rw[←image_u']
L : Language
T : Theory L
σ : Sentence L
h : T ⊨ σ
this✝³ : (α : Type u) → DecidableEq α := Classical.typeDecidableEq
u : Finset (Sentence L)
ssu : ↑u ⊆ insert (~σ) T
hu : ¬Satisfiable ↑u
this✝² : (k : ℕ) → Encodable ((languageFinset u).Func k)
this✝¹ : (k : ℕ) → Encodable ((languageFinset u).Rel k)
u' : Finset (Sentence (languageFinset u)) := u.imageOfFinset fun x hσ => toSubLanguageFinsetSelf hσ
image_u' : Finset.image (⇑(lMap L.ofSubLanguage)) u' = u
this✝ : ¬Satisfiable ↑u'
this : System.Inconsistent ↑u'
⊢ System.Inconsistent ↑u
L : Language
T : Theory L
σ : Sentence L
h : T ⊨ σ
this✝³ : (α : Type u) → DecidableEq α := Classical.typeDecidableEq
u : Finset (Sentence L)
ssu : ↑u ⊆ insert (~σ) T
hu : ¬Satisfiable ↑u
this✝² : (k : ℕ) → Encodable ((languageFinset u).Func k)
this✝¹ : (k : ℕ) → Encodable ((languageFinset u).Rel k)
u' : Finset (Sentence (languageFinset u)) := u.imageOfFinset fun x hσ => toSubLanguageFinsetSelf hσ
image_u' : Finset.image (⇑(lMap L.ofSubLanguage)) u' = u
this✝ : ¬Satisfiable ↑u'
this : System.Inconsistent ↑u'
⊢ System.Inconsistent ↑(Finset.image (⇑(lMap L.ofSubLanguage)) u')