include "basic_2/multiple/lleq_drop.ma".
include "basic_2/reduction/cpx_llpx_sn.ma".
-(* CONTEXT-SENSITIVE EXTENDED PARALLEL REDUCTION FOR TERMS ******************)
+(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS *************)
(* Properties on lazy equivalence for local environments ********************)
-lemma lleq_cpx_trans: â\88\80h,o,G,L2,T1,T2. â¦\83G, L2â¦\84 â\8a¢ T1 â\9e¡[h, o] T2 →
- â\88\80L1. L1 â\89¡[T1, 0] L2 â\86\92 â¦\83G, L1â¦\84 â\8a¢ T1 â\9e¡[h, o] T2.
+lemma lleq_cpx_trans: â\88\80h,o,G,L2,T1,T2. â¦\83G, L2â¦\84 â\8a¢ T1 â¬\88[h, o] T2 →
+ â\88\80L1. L1 â\89¡[T1, 0] L2 â\86\92 â¦\83G, L1â¦\84 â\8a¢ T1 â¬\88[h, o] T2.
#h #o #G #L2 #T1 #T2 #H elim H -G -L2 -T1 -T2 /2 width=2 by cpx_st/
[ #I #G #L2 #K2 #V1 #V2 #W2 #i #HLK2 #_ #HVW2 #IHV12 #L1 #H elim (lleq_fwd_lref_dx … H … HLK2) -L2
[ #H elim (ylt_yle_false … H) //
]
qed-.
-lemma cpx_lleq_conf: â\88\80h,o,G,L2,T1,T2. â¦\83G, L2â¦\84 â\8a¢ T1 â\9e¡[h, o] T2 →
- â\88\80L1. L2 â\89¡[T1, 0] L1 â\86\92 â¦\83G, L1â¦\84 â\8a¢ T1 â\9e¡[h, o] T2.
+lemma cpx_lleq_conf: â\88\80h,o,G,L2,T1,T2. â¦\83G, L2â¦\84 â\8a¢ T1 â¬\88[h, o] T2 →
+ â\88\80L1. L2 â\89¡[T1, 0] L1 â\86\92 â¦\83G, L1â¦\84 â\8a¢ T1 â¬\88[h, o] T2.
/3 width=3 by lleq_cpx_trans, lleq_sym/ qed-.
lemma cpx_lleq_conf_sn: ∀h,o,G. b_c_confluent1 … (cpx h o G) (lleq 0).
/3 width=6 by cpx_llpx_sn_conf, lift_mono, ex2_intro/ qed-.
-lemma cpx_lleq_conf_dx: â\88\80h,o,G,L2,T1,T2. â¦\83G, L2â¦\84 â\8a¢ T1 â\9e¡[h, o] T2 →
+lemma cpx_lleq_conf_dx: â\88\80h,o,G,L2,T1,T2. â¦\83G, L2â¦\84 â\8a¢ T1 â¬\88[h, o] T2 →
∀L1. L1 ≡[T1, 0] L2 → L1 ≡[T2, 0] L2.
/4 width=6 by cpx_lleq_conf_sn, lleq_sym/ qed-.