matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_fsb.ma

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  14
  15 include "basic_2/rt_computation/fsb_aaa.ma".
  16 include "basic_2/dynamic/cnv_aaa.ma".
  17
  18 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
  19
  20 (* Forward lemmas with strongly rst-normalizing closures ********************)
  21
  22 (* Note: this is the "big tree" theorem *)
  23 (* Basic_2A1: uses: snv_fwd_fsb *)
  24 lemma cnv_fwd_fsb (h) (a):
  25       ∀G,L,T. ❪G,L❫ ⊢ T ![h,a] → ≥[h] 𝐒❪G,L,T❫.
  26 #h #a #G #L #T #H elim (cnv_fwd_aaa … H) -H /2 width=2 by aaa_fsb/
  27 qed-.
  28
  29 (* Forward lemmas with strongly rt-normalizing terms ************************)
  30
  31 lemma cnv_fwd_csx (h) (a):
  32       ∀G,L,T. ❪G,L❫ ⊢ T ![h,a] → ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T❫.
  33 #h #a #G #L #T #H
  34 /3 width=2 by cnv_fwd_fsb, fsb_inv_csx/
  35 qed-.
  36
  37 (* Inversion lemmas with proper parallel rst-computation for closures *******)
  38
  39 lemma cnv_fpbg_refl_false (h) (a):
  40       ∀G,L,T. ❪G,L❫ ⊢ T ![h,a] → ❪G,L,T❫ >[h] ❪G,L,T❫ → ⊥.
  41 /3 width=7 by cnv_fwd_fsb, fsb_fpbg_refl_false/ qed-.