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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
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15 include "delayed_updating/reduction/dfr.ma".
17 include "delayed_updating/substitution/fsubst_lift.ma".
18 include "delayed_updating/substitution/fsubst_eq.ma".
19 include "delayed_updating/substitution/lift_constructors.ma".
20 include "delayed_updating/substitution/lift_path_closed.ma".
21 include "delayed_updating/substitution/lift_rmap_closed.ma".
23 (* DELAYED FOCUSED REDUCTION ************************************************)
25 (* Constructions with lift **************************************************)
27 theorem dfr_lift_bi (f) (t1) (t2) (r):
28 t1 โก๐๐[r] t2 โ ๐ ก[f]t1 โก๐๐[๐ ก[f]r] ๐ ก[f]t2.
30 * #p #q #n #Hr #Hn #Ht1 #Ht2 destruct
31 @(ex4_3_intro โฆ (๐ ก[f]p) (๐ ก[๐ ข[f](pโ๐โ๐)]q) (๐ ข[f](pโ๐โ๐โq)๏ผ ยงโจnโฉ))
34 /2 width=1 by lift_path_rmap_closed_L/
35 | lapply (in_comp_lift_path_term f โฆ Ht1) -Ht2 -Ht1 -Hn
36 <lift_path_d_dx #Ht1 //
37 | lapply (lift_term_eq_repl_dx f โฆ Ht2) -Ht2 #Ht2 -Ht1
38 @(subset_eq_trans โฆ Ht2) -t2
39 @(subset_eq_trans โฆ (lift_term_fsubst โฆ))
40 @fsubst_eq_repl [ // | // ]
41 @(subset_eq_trans โฆ (lift_term_iref_nap โฆ))
43 @(subset_eq_canc_sn โฆ (lift_term_grafted_S โฆ))
45 (* Note: crux of the proof begins *)
46 /2 width=2 by tls_succ_lift_rmap_append_closed_Lq_dx/
47 (* Note: crux of the proof ends *)