milestone update in ground

[helm.git] / matita / matita / contribs / lambdadelta / ground / relocation / gr_sle_eq.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/gr_sle_eq.ma b/matita/matita/contribs/lambdadelta/ground/relocation/gr_sle_eq.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 "ground/relocation/gr_sle.ma".
+(**) (* this should go first *)
+include "ground/relocation/gr_tl_eq.ma".
+
+(* INCLUSION FOR GENERIC RELOCATION MAPS ***********************************************************)
+
+(* Properties with gr_eq *********************************************************)
+
+(*** sle_eq_repl_back1 *)
+corec lemma gr_sle_eq_repl_back_sn:
+            ∀f2:gr_map. gr_eq_repl_back … (λf1:gr_map. f1 ⊆ f2).
+#f2 #f1 * -f2 -f1
+#f1 #f2 #g1 #g2 #Hf #H1 #H2 #g #H0
+[ cases (gr_eq_inv_push_sn …  H0 …  H1) -g1 /3 width=5 by gr_sle_push/
+| cases (gr_eq_inv_next_sn …  H0 …  H1) -g1 /3 width=5 by gr_sle_next/
+| cases (gr_eq_inv_push_sn …  H0 …  H1) -g1 /3 width=5 by gr_sle_weak/
+]
+qed-.
+
+(*** sle_eq_repl_fwd1 *)
+lemma gr_sle_eq_repl_fwd_sn:
+      ∀f2. gr_eq_repl_fwd … (λf1. f1 ⊆ f2).
+#f2 @gr_eq_repl_sym /2 width=3 by gr_sle_eq_repl_back_sn/
+qed-.
+
+(*** sle_eq_repl_back2 *)
+corec lemma gr_sle_eq_repl_back_dx:
+            ∀f1. gr_eq_repl_back … (λf2. f1 ⊆ f2).
+#f1 #f2 * -f1 -f2
+#f1 #f2 #g1 #g2 #Hf #H1 #H2 #g #H0
+[ cases (gr_eq_inv_push_sn …  H0 …  H2) -g2 /3 width=5 by gr_sle_push/
+| cases (gr_eq_inv_next_sn …  H0 …  H2) -g2 /3 width=5 by gr_sle_next/
+| cases (gr_eq_inv_next_sn …  H0 …  H2) -g2 /3 width=5 by gr_sle_weak/
+]
+qed-.
+
+(*** sle_eq_repl_fwd2 *)
+lemma gr_sle_eq_repl_fwd_dx:
+      ∀f1. gr_eq_repl_fwd … (λf2. f1 ⊆ f2).
+#f1 @gr_eq_repl_sym /2 width=3 by gr_sle_eq_repl_back_dx/
+qed-.
+
+(*** sle_refl_eq *)
+lemma gr_sle_refl_eq:
+      ∀f1,f2. f1 ≡ f2 → f1 ⊆ f2.
+/2 width=3 by gr_sle_eq_repl_back_dx/ qed.