case forall_ x phi phi_ih =>
  unfold NoMetaVarAndAllFreeInList at h1
  unfold sub
  unfold NoMetaVarAndAllFreeInList
  simp only [← List.map_cons]
  exact phi_ih (x :: vs) h1
σ : Instantiation
τ : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
  ∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ phi)
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (forall_ x phi)
⊢ NoMetaVarAndAllFreeInList (List.map (↑σ) vs) (sub σ τ (forall_ x phi))
no goals