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14
15 include "ground/notation/relations/predicate_f_1.ma".
16 include "ground/relocation/pr_fcla.ma".
17
18 (* FINITE COLENGTH CONDITION FOR PARTIAL RELOCATION MAPS ********************)
19
20 (*** isfin *)
21 definition pr_isf: predicate pr_map ā‰
22            Ī»f. āˆƒn. š‚āØfā© ā‰˜ n.
23
24 interpretation
25   "finite colength condition (partial relocation maps)"
26   'PredicateF f = (pr_isf f).
27
28 (* Basic eliminations *******************************************************)
29
30 (*** isfin_ind *)
31 lemma pr_isf_ind (Q:predicate ā€¦):
32       (āˆ€f.  šˆāØfā© ā†’ Q f) ā†’
33       (āˆ€f. š…āØfā© ā†’ Q f ā†’ Q (ā«Æf)) ā†’
34       (āˆ€f. š…āØfā© ā†’ Q f ā†’ Q (ā†‘f)) ā†’
35       āˆ€f. š…āØfā© ā†’ Q f.
36 #Q #IH1 #IH2 #IH3 #f #H elim H -H
37 #n #H elim H -f -n /3 width=2 by ex_intro/
38 qed-.
39
40 (* Basic inversions *********************************************************)
41
42 (*** isfin_inv_push *)
43 lemma pr_isf_inv_push (g): š…āØgā© ā†’ āˆ€f. ā«Æf = g ā†’ š…āØfā©.
44 #g * /3 width=4 by pr_fcla_inv_push, ex_intro/
45 qed-.
46
47 (*** isfin_inv_next *)
48 lemma pr_isf_inv_next (g): š…āØgā© ā†’ āˆ€f. ā†‘f = g ā†’ š…āØfā©.
49 #g * #n #H #f #H0 elim (pr_fcla_inv_next ā€¦ H ā€¦ H0) -g
50 /2 width=2 by ex_intro/
51 qed-.
52
53 (* Basic constructions ******************************************************)
54
55 (*** isfin_isid *)
56 lemma pr_isf_isi (f): šˆāØfā© ā†’ š…āØfā©.
57 /3 width=2 by pr_fcla_isi, ex_intro/ qed.
58
59 (*** isfin_push *)
60 lemma pr_isf_push (f): š…āØfā© ā†’ š…āØā«Æfā©.
61 #f * /3 width=2 by pr_fcla_push, ex_intro/
62 qed.
63
64 (*** isfin_next *)
65 lemma pr_isf_next (f): š…āØfā© ā†’ š…āØā†‘fā©.
66 #f * /3 width=2 by pr_fcla_next, ex_intro/
67 qed.