(**************************************************************************)
include "basic_2/computation/csn_aaa.ma".
-include "basic_2/computation/dxprs_aaa.ma".
+include "basic_2/computation/cpds_aaa.ma".
include "basic_2/equivalence/cpcs_aaa.ma".
include "basic_2/dynamic/snv.ma".
(* Forward lemmas on atomic arity assignment for terms **********************)
-lemma snv_fwd_aaa: ∀h,g,L,T. ⦃h, L⦄ ⊩ T :[g] → ∃A. L ⊢ T ⁝ A.
+lemma snv_fwd_aaa: ∀h,g,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] → ∃A. ⦃G, L⦄ ⊢ T ⁝ A.
#h #g #L #T #H elim H -L -T
[ /2 width=2/
| #I #L #K #V #i #HLK #_ * /3 width=6/
| #a * #L #V #T #_ #_ * #B #HV * #A #HA /3 width=2/
| #a #L #V #W #W0 #T #U #l #_ #_ #HVW #HW0 #HTU * #B #HV * #X #HT
- lapply (dxprs_aaa h g … HV W0 ?) [ -HTU /3 width=4/ ] -W #HW0 (**) (* auto fail without -HTU *)
- lapply (dxprs_aaa … HT … HTU) -HTU #H
+ lapply (cpds_aaa h g … HV W0 ?) [ -HTU /3 width=4/ ] -W #HW0 (**) (* auto fail without -HTU *)
+ lapply (cpds_aaa … HT … HTU) -HTU #H
elim (aaa_inv_abst … H) -H #B0 #A #H1 #HU #H2 destruct
lapply (aaa_mono … H1 … HW0) -W0 #H destruct /3 width=4/
| #L #W #T #U #l #_ #_ #HTU #HUW * #B #HW * #A #HT
]
qed-.
-lemma snv_fwd_csn: ∀h,g,L,T. ⦃h, L⦄ ⊩ T :[g] → L ⊢ ⬊* T.
+lemma snv_fwd_csn: ∀h,g,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] → ⦃G, L⦄ ⊢ ⬊*[h, g] T.
#h #g #L #T #H elim (snv_fwd_aaa … H) -H /2 width=2/
qed-.