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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 *)
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11 (* v GNU General Public License Version 2 *)
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15 include "basic_2/dynamic/cnv_aaa.ma".
16 include "basic_2/dynamic/lsubv.ma".
18 (* LOCAL ENVIRONMENT REFINEMENT FOR NATIVE VALIDITY *************************)
20 (* Forward lemmas with lenv refinement for atomic arity assignment **********)
22 (* Basic_2A1: uses: lsubsv_fwd_lsuba *)
23 lemma lsubsv_fwd_lsuba (a) (h) (G): ∀L1,L2. G ⊢ L1 ⫃![a,h] L2 → G ⊢ L1 ⫃⁝ L2.
24 #a #h #G #L1 #L2 #H elim H -L1 -L2 /2 width=1 by lsuba_bind/
25 #L1 #L2 #W #V #H #_ #IH
26 elim (cnv_inv_cast … H) -H #W0 #HW #HV #HW0 #HVW0
27 elim (cnv_fwd_aaa … HW) -HW #B #HW
28 elim (cnv_fwd_aaa … HV) -HV #A #HV
29 lapply (cpms_aaa_conf … HW … HW0) -HW0 #H
30 lapply (cpms_aaa_conf … HV … HVW0) -HVW0 #HW0
31 lapply (aaa_mono … H … HW0) -W0 #H destruct
32 /4 width=5 by lsuba_aaa_conf, lsuba_beta, aaa_cast/