(* Note: alternative definition of fsb *)
inductive fsba (h) (o): relation3 genv lenv term ≝
| fsba_intro: ∀G1,L1,T1. (
- â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 >â\89¡[h, o] ⦃G2, L2, T2⦄ → fsba h o G2 L2 T2
+ â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 >â\89\9b[h, o] ⦃G2, L2, T2⦄ → fsba h o G2 L2 T2
) → fsba h o G1 L1 T1.
interpretation
lemma fsba_ind_alt: ∀h,o. ∀R: relation3 …. (
∀G1,L1,T1. ⦥⦥[h,o] ⦃G1, L1, T1⦄ → (
- â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 >â\89¡[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2
+ â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 >â\89\9b[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2
) → R G1 L1 T1
) →
∀G,L,T. ⦥⦥[h, o] ⦃G, L, T⦄ → R G L T.
lemma fsb_ind_fpbg: ∀h,o. ∀R:relation3 genv lenv term.
(∀G1,L1,T1. ⦥[h, o] ⦃G1, L1, T1⦄ →
- (â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 >â\89¡[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
+ (â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 >â\89\9b[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
R G1 L1 T1
) →
∀G1,L1,T1. ⦥[h, o] ⦃G1, L1, T1⦄ → R G1 L1 T1.