(* Note: this is the "big tree" theorem *)
(* Basic_2A1: uses: snv_fwd_fsb *)
lemma cnv_fwd_fsb (h) (a):
- ∀G,L,T. ❪G,L❫ ⊢ T ![h,a] → ≥[h] 𝐒❪G,L,T❫.
+ ∀G,L,T. ❪G,L❫ ⊢ T ![h,a] → ≥𝐒 ❪G,L,T❫.
#h #a #G #L #T #H elim (cnv_fwd_aaa … H) -H /2 width=2 by aaa_fsb/
qed-.
(* Forward lemmas with strongly rt-normalizing terms ************************)
lemma cnv_fwd_csx (h) (a):
- ∀G,L,T. ❪G,L❫ ⊢ T ![h,a] → ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T❫.
+ ∀G,L,T. ❪G,L❫ ⊢ T ![h,a] → ❪G,L❫ ⊢ ⬈*𝐒 T.
#h #a #G #L #T #H
-/3 width=2 by cnv_fwd_fsb, fsb_inv_csx/
+/3 width=3 by cnv_fwd_fsb, fsb_inv_csx/
qed-.
(* Inversion lemmas with proper parallel rst-computation for closures *******)
lemma cnv_fpbg_refl_false (h) (a):
- ∀G,L,T. ❪G,L❫ ⊢ T ![h,a] → ❪G,L,T❫ >[h] ❪G,L,T❫ → ⊥.
+ ∀G,L,T. ❪G,L❫ ⊢ T ![h,a] → ❪G,L,T❫ > ❪G,L,T❫ → ⊥.
/3 width=7 by cnv_fwd_fsb, fsb_fpbg_refl_false/ qed-.