inductive fsb (h): relation3 genv lenv term ≝
| fsb_intro: ∀G1,L1,T1. (
- â\88\80G2,L2,T2. â¦\83G1,L1,T1â¦\84 â\89»[h] â¦\83G2,L2,T2â¦\84 → fsb h G2 L2 T2
+ â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« â\89»[h] â\9dªG2,L2,T2â\9d« → fsb h G2 L2 T2
) → fsb h G1 L1 T1
.
(* Note: eliminator with shorter ground hypothesis *)
(* Note: to be named fsb_ind when fsb becomes a definition like csx, lfsx ***)
lemma fsb_ind_alt: ∀h. ∀Q: relation3 …. (
- â\88\80G1,L1,T1. â\89¥[h] ð\9d\90\92â¦\83G1,L1,T1â¦\84 → (
- â\88\80G2,L2,T2. â¦\83G1,L1,T1â¦\84 â\89»[h] â¦\83G2,L2,T2â¦\84 → Q G2 L2 T2
+ â\88\80G1,L1,T1. â\89¥[h] ð\9d\90\92â\9dªG1,L1,T1â\9d« → (
+ â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« â\89»[h] â\9dªG2,L2,T2â\9d« → Q G2 L2 T2
) → Q G1 L1 T1
) →
- â\88\80G,L,T. â\89¥[h] ð\9d\90\92â¦\83G,L,Tâ¦\84 → Q G L T.
+ â\88\80G,L,T. â\89¥[h] ð\9d\90\92â\9dªG,L,Tâ\9d« → Q G L T.
#h #Q #IH #G #L #T #H elim H -G -L -T
/4 width=1 by fsb_intro/
qed-.