case not_ phi phi_ih =>
  simp only [Formula.subst]
  simp only [Formula.freeVarSet]
  exact phi_ih
z : String
t : Var
phi : Formula
phi_ih : (Formula.subst (free_ z) t phi).freeVarSet ⊆ t.freeVarSet ∪ phi.freeVarSet \ {free_ z}
⊢ (Formula.subst (free_ z) t phi.not_).freeVarSet ⊆ t.freeVarSet ∪ phi.not_.freeVarSet \ {free_ z}
no goals