update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / reduction / ifr_unwind.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_unwind.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_unwind.ma
new file mode 100644 (file)
index 0000000..7634974
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_unwind.ma
@@ -0,0 +1,77 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/reduction/ifr.ma".
+
+include "delayed_updating/unwind/unwind2_constructors.ma".
+include "delayed_updating/unwind/unwind2_preterm_fsubst.ma".
+include "delayed_updating/unwind/unwind2_preterm_eq.ma".
+include "delayed_updating/unwind/unwind2_prototerm_lift.ma".
+include "delayed_updating/unwind/unwind2_rmap_head.ma".
+
+include "delayed_updating/substitution/fsubst_eq.ma".
+include "delayed_updating/substitution/lift_prototerm_eq.ma".
+
+include "delayed_updating/syntax/prototerm_proper_constructors.ma".
+include "delayed_updating/syntax/path_head_structure.ma".
+include "delayed_updating/syntax/path_structure_depth.ma".
+include "delayed_updating/syntax/path_structure_reverse.ma".
+include "delayed_updating/syntax/path_depth_reverse.ma".
+
+(* IMMEDIATE FOCUSED REDUCTION **********************************************)
+
+(* Constructions with unwind ************************************************)
+
+theorem ifr_unwind_bi (f) (p) (q) (t1) (t2):
+        t1 ϵ 𝐓 → t1⋔(p◖𝗦) ϵ 𝐏 →
+        t1 ➡𝐟[p,q] t2 → ▼[f]t1 ➡𝐟[⊗p,⊗q] ▼[f]t2.
+#f #p #q #t1 #t2 #H1t1 #H2t1 
+* #n * #H1n #Ht1 #Ht2
+@(ex_intro … (↑♭⊗q)) @and3_intro
+[ -H0t1 -Ht1 -Ht2
+  >structure_L_sn >structure_reverse
+  >H1n >path_head_structure_depth <H1n -H1n //
+| lapply (in_comp_unwind2_path_term f … Ht1) -Ht2 -Ht1 -H0t1
+  <unwind2_path_d_dx <depth_structure
+  >list_append_rcons_sn in H1n; <reverse_append #H1n
+  lapply (unwind2_rmap_append_pap_closed f … H1n)
+  <reverse_lcons <depth_L_dx #H2n
+  lapply (eq_inv_ninj_bi … H2n) -H2n #H2n <H2n -H2n -H1n #Ht1 //
+| lapply (unwind2_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
+  @(subset_eq_trans … Ht2) -t2
+  @(subset_eq_trans … (unwind2_term_fsubst …))
+  [ @fsubst_eq_repl [ // | // ]
+(*  
+    @(subset_eq_trans … (unwind2_term_iref …))
+    @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
+    [ @unwind2_term_grafted_S /2 width=2 by ex_intro/ | skip ] -Ht1
+    @(subset_eq_trans … (unwind2_lift_term_after …))
+    @unwind2_term_eq_repl_sn
+(* Note: crux of the proof begins *)
+    @nstream_eq_inv_ext #m
+    <tr_compose_pap <tr_compose_pap
+    <tr_uni_pap <tr_uni_pap <tr_pap_plus
+    >list_append_rcons_sn in H1n; <reverse_append #H1n
+    lapply (unwind2_rmap_append_pap_closed f … H1n) #H2n
+    >nrplus_inj_dx in ⊢ (???%); <H2n -H2n
+    lapply (tls_unwind2_rmap_append_closed f … H1n) #H2n
+    <(tr_pap_eq_repl … H2n) -H2n -H1n //
+(* Note: crux of the proof ends *)
+*)
+  | //
+  | /2 width=2 by ex_intro/
+  | //
+  ]
+]
+qed.