1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "static_2/notation/functions/weight_2.ma".
16 include "static_2/syntax/lenv_weight.ma".
18 (* WEIGHT OF A RESTRICTED CLOSURE *******************************************)
20 definition rfw: lenv → term → ? ≝ λL,T. ♯{L} + ♯{T}.
22 interpretation "weight (restricted closure)" 'Weight L T = (rfw L T).
24 (* Basic properties *********************************************************)
26 (* Basic_1: was: flt_shift *)
27 lemma rfw_shift: ∀p,I,K,V,T. ♯{K.ⓑ{I}V,T} < ♯{K,ⓑ{p,I}V.T}.
28 normalize /2 width=1 by monotonic_le_plus_r/
31 lemma rfw_clear: ∀p,I1,I2,K,V,T. ♯{K.ⓤ{I1},T} < ♯{K,ⓑ{p,I2}V.T}.
32 normalize /4 width=1 by monotonic_le_plus_r, le_S_S/
35 lemma rfw_tpair_sn: ∀I,L,V,T. ♯{L,V} < ♯{L,②{I}V.T}.
36 normalize in ⊢ (?→?→?→?→?%%); //
39 lemma rfw_tpair_dx: ∀I,L,V,T. ♯{L,T} < ♯{L,②{I}V.T}.
40 normalize in ⊢ (?→?→?→?→?%%); //
43 lemma rfw_lpair_sn: ∀I,L,V,T. ♯{L,V} < ♯{L.ⓑ{I}V,T}.
44 normalize /3 width=1 by monotonic_lt_plus_l, monotonic_le_plus_r/
47 lemma rfw_lpair_dx: ∀I,L,V,T. ♯{L,T} < ♯{L.ⓑ{I}V,T}.
48 normalize /3 width=1 by monotonic_lt_plus_l, monotonic_le_plus_r/
51 (* Basic_1: removed theorems 7:
52 flt_thead_sx flt_thead_dx flt_trans
53 flt_arith0 flt_arith1 flt_arith2 flt_wf_ind
55 (* Basic_1: removed local theorems 1: q_ind *)