update in ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/pr_after_pat_tls.ma b/matita/matita/contribs/lambdadelta/ground/relocation/pr_after_pat_tls.ma
new file mode 100644 (file)
index 0000000..ec6fb76
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/ground/relocation/pr_after_pat_tls.ma
@@ -0,0 +1,33 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_tls.ma".
+include "ground/relocation/pr_pat.ma".
+include "ground/relocation/pr_after.ma".
+
+(* RELATIONAL COMPOSITION FOR PARTIAL RELOCATION MAPS ***********************)
+
+(* Constructions with pr_pat and pr_tls *************************************)
+
+(* Note: this requires ↑ on first n *)
+(*** after_tls *)
+lemma pr_after_tls_sn_tls (n):
+      ∀f1,f2,f. @❪𝟏, f1❫ ≘ ↑n →
+      f1 ⊚ f2 ≘ f → ⫰*[n]f1 ⊚ f2 ≘ ⫰*[n]f.
+#n @(nat_ind_succ … n) -n //
+#n #IH #f1 #f2 #f #Hf1 #Hf
+cases (pr_pat_inv_unit_succ … Hf1) -Hf1 [ |*: // ] #g1 #Hg1 #H1
+cases (pr_after_inv_next_sn … Hf … H1) -Hf #g #Hg #H0 destruct
+<pr_tls_swap <pr_tls_swap /2 width=1 by/
+qed.