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15 include "basic_2/dynamic/cnv_fsb.ma".
16 include "basic_2/dynamic/nta.ma".
18 (* NATIVE TYPE ASSIGNMENT FOR TERMS *****************************************)
20 (* Forward lemmas with strongly rst-normalizing closures ********************)
22 (* Note: this is an extended stong normalization property *)
23 (* Note: this might use fsb_inv_cast (still to be proved) *)
24 (* Basic_1: uses: ty3_sn3 *)
25 (* Basic_2A1: uses: nta_fwd_csn *)
26 theorem nta_fwd_fsb (a) (h) (o) (G) (L):
27 ∀T,U. ⦃G,L⦄ ⊢ T :[a,h] U →
28 ∧∧ ≥[h,o] 𝐒⦃G,L,T⦄ & ≥[h,o] 𝐒⦃G,L,U⦄.
29 #a #h #o #G #L #T #U #H
30 elim (cnv_inv_cast … H) #X #HU #HT #_ #_ -X
31 /3 width=2 by cnv_fwd_fsb, conj/