matita/matita/contribs/lambdadelta/basic_2A/grammar/cl_restricted_weight.ma

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  14
  15 include "basic_2A/notation/functions/weight_2.ma".
  16 include "basic_2A/grammar/lenv_weight.ma".
  17
  18 (* WEIGHT OF A RESTRICTED CLOSURE *******************************************)
  19
  20 definition rfw: lenv → term → ? ≝ λL,T. ♯{L} + ♯{T}.
  21
  22 interpretation "weight (restricted closure)" 'Weight L T = (rfw L T).
  23
  24 (* Basic properties *********************************************************)
  25
  26 lemma rfw_shift: ∀a,I,K,V,T. ♯{K.ⓑ{I}V, T} < ♯{K, ⓑ{a,I}V.T}.
  27 normalize //
  28 qed.
  29
  30 lemma rfw_tpair_sn: ∀I,L,V,T. ♯{L, V} < ♯{L, ②{I}V.T}.
  31 normalize in ⊢ (?→?→?→?→?%%); //
  32 qed.
  33
  34 lemma rfw_tpair_dx: ∀I,L,V,T. ♯{L, T} < ♯{L, ②{I}V.T}.
  35 normalize in ⊢ (?→?→?→?→?%%); //
  36 qed.
  37
  38 lemma rfw_lpair_sn: ∀I,L,V,T. ♯{L, V} < ♯{L.ⓑ{I}V, T}.
  39 normalize /3 width=1 by monotonic_lt_plus_l, monotonic_le_plus_r/
  40 qed.
  41
  42 lemma rfw_lpair_dx: ∀I,L,V,T. ♯{L, T} < ♯{L.ⓑ{I}V, T}.
  43 normalize /3 width=1 by monotonic_lt_plus_l, monotonic_le_plus_r/
  44 qed.