cases h1
zs : List String
phi psi : Formula
phi_ih : ∀ (j : ℕ), lc_at j phi → openList j (List.map free_ zs) phi = phi
psi_ih : ∀ (j : ℕ), lc_at j psi → openList j (List.map free_ zs) psi = psi
j : ℕ
h1 : lc_at j phi ∧ lc_at j psi
⊢ (openList j (List.map free_ zs) phi).imp_ (openList j (List.map free_ zs) psi) = phi.imp_ psi
case intro
zs : List String
phi psi : Formula
phi_ih : ∀ (j : ℕ), lc_at j phi → openList j (List.map free_ zs) phi = phi
psi_ih : ∀ (j : ℕ), lc_at j psi → openList j (List.map free_ zs) psi = psi
j : ℕ
left✝ : lc_at j phi
right✝ : lc_at j psi
⊢ (openList j (List.map free_ zs) phi).imp_ (openList j (List.map free_ zs) psi) = phi.imp_ psi