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 "static_2/static/req_length.ma".
16 include "static_2/static/req_drops.ma".
17 include "basic_2/rt_transition/rpx_fsle.ma".
19 (* EXTENDED CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS **************)
21 (* Properties with syntactic equivalence for lenvs on referred entries ******)
23 (* Basic_2A1: was: lleq_cpx_trans *)
24 lemma req_cpx_trans (G): R_transitive_req (cpx G).
25 #G #L2 #T1 #T2 #H @(cpx_ind … H) -G -L2 -T1 -T2 /2 width=2 by cpx_qu/
26 [ #I #G #K2 #V1 #V2 #W2 #_ #IH #HVW2 #L1 #H
27 elim (req_inv_zero_pair_dx … H) -H #K1 #HK12 #H destruct
28 /3 width=3 by cpx_delta/
29 | #I2 #G #K2 #T #U #i #_ #IH #HTU #L1 #H
30 elim (req_inv_lref_bind_dx … H) -H #I1 #K1 #HK12 #H destruct
31 /3 width=3 by cpx_lref/
32 | #p #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #H
33 elim (req_inv_bind … H) -H /3 width=1 by cpx_bind/
34 | #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #H
35 elim (req_inv_flat … H) -H /3 width=1 by cpx_flat/
36 | #G #L2 #V2 #T1 #T #T2 #HT1 #_ #IH #L1 #H
37 elim (req_inv_bind … H) -H #HV2 #H
38 lapply (req_inv_lifts_bi … H (Ⓣ) … HT1) -H [6:|*: /3 width=2 by drops_refl, drops_drop/ ] #HT
39 /3 width=3 by cpx_zeta/
40 | #G #L2 #W1 #T1 #T2 #_ #IH #L1 #H
41 elim (req_inv_flat … H) -H /3 width=1 by cpx_eps/
42 | #G #L2 #W1 #W2 #T1 #_ #IH #L1 #H
43 elim (req_inv_flat … H) -H /3 width=1 by cpx_ee/
44 | #p #G #L2 #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #L1 #H
45 elim (req_inv_flat … H) -H #HV1 #H
46 elim (req_inv_bind … H) -H /3 width=1 by cpx_beta/
47 | #p #G #L2 #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV1 #IHW12 #IHT12 #HV2 #L1 #H
48 elim (req_inv_flat … H) -H #HV1 #H
49 elim (req_inv_bind … H) -H /3 width=3 by cpx_theta/
53 lemma cpx_req_conf (G): R_confluent1_rex (cpx G) ceq.
54 /3 width=3 by req_cpx_trans, req_sym/ qed-.
56 (* Basic_2A1: was: cpx_lleq_conf_sn *)
57 lemma cpx_req_conf_sn (G): s_r_confluent1 … (cpx G) req.
58 /2 width=5 by cpx_rex_conf_sn/ qed-.