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14
15 include "static_2/notation/functions/weight_2.ma".
16 include "static_2/syntax/lenv_weight.ma".
17
18 (* WEIGHT OF A RESTRICTED CLOSURE *******************************************)
19
20 definition rfw: lenv → term → ? ≝ λL,T. ♯❨L❩ + ♯❨T❩.
21
22 interpretation "weight (restricted closure)" 'Weight L T = (rfw L T).
23
24 (* Basic properties *********************************************************)
25
26 lemma rfw_unfold (L) (T): ♯❨L❩ + ♯❨T❩ = ♯❨L,T❩.
27 // qed.
28
29 (* Basic_1: was: flt_shift *)
30 lemma rfw_shift: ∀p,I,K,V,T. ♯❨K.ⓑ[I]V,T❩ < ♯❨K,ⓑ[p,I]V.T❩.
31 /2 width=1 by plt_plus_bi_sn/ qed.
32
33 lemma rfw_clear: ∀p,I1,I2,K,V,T. ♯❨K.ⓤ[I1],T❩ < ♯❨K,ⓑ[p,I2]V.T❩.
34 /2 width=1 by plt_plus_bi_sn/ qed.
35
36 lemma rfw_tpair_sn: ∀I,L,V,T. ♯❨L,V❩ < ♯❨L,②[I]V.T❩.
37 /2 width=1 by plt_plus_bi_sn/ qed.
38
39 lemma rfw_tpair_dx: ∀I,L,V,T. ♯❨L,T❩ < ♯❨L,②[I]V.T❩.
40 /2 width=1 by plt_plus_bi_sn/ qed.
41
42 lemma rfw_lpair_sn: ∀I,L,V,T. ♯❨L,V❩ < ♯❨L.ⓑ[I]V,T❩.
43 // qed.
44
45 lemma rfw_lpair_dx: ∀I,L,V,T. ♯❨L,T❩ < ♯❨L.ⓑ[I]V,T❩.
46 /2 width=1 by plt_plus_bi_dx/ qed.
47
48 (* Basic_1: removed theorems 7:
49             flt_thead_sx flt_thead_dx flt_trans
50             flt_arith0 flt_arith1 flt_arith2 flt_wf_ind
51 *)
52 (* Basic_1: removed local theorems 1: q_ind *)