matita/matita/contribs/lambda_delta/Basic_2/computation/lsubc.ma

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  14
  15 include "Basic_2/computation/acp_cr.ma".
  16
  17 (* LOCAL ENVIRONMENT REFINEMENT FOR ABSTRACT CANDIDATES OF REDUCIBILITY *****)
  18
  19 inductive lsubc (RP:lenv→predicate term): relation lenv ≝
  20 | lsubc_atom: lsubc RP (⋆) (⋆)
  21 | lsubc_pair: ∀I,L1,L2,V. lsubc RP L1 L2 → lsubc RP (L1. 𝕓{I} V) (L2. 𝕓{I} V)
  22 | lsubc_abbr: ∀L1,L2,V,W,A. ⦃L1, V⦄ [RP] ϵ 〚A〛 → ⦃L2, W⦄ [RP] ϵ 〚A〛 →
  23               lsubc RP L1 L2 → lsubc RP (L1. 𝕓{Abbr} V) (L2. 𝕓{Abst} W)
  24 .
  25
  26 interpretation
  27   "local environment refinement (abstract candidates of reducibility)"
  28   'CrSubEq L1 RP L2 = (lsubc RP L1 L2).
  29
  30 (* Basic properties *********************************************************)
  31
  32 lemma lsubc_refl: ∀RP,L. L [RP] ⊑ L.
  33 #RP #L elim L -L // /2 width=1/
  34 qed.
  35
  36 (* Basic inversion lemmas ***************************************************)