(* STRONGLY NORMALIZING TERM VECTORS FOR UNBOUND PARALLEL RT-TRANSITION *****)
-include "basic_2/rt_computation/cpxs_theq_vector.ma".
-include "basic_2/rt_computation/csx_simple_theq.ma".
+include "basic_2/rt_computation/cpxs_toeq_vector.ma".
+include "basic_2/rt_computation/csx_simple_toeq.ma".
include "basic_2/rt_computation/csx_cnx.ma".
include "basic_2/rt_computation/csx_cpxs.ma".
include "basic_2/rt_computation/csx_vector.ma".
(* Properties with normal terms for unbound parallel rt-transition **********)
(* Basic_1: was just: sn3_appls_lref *)
-lemma csx_applv_cnx: ∀h,G,L,T. 𝐒⦃T⦄ → ⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃T⦄ →
- ∀Vs. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃Vs⦄ → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⒶVs.T⦄.
+lemma csx_applv_cnx (h) (G) (L):
+ ∀T. 𝐒⦃T⦄ → ⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃T⦄ →
+ ∀Vs. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃Vs⦄ → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⒶVs.T⦄.
#h #G #L #T #H1T #H2T #Vs elim Vs -Vs
[ #_ normalize in ⊢ (????%); /2 width=1 by cnx_csx/
| #V #Vs #IHV #H
elim (csxv_inv_cons … H) -H #HV #HVs
- @csx_appl_simple_theq /2 width=1 by applv_simple/ -IHV -HV -HVs
+ @csx_appl_simple_toeq /2 width=1 by applv_simple/ -IHV -HV -HVs
#X #H #H0
lapply (cpxs_fwd_cnx_vector … H) -H // -H1T -H2T #H
elim (H0) -H0 //
(* Advanced properties ******************************************************)
(* Note: strong normalization does not depend on this any more *)
-lemma csx_applv_sort: ∀h,G,L,s,Vs. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃Vs⦄ → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⒶVs.⋆s⦄.
+lemma csx_applv_sort (h) (G) (L):
+ ∀s,Vs. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃Vs⦄ → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⒶVs.⋆s⦄.
/3 width=6 by csx_applv_cnx, cnx_sort, simple_atom/ qed.