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
index f05d86db3078678331cd649e9abe405996c383b1..6a135ea2ef84a65b34c736caafe92b9df171584b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_unwind.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_unwind.ma
@@ -14,15 +14,15 @@
 
 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_inner.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_inner.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".
@@ -33,43 +33,40 @@ include "delayed_updating/syntax/path_depth_reverse.ma".
 (* Constructions with unwind ************************************************)
 
 lemma ifr_unwind_bi (f) (p) (q) (t1) (t2):
-      t1 ϵ 𝐓 → t1⋔(p◖𝗦) ⧸≬ 𝐈 →
+      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
 * #n * #H1n #Ht1 #Ht2
 @(ex_intro … (↑♭q)) @and3_intro
 [ -H1t1 -H2t1 -Ht1 -Ht2
   >structure_L_sn >structure_reverse
-  >H1n >path_head_structure_depth <H1n -H1n //
+  >H1n in ⊢ (??%?); >path_head_structure_depth <H1n -H1n //
 | lapply (in_comp_unwind2_path_term f … Ht1) -Ht2 -Ht1 -H1t1 -H2t1
-  <unwind2_path_d_dx
-  >list_append_rcons_sn in H1n; <reverse_append #H1n
-  lapply (unwind2_rmap_append_pap_closed f … H1n)
+  <unwind2_path_d_dx >(list_append_rcons_sn … p) <reverse_append
+  lapply (unwind2_rmap_append_pap_closed f … (p◖𝗔)ᴿ … H1n) -H1n
   <reverse_lcons <depth_L_dx #H2n
-  lapply (eq_inv_ninj_bi … H2n) -H2n #H2n <H2n -H2n -H1n #Ht1 //
+  lapply (eq_inv_ninj_bi … H2n) -H2n #H2n <H2n -H2n #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_canc_dx … (unwind2_term_after …))
-    @(subset_eq_canc_sn … (unwind2_term_eq_repl_dx …))
+    @(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_term_after …))
+    @(subset_eq_trans … (lift_unwind2_term_after …))
+    @(subset_eq_canc_dx … (unwind2_term_after_lift …))
     @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) -H1n #H2n
-    <(tr_pap_eq_repl … H2n) -H2n //
+    >list_append_rcons_sn <reverse_append
+    @(stream_eq_trans … (tr_compose_uni_dx …))
+    @tr_compose_eq_repl
+    [ <unwind2_rmap_append_pap_closed //
+    | >unwind2_rmap_A_sn <reverse_rcons
+      /2 width=1 by tls_unwind2_rmap_closed/
+    ]
 (* Note: crux of the proof ends *)
   | //
   | /2 width=2 by ex_intro/
-  | @term_proper_outer #H0 (**) (* full auto does not work *)
-    /3 width=2 by unwind2_term_des_inner/
+  | /2 width=6 by lift_term_proper/
   ]
 ]
 qed.