matita/matita/contribs/lambda_delta/Basic_2/reducibility/apr_cr.ma

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  14
  15 include "Basic_2/grammar/term_simple.ma".
  16
  17 (* CANDIDATES OF REDUCIBILITY ***********************************************)
  18
  19 (* abstract conditions for candidates *)
  20
  21 definition CR1: predicate term → predicate term → Prop ≝
  22                 λRD,RC. ∀T. RC T → RD T.
  23
  24 definition CR2: relation term → predicate term → Prop ≝
  25                 λRR,RC. ∀T1,T2. RC T1 → 𝕊[T1] → RR T1 T2 → RC T2.
  26
  27 definition CR3: relation term → predicate term → Prop ≝
  28                 λRR,RC. ∀T1. (∀T2. RR T1 T2 → RC T2) → 𝕊[T1] → RC T1.
  29
  30 (* a candidate *)
  31 record cr (RR:relation term) (RD:predicate term): Type[0] ≝ {
  32    in_cr: predicate term;
  33    cr1: CR1 RD in_cr;
  34    cr2: CR2 RR in_cr;
  35    cr3: CR3 RR in_cr
  36 }.
  37
  38 interpretation
  39    "context-free parallel reduction (term)"
  40    'InSubset T R = (in_cr ? ? R T).
  41
  42 definition in_fun_cr: ∀RR,RD. ∀D,C:(cr RR RD). predicate term ≝
  43                       λRR,RD,D,C,T. ∀V. V ϵ D → 𝕔{Appl}V.T ϵ C.