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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 "basic_2/unfold/ltpss_ltpss.ma".
16 include "basic_2/reducibility/cpr.ma".
17 include "basic_2/reducibility/lcpr.ma".
19 (* CONTEXT-SENSITIVE PARALLEL REDUCTION ON LOCAL ENVIRONMENTS *************)
21 (* Advanced properties ****************************************************)
23 lemma lcpr_pair: ∀L1,L2. L1 ⊢ ➡ L2 → ∀V1,V2. L2 ⊢ V1 ➡ V2 →
24 ∀I. L1. ⓑ{I} V1 ⊢ ➡ L2. ⓑ{I} V2.
25 #L1 #L2 * #L #HL1 #HL2 #V1 #V2 *
26 <(ltpss_fwd_length … HL2) /4 width=5/
29 lemma ltpss_lcpr: ∀L1,L2,d,e. L1 ▶* [d, e] L2 → L1 ⊢ ➡ L2.
30 #L1 #L2 #d #e #H elim H -L1 -L2 -d -e // /3 width=3/