X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fdelayed_updating%2Freduction%2Fdfr_ifr.ma;h=68cea487c474ddaf6d9a0bff4f740a3e97953946;hb=41a54a797af98d2867d4bf979d424283fb44a1fc;hp=2b15d3d5279b109c66127c7747230d3e39d58e3b;hpb=3af42b8f2cb1956eed14edcc0adb9df92601f248;p=helm.git

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 2b15d3d52..68cea487c 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
@@ -27,29 +27,28 @@ 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".
 
 (* 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 ➡𝐢𝐟[⊗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 in ⊢ (??%?); >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 #k #Hr #H1k #Ht1 #Ht2 destruct
+@(ex4_3_intro … (⊗p) (⊗q) (↑♭q))
+[ -H0t1 -H1k -Ht1 -Ht2 //
+| -H0t1 -Ht1 -Ht2
+  >structure_L_sn
+  >H1k in ⊢ (??%?); >path_head_structure_depth <H1k -H1k //
 | lapply (in_comp_unwind2_path_term f … Ht1) -Ht2 -Ht1 -H0t1
-  <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 #Ht1 //
+  <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 …))
+  @(subset_eq_trans … (unwind2_term_fsubst_ppc …))
   [ @fsubst_eq_repl [ // | // ]
     @(subset_eq_trans … (unwind2_term_iref …))
     @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
@@ -57,11 +56,11 @@ theorem dfr_des_ifr (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
     @(subset_eq_trans … (lift_unwind2_term_after …))
     @unwind2_term_eq_repl_sn
 (* Note: crux of the proof begins *)
-    >list_append_rcons_sn <reverse_append
+    <list_append_rcons_sn
     @(stream_eq_trans … (tr_compose_uni_dx …))
     @tr_compose_eq_repl
     [ <unwind2_rmap_append_pap_closed //
-    | >unwind2_rmap_A_sn <reverse_rcons
+    | >unwind2_rmap_A_dx
       /2 width=1 by tls_unwind2_rmap_closed/
     ]
 (* Note: crux of the proof ends *)