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14
15 include "ground/relocation/pr_tl_eq.ma".
16 include "ground/relocation/pr_sdj.ma".
17
18 (* DISJOINTNESS FOR PARTIAL RELOCATION MAPS *********************************)
19
20 (* Constructions with pr_eq *************************************************)
21
22 (*** sdj_eq_repl_back1 *)
23 corec lemma pr_sdj_eq_repl_back_sn:
24             ∀f2. pr_eq_repl_back … (λf1. f1 ∥ f2).
25 #f2 #f1 * -f2 -f1
26 #f1 #f2 #g1 #g2 #Hf #H1 #H2 #g #H0
27 [ cases (pr_eq_inv_push_sn …  H0 …  H1) -g1 /3 width=5 by pr_sdj_push_bi/
28 | cases (pr_eq_inv_next_sn …  H0 …  H1) -g1 /3 width=5 by pr_sdj_next_push/
29 | cases (pr_eq_inv_push_sn …  H0 …  H1) -g1 /3 width=5 by pr_sdj_push_next/
30 ]
31 qed-.
32
33 (*** sdj_eq_repl_fwd1 *)
34 lemma pr_sdj_eq_repl_fwd_sn:
35       ∀f2. pr_eq_repl_fwd … (λf1. f1 ∥ f2).
36 #f2 @pr_eq_repl_sym /2 width=3 by pr_sdj_eq_repl_back_sn/
37 qed-.
38
39 (*** sdj_eq_repl_back2 *)
40 corec lemma pr_sdj_eq_repl_back_dx:
41             ∀f1. pr_eq_repl_back … (λf2. f1 ∥ f2).
42 #f1 #f2 * -f1 -f2
43 #f1 #f2 #g1 #g2 #Hf #H1 #H2 #g #H0
44 [ cases (pr_eq_inv_push_sn …  H0 …  H2) -g2 /3 width=5 by pr_sdj_push_bi/
45 | cases (pr_eq_inv_push_sn …  H0 …  H2) -g2 /3 width=5 by pr_sdj_next_push/
46 | cases (pr_eq_inv_next_sn …  H0 …  H2) -g2 /3 width=5 by pr_sdj_push_next/
47 ]
48 qed-.
49
50 (*** sdj_eq_repl_fwd2 *)
51 lemma pr_sdj_eq_repl_fwd_dx:
52       ∀f1. pr_eq_repl_fwd … (λf2. f1 ∥ f2).
53 #f1 @pr_eq_repl_sym /2 width=3 by pr_sdj_eq_repl_back_dx/
54 qed-.