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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 (h) (a) (G) (L):
27 ∀T,U. ❨G,L❩ ⊢ T :[h,a] U →
28 ∧∧ ≥𝐒 ❨G,L,T❩ & ≥𝐒 ❨G,L,U❩.
30 elim (cnv_inv_cast … H) #X #HU #HT #_ #_ -X
31 /3 width=3 by cnv_fwd_fsb, conj/