(* *)
(**************************************************************************)
-include "basic_2/syntax/tdeq_tdeq.ma".
+include "basic_2/rt_transition/lfpx_lfdeq.ma".
include "basic_2/rt_computation/cpxs.ma".
-include "basic_2/rt_transition/cpx_lfdeq.ma".
-include "basic_2/rt_transition/lfpx_fqup.ma".
(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS ************)
-lemma tdeq_cpxs_trans: ∀h,o,U1,T1. U1 ≡[h, o] T1 → ∀G,L,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 →
- ∃∃U2. ⦃G, L⦄ ⊢ U1 ⬈*[h] U2 & U2 ≡[h, o] T2.
+(* Properties with degree-based equivalence for terms ***********************)
+
+lemma tdeq_cpxs_trans: ∀h,o,U1,T1. U1 ≛[h, o] T1 → ∀G,L,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 →
+ ∃∃U2. ⦃G, L⦄ ⊢ U1 ⬈*[h] U2 & U2 ≛[h, o] T2.
#h #o #U1 #T1 #HUT1 #G #L #T2 #HT12 @(cpxs_ind … HT12) -T2 /2 width=3 by ex2_intro/
#T #T2 #_ #HT2 * #U #HU1 #HUT elim (tdeq_cpx_trans … HUT … HT2) -T -T1
/3 width=3 by ex2_intro, cpxs_strap1/
qed-.
(* Note: this requires tdeq to be symmetric *)
-lemma cpxs_tdneq_inv_step_sn: â\88\80h,o,G,L,T1,T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88*[h] T2 â\86\92 (T1 â\89¡[h, o] T2 → ⊥) →
- â\88\83â\88\83T,T0. â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88[h] T & T1 â\89¡[h, o] T â\86\92 â\8a¥ & â¦\83G, Lâ¦\84 â\8a¢ T â¬\88*[h] T0 & T0 â\89¡[h, o] T2.
+lemma cpxs_tdneq_inv_step_sn: â\88\80h,o,G,L,T1,T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88*[h] T2 â\86\92 (T1 â\89\9b[h, o] T2 → ⊥) →
+ â\88\83â\88\83T,T0. â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88[h] T & T1 â\89\9b[h, o] T â\86\92 â\8a¥ & â¦\83G, Lâ¦\84 â\8a¢ T â¬\88*[h] T0 & T0 â\89\9b[h, o] T2.
#h #o #G #L #T1 #T2 #H @(cpxs_ind_dx … H) -T1
[ #H elim H -H //
| #T1 #T #H1 #H2 #IH #Hn12 elim (tdeq_dec h o T1 T) #H destruct
]
]
qed-.
-
-(* Basic_2A1: removed theorems 1: cpxs_neq_inv_step_sn *)