matita/matita/contribs/lambdadelta/basic_2/grammar/cl_weight.ma

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  14
  15 include "basic_2/grammar/lenv_weight.ma".
  16 include "basic_2/grammar/cl_shift.ma".
  17
  18 (* WEIGHT OF A CLOSURE ******************************************************)
  19
  20 definition fw: lenv → term → ? ≝ λL,T. #{L} + #{T}.
  21
  22 interpretation "weight (closure)" 'Weight L T = (fw L T).
  23
  24 (* Basic properties *********************************************************)
  25
  26 (* Basic_1: was: flt_shift *)
  27 lemma fw_shift: ∀a,K,I,V,T. #{K. ⓑ{I} V, T} < #{K, ⓑ{a,I} V. T}.
  28 normalize //
  29 qed.
  30
  31 lemma tw_shift: ∀L,T. #{L, T} ≤ #{L @@ T}.
  32 #L elim L //
  33 #K #I #V #IHL #T
  34 @transitive_le [3: @IHL |2: /2 width=2/ | skip ]
  35 qed.
  36
  37 lemma fw_tpair_sn: ∀I,L,V,T. #{L, V} < #{L, ②{I}V.T}.
  38 normalize in ⊢ (?→?→?→?→?%%); //
  39 qed.
  40
  41 lemma fw_tpair_dx: ∀I,L,V,T. #{L, T} < #{L, ②{I}V.T}.
  42 normalize in ⊢ (?→?→?→?→?%%); //
  43 qed.
  44
  45 lemma fw_tpair_dx_sn: ∀I1,I2,L,V1,V2,T. #{L, V2} < #{L, ②{I1}V1.②{I2}V2.T}.
  46 normalize in ⊢ (?→?→?→?→?→?→?%%); /2 width=1/
  47 qed.
  48
  49 lemma fw_tpair_sn_sn_shift: ∀I,I1,I2,L,V1,V2,T.
  50                             #{L.ⓑ{I}V1, T} < #{L, ②{I1}V1.②{I2}V2.T}.
  51 normalize in ⊢ (?→?→?→?→?→?→?→?%%); /3 width=1/
  52 qed.
  53
  54 lemma fw_tpair_sn_dx_shift: ∀I,I1,I2,L,V1,V2,T.
  55                             #{L.ⓑ{I}V2, T} < #{L, ②{I1}V1.②{I2}V2.T}.
  56 normalize in ⊢ (?→?→?→?→?→?→?→?%%); /2 width=1/
  57 qed.
  58
  59 (* Basic_1: removed theorems 7:
  60             flt_thead_sx flt_thead_dx flt_arith0 flt_arith1 flt_arith2 flt_trans
  61             flt_wf_ind
  62 *)
  63 (* Basic_1: removed local theorems 1: q_ind *)