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 axiom cw_wf_ind: ∀R:lenv→term→Prop.
  27                  (∀L2,T2. (∀L1,T1. #[L1,T1] < #[L2,T2] → R L1 T1) → R L2 T2) →
  28                  ∀L,T. R L T.
  29
  30 lemma cw_shift: ∀K,I,V,T. #[K. 𝕓{I} V, T] < #[K, 𝕔{I} V. T].
  31 normalize //
  32 qed.
  33
  34 lemma tw_shift: ∀L,T. #[L, T] ≤ #[L @ T].
  35 #L elim L //
  36 #K #I #V #IHL #T
  37 @transitive_le [3: @IHL |2: /2/ | skip ]
  38 qed.