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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 fw: lenv → term → ? ≝ λL,T. ♯{L} + ♯{T}.
21
22 interpretation "weight (closure)" 'Weight L T = (fw L T).
23
24 (* Basic properties *********************************************************)
25
26 (* Basic_1: was: flt_shift *)
27 lemma fw_shift: ∀a,K,I,V,T. ♯{K. ⓑ{I} V, T} < ♯{K, ⓑ{a,I} V. T}.
28 normalize //
29 qed.
30
31 lemma tw_shift: ∀L,T. ♯{L, T} ≤ ♯{L @@ T}.
32 #L elim L //
33 #K #I #V #IHL #T
34 @transitive_le [3: @IHL |2: /2 width=2/ | skip ]
35 qed.
36
37 lemma fw_tpair_sn: ∀I,L,V,T. ♯{L, V} < ♯{L, ②{I}V.T}.
38 normalize in ⊢ (?→?→?→?→?%%); //
39 qed.
40
41 lemma fw_tpair_dx: ∀I,L,V,T. ♯{L, T} < ♯{L, ②{I}V.T}.
42 normalize in ⊢ (?→?→?→?→?%%); //
43 qed.
44
45 lemma fw_tpair_dx_sn: ∀I1,I2,L,V1,V2,T. ♯{L, V2} < ♯{L, ②{I1}V1.②{I2}V2.T}.
46 normalize in ⊢ (?→?→?→?→?→?→?%%); /2 width=1/
47 qed.
48
49 lemma fw_tpair_sn_sn_shift: ∀I,I1,I2,L,V1,V2,T.
50                             ♯{L.ⓑ{I}V1, T} < ♯{L, ②{I1}V1.②{I2}V2.T}.
51 normalize in ⊢ (?→?→?→?→?→?→?→?%%); /3 width=1/
52 qed.
53
54 lemma fw_tpair_sn_dx_shift: ∀I,I1,I2,L,V1,V2,T.
55                             ♯{L.ⓑ{I}V2, T} < ♯{L, ②{I1}V1.②{I2}V2.T}.
56 normalize in ⊢ (?→?→?→?→?→?→?→?%%); /2 width=1/
57 qed.
58
59 (* Basic_1: removed theorems 7:
60             flt_thead_sx flt_thead_dx flt_arith0 flt_arith1 flt_arith2 flt_trans
61             flt_wf_ind
62 *)
63 (* Basic_1: removed local theorems 1: q_ind *)