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15 include "basic_2/rt_computation/fsb_aaa.ma".
16 include "basic_2/dynamic/cnv_aaa.ma".
18 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
20 (* Forward lemmas with strongly rst-normalizing closures ********************)
22 (* Basic_2A1: uses: snv_fwd_fsb *)
23 lemma cnv_fwd_fsb (a) (h) (o): ∀G,L,T. ⦃G, L⦄ ⊢ T ![a, h] → ≥[h, o] 𝐒⦃G, L, T⦄.
24 #a #h #o #G #L #T #H elim (cnv_fwd_aaa … H) -H /2 width=2 by aaa_fsb/
27 (* Inversion lemmas with proper parallel rst-computation for closures *******)
29 lemma cnv_fpbg_refl_false (a) (h) (o) (G) (L) (T):
30 ⦃G, L⦄ ⊢ T ![a,h] → ⦃G, L, T⦄ >[h,o] ⦃G, L, T⦄ → ⊥.
31 /3 width=7 by cnv_fwd_fsb, fsb_fpbg_refl_false/ qed-.