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/computation/cprs_ltpss_dx.ma".
16 include "basic_2/equivalence/cpcs_cpcs.ma".
18 (* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON TERMS **************************)
20 (* Properties concerning dx partial unfold on local environments ************)
22 lemma cpcs_ltpss_dx_conf: ∀L1,L2,d,e. L1 ▶* [d, e] L2 →
23 ∀T1,T2. L1 ⊢ T1 ⬌* T2 → L2 ⊢ T1 ⬌* T2.
24 #L1 #L2 #d #e #HL12 #T1 #T2 #H
25 elim (cpcs_inv_cprs … H) -H #T #HT1 #HT2
26 elim (cprs_ltpss_dx_conf … HT1 … HL12) -HT1 #U1 #HTU1 #H1
27 elim (cprs_ltpss_dx_conf … HT2 … HL12) -L1 #U2 #HTU2 #H2
28 elim (tpss_conf_eq … H1 … H2) -T #U #HU1 #HU2
29 lapply (cprs_tpss_trans … HTU1 … HU1) -U1
30 lapply (cprs_tpss_trans … HTU2 … HU2) -U2 /2 width=3/
33 lemma cpcs_ltpss_dx_tpss_conf: ∀L1,L2,d,e. L1 ▶* [d, e] L2 →
35 ∀T1. L2 ⊢ T ▶* [d, e] T1 →
37 #L1 #L2 #d #e #HL12 #T #T2 #HT2 #T1 #HT1
38 lapply (cpcs_ltpss_dx_conf … HL12 … HT2) -L1 #HT2
39 lapply (cpcs_tpss_conf … HT1 … HT2) -T //
42 lemma cpcs_ltpss_dx_tpss2_conf: ∀L1,L2,d,e. L1 ▶* [d, e] L2 →
43 ∀T1,T2. L1 ⊢ T1 ⬌* T2 →
44 ∀T3. L2 ⊢ T1 ▶* [d, e] T3 →
45 ∀T4. L2 ⊢ T2 ▶* [d, e] T4 →
47 #L1 #L2 #d #e #HL12 #T1 #T2 #HT12 #T3 #HT13 #T4 #HT24
48 lapply (cpcs_ltpss_dx_tpss_conf … HL12 … HT12 … HT13) -L1 -T1 #HT32
49 lapply (cpcs_tpss_strap1 … HT32 … HT24) -T2 //