include "basic_2/rt_transition/cpx_lfdeq.ma".
include "basic_2/rt_computation/cpxs_tdeq.ma".
-(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS ************)
+(* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
(* Properties with degree-based equivalence for local environments **********)
(* Basic_2A1: was just: lleq_cpxs_trans *)
lemma lfdeq_cpxs_trans: ∀h,o,G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈*[h] T1 →
- â\88\80L2. L2 â\89¡[h, o, T0] L0 →
- â\88\83â\88\83T. â¦\83G, L2â¦\84 â\8a¢ T0 â¬\88*[h] T & T â\89¡[h, o] T1.
+ â\88\80L2. L2 â\89\9b[h, o, T0] L0 →
+ â\88\83â\88\83T. â¦\83G, L2â¦\84 â\8a¢ T0 â¬\88*[h] T & T â\89\9b[h, o] T1.
#h #o #G #L0 #T0 #T1 #H @(cpxs_ind_dx … H) -T0 /2 width=3 by ex2_intro/
#T0 #T #HT0 #_ #IH #L2 #HL2
elim (lfdeq_cpx_trans … HL2 … HT0) #U1 #H1 #H2
qed-.
(* Basic_2A1: was just: cpxs_lleq_conf *)
-lemma cpxs_lfdeq_trans: ∀h,o,G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈*[h] T1 →
- ∀L2. L0 ≡[h, o, T0] L2 →
- ∃∃T. ⦃G, L2⦄ ⊢ T0 ⬈*[h] T & T ≡[h, o] T1.
+lemma cpxs_lfdeq_conf: ∀h,o,G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈*[h] T1 →
+ ∀L2. L0 ≛[h, o, T0] L2 →
+ ∃∃T. ⦃G, L2⦄ ⊢ T0 ⬈*[h] T & T ≛[h, o] T1.
/3 width=3 by lfdeq_cpxs_trans, lfdeq_sym/ qed-.
(* Basic_2A1: was just: cpxs_lleq_conf_dx *)
lemma cpxs_lfdeq_conf_dx: ∀h,o,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ⬈*[h] T2 →
- â\88\80L1. L1 â\89¡[h, o, T1] L2 â\86\92 L1 â\89¡[h, o, T2] L2.
+ â\88\80L1. L1 â\89\9b[h, o, T1] L2 â\86\92 L1 â\89\9b[h, o, T2] L2.
#h #o #G #L2 #T1 #T2 #H @(cpxs_ind … H) -T2 /3 width=6 by cpx_lfdeq_conf_dx/
qed-.
(* Basic_2A1: was just: lleq_conf_sn *)
lemma cpxs_lfdeq_conf_sn: ∀h,o,G,L1,T1,T2. ⦃G, L1⦄ ⊢ T1 ⬈*[h] T2 →
- â\88\80L2. L1 â\89¡[h, o, T1] L2 â\86\92 L1 â\89¡[h, o, T2] L2.
+ â\88\80L2. L1 â\89\9b[h, o, T1] L2 â\86\92 L1 â\89\9b[h, o, T2] L2.
/4 width=6 by cpxs_lfdeq_conf_dx, lfdeq_sym/ qed-.