simp
σ σ' : VarName → VarName
phi : Formula
phi_ih :
  ∀ (binders : Finset VarName),
    (∀ v ∉ binders, σ v = σ' v) → replaceFreeAux σ binders phi = replaceFreeAux σ' binders phi
binders : Finset VarName
h1 : ∀ v ∉ binders, σ v = σ' v
⊢ (replaceFreeAux σ binders phi).not_ = (replaceFreeAux σ' binders phi).not_
σ σ' : VarName → VarName
phi : Formula
phi_ih :
  ∀ (binders : Finset VarName),
    (∀ v ∉ binders, σ v = σ' v) → replaceFreeAux σ binders phi = replaceFreeAux σ' binders phi
binders : Finset VarName
h1 : ∀ v ∉ binders, σ v = σ' v
⊢ replaceFreeAux σ binders phi = replaceFreeAux σ' binders phi