case forall_ x phi phi_ih | exists_ x phi phi_ih =>
  simp only [fastReplaceFree]
  split_ifs
  case pos c1 =>
    simp only [isFreeIn]
    simp
    intro a1
    contradiction
  case neg c1 =>
    simp only [isFreeIn]
    simp
    intro _
    exact phi_ih
v t : VarName
h1 : ¬v = t
x : VarName
phi : Formula
phi_ih : ¬isFreeIn v (fastReplaceFree v t phi)
⊢ ¬isFreeIn v (fastReplaceFree v t (exists_ x phi))
no goals