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14
15 include "basic_2A/notation/functions/weight_3.ma".
16 include "basic_2A/grammar/lenv_weight.ma".
17 include "basic_2A/grammar/genv.ma".
18
19 (* WEIGHT OF A CLOSURE ******************************************************)
20
21 (* activate genv *)
22 definition fw: genv → lenv → term → ? ≝ λG,L,T. ♯{L} + ♯{T}.
23
24 interpretation "weight (closure)" 'Weight G L T = (fw G L T).
25
26 (* Basic properties *********************************************************)
27
28 lemma fw_shift: ∀a,I,G,K,V,T. ♯{G, K.ⓑ{I}V, T} < ♯{G, K, ⓑ{a,I}V.T}.
29 normalize //
30 qed.
31
32 lemma fw_tpair_sn: ∀I,G,L,V,T. ♯{G, L, V} < ♯{G, L, ②{I}V.T}.
33 normalize in ⊢ (?→?→?→?→?→?%%); //
34 qed.
35
36 lemma fw_tpair_dx: ∀I,G,L,V,T. ♯{G, L, T} < ♯{G, L, ②{I}V.T}.
37 normalize in ⊢ (?→?→?→?→?→?%%); //
38 qed.
39
40 lemma fw_lpair_sn: ∀I,G,L,V,T. ♯{G, L, V} < ♯{G, L.ⓑ{I}V, T}.
41 normalize /3 width=1 by monotonic_lt_plus_l, monotonic_le_plus_r/
42 qed.