. intro hp;
  have := provable_iff_insert_neg_not_Lconsistent.not.mp $ membership_iff.not.mp hp;
  have := (not_imp_not.mpr $ Ω.maximal (U := insert (~p) Ω.theory)) this;
  simp [Set.ssubset_def] at this;
  apply this;
  simp;
case mpr
α : Type u_1
inst✝² : DecidableEq α
inst✝¹ : Inhabited α
L : DeductionParameter α
inst✝ : L.Normal
Ω Ω₁ Ω₂ : MCT L
p : Formula α
⊢ p ∉ Ω.theory → ~p ∈ Ω.theory
no goals