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 *)
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15 include "apps_2/models/vdrop_vlift.ma".
16 include "apps_2/models/veq.ma".
18 (* EVALUATION EQUIVALENCE ***************************************************)
20 (* Properties with evaluation drop ******************************************)
22 lemma vdrop_comp (M): ∀i. compatible_2 … (vdrop M i) (veq M) (veq M).
23 #M #i #lv1 #lv2 #Hlv12 #j elim (lt_or_ge j i) #Hji
24 [ >vdrop_lt // >vdrop_lt //
25 | >vdrop_ge // >vdrop_ge //
29 (* Advanced inversion lemmas with evaluation evaluation lift ****************)
31 lemma veq_inv_vlift_sn (M): ∀lv1,y2,d1,i. ⫯[i←d1]lv1 ≗{M} y2 →
32 ∃∃lv2,d2. lv1 ≗ lv2 & d1 ≗ d2 & ⫯[i←d2]lv2 ≐ y2.
35 [5: @exteq_sym @vlift_vdrop_eq |1,2: skip
36 | #j elim (lt_or_ge j i) #Hji
37 [ lapply (H j) -H >vlift_lt // >vdrop_lt //
38 | lapply (H (↑j)) -H >vlift_gt /2 width=1 by monotonic_le_plus_l/ >vdrop_ge //
40 | lapply (H i) >vlift_eq //