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 "basic_2/rt_equivalence/cpcs_cprs.ma".
17 (* CONTEXT-SENSITIVE PARALLEL R-EQUIVALENCE FOR TERMS ***********************)
19 (* Properties with generic slicing for local environments *******************)
21 (* Basic_1: was: pc3_lift *)
22 (* Basic_2A1: was: cpcs_lift *)
23 lemma cpcs_lifts_bi (h) (G): d_liftable2_bi … lifts (cpcs h G).
24 #h #G #K #T1 #T2 #HT12 #b #f #L #HLK #U1 #HTU1 #U2 #HTU2
25 elim (cpcs_inv_cprs … HT12) -HT12 #T #HT1 #HT2
26 elim (lifts_total T f) #U #HU
27 /3 width=12 by cprs_div, cpms_lifts_bi/
30 (* Inversion lemmas with generic slicing for local environments *************)
32 (* Basic_1: was: pc3_gen_lift *)
33 (* Basic_2A1: was cpcs_inv_lift *)
34 lemma cpcs_inv_lifts_bi (h) (G): d_deliftable2_bi … lifts (cpcs h G).
35 #h #G #L #U1 #U2 #HU12 #b #f #K #HLK #T1 #HTU1 #T2 #HTU2
36 elim (cpcs_inv_cprs … HU12) -HU12 #U #HU1 #HU2
37 elim (cpms_inv_lifts_sn … HU1 … HLK … HTU1) -U1 #T #HTU #HT1
38 lapply (cpms_inv_lifts_bi … HU2 … HLK … HTU2 … HTU) -L -U -U2 -b -f #HT2
39 /2 width=3 by cprs_div/