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/multiple/lleq_fqus.ma".
16 include "basic_2/multiple/lleq_lleq.ma".
17 include "basic_2/reduction/lpx_lleq.ma".
18 include "basic_2/reduction/fpb.ma".
20 (* "RST" PROPER PARALLEL COMPUTATION FOR CLOSURES ***************************)
22 (* Properties on lazy equivalence for local environments ********************)
24 lemma lleq_fpb_trans: ∀h,o,F,K1,K2,T. K1 ≡[T, 0] K2 →
25 ∀G,L2,U. ⦃F, K2, T⦄ ≻[h, o] ⦃G, L2, U⦄ →
26 ∃∃L1. ⦃F, K1, T⦄ ≻[h, o] ⦃G, L1, U⦄ & L1 ≡[U, 0] L2.
27 #h #o #F #K1 #K2 #T #HT #G #L2 #U * -G -L2 -U
28 [ #G #L2 #U #H2 elim (lleq_fqu_trans … H2 … HT) -K2
29 /3 width=3 by fpb_fqu, ex2_intro/
30 | /4 width=10 by fpb_cpx, cpx_lleq_conf_sn, lleq_cpx_trans, ex2_intro/
31 | #L2 #HKL2 #HnKL2 elim (lleq_lpx_trans … HKL2 … HT) -HKL2
32 /6 width=3 by fpb_lpx, lleq_canc_sn, ex2_intro/ (* 2 lleq_canc_sn *)