matita/matita/contribs/lambdadelta/basic_2/syntax/cl_restricted_weight.ma

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  14
  15 include "basic_2/notation/functions/weight_2.ma".
  16 include "basic_2/syntax/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 (* Basic_1: was: flt_shift *)
  27 lemma rfw_shift: ∀p,I,K,V,T. ♯{K.ⓑ{I}V, T} < ♯{K, ⓑ{p,I}V.T}.
  28 normalize /2 width=1 by monotonic_le_plus_r/
  29 qed.
  30
  31 lemma rfw_clear: ∀p,I1,I2,K,V,T. ♯{K.ⓤ{I1}, T} < ♯{K, ⓑ{p,I2}V.T}.
  32 normalize /4 width=1 by monotonic_le_plus_r, le_S_S/
  33 qed.
  34
  35 lemma rfw_tpair_sn: ∀I,L,V,T. ♯{L, V} < ♯{L, ②{I}V.T}.
  36 normalize in ⊢ (?→?→?→?→?%%); //
  37 qed.
  38
  39 lemma rfw_tpair_dx: ∀I,L,V,T. ♯{L, T} < ♯{L, ②{I}V.T}.
  40 normalize in ⊢ (?→?→?→?→?%%); //
  41 qed.
  42
  43 lemma rfw_lpair_sn: ∀I,L,V,T. ♯{L, V} < ♯{L.ⓑ{I}V, T}.
  44 normalize /3 width=1 by monotonic_lt_plus_l, monotonic_le_plus_r/
  45 qed.
  46
  47 lemma rfw_lpair_dx: ∀I,L,V,T. ♯{L, T} < ♯{L.ⓑ{I}V, T}.
  48 normalize /3 width=1 by monotonic_lt_plus_l, monotonic_le_plus_r/
  49 qed.
  50
  51 (* Basic_1: removed theorems 7:
  52             flt_thead_sx flt_thead_dx flt_trans
  53             flt_arith0 flt_arith1 flt_arith2 flt_wf_ind
  54 *)
  55 (* Basic_1: removed local theorems 1: q_ind *)