(* Note: this is the "big tree" theorem *)
(* Basic_2A1: uses: snv_fwd_fsb *)
lemma cnv_fwd_fsb (h) (a):
- â\88\80G,L,T. â¦\83G,Lâ¦\84 â\8a¢ T ![h,a] â\86\92 â\89¥[h] ð\9d\90\92â¦\83G,L,Tâ¦\84.
+ â\88\80G,L,T. â\9dªG,Lâ\9d« â\8a¢ T ![h,a] â\86\92 â\89¥[h] ð\9d\90\92â\9dªG,L,Tâ\9d«.
#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):
- â\88\80G,L,T. â¦\83G,Lâ¦\84 â\8a¢ T ![h,a] â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83Tâ¦\84.
+ â\88\80G,L,T. â\9dªG,Lâ\9d« â\8a¢ T ![h,a] â\86\92 â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªTâ\9d«.
#h #a #G #L #T #H
/3 width=2 by cnv_fwd_fsb, fsb_inv_csx/
qed-.
(* Inversion lemmas with proper parallel rst-computation for closures *******)
lemma cnv_fpbg_refl_false (h) (a):
- â\88\80G,L,T. â¦\83G,Lâ¦\84 â\8a¢ T ![h,a] â\86\92 â¦\83G,L,Tâ¦\84 >[h] â¦\83G,L,Tâ¦\84 → ⊥.
+ â\88\80G,L,T. â\9dªG,Lâ\9d« â\8a¢ T ![h,a] â\86\92 â\9dªG,L,Tâ\9d« >[h] â\9dªG,L,Tâ\9d« → ⊥.
/3 width=7 by cnv_fwd_fsb, fsb_fpbg_refl_false/ qed-.