include "basic_2/rt_computation/cpxs_cpxs.ma".
include "basic_2/rt_computation/csx_csx.ma".
-(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS ************)
+(* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
-(* Properties with uncounted context-sensitive rt-computation for terms *****)
+(* Properties with unbound context-sensitive rt-computation for terms *******)
(* Basic_1: was just: sn3_intro *)
lemma csx_intro_cpxs: ∀h,o,G,L,T1.
/2 width=3 by csx_cpx_trans/
qed-.
-(* Eliminators with uncounted context-sensitive rt-computation for terms ****)
+(* Eliminators with unbound context-sensitive rt-computation for terms ******)
lemma csx_ind_cpxs_tdeq: ∀h,o,G,L. ∀R:predicate term.
(∀T1. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ →
elim (tdeq_dec h o T1 T0) #H
[ lapply (tdeq_tdneq_trans … H … HnTV0) -H -HnTV0 #Hn10
lapply (cpxs_trans … HT10 … HTV0) -T0 #H10
- elim (cpxs_tdneq_inv_step_sn … H10 … Hn10) -H10 -Hn10
+ elim (cpxs_tdneq_fwd_step_sn … H10 … Hn10) -H10 -Hn10
/3 width=8 by tdeq_trans/
-| elim (cpxs_tdneq_inv_step_sn … HT10 … H) -HT10 -H #T #V #HT1 #HnT1 #HTV #HVT0
+| elim (cpxs_tdneq_fwd_step_sn … HT10 … H) -HT10 -H #T #V #HT1 #HnT1 #HTV #HVT0
elim (tdeq_cpxs_trans … HVT0 … HTV0) -T0
/3 width=8 by cpxs_trans, tdeq_trans/
]