update in ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/pr_coafter_nat_tls.ma b/matita/matita/contribs/lambdadelta/ground/relocation/pr_coafter_nat_tls.ma
new file mode 100644 (file)
index 0000000..f3b7ba7
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/ground/relocation/pr_coafter_nat_tls.ma
@@ -0,0 +1,45 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_nat.ma".
+include "ground/relocation/pr_coafter.ma".
+
+(* RELATIONAL CO-COMPOSITION FOR PARTIAL RELOCATION MAPS ********************)
+
+(* Constructions with pr_nat and pr_tls *************************************)
+
+(*** coafter_tls *)
+lemma pr_coafter_tls_bi_tls (n2) (n1):
+      ∀f1,f2,f. @↑❪n1, f1❫ ≘ n2 →
+      f1 ~⊚ f2 ≘ f → ⫰*[n2]f1 ~⊚ ⫰*[n1]f2 ≘ ⫰*[n2]f.
+#n2 @(nat_ind_succ … n2) -n2 [ #n1 | #n2 #IH * [| #n1 ] ] #f1 #f2 #f #Hf1 #Hf
+[ elim (pr_nat_inv_zero_dx … Hf1) -Hf1 [ |*: // ] #g1 #Hg1 #H1 destruct //
+| elim (pr_nat_inv_zero_succ … Hf1) -Hf1 [ |*: // ] #g1 #Hg1 #H1
+  elim (pr_coafter_inv_next_sn … Hf … H1) -Hf #g #Hg #H0 destruct
+  lapply (IH … Hg1 Hg) -IH -Hg1 -Hg //
+| elim (pr_nat_inv_succ_dx … Hf1) -Hf1 [1,3: * |*: // ] #g1 [ #n1 ] #Hg1 [ #H ] #H1
+  [ elim (pr_coafter_inv_push_sn … Hf … H1) -Hf * #g2 #g #Hg #H2 #H0 destruct
+    lapply (IH … Hg1 Hg) -IH -Hg1 -Hg #H //
+  | elim (pr_coafter_inv_next_sn … Hf … H1) -Hf #g #Hg #H0 destruct
+    lapply (IH … Hg1 Hg) -IH -Hg1 -Hg #H //
+  ]
+]
+qed.
+
+(*** coafter_tls_O *)
+lemma pr_coafter_tls_sn_tls:
+      ∀n,f1,f2,f. @↑❪𝟎, f1❫ ≘ n →
+      f1 ~⊚ f2 ≘ f → ⫰*[n]f1 ~⊚ f2 ≘ ⫰*[n]f.
+/2 width=1 by pr_coafter_tls_bi_tls/ qed.