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1 (**************************************************************************)
2 (*       ___                                                              *)
3 (*      ||M||                                                             *)
4 (*      ||A||       A project by Andrea Asperti                           *)
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11 (*        v         GNU General Public License Version 2                  *)
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13 (**************************************************************************)
14
15 include "static_2/syntax/bind_weight.ma".
16 include "static_2/syntax/lenv.ma".
17
18 (* WEIGHT OF A LOCAL ENVIRONMENT ********************************************)
19
20 rec definition lw L ≝ match L with
21 [ LAtom     ⇒ 𝟏
22 | LBind L I ⇒ lw L + ♯❨I❩
23 ].
24
25 interpretation "weight (local environment)" 'Weight L = (lw L).
26
27 (* Basic properties *********************************************************)
28
29 lemma lw_atom_unfold: 𝟏 = ♯❨⋆❩.
30 // qed.
31
32 lemma lw_bind_unfold (I) (L): ♯❨L❩ + ♯❨I❩ = ♯❨L.ⓘ[I]❩.
33 // qed.
34
35 (* Basic_2A1: uses: lw_pair *)
36 lemma lw_bind: ∀I,L. ♯❨L❩ < ♯❨L.ⓘ[I]❩.
37 // qed.
38
39 (* Basic_1: removed theorems 4: clt_cong clt_head clt_thead clt_wf_ind *)
40 (* Basic_1: removed local theorems 1: clt_wf__q_ind *)
41 (* Basic_1: note: clt_thead should be renamed clt_ctail *)