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 *)
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15 include "basic_2/static/lsubr.ma".
16 include "basic_2/rt_transition/cpg.ma".
18 (* BOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS *****************)
20 (* Properties with restricted refinement for local environments *************)
22 lemma lsubr_cpg_trans: ∀Rt,c,h,G. lsub_trans … (cpg Rt h c G) lsubr.
23 #Rt #c #h #G #L1 #T1 #T2 #H elim H -c -G -L1 -T1 -T2
25 | /2 width=2 by cpg_ess/
26 | #c #G #L1 #V1 #V2 #W2 #_ #HVW2 #IH #X #H
27 elim (lsubr_inv_abbr2 … H) -H #L2 #HL21 #H destruct
28 /3 width=3 by cpg_delta/
29 | #c #G #L1 #V1 #V2 #W2 #_ #HVW2 #IH #X #H
30 elim (lsubr_inv_abst2 … H) -H * #L2 [2: #V ] #HL21 #H destruct
31 /4 width=3 by cpg_delta, cpg_ell, cpg_ee/
32 | #c #I1 #G #L1 #T1 #U1 #i #_ #HTU1 #IH #X #H
33 elim (lsubr_fwd_bind2 … H) -H #I2 #L2 #HL21 #H destruct
34 /3 width=3 by cpg_lref/
35 |6,12: /4 width=1 by cpg_bind, cpg_beta, lsubr_bind/
36 |7,8,10,11: /3 width=1 by cpg_appl, cpg_cast, cpg_eps, cpg_ee/
37 |9,13: /4 width=3 by cpg_zeta, cpg_theta, lsubr_bind/