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14
15 include "ground/relocation/pr_tl_eq_eq.ma".
16 include "ground/relocation/pr_isd.ma".
17
18 (* DIVERGENCE CONDITION FOR PARTIAL RELOCATION MAPS *************************)
19
20 (* Constructions with pr_eq *************************************************)
21
22 (*** isdiv_eq_repl_back *)
23 corec lemma pr_isd_eq_repl_back:
24             pr_eq_repl_back … pr_isd.
25 #f1 #H cases (pr_isd_inv_gen … H) -H
26 #g1 #Hg1 #H1 #f2 #Hf cases (pr_eq_inv_next_sn … Hf … H1) -f1
27 /3 width=3 by pr_isd_next/
28 qed-.
29
30 (*** isdiv_eq_repl_fwd *)
31 lemma pr_isd_eq_repl_fwd:
32       pr_eq_repl_fwd … pr_isd.
33 /3 width=3 by pr_isd_eq_repl_back, pr_eq_repl_sym/ qed-.
34
35 (* Main inversions with pr_eq ***********************************************)
36
37 (*** isdiv_inv_eq_repl *)
38 corec theorem pr_isd_inv_eq_repl (g1) (g2): 𝛀❨g1❩ → 𝛀❨g2❩ → g1 ≡ g2.
39 #H1 #H2
40 cases (pr_isd_inv_gen … H1) -H1
41 cases (pr_isd_inv_gen … H2) -H2
42 /3 width=5 by pr_eq_next/
43 qed-.
44
45 (* Alternative definition with pr_eq ****************************************)
46
47 (*** eq_next_isdiv *)
48 corec lemma pr_eq_next_isd (f): ↑f ≡ f → 𝛀❨f❩.
49 #H cases (pr_eq_inv_next_sn … H) -H
50 /4 width=3 by pr_isd_next, pr_eq_trans/
51 qed.
52
53 (*** eq_next_inv_isdiv *)
54 corec lemma pr_eq_next_inv_isd (g): 𝛀❨g❩ → ↑g ≡ g.
55 * -g #f #g #Hf *
56 /3 width=5 by pr_eq_next/
57 qed-.