unfold sub
σ : Instantiation
τ τ' : MetaInstantiation
x : VarName
phi : Formula
phi_ih : phi.metaVarSet = ∅ → sub σ τ phi = sub σ τ' phi
h1 : phi.metaVarSet = ∅
⊢ sub σ τ (forall_ x phi) = sub σ τ' (forall_ x phi)
σ : Instantiation
τ τ' : MetaInstantiation
x : VarName
phi : Formula
phi_ih : phi.metaVarSet = ∅ → sub σ τ phi = sub σ τ' phi
h1 : phi.metaVarSet = ∅
⊢ forall_ (↑σ x) (sub σ τ phi) = forall_ (↑σ x) (sub σ τ' phi)