commit 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
index 7634974a54f9a0c6c9dffe13a44d75517c104e51..a554bdbe265cd085f11e3d213edece250d39a3b1 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_unwind.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_unwind.ma
@@ -14,64 +14,57 @@
 
 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_proper.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 ************************************************)
+(* Constructions with unwind2 ***********************************************)
 
-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 //
+lemma ifr_unwind_bi (f) (p) (q) (t1) (t2):
+      t1 ϵ 𝐓 → t1⋔(p◖𝗦) ϵ 𝐏 →
+      t1 ➡𝐢𝐟[p,q] t2 → ▼[f]t1 ➡𝐢𝐟[⊗p,⊗q] ▼[f]t2.
+#f #p #q #t1 #t2 #H1t1 #H2t1
+* #k * #H1k #Ht1 #Ht2
+@(ex_intro … (↑♭q)) @and3_intro
+[ -H1t1 -H2t1 -Ht1 -Ht2
+  >structure_L_sn
+  >H1k in ⊢ (??%?); >path_head_structure_depth <H1k -H1k //
+| lapply (in_comp_unwind2_path_term f … Ht1) -Ht2 -Ht1 -H1t1 -H2t1
+  <unwind2_path_d_dx <list_append_rcons_sn
+  lapply (unwind2_rmap_append_pap_closed f … (p◖𝗔) … H1k) -H1k
+  <depth_L_sn #H2k
+  lapply (eq_inv_ninj_bi … H2k) -H2k #H2k <H2k -H2k #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 …))
+    @(subset_eq_trans … (lift_unwind2_term_after …))
+    @(subset_eq_canc_dx … (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 //
+    <list_append_rcons_sn
+    @(stream_eq_trans … (tr_compose_uni_dx …))
+    @tr_compose_eq_repl
+    [ <unwind2_rmap_append_pap_closed //
+    | >unwind2_rmap_A_dx
+      /2 width=1 by tls_unwind2_rmap_closed/
+    ]
 (* Note: crux of the proof ends *)
-*)
   | //
   | /2 width=2 by ex_intro/
-  | //
+  | /2 width=6 by lift_term_proper/
   ]
 ]
 qed.