update un 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 015958b54db1ff5e19eed95585526d4ecb90d181..a8d9469ddaa6fe171c11ece64ebff473d74a3429 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
@@ -12,12 +12,32 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "delayed_updating/reduction/ifr.ma".
 include "delayed_updating/reduction/dfr.ma".
+include "delayed_updating/reduction/ifr.ma".
+include "delayed_updating/substitution/fsubst_lift.ma".
+include "delayed_updating/substitution/lift_structure_depth.ma".
+include "delayed_updating/syntax/prototerm_proper_constructors.ma".
+include "delayed_updating/syntax/path_structure_depth.ma".
+include "ground/relocation/tr_pap_pushs.ma".
 
 (* DELAYED FOCUSED REDUCTION ************************************************)
 
-lemma dfr_lift_bi (f) (p) (q) (t1) (t2):
+lemma dfr_lift_bi (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
-* #b #Hr #Hb
+#f #p #q #t1 #t2 #H0t1
+* #b #n * #Hb #Hn  #Ht1 #Ht2
+@(ex1_2_intro … (⊗b) (❘⊗q❘)) @and4_intro
+[ //
+| #g <lift_rmap_structure <depth_structure
+  >tr_pushs_swap <tr_pap_pushs_le //
+| lapply (in_comp_lift_bi f … Ht1) -Ht1 -H0t1 -Hb -Ht2
+  <lift_d_empty_dx //
+| lapply (eq_lift_bi f … Ht2) -Ht2 #Ht2
+  @(subset_eq_trans … Ht2) -t2
+  @(subset_eq_trans … (lift_fsubst …))
+  [ <structure_append <structure_A_sn <structure_append <structure_L_sn
+  | //
+  | /2 width=2 by ex_intro/
+  | //
+  ]
+]