(* *)
(**************************************************************************)
-include "basic_2/static/lfdeq_lfdeq.ma".
include "basic_2/rt_transition/lfpx_lfdeq.ma".
include "basic_2/rt_computation/lfpxs_fqup.ma".
(* Basic_2A1: was: lleq_lpxs_trans *)
lemma lfdeq_lfpxs_trans: ∀h,o,G,L2,K2,T. ⦃G, L2⦄ ⊢ ⬈*[h, T] K2 →
- â\88\80L1. L1 â\89¡[h, o, T] L2 →
- â\88\83â\88\83K1. â¦\83G, L1â¦\84 â\8a¢ â¬\88*[h, T] K1 & K1 â\89¡[h, o, T] K2.
+ â\88\80L1. L1 â\89\9b[h, o, T] L2 →
+ â\88\83â\88\83K1. â¦\83G, L1â¦\84 â\8a¢ â¬\88*[h, T] K1 & K1 â\89\9b[h, o, T] K2.
#h #o #G #L2 #K2 #T #H @(lfpxs_ind_sn … H) -K2 /2 width=3 by ex2_intro/
#K #K2 #_ #HK2 #IH #L1 #HT elim (IH … HT) -L2
#L #HL1 #HT elim (lfdeq_lfpx_trans … HK2 … HT) -K
qed-.
(* Basic_2A1: was: lpxs_nlleq_inv_step_sn *)
-lemma lfpxs_lfdneq_inv_step_sn: â\88\80h,o,G,L1,L2,T. â¦\83G, L1â¦\84 â\8a¢ â¬\88*[h, T] L2 â\86\92 (L1 â\89¡[h, o, T] L2 → ⊥) →
- â\88\83â\88\83L,L0. â¦\83G, L1â¦\84 â\8a¢ â¬\88[h, T] L & L1 â\89¡[h, o, T] L â\86\92 â\8a¥ & â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h, T] L0 & L0 â\89¡[h, o, T] L2.
+lemma lfpxs_lfdneq_inv_step_sn: â\88\80h,o,G,L1,L2,T. â¦\83G, L1â¦\84 â\8a¢ â¬\88*[h, T] L2 â\86\92 (L1 â\89\9b[h, o, T] L2 → ⊥) →
+ â\88\83â\88\83L,L0. â¦\83G, L1â¦\84 â\8a¢ â¬\88[h, T] L & L1 â\89\9b[h, o, T] L â\86\92 â\8a¥ & â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h, T] L0 & L0 â\89\9b[h, o, T] L2.
#h #o #G #L1 #L2 #T #H @(lfpxs_ind_dx … H) -L1
[ #H elim H -H //
| #L1 #L #H1 #H2 #IH2 #H12 elim (lfdeq_dec h o L1 L T) #H