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4 (* ||A|| A project by Andrea Asperti *)
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15 include "basic_2/dynamic/lsubv_cpms.ma".
17 (* LOCAL ENVIRONMENT REFINEMENT FOR NATIVE VALIDITY *************************)
19 (* Forward lemmas with native validity **************************************)
21 (* Basic_2A1: uses: lsubsv_snv_trans *)
22 lemma lsubv_cnv_trans (h) (a) (G):
23 ∀L2,T. ❨G,L2❩ ⊢ T ![h,a] →
24 ∀L1. G ⊢ L1 ⫃![h,a] L2 → ❨G,L1❩ ⊢ T ![h,a].
25 #h #a #G #L2 #T #H elim H -G -L2 -T //
26 [ #I #G #K2 #V #HV #IH #L1 #H
27 elim (lsubv_inv_bind_dx … H) -H * /3 width=1 by cnv_zero/
28 | #I #G #K2 #i #_ #IH #L1 #H
29 elim (lsubv_inv_bind_dx … H) -H * /3 width=1 by cnv_lref/
30 | #p #I #G #L2 #V #T #_ #_ #IHV #IHT #L1 #HL12
31 /4 width=1 by cnv_bind, lsubv_bind/
32 | #n #p #G #L2 #V #W #T #U #Ha #_ #_ #HVW #HTU #IHV #IHT #L1 #HL
33 /4 width=10 by lsubv_cpms_trans, cnv_appl/
34 | #G #L2 #U #T #U0 #_ #_ #HU0 #HTU0 #IHU #IHT #L1 #HL12
35 /4 width=6 by lsubv_cpms_trans, cnv_cast/