitution/gget.ma".
+
+(* GLOBAL ENVIRONMENT READING ***********************************************)
+
+(* Main properties **********************************************************)
+
+theorem gget_mono: ∀G,G1,m. ⬇[m] G ≡ G1 → ∀G2. ⬇[m] G ≡ G2 → G1 = G2.
+#G #G1 #m #H elim H -G -G1
+[ #G #Hm #G2 #H
+  >(gget_inv_gt … H Hm) -H -Hm //
+| #G #Hm #G2 #H
+  >(gget_inv_eq … H Hm) -H -Hm //
+| #I #G #G1 #V #Hm #_ #IHG1 #G2 #H
+  lapply (gget_inv_lt … H Hm) -H -Hm /2 width=1 by/
+]
+qed-.
+
+lemma gget_dec: ∀G1,G2,m. Decidable (⬇[m] G1 ≡ G2).
+#G1 #G2 #m
+elim (gget_total m G1) #G #HG1
+elim (eq_genv_dec G G2) #HG2
+[ destruct /2 width=1 by or_introl/
+| @or_intror #HG12
+  lapply (gget_mono … HG1 … HG12) -HG1 -HG12 /2 width=1 by/
+]
+qed-.