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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "basic_2/rt_computation/cpms_aaa.ma".
16 include "basic_2/dynamic/cnv.ma".
18 (* CONTEXT_SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
20 (* Forward lemmas on atomic arity assignment for terms **********************)
22 (* Basic_2A1: uses: snv_fwd_aaa *)
23 lemma cnv_fwd_aaa (a) (h): ∀G,L,T. ⦃G, L⦄ ⊢ T ![a, h] → ∃A. ⦃G, L⦄ ⊢ T ⁝ A.
24 #a #h #G #L #T #H elim H -G -L -T
25 [ /2 width=2 by aaa_sort, ex_intro/
26 | #I #G #L #V #_ * /3 width=2 by aaa_zero, ex_intro/
27 | #I #G #L #K #_ * /3 width=2 by aaa_lref, ex_intro/
28 | #p * #G #L #V #T #_ #_ * #B #HV * #A #HA
29 /3 width=2 by aaa_abbr, aaa_abst, ex_intro/
30 | #n #p #G #L #V #W #T0 #U0 #_ #_ #_ #HVW #HTU0 * #B #HV * #X #HT
31 lapply (cpms_aaa_conf … HV … HVW) -HVW #H1W
32 lapply (cpms_aaa_conf … HT … HTU0) -HTU0 #H
33 elim (aaa_inv_abst … H) -H #B0 #A #H2W #HU #H destruct
34 lapply (aaa_mono … H2W … H1W) -W #H destruct
35 /3 width=4 by aaa_appl, ex_intro/
36 | #G #L #U #T #U0 #_ #_ #HU0 #HTU0 * #B #HU * #A #HT
37 lapply (cpms_aaa_conf … HU … HU0) -HU0 #HU0
38 lapply (cpms_aaa_conf … HT … HTU0) -HTU0 #H
39 lapply (aaa_mono … H … HU0) -U0 #H destruct
40 /3 width=3 by aaa_cast, ex_intro/