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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/dynamic/snv_aaa.ma".
16 include "basic_2/dynamic/lsubsv.ma".
18 (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
20 (* Forward lemmas on lenv refinement for atomic arity assignment ************)
22 lemma lsubsv_fwd_lsuba: ∀h,g,G,L1,L2. G ⊢ L1 ¡⊑[h, g] L2 → G ⊢ L1 ⁝⊑ L2.
23 #h #g #G #L1 #L2 #H elim H -L1 -L2 // /2 width=1/
24 #L1 #L2 #W #V #l #H1W #HV #HVW #H2W #H1l #_ #_ #IHL12
25 lapply (snv_scast … HV H1W HVW H1l) -HV -H1W -HVW -H1l #HV
26 elim (snv_fwd_aaa … HV) -HV #A #HV
27 elim (snv_fwd_aaa … H2W) -H2W #B #HW
28 elim (aaa_inv_cast … HV) #HWA #_
29 lapply (lsuba_aaa_trans … HW … IHL12) #HWB
30 lapply (aaa_mono … HWB … HWA) -HWB -HWA #H destruct /2 width=3/