include "basic_2/notation/relations/predtystar_5.ma".
include "basic_2/rt_transition/cpx.ma".
-(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS ************)
+(* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
definition cpxs: sh → relation4 genv lenv term term ≝
- λh,G. LTC … (cpx h G).
+ λh,G. CTC … (cpx h G).
-interpretation "uncounted context-sensitive parallel rt-computation (term)"
+interpretation "unbound context-sensitive parallel rt-computation (term)"
'PRedTyStar h G L T1 T2 = (cpxs h G L T1 T2).
(* Basic eliminators ********************************************************)
/3 width=3 by cpxs_strap1, cpx_pair_sn/
qed.
-lemma cpxs_zeta: â\88\80h,G,L,V,T1,T,T2. â¬\86*[1] T2 â\89¡ T →
+lemma cpxs_zeta: â\88\80h,G,L,V,T1,T,T2. â¬\86*[1] T2 â\89\98 T →
⦃G, L.ⓓV⦄ ⊢ T1 ⬈*[h] T → ⦃G, L⦄ ⊢ +ⓓV.T1 ⬈*[h] T2.
#h #G #L #V #T1 #T #T2 #HT2 #H @(cpxs_ind_dx … H) -T1
/3 width=3 by cpxs_strap2, cpx_cpxs, cpx_bind, cpx_zeta/
qed.
lemma cpxs_theta_dx: ∀h,p,G,L,V1,V,V2,W1,W2,T1,T2.
- â¦\83G, Lâ¦\84 â\8a¢ V1 â¬\88[h] V â\86\92 â¬\86*[1] V â\89¡ V2 → ⦃G, L.ⓓW1⦄ ⊢ T1 ⬈*[h] T2 →
+ â¦\83G, Lâ¦\84 â\8a¢ V1 â¬\88[h] V â\86\92 â¬\86*[1] V â\89\98 V2 → ⦃G, L.ⓓW1⦄ ⊢ T1 ⬈*[h] T2 →
⦃G, L⦄ ⊢ W1 ⬈[h] W2 → ⦃G, L⦄ ⊢ ⓐV1.ⓓ{p}W1.T1 ⬈*[h] ⓓ{p}W2.ⓐV2.T2.
#h #p #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 #HV1 #HV2 * -T2
/4 width=9 by cpx_cpxs, cpxs_strap1, cpxs_bind_dx, cpxs_flat_dx, cpx_theta/
#h #G #L #X2 #s #H @(cpxs_ind … H) -X2 /2 width=2 by ex_intro/
#X #X2 #_ #HX2 * #n #H destruct
elim (cpx_inv_sort1 … HX2) -HX2 #H destruct /2 width=2 by ex_intro/
-@(ex_intro â\80¦ (⫯n)) >iter_S //
+@(ex_intro â\80¦ (â\86\91n)) >iter_S //
qed-.
lemma cpxs_inv_cast1: ∀h,G,L,W1,T1,U2. ⦃G, L⦄ ⊢ ⓝW1.T1 ⬈*[h] U2 →
lapply (cpxs_strap1 … HW1 … HW2) -W
lapply (cpxs_strap1 … HT1 … HT2) -T /3 width=5 by or3_intro0, ex3_2_intro/
qed-.
-
-(* Basic_2A1: removed theorems 1: cpxs_neq_inv_step_sn *)