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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
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-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-include "delayed_updating/reduction/dfr.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_closed.ma".
-include "delayed_updating/substitution/lift_rmap_closed.ma".
-
-(* DELAYED FOCUSED REDUCTION ************************************************)
-
-(* Constructions with lift **************************************************)
-
-theorem dfr_lift_bi (f) (t1) (t2) (r):
-        t1 โžก๐๐Ÿ[r] t2 โ†’ ๐Ÿ ก[f]t1 โžก๐๐Ÿ[๐Ÿ ก[f]r] ๐Ÿ ก[f]t2.
-#f #t1 #t2 #r
-* #p #q #n #Hr #Hn #Ht1 #Ht2 destruct
-@(ex4_3_intro โ€ฆ (๐Ÿ ก[f]p) (๐Ÿ ก[๐Ÿ ข[f](pโ—–๐—”โ—–๐—Ÿ)]q) (๐Ÿ ข[f](pโ—๐—”โ——๐—Ÿโ——q)๏ผ ยงโจnโฉ))
-[ -Hn -Ht1 -Ht2 //
-| -Ht1 -Ht2
-  /2 width=1 by lift_path_rmap_closed_L/
-| lapply (in_comp_lift_path_term f โ€ฆ Ht1) -Ht2 -Ht1 -Hn
-  <lift_path_d_dx #Ht1 //
-| lapply (lift_term_eq_repl_dx f โ€ฆ Ht2) -Ht2 #Ht2 -Ht1
-  @(subset_eq_trans โ€ฆ Ht2) -t2
-  @(subset_eq_trans โ€ฆ (lift_term_fsubst โ€ฆ))
-  @fsubst_eq_repl [ // | // ]
-  @(subset_eq_trans โ€ฆ (lift_term_iref_nap โ€ฆ))
-  @iref_eq_repl
-  @(subset_eq_canc_sn โ€ฆ (lift_term_grafted_S โ€ฆ))
-  @lift_term_eq_repl_sn
-(* Note: crux of the proof begins *)
-  /2 width=2 by tls_succ_lift_rmap_append_closed_Lq_dx/
-(* Note: crux of the proof ends *)
-]
-qed.