lemma csx_ind (G) (L) (Q:predicate …):
(∀T1. ❪G,L❫ ⊢ ⬈*𝐒 T1 →
- (â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\88 T2 â\86\92 (T1 â\89\9b T2 → ⊥) → Q T2) →
+ (â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\88 T2 â\86\92 (T1 â\89\85 T2 → ⊥) → Q T2) →
Q T1
) →
∀T. ❪G,L❫ ⊢ ⬈*𝐒 T → Q T.
(* Basic_1: was just: sn3_pr2_intro *)
lemma csx_intro (G) (L):
- â\88\80T1. (â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\88 T2 â\86\92 (T1 â\89\9b T2 → ⊥) → ❪G,L❫ ⊢ ⬈*𝐒 T2) →
+ â\88\80T1. (â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\88 T2 â\86\92 (T1 â\89\85 T2 → ⊥) → ❪G,L❫ ⊢ ⬈*𝐒 T2) →
❪G,L❫ ⊢ ⬈*𝐒 T1.
/4 width=1 by SN_intro/ qed.