1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "basic_2/computation/csn_aaa.ma".
16 include "basic_2/computation/xprs_aaa.ma".
17 include "basic_2/computation/xprs_cprs.ma".
18 include "basic_2/equivalence/lcpcs_aaa.ma".
19 include "basic_2/dynamic/snv.ma".
21 (* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************)
23 (* Properties on atomic arity assignment for terms **************************)
25 lemma snv_aaa: ∀h,g,L,T. ⦃h, L⦄ ⊩ T :[g] → ∃A. L ⊢ T ⁝ A.
26 #h #g #L #T #H elim H -L -T
28 | #I #L #K #V #i #HLK #_ * /3 width=6/
29 | #a * #L #V #T #_ #_ * #B #HV * #A #HA /3 width=2/
30 | #a #L #V #W #W0 #T #U #l #_ #_ #HVW #HW0 #HTU * #B #HV * #X #HT
31 lapply (xprs_aaa h g … HV W0 ?)
32 [ /3 width=3 by xprs_strap2, ssta_xpr, cprs_xprs/ ] -W #HW0 (**) (* NTypeChecker failure without trace *)
33 lapply (xprs_aaa … HT … HTU) -HTU #H
34 elim (aaa_inv_abst … H) -H #B0 #A #H1 #HU #H2 destruct
35 lapply (aaa_mono … H1 … HW0) -W0 #H destruct /3 width=4/
36 | #L #W #T #U #l #_ #_ #HTU #HUW * #B #HW * #A #HT
37 lapply (aaa_cpcs_mono … HUW A … HW) -HUW /2 width=7/ -HTU #H destruct /3 width=3/
41 lemma snv_csn: ∀h,g,L,T. ⦃h, L⦄ ⊩ T :[g] → L ⊢ ⬊* T.
42 #h #g #L #T #H elim (snv_aaa … H) -H /2 width=2/