milestone update in ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/gr_sor_isi.ma b/matita/matita/contribs/lambdadelta/ground/relocation/gr_sor_isi.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_isi_eq.ma".
+include "ground/relocation/gr_sor_eq.ma".
+include "ground/relocation/gr_sor_sor.ma".
+
+(* RELATIONAL UNION FOR GENERIC RELOCATION MAPS ***********************************************************)
+
+(* Properties with test for identity *****************************************)
+
+(*** sor_isid_sn *)
+corec lemma gr_sor_isi_sn:
+            ∀f1. 𝐈❪f1❫ → ∀f2. f1 ⋓ f2 ≘ f2.
+#f1 * -f1
+#f1 #g1 #Hf1 #H1 #f2 cases (gr_map_split_tl f2)
+/3 width=7 by gr_sor_push_bi, gr_sor_push_next/
+qed.
+
+(*** sor_isid_dx *)
+corec lemma gr_sor_isi_dx:
+            ∀f2. 𝐈❪f2❫ → ∀f1. f1 ⋓ f2 ≘ f1.
+#f2 * -f2
+#f2 #g2 #Hf2 #H2 #f1 cases (gr_map_split_tl f1)
+/3 width=7 by gr_sor_push_bi, gr_sor_next_push/
+qed.
+
+(*** sor_isid *)
+lemma gr_sor_isi_bi_isi:
+      ∀f1,f2,f. 𝐈❪f1❫ → 𝐈❪f2❫ → 𝐈❪f❫ → f1 ⋓ f2 ≘ f.
+/4 width=3 by gr_sor_eq_repl_back_dx, gr_sor_eq_repl_back_sn, gr_isi_inv_eq_repl/ qed.
+
+
+(* Forward lemmas with test for identity **********************************)
+
+(*** sor_fwd_isid1 *)
+corec lemma gr_sor_des_isi_sn:
+            ∀f1,f2,f. f1 ⋓ f2 ≘ f → 𝐈❪f❫ → 𝐈❪f1❫.
+#f1 #f2 #f * -f1 -f2 -f
+#f1 #f2 #f #g1 #g2 #g #Hf #H1 #H2 #H #Hg
+[ /4 width=6 by gr_isi_inv_push, gr_isi_push/ ]
+cases (gr_isi_inv_next … Hg … H)
+qed-.
+
+(*** sor_fwd_isid2 *)
+corec lemma gr_sor_des_isi_dx:
+            ∀f1,f2,f. f1 ⋓ f2 ≘ f → 𝐈❪f❫ → 𝐈❪f2❫.
+#f1 #f2 #f * -f1 -f2 -f
+#f1 #f2 #f #g1 #g2 #g #Hf #H1 #H2 #H #Hg
+[ /4 width=6 by gr_isi_inv_push, gr_isi_push/ ]
+cases (gr_isi_inv_next … Hg … H)
+qed-.
+
+(* Inversion lemmas with test for identity **********************************)
+
+(*** sor_isid_inv_sn *)
+lemma gr_sor_inv_isi_sn:
+      ∀f1,f2,f. f1 ⋓ f2 ≘ f → 𝐈❪f1❫ → f2 ≡ f.
+/3 width=4 by gr_sor_isi_sn, gr_sor_mono/
+qed-.
+
+(*** sor_isid_inv_dx *)
+lemma gr_sor_inv_isi_dx:
+      ∀f1,f2,f. f1 ⋓ f2 ≘ f → 𝐈❪f2❫ → f1 ≡ f.
+/3 width=4 by gr_sor_isi_dx, gr_sor_mono/
+qed-.
+
+(*** sor_inv_isid3 *)
+lemma gr_sor_inv_isi:
+      ∀f1,f2,f. f1 ⋓ f2 ≘ f → 𝐈❪f❫ →
+      ∧∧ 𝐈❪f1❫ & 𝐈❪f2❫.
+/3 width=4 by gr_sor_des_isi_dx, gr_sor_des_isi_sn, conj/ qed-.