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14
15 include "static_2/static/lsubr.ma".
16 include "basic_2/rt_transition/cpg.ma".
17
18 (* BOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS *****************)
19
20 (* Properties with restricted refinement for local environments *************)
21
22 lemma lsubr_cpg_trans (Rs) (Rk) (c) (G):
23       lsub_trans … (cpg Rs Rk c G) lsubr.
24 #Rs #Rk #c #G #L1 #T1 #T2 #H elim H -c -G -L1 -T1 -T2
25 [ //
26 | /2 width=2 by cpg_ess/
27 | #c #G #L1 #V1 #V2 #W2 #_ #HVW2 #IH #X #H
28   elim (lsubr_inv_abbr2 … H) -H #L2 #HL21 #H destruct
29   /3 width=3 by cpg_delta/
30 | #c #G #L1 #V1 #V2 #W2 #_ #HVW2 #IH #X #H
31   elim (lsubr_inv_abst2 … H) -H * #L2 [2: #V ] #HL21 #H destruct
32   /4 width=3 by cpg_delta, cpg_ell, cpg_ee/
33 | #c #I1 #G #L1 #T1 #U1 #i #_ #HTU1 #IH #X #H
34   elim (lsubr_fwd_bind2 … H) -H #I2 #L2 #HL21 #H destruct
35   /3 width=3 by cpg_lref/
36 |6,12: /4 width=1 by cpg_bind, cpg_beta, lsubr_bind/
37 |7,8,10,11: /3 width=1 by cpg_appl, cpg_cast, cpg_eps, cpg_ee/
38 |9,13: /4 width=3 by cpg_zeta, cpg_theta, lsubr_bind/
39 ]
40 qed-.