update in delayed_updating

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

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
index 8403b778197501e01535e3c42490548cd0181ac7..1cb62ed3b68759ce39c3d3ab2461f28ed62cab2c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
@@ -19,53 +19,46 @@ 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/unwind/unwind2_rmap_closed.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_closed_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".
 
 (* DELAYED FOCUSED REDUCTION ************************************************)
 
 (* Main destructions with ifr ***********************************************)
 
-theorem dfr_des_ifr (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
-        t1 ➡𝐝𝐟[p,q] t2 → ▼[f]t1 ➡𝐟[⊗p,⊗q] ▼[f]t2.
-#f #p #q #t1 #t2 #H0t1
-* #n * #H1n #Ht1 #Ht2
-@(ex_intro … (↑♭⊗q)) @and3_intro
-[ -H0t1 -Ht1 -Ht2
-  >structure_L_sn >structure_reverse
-  >H1n >path_head_structure_depth <H1n -H1n //
+theorem dfr_des_ifr (f) (t1) (t2) (r): t1 ϵ 𝐓 →
+        t1 ➡𝐝𝐟[r] t2 → ▼[f]t1 ➡𝐢𝐟[⊗r] ▼[f]t2.
+#f #t1 #t2 #r #H0t1
+* #p #q #n #Hr #Hn #Ht1 #Ht2 destruct
+@(ex4_3_intro … (⊗p) (⊗q) (♭q))
+[ -H0t1 -Hn -Ht1 -Ht2 //
+| -H0t1 -Ht1 -Ht2
+  /2 width=2 by path_closed_structure_depth/
 | 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 //
+  <unwind2_path_d_dx <tr_pap_succ_nap <list_append_rcons_sn
+  <nap_unwind2_rmap_append_closed_Lq_dx_depth //
 | lapply (unwind2_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
   @(subset_eq_trans … Ht2) -t2
-  @(subset_eq_trans … (unwind2_term_fsubst …))
+  @(subset_eq_trans … (unwind2_term_fsubst_ppc …))
   [ @fsubst_eq_repl [ // | // ]
-    @(subset_eq_trans … (unwind2_term_iref …))
+    @(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 …))
     @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_pap …)) <tr_pap_succ_nap
+    @tr_compose_eq_repl
+    [ <nap_unwind2_rmap_append_closed_Lq_dx_depth //
+    | /2 width=2 by tls_succ_unwind2_rmap_append_closed_Lq_dx/
+    ]
 (* Note: crux of the proof ends *)
   | //
   | /2 width=2 by ex_intro/