lambda_delta: global environments handling: redefined and first results

[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / substitution / gdrop_gdrop.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/substitution/gdrop_gdrop.ma b/matita/matita/contribs/lambda_delta/Basic_2/substitution/gdrop_gdrop.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/substitution/gdrop.ma".
+
+(* GLOBAL ENVIRONMENT SLICING ***********************************************)
+
+(* Main properties **********************************************************)
+
+theorem gdrop_mono: ∀G,G1,e. ⇓[e] G ≡ G1 → ∀G2. ⇓[e] G ≡ G2 → G1 = G2.
+#G #G1 #e #H elim H -G -G1
+[ #G #He #G2 #H
+  >(gdrop_inv_gt … H He) -H -He //
+| #G #He #G2 #H
+  >(gdrop_inv_eq … H He) -H -He //
+| #I #G #G1 #V #He #_ #IHG1 #G2 #H
+  lapply (gdrop_inv_lt … H He) -H -He /2 width=1/
+]
+qed-.
+
+lemma gdrop_dec: ∀G1,G2,e. Decidable (⇓[e] G1 ≡ G2).
+#G1 #G2 #e
+elim (gdrop_total e G1) #G #HG1
+elim (genv_eq_dec G G2) #HG2
+[ destruct /2 width=1/
+| @or_intror #HG12
+  lapply (gdrop_mono … HG1 … HG12) -HG1 -HG12 /2 width=1/
+]
+qed-.