X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fdelayed_updating%2Freduction%2Fdfr_ifr.ma;h=e54dd267877972e510e4b7d12516e0506efe9654;hb=ccbaf3fd118c7c6425b3572a057ccc2941b7762e;hp=015958b54db1ff5e19eed95585526d4ecb90d181;hpb=cc178d85bc4fec05b6a9dd176f338b3275beb3d9;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 015958b54..e54dd2678 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
@@ -12,12 +12,63 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "delayed_updating/reduction/ifr.ma".
 include "delayed_updating/reduction/dfr.ma".
+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".
 
 (* DELAYED FOCUSED REDUCTION ************************************************)
 
-lemma dfr_lift_bi (f) (p) (q) (t1) (t2):
-      t1 ➡𝐝𝐟[p,q] t2 → ↑[f]t1 ➡𝐟[⊗p,⊗q] ↑[f]t2.
-#f #p #q #t1 #t2
-* #b #Hr #Hb
+(* 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 >path_head_structure_depth <H1n -H1n //
+| lapply (in_comp_unwind2_path_term f … Ht1) -Ht2 -Ht1 -H0t1
+  <unwind2_path_d_dx
+  >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 … (lift_unwind2_term_after …))
+    @unwind2_term_eq_repl_sn
+(* Note: crux of the proof begins *)
+    >list_append_rcons_sn in H1n; <reverse_append #H1n
+    @(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_append_closed/
+    ]
+(* Note: crux of the proof ends *)
+  | //
+  | /2 width=2 by ex_intro/
+  | //
+  ]
+]
+qed.