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 *)
13 (**************************************************************************)
15 include "ground/relocation/gr_pat_tls.ma".
16 include "ground/relocation/gr_isf_tls.ma".
17 include "ground/relocation/gr_ist_tls.ma".
18 include "ground/relocation/gr_coafter_nat_tls.ma".
19 include "ground/relocation/gr_coafter_isi.ma".
21 (* RELATIONAL CO-COMPOSITION FOR GENERIC RELOCATION MAPS ********************)
23 (*** H_coafter_isfin2_fwd *)
24 definition H_gr_coafter_des_ist_isf: predicate gr_map â
25 Îťf1. âf2. đ
âŞf2⍠â đâŞf1⍠â âf. f1 ~â f2 â f â đ
âŞfâŤ.
27 (* Destructions with gr_ist and gr_isf **************************************)
29 (*** coafter_isfin2_fwd_O_aux *)
30 fact gr_coafter_des_ist_isf_unit_aux:
31 âf1. @âŞđ, f1⍠â đ â H_gr_coafter_des_ist_isf f1.
33 generalize in match Hf1; generalize in match f1; -f1
34 @(gr_isf_ind ⌠H) -f2
35 [ /3 width=4 by gr_coafter_isi_inv_dx, gr_isf_isi/ ]
36 #f2 #_ #IH #f1 #H #Hf1 #f #Hf
37 elim (gr_pat_inv_unit_bi ⌠H) -H [ |*: // ] #g1 #H1
38 lapply (gr_ist_inv_push ⌠Hf1 ⌠H1) -Hf1 #Hg1
39 elim (Hg1 (đ)) #n #Hn
40 [ elim (gr_coafter_inv_push_bi ⌠Hf) | elim (gr_coafter_inv_push_next ⌠Hf)
41 ] -Hf [1,6: |*: // ] #g #Hg #H0 destruct
42 /5 width=6 by gr_isf_next, gr_isf_push, gr_isf_inv_tls, gr_ist_tls, gr_pat_unit_succ_tls, gr_coafter_tls_sn_tls/
45 (*** coafter_isfin2_fwd_aux *)
46 fact gr_coafter_des_ist_isf_aux:
47 (âf1. @âŞđ, f1⍠â đ â H_gr_coafter_des_ist_isf f1) â
48 âi2,f1. @âŞđ, f1⍠â i2 â H_gr_coafter_des_ist_isf f1.
49 #H0 #i2 elim i2 -i2 /2 width=1 by/ -H0
50 #i2 #IH #f1 #H1f1 #f2 #Hf2 #H2f1 #f #Hf
51 elim (gr_pat_inv_unit_succ ⌠H1f1) -H1f1 [ |*: // ] #g1 #Hg1 #H1
52 elim (gr_coafter_inv_next_sn ⌠Hf ⌠H1) -Hf #g #Hg #H0
53 lapply (IH ⌠Hg1 ⌠Hg) -i2 -Hg
54 /2 width=4 by gr_ist_inv_next, gr_isf_push/ (* * full auto fails *)
57 (*** coafter_isfin2_fwd *)
58 lemma gr_coafter_des_ist_isf: âf1. H_gr_coafter_des_ist_isf f1.
59 #f1 #f2 #Hf2 #Hf1 cases (Hf1 (đ))
60 /3 width=7 by gr_coafter_des_ist_isf_aux, gr_coafter_des_ist_isf_unit_aux/