matita/matita/contribs/lambda_delta/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_wf__q_ind *)
  27
  28 (* Basic_1: was: flt_wf_ind *)
  29 axiom fw_ind: ∀R:relation2 lenv term.
  30               (∀L2,T2. (∀L1,T1. #{L1,T1} < #{L2,T2} → R L1 T1) → R L2 T2) →
  31               ∀L,T. R L T.
  32
  33 (* Basic_1: was: flt_shift *)
  34 lemma fw_shift: ∀a,K,I,V,T. #{K. ⓑ{I} V, T} < #{K, ⓑ{a,I} V. T}.
  35 normalize //
  36 qed.
  37
  38 lemma tw_shift: ∀L,T. #{L, T} ≤ #{L @@ T}.
  39 #L elim L //
  40 #K #I #V #IHL #T
  41 @transitive_le [3: @IHL |2: /2 width=2/ | skip ]
  42 qed.
  43
  44 lemma fw_tpair_sn: ∀I,L,V,T. #{L, V} < #{L, ②{I}V.T}.
  45 normalize in ⊢ (?→?→?→?→?%%); //
  46 qed.
  47
  48 lemma fw_tpair_dx: ∀I,L,V,T. #{L, T} < #{L, ②{I}V.T}.
  49 normalize in ⊢ (?→?→?→?→?%%); //
  50 qed.
  51
  52 lemma fw_tpair_dx_sn: ∀I1,I2,L,V1,V2,T. #{L, V2} < #{L, ②{I1}V1.②{I2}V2.T}.
  53 normalize in ⊢ (?→?→?→?→?→?→?%%); /2 width=1/
  54 qed.
  55
  56 lemma fw_tpair_sn_sn_shift: ∀I,I1,I2,L,V1,V2,T.
  57                             #{L.ⓑ{I}V1, T} < #{L, ②{I1}V1.②{I2}V2.T}.
  58 normalize in ⊢ (?→?→?→?→?→?→?→?%%); /3 width=1/
  59 qed.
  60
  61 lemma fw_tpair_sn_dx_shift: ∀I,I1,I2,L,V1,V2,T.
  62                             #{L.ⓑ{I}V2, T} < #{L, ②{I1}V1.②{I2}V2.T}.
  63 normalize in ⊢ (?→?→?→?→?→?→?→?%%); /2 width=1/
  64 qed.
  65
  66 (* Basic_1: removed theorems 6:
  67             flt_thead_sx flt_thead_dx flt_arith0 flt_arith1 flt_arith2 flt_trans
  68 *)