update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / unwind_k / unwind2_rmap_lift.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind_k/unwind2_rmap_lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind_k/unwind2_rmap_lift.ma
new file mode 100644 (file)
index 0000000..1d3d544
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/unwind_k/unwind2_rmap_lift.ma
@@ -0,0 +1,43 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "delayed_updating/unwind_k/unwind2_rmap.ma".
+include "delayed_updating/unwind_k/preunwind2_rmap_lift.ma".
+include "delayed_updating/unwind_k/preunwind2_rmap_eq.ma".
+include "delayed_updating/substitution/lift_path.ma".
+include "delayed_updating/syntax/path_structure.ma".
+
+(* TAILED UNWIND FOR RELOCATION MAP *****************************************)
+
+(* Constructions with lift_path *********************************************)
+
+lemma lift_unwind2_rmap_after (g) (f) (p):
+      🠢[g]⊗p∘▶[f]p ≗ ▶[g∘f]p.
+#g #f #p elim p -p //
+* [ #k ] #p #IH //
+[ <unwind2_rmap_d_dx <unwind2_rmap_d_dx
+  @(stream_eq_canc_sn … (tr_compose_assoc …))
+  /2 width=1 by tr_compose_eq_repl/
+| <unwind2_rmap_L_dx <unwind2_rmap_L_dx <lift_rmap_L_dx
+  /2 width=1 by tr_push_eq_repl/
+]
+qed.
+
+lemma unwind2_lift_rmap_after (g) (f) (p:path):
+      ▶[g]🠡[f]p∘🠢[f]p ≗ ▶[g∘f]p.
+#g #f #p elim p -p // #l #p #IH
+<lift_path_rcons <lift_rmap_rcons <unwind2_rmap_rcons <unwind2_rmap_rcons
+@(stream_eq_trans … (preunwind2_lift_rmap_after …))
+/2 width=1 by preunwind2_rmap_eq_repl/
+qed.