matita/matita/contribs/lambdadelta/basic_2/etc_2A1/fpa/gcp.etc

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  14
  15 include "basic_2/grammar/genv.ma".
  16 include "basic_2/multiple/fpas.ma".
  17
  18 (* GENERIC COMPUTATION PROPERTIES *******************************************)
  19
  20 definition candidate: Type[0] ≝ relation3 genv lenv term.
  21
  22 definition CP0 ≝ λRR:relation4 genv lenv term term. λRS:relation term.
  23                  ∀G,L1,L2,T1,T2,s. ⦃L1, T1⦄ ⇳[s] ⦃L2, T2⦄ →
  24                  NF … (RR G L1) RS T1 → NF … (RR G L2) RS T2.
  25
  26 definition CP0s ≝ λRR:relation4 genv lenv term term. λRS:relation term.
  27                   ∀G,L1,L2,T1,T2,s. ⦃L1, T1⦄ ⇳*[s] ⦃L2, T2⦄ →
  28                   NF … (RR G L1) RS T1 → NF … (RR G L2) RS T2.
  29
  30 definition CP1 ≝ λRR:relation4 genv lenv term term. λRS:relation term.
  31                  ∀G,L. ∃k. NF … (RR G L) RS (⋆k).
  32
  33 definition CP2 ≝ λRP:candidate.
  34                  ∀G,L,T,k. RP G L (ⓐ⋆k.T) → RP G L T.
  35
  36 (* requirements for generic computation properties *)
  37 record gcp (RR:relation4 genv lenv term term) (RS:relation term) (RP:candidate) : Prop ≝
  38 { cp0: CP0 RR RS;
  39   cp1: CP1 RR RS;
  40   cp2: CP2 RP
  41 }.
  42
  43 (* Basic properties *********************************************************)
  44
  45 (* Basic_1: was just: nf2_lift1 *)
  46 lemma gcp_fpas: ∀RR,RS. CP0 RR RS → CP0s RR RS.
  47 #RR #RS #HRR #G #L1 #L2 #T1 #T2 #s #H @(fpas_ind … H) -L2 -T2 /3 width=5 by/
  48 qed.