1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 include "delayed_updating/reduction/dfr.ma".
16 include "delayed_updating/reduction/ifr.ma".
18 include "delayed_updating/unwind/unwind2_constructors.ma".
19 include "delayed_updating/unwind/unwind2_preterm_fsubst.ma".
20 include "delayed_updating/unwind/unwind2_preterm_eq.ma".
21 include "delayed_updating/unwind/unwind2_prototerm_lift.ma".
22 include "delayed_updating/unwind/unwind2_rmap_closed.ma".
24 include "delayed_updating/substitution/fsubst_eq.ma".
25 include "delayed_updating/substitution/lift_prototerm_eq.ma".
27 include "delayed_updating/syntax/prototerm_proper_constructors.ma".
28 include "delayed_updating/syntax/path_closed_structure.ma".
29 include "delayed_updating/syntax/path_structure_depth.ma".
31 (* DELAYED FOCUSED REDUCTION ************************************************)
33 (* Main destructions with ifr ***********************************************)
35 theorem dfr_des_ifr (f) (t1) (t2) (r): t1 Ο΅ π β
36 t1 β‘ππ[r] t2 β βΌ[f]t1 β‘π’π[βr] βΌ[f]t2.
38 * #p #q #n #Hr #Hn #Ht1 #Ht2 destruct
39 @(ex4_3_intro β¦ (βp) (βq) (βq))
40 [ -H0t1 -Hn -Ht1 -Ht2 //
42 /2 width=2 by path_closed_structure_depth/
43 | lapply (in_comp_unwind2_path_term f β¦ Ht1) -Ht2 -Ht1 -H0t1
44 <unwind2_path_d_dx <tr_pap_succ_nap <list_append_rcons_sn
45 <unwind2_rmap_append_closed_nap //
46 | lapply (unwind2_term_eq_repl_dx f β¦ Ht2) -Ht2 #Ht2
47 @(subset_eq_trans β¦ Ht2) -t2
48 @(subset_eq_trans β¦ (unwind2_term_fsubst_ppc β¦))
49 [ @fsubst_eq_repl [ // | // ]
50 @(subset_eq_trans β¦ (unwind2_term_irefβ¦))
51 @(subset_eq_canc_sn β¦ (lift_term_eq_repl_dx β¦))
52 [ @unwind2_term_grafted_S /2 width=2 by ex_intro/ | skip ] -Ht1
53 @(subset_eq_trans β¦ (lift_unwind2_term_after β¦))
54 @unwind2_term_eq_repl_sn
55 (* Note: crux of the proof begins *)
57 @(stream_eq_trans β¦ (tr_compose_uni_dx_pap β¦)) <tr_pap_succ_nap
59 [ <unwind2_rmap_append_closed_nap //
60 | /2 width=1 by tls_succ_unwind2_rmap_append_L_closed_dx/
62 (* Note: crux of the proof ends *)
64 | /2 width=2 by ex_intro/