(* Note: alternative definition of fsb *)
inductive fsba (h) (g): relation3 genv lenv term ≝
| fsba_intro: ∀G1,L1,T1. (
- â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 >â\8b\95[h, g] ⦃G2, L2, T2⦄ → fsba h g G2 L2 T2
+ â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 >â\89¡[h, g] ⦃G2, L2, T2⦄ → fsba h g G2 L2 T2
) → fsba h g G1 L1 T1.
interpretation
lemma fsba_ind_alt: ∀h,g. ∀R: relation3 …. (
∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⦥⦥[h,g] T1 → (
- â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 >â\8b\95[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2
+ â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 >â\89¡[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2
) → R G1 L1 T1
) →
∀G,L,T. ⦃G, L⦄ ⊢ ⦥⦥[h, g] T → R G L T.
lemma fsb_ind_fpbg: ∀h,g. ∀R:relation3 genv lenv term.
(∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⦥[h, g] T1 →
- (â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 >â\8b\95[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
+ (â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 >â\89¡[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
R G1 L1 T1
) →
∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⦥[h, g] T1 → R G1 L1 T1.