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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 *)
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15 include "basic_2/static/ssta.ma".
16 include "basic_2/static/aaa_lift.ma".
17 include "basic_2/static/aaa_da.ma".
19 (* ATONIC ARITY ASSIGNMENT FOR TERMS ****************************************)
21 (* Properties on stratified static type assignment for terms ****************)
23 lemma aaa_ssta_conf: ∀h,g,G,L. Conf3 … (aaa G L) (ssta h g G L).
24 #h #g #G #L #T #A #H elim H -G -L -T -A
26 lapply (ssta_inv_sort1 … H) -H #H destruct //
27 | #I #G #L #K #V #B #i #HLK #HV #IHV #U #H
28 elim (ssta_inv_lref1 … H) -H * #K0 #V0 #W0 #HLK0 #HVW0 #HU
29 lapply (ldrop_mono … HLK0 … HLK) -HLK0 #H0 destruct
30 lapply (ldrop_fwd_drop2 … HLK) -HLK #HLK
31 @(aaa_lift … HLK … HU) -HU -L // -HV /2 width=2/
32 | #a #G #L #V #T #B #A #HV #_ #_ #IHT #X #H
33 elim (ssta_inv_bind1 … H) -H #U #HTU #H destruct /3 width=2/
34 | #a #G #L #V #T #B #A #HV #_ #_ #IHT #X #H
35 elim (ssta_inv_bind1 … H) -H #U #HTU #H destruct /3 width=2/
36 | #G #L #V #T #B #A #HV #_ #_ #IHT #X #H
37 elim (ssta_inv_appl1 … H) -H #U #HTU #H destruct /3 width=3/
38 | #G #L #V #T #A #_ #_ #IHV #IHT #X #H
39 lapply (ssta_inv_cast1 … H) -H /2 width=2/
43 (* Forward lemmas on stratified static type assignment for terms ************)
45 lemma aaa_fwd_ssta: ∀h,g,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ∃U. ⦃G, L⦄ ⊢ T •[h, g] U.
46 #h #g #G #L #T #A #H elim (aaa_fwd_da … H) -H /2 width=3 by da_ssta/