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 "apps_2/models/model_li.ma".
16 include "apps_2/models/veq_vdrop.ma".
18 (* EVALUATION EQUIVALENCE **************************************************)
20 (* Properties with local environment interpretation *************************)
22 lemma li_repl_back (M) (gv): is_model M →
23 ∀L,lv1. lv1 ϵ ⟦L⟧[gv] →
24 ∀lv2. lv1 ≗{M} lv2 → lv2 ϵ ⟦L⟧[gv].
25 #M #gv #HM #L #lv1 #H elim H -L -lv1 //
26 [ #lv1 #d1 #K #V #_ #Hd #IH #y #H
27 elim (veq_inv_vlift_sn … H) -H #lv2 #d2 #Hlv12 #Hd12 #Hy
28 /5 width=5 by li_repl, li_abbr, ti_comp_l, mr/
29 | #lv1 #d1 #K #W #_ #IH #y #H
30 elim (veq_inv_vlift_sn … H) -H #lv2 #d2 #Hlv12 #_ #Hy
31 /4 width=3 by li_repl, li_abst/
32 | #lv1 #d1 #I #K #_ #IH #y #H
33 elim (veq_inv_vlift_sn … H) -H #lv2 #d2 #Hlv12 #_ #Hy
34 /4 width=3 by li_repl, li_unit/
35 | #lv1 #lv #L #_ #Hlv1 #IH #lv2 #Hlv2
36 @IH /2 width=3 by exteq_veq_trans/