simp [satisfiable] at *
case h.right.left
φ ψ : Formula
hyp : φ⊨ψ
X : TNode := ([φ], [~ψ], none)
ctX : ClosedTableau ([], []) X
θ : Formula
this : ¬satisfiable ((~θ) :: X.left)
⊢ ¬satisfiable [φ, ~θ]
case h.right.left
φ ψ : Formula
hyp : φ⊨ψ
X : TNode := ([φ], [~ψ], none)
ctX : ClosedTableau ([], []) X
θ : Formula
this : ∀ (x : Type) (x_1 : KripkeModel x) (x_2 : x), ¬evaluate x_1 x_2 θ → ¬evaluate x_1 x_2 φ
⊢ ∀ (x : Type) (x_1 : KripkeModel x) (x_2 : x), evaluate x_1 x_2 φ → evaluate x_1 x_2 θ