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14
15 include "basic_2/notation/functions/weight_3.ma".
16 include "basic_2/grammar/lenv_weight.ma".
17 include "basic_2/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 (* Basic_1: was: flt_shift *)
29 lemma fw_shift: ∀p,I,G,K,V,T. ♯{G, K.ⓑ{I}V, T} < ♯{G, K, ⓑ{p,I}V.T}.
30 normalize //
31 qed.
32
33 lemma fw_tpair_sn: ∀I,G,L,V,T. ♯{G, L, V} < ♯{G, L, ②{I}V.T}.
34 normalize in ⊢ (?→?→?→?→?→?%%); //
35 qed.
36
37 lemma fw_tpair_dx: ∀I,G,L,V,T. ♯{G, L, T} < ♯{G, L, ②{I}V.T}.
38 normalize in ⊢ (?→?→?→?→?→?%%); //
39 qed.
40
41 lemma fw_lpair_sn: ∀I,G,L,V,T. ♯{G, L, V} < ♯{G, L.ⓑ{I}V, T}.
42 normalize /3 width=1 by monotonic_lt_plus_l, monotonic_le_plus_r/
43 qed.
44
45 (* Basic_1: removed theorems 7:
46             flt_thead_sx flt_thead_dx flt_trans
47             flt_arith0 flt_arith1 flt_arith2 flt_wf_ind
48 *)
49 (* Basic_1: removed local theorems 1: q_ind *)