linarith
case s1
a✝ : String
phi : Formula
phi_ih :
  ∀ (j : ℕ) (zs : List String),
    Formula.lc_at j (Formula.openList j (List.map free_ zs) phi) ↔ Formula.lc_at (j + zs.length) phi
j : ℕ
zs : List String
⊢ j + 1 + zs.length = j + zs.length + 1

a✝ : String
phi : Formula
phi_ih :
  ∀ (j : ℕ) (zs : List String),
    Formula.lc_at j (Formula.openList j (List.map free_ zs) phi) ↔ Formula.lc_at (j + zs.length) phi
j : ℕ
zs : List String
s1 : j + 1 + zs.length = j + zs.length + 1
⊢ Formula.lc_at (j + 1 + zs.length) phi ↔ Formula.lc_at (j + zs.length + 1) phi
a✝ : String
phi : Formula
phi_ih :
  ∀ (j : ℕ) (zs : List String),
    Formula.lc_at j (Formula.openList j (List.map free_ zs) phi) ↔ Formula.lc_at (j + zs.length) phi
j : ℕ
zs : List String
s1 : j + 1 + zs.length = j + zs.length + 1
⊢ Formula.lc_at (j + 1 + zs.length) phi ↔ Formula.lc_at (j + zs.length + 1) phi