update in ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/pr_coafter_ist_isf.ma b/matita/matita/contribs/lambdadelta/ground/relocation/pr_coafter_ist_isf.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_isf_tls.ma".
+include "ground/relocation/pr_ist_tls.ma".
+include "ground/relocation/pr_coafter_nat_tls.ma".
+include "ground/relocation/pr_coafter_isi.ma".
+
+(* RELATIONAL CO-COMPOSITION FOR PARTIAL RELOCATION MAPS ********************)
+
+(*** H_coafter_isfin2_fwd *)
+definition H_pr_coafter_des_ist_isf: predicate pr_map ≝
+           λf1. ∀f2. 𝐅❪f2❫ → 𝐓❪f1❫ → ∀f. f1 ~⊚ f2 ≘ f →  𝐅❪f❫.
+
+(* Destructions with pr_ist and pr_isf **************************************)
+
+(*** coafter_isfin2_fwd_O_aux *)
+fact pr_coafter_des_ist_isf_unit_aux:
+     ∀f1. @❪𝟏, f1❫ ≘ 𝟏 → H_pr_coafter_des_ist_isf f1.
+#f1 #Hf1 #f2 #H
+generalize in match Hf1; generalize in match f1; -f1
+@(pr_isf_ind … H) -f2
+[ /3 width=4 by pr_coafter_isi_inv_dx, pr_isf_isi/ ]
+#f2 #_ #IH #f1 #H #Hf1 #f #Hf
+elim (pr_pat_inv_unit_bi … H) -H [ |*: // ] #g1 #H1
+lapply (pr_ist_inv_push … Hf1 … H1) -Hf1 #Hg1
+elim (Hg1 (𝟏)) #n #Hn
+[ elim (pr_coafter_inv_push_bi … Hf) | elim (pr_coafter_inv_push_next … Hf)
+] -Hf [1,6: |*: // ] #g #Hg #H0 destruct
+/5 width=6 by pr_isf_next, pr_isf_push, pr_isf_inv_tls, pr_ist_tls, pr_pat_unit_succ_tls, pr_coafter_tls_sn_tls/
+qed-.
+
+(*** coafter_isfin2_fwd_aux *)
+fact pr_coafter_des_ist_isf_aux:
+     (∀f1. @❪𝟏, f1❫ ≘ 𝟏 → H_pr_coafter_des_ist_isf f1) →
+     ∀i2,f1. @❪𝟏, f1❫ ≘ i2 → H_pr_coafter_des_ist_isf f1.
+#H0 #i2 elim i2 -i2 /2 width=1 by/ -H0
+#i2 #IH #f1 #H1f1 #f2 #Hf2 #H2f1 #f #Hf
+elim (pr_pat_inv_unit_succ … H1f1) -H1f1 [ |*: // ] #g1 #Hg1 #H1
+elim (pr_coafter_inv_next_sn … Hf … H1) -Hf #g #Hg #H0
+lapply (IH … Hg1 … Hg) -i2 -Hg
+/2 width=4 by pr_ist_inv_next, pr_isf_push/ (* * full auto fails *)
+qed-.
+
+(*** coafter_isfin2_fwd *)
+lemma pr_coafter_des_ist_isf: ∀f1. H_pr_coafter_des_ist_isf f1.
+#f1 #f2 #Hf2 #Hf1 cases (Hf1 (𝟏))
+/3 width=7 by pr_coafter_des_ist_isf_aux, pr_coafter_des_ist_isf_unit_aux/
+qed-.