constructor
L : Language
T : Theory L
A : FinSubtheory T → Type u
s : (i : FinSubtheory T) → Structure L (A i)
⊢ Satisfiable T ↔ ∀ (i : FinSubtheory T), Satisfiable ↑↑i
case mp
L : Language
T : Theory L
A : FinSubtheory T → Type u
s : (i : FinSubtheory T) → Structure L (A i)
⊢ Satisfiable T → ∀ (i : FinSubtheory T), Satisfiable ↑↑i

case mpr
L : Language
T : Theory L
A : FinSubtheory T → Type u
s : (i : FinSubtheory T) → Structure L (A i)
⊢ (∀ (i : FinSubtheory T), Satisfiable ↑↑i) → Satisfiable T