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/reducibility/ltpr_ltpss.ma".
16 include "basic_2/reducibility/ltpr_ltpr.ma".
17 include "basic_2/reducibility/lcpr.ma".
19 (* CONTEXT-SENSITIVE PARALLEL REDUCTION ON LOCAL ENVIRONMENTS ***************)
21 (* Main properties **********************************************************)
23 theorem lcpr_conf: ∀L0,L1,L2. L0 ⊢ ➡ L1 → L0 ⊢ ➡ L2 →
24 ∃∃L. L1 ⊢ ➡ L & L2 ⊢ ➡ L.
25 #K0 #L1 #L2 * #K1 #HK01 #HKL1 * #K2 #HK02 #HKL2
26 lapply (ltpr_fwd_length … HK01) #H
27 >(ltpr_fwd_length … HK02) in H; #H
28 elim (ltpr_conf … HK01 … HK02) -K0 #K #HK1 #HK2
29 lapply (ltpss_fwd_length … HKL1) #H1
30 lapply (ltpss_fwd_length … HKL2) #H2
31 >H1 in HKL1 H; -H1 #HKL1
32 >H2 in HKL2; -H2 #HKL2 #H
33 elim (ltpr_ltpss_conf … HKL1 … HK1) -K1 #K1 #HK1 #HLK1
34 elim (ltpr_ltpss_conf … HKL2 … HK2) -K2 #K2 #HK2 #HLK2
35 elim (ltpss_conf … HK1 … HK2) -K #K #HK1 #HK2
36 lapply (ltpr_fwd_length … HLK1) #H1
37 lapply (ltpr_fwd_length … HLK2) #H2