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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
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15 include "basic_2A/notation/functions/weight_2.ma".
16 include "basic_2A/grammar/lenv_weight.ma".
18 (* WEIGHT OF A RESTRICTED CLOSURE *******************************************)
20 definition rfw: lenv → term → ? ≝ λL,T. ♯{L} + ♯{T}.
22 interpretation "weight (restricted closure)" 'Weight L T = (rfw L T).
24 (* Basic properties *********************************************************)
26 lemma rfw_shift: ∀a,I,K,V,T. ♯{K.ⓑ{I}V, T} < ♯{K, ⓑ{a,I}V.T}.
30 lemma rfw_tpair_sn: ∀I,L,V,T. ♯{L, V} < ♯{L, ②{I}V.T}.
31 normalize in ⊢ (?→?→?→?→?%%); //
34 lemma rfw_tpair_dx: ∀I,L,V,T. ♯{L, T} < ♯{L, ②{I}V.T}.
35 normalize in ⊢ (?→?→?→?→?%%); //
38 lemma rfw_lpair_sn: ∀I,L,V,T. ♯{L, V} < ♯{L.ⓑ{I}V, T}.
39 normalize /3 width=1 by monotonic_lt_plus_l, monotonic_le_plus_r/
42 lemma rfw_lpair_dx: ∀I,L,V,T. ♯{L, T} < ♯{L.ⓑ{I}V, T}.
43 normalize /3 width=1 by monotonic_lt_plus_l, monotonic_le_plus_r/