matita/matita/contribs/lambdadelta/ground/relocation/gr_isf.ma

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  14
  15 include "ground/notation/relations/predicate_f_1.ma".
  16 include "ground/relocation/gr_fcla.ma".
  17
  18 (* FINITE COLENGTH CONDITION FOR GENERIC RELOCATION MAPS *)
  19
  20 (*** isfin *)
  21 definition gr_isf: predicate gr_map ≝
  22            λf. ∃n. 𝐂❪f❫ ≘ n.
  23
  24 interpretation
  25   "finite colength condition (generic relocation maps)"
  26   'PredicateF f = (gr_isf f).
  27
  28 (* Basic eliminators ********************************************************)
  29
  30 (*** isfin_ind *)
  31 lemma gr_isf_ind (Q:predicate …):
  32       (∀f.  𝐈❪f❫ → Q f) →
  33       (∀f. 𝐅❪f❫ → Q f → Q (⫯f)) →
  34       (∀f. 𝐅❪f❫ → Q f → Q (↑f)) →
  35       ∀f. 𝐅❪f❫ → 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 inversion lemmas ***************************************************)
  41
  42 (*** isfin_inv_push *)
  43 lemma gr_isf_inv_push (g): 𝐅❪g❫ → ∀f. ⫯f = g → 𝐅❪f❫.
  44 #g * /3 width=4 by gr_fcla_inv_push, ex_intro/
  45 qed-.
  46
  47 (*** isfin_inv_next *)
  48 lemma gr_isf_inv_next (g): 𝐅❪g❫ → ∀f. ↑f = g → 𝐅❪f❫.
  49 #g * #n #H #f #H0 elim (gr_fcla_inv_next … H … H0) -g
  50 /2 width=2 by ex_intro/
  51 qed-.
  52
  53 (* Basic properties *********************************************************)
  54
  55 (*** isfin_isid *)
  56 lemma gr_isf_isi (f): 𝐈❪f❫ → 𝐅❪f❫.
  57 /3 width=2 by gr_fcla_isi, ex_intro/ qed.
  58
  59 (*** isfin_push *)
  60 lemma gr_isf_push (f): 𝐅❪f❫ → 𝐅❪⫯f❫.
  61 #f * /3 width=2 by gr_fcla_push, ex_intro/
  62 qed.
  63
  64 (*** isfin_next *)
  65 lemma gr_isf_next (f): 𝐅❪f❫ → 𝐅❪↑f❫.
  66 #f * /3 width=2 by gr_fcla_next, ex_intro/
  67 qed.