update in ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/pr_compose.ma b/matita/matita/contribs/lambdadelta/ground/relocation/pr_compose.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/pr_after.ma".
+
+(* RELATIONAL COMPOSITION FOR PARTIAL RELOCATION MAPS ***********************)
+
+corec definition pr_compose: pr_map → pr_map → pr_map.
+* * #g2 [ #f1 | * * #g1 ]
+[ @pr_next @(pr_compose g2 f1)
+| @pr_next @(pr_compose g2 g1)
+| @pr_push @(pr_compose g2 g1)
+]
+defined.
+
+interpretation
+  "functional composition (partial relocation maps)"
+  'compose f2 f1 = (pr_compose f2 f1).
+
+(* Basic constructions (specific) *******************************************)
+
+lemma pr_compose_unfold_refl (f2) (f1): ⫯(f2∘f1) = (⫯f2)∘(⫯f1).
+#f2 #f1
+<(stream_unfold … ((⫯f2)∘(⫯f1))) in ⊢ (???%); //
+qed.
+
+lemma pr_compose_unfold_push (f2) (f1): ↑(f2∘f1) = (⫯f2)∘(↑f1).
+#f2 #f1
+<(stream_unfold … ((⫯f2)∘(↑f1))) in ⊢ (???%); //
+qed.
+
+lemma pr_compose_unfold_next (f2) (f1):
+      ↑(f2∘f1) = (↑f2)∘f1.
+#f2 #f1
+<(stream_unfold … ((↑f2)∘f1)) in ⊢ (???%); //
+qed.
+
+(* Main constructions *******************************************************)
+
+corec theorem pr_after_compose (f2) (f1):
+              f2 ⊚ f1 ≘ f2∘f1.
+cases (pr_map_split_tl f2)*
+[ cases (pr_map_split_tl f1) * ]
+[ @pr_after_refl /2 width=7 by/
+| @pr_after_push /2 width=7 by/
+| @pr_after_next /2 width=5 by/
+]
+qed.