let u' : Finset (Sentence (languageFinset u)) := Finset.imageOfFinset u (fun _ hσ ↦ toSubLanguageFinsetSelf hσ)
case intro
L : Language
T : Theory L
σ : Sentence L
h : T ⊨ σ
this✝¹ : (α : Type u) → DecidableEq α := Classical.typeDecidableEq
u : Finset (Sentence L)
ssu : ↑u ⊆ insert (~σ) T
hu : ¬Satisfiable ↑u
this✝ : (k : ℕ) → Encodable ((languageFinset u).Func k)
this : (k : ℕ) → Encodable ((languageFinset u).Rel k)
⊢ T ⊢! σ
case intro
L : Language
T : Theory L
σ : Sentence L
h : T ⊨ σ
this✝¹ : (α : Type u) → DecidableEq α := Classical.typeDecidableEq
u : Finset (Sentence L)
ssu : ↑u ⊆ insert (~σ) T
hu : ¬Satisfiable ↑u
this✝ : (k : ℕ) → Encodable ((languageFinset u).Func k)
this : (k : ℕ) → Encodable ((languageFinset u).Rel k)
u' : Finset (Sentence (languageFinset u)) := u.imageOfFinset fun x hσ => toSubLanguageFinsetSelf hσ
⊢ T ⊢! σ