update in ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/pr_coafter_ist_isi.ma b/matita/matita/contribs/lambdadelta/ground/relocation/pr_coafter_ist_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/pr_pat_tls.ma".
+include "ground/relocation/pr_isi_tls.ma".
+include "ground/relocation/pr_ist_tls.ma".
+include "ground/relocation/pr_coafter_nat_tls.ma".
+
+(* RELATIONAL CO-COMPOSITION FOR PARTIAL RELOCATION MAPS ********************)
+
+(*** H_coafter_fwd_isid2 *)
+definition H_pr_coafter_des_ist_sn_isi: predicate pr_map ≝
+           λf1. ∀f2,f. f1 ~⊚ f2 ≘ f → 𝐓❪f1❫ → 𝐈❪f❫ → 𝐈❪f2❫.
+
+(* Destructions with pr_ist and pr_isi **************************************)
+
+(*** coafter_fwd_isid2_O_aux *)
+corec fact pr_coafter_des_ist_sn_isi_unit_aux:
+           ∀f1. @❪𝟏, f1❫ ≘ 𝟏 → H_pr_coafter_des_ist_sn_isi f1.
+#f1 #H1f1 #f2 #f #H #H2f1 #Hf
+cases (pr_pat_inv_unit_bi … H1f1) -H1f1 [ |*: // ] #g1 #H1
+lapply (pr_ist_inv_push … H2f1 … H1) -H2f1 #H2g1
+cases (H2g1 (𝟏)) #n #Hn
+cases (pr_coafter_inv_push_sn … H … H1) -H * #g2 #g #H #H2 #H0
+[ lapply (pr_isi_inv_push … Hf … H0) -Hf #Hg
+  @(pr_isi_push … H2) -H2
+  /3 width=7 by pr_coafter_tls_sn_tls, pr_pat_unit_succ_tls, pr_ist_tls, pr_isi_tls/
+| cases (pr_isi_inv_next … Hf … H0)
+]
+qed-.
+
+(*** coafter_fwd_isid2_aux *)
+fact pr_coafter_des_ist_sn_isi_aux:
+     (∀f1. @❪𝟏, f1❫ ≘ 𝟏 → H_pr_coafter_des_ist_sn_isi f1) →
+     ∀i2,f1. @❪𝟏, f1❫ ≘ i2 → H_pr_coafter_des_ist_sn_isi f1.
+#H0 #i2 elim i2 -i2 /2 width=1 by/ -H0
+#i2 #IH #f1 #H1f1 #f2 #f #H #H2f1 #Hf
+elim (pr_pat_inv_unit_succ … H1f1) -H1f1 [ |*: // ] #g1 #Hg1 #H1
+elim (pr_coafter_inv_next_sn … H … H1) -H #g #Hg #H0
+@(IH … Hg1 … Hg) /2 width=3 by pr_ist_inv_next, pr_isi_inv_push/ (* * full auto fails *)
+qed-.
+
+(*** coafter_fwd_isid2 *)
+lemma pr_coafter_des_ist_sn_isi:
+      ∀f1. H_pr_coafter_des_ist_sn_isi f1.
+#f1 #f2 #f #Hf #H cases (H (𝟏))
+/3 width=7 by pr_coafter_des_ist_sn_isi_aux, pr_coafter_des_ist_sn_isi_unit_aux/
+qed-.