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 cw: lenv → term → ? ≝ λL,T. #[L] + #[T].
  21
  22 interpretation "weight (closure)" 'Weight L T = (cw 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 cw_wf_ind: ∀R:lenv→predicate 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 cw_shift: ∀K,I,V,T. #[K. ⓑ{I} V, T] < #[K, ②{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 (* Basic_1: removed theorems 6:
  45             flt_thead_sx flt_thead_dx flt_arith0 flt_arith1 flt_arith2 flt_trans
  46 *)