update in delayed_updating

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

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_lift.ma
index d25ddc502452773090319fb5a90b97e0b50d20c4..7273cd780dae13c2dc5359b91efea902d2c0437a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_lift.ma
@@ -13,58 +13,39 @@
 (**************************************************************************)
 
 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/substitution/fsubst_lift.ma".
+include "delayed_updating/substitution/fsubst_eq.ma".
+include "delayed_updating/substitution/lift_constructors.ma".
+include "delayed_updating/substitution/lift_path_head.ma".
+include "delayed_updating/substitution/lift_rmap_head.ma".
 
 (* DELAYED FOCUSED REDUCTION ************************************************)
 
 (* Constructions with lift **************************************************)
 
-theorem dfr_lift_bi (f) (p) (q) (t1) (t2): (*t1 ϵ 𝐓 → *)
-        t1 ➡𝐝𝐟[p,q] t2 → ↑[f]t1 ➡𝐟[↑[f]p,↑[↑[p◖𝗔◖𝗟]f]q] ↑[f]t2.
+theorem dfr_lift_bi (f) (p) (q) (t1) (t2):
+        t1 â\9e¡ð\9d\90\9dð\9d\90\9f[p,q] t2 â\86\92 â\86\91[f]t1 â\9e¡ð\9d\90\9dð\9d\90\9f[â\86\91[f]p,â\86\91[â\86\91[pâ\97\96ð\9d\97\94â\97\96ð\9d\97\9f]f]q] â\86\91[f]t2.
 #f #p #q #t1 #t2
 * #n * #H1n #Ht1 #Ht2
 @(ex_intro … ((↑[p●𝗔◗𝗟◗q]f)＠⧣❨n❩)) @and3_intro
 [ -Ht1 -Ht2
-  >H1n >path_head_structure_depth <H1n -H1n //
-| lapply (in_comp_unwind2_path_term f … Ht1) -Ht2 -Ht1 -H0t1
-  <unwind2_path_d_dx <depth_structure
+  <lift_rmap_L_dx >lift_path_L_sn
   >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
+  <(lift_path_head … H1n) -H1n //
+| lapply (in_comp_lift_path_term f … Ht1) -Ht2 -Ht1 -H1n
+  <lift_path_d_dx #Ht1 //
+| lapply (lift_term_eq_repl_dx f … Ht2) -Ht2 #Ht2 -Ht1
   @(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 … (unwind2_lift_term_after …))
-    @unwind2_term_eq_repl_sn
+  @(subset_eq_trans … (lift_term_fsubst …))
+  @fsubst_eq_repl [ // | // ]
+  @(subset_eq_trans … (lift_term_iref …))
+  @iref_eq_repl
+  @(subset_eq_canc_sn … (lift_term_grafted_S …))
+  @lift_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 in H1n; #H1n >lift_rmap_A_dx
+  /2 width=1 by tls_lift_rmap_append_closed/
 (* Note: crux of the proof ends *)
-  | //
-  | /2 width=2 by ex_intro/
-  | //
-  ]
 ]
 qed.