case botC ih => by_contra hA; apply ih (satisfies_insert_iff.mpr ⟨by exact hA, hv⟩)
v✝ : Variable → Prop
A B : Formula
Γ Δ Γ✝ : Set Formula
A✝ : Formula
a✝ : insert (~A✝) Γ✝ ⊢ ⊥
ih : insert (~A✝) Γ✝ ⊨ ⊥
v : Variable → Prop
hv : Satisfies v Γ✝
⊢ IsTrue v A✝
no goals