case nil =>
  unfold IsMetaVarOrAllDefInEnv at h1
  simp at h1
D : Type
I : Interpretation D
M : MetaValuation D
σ : Instantiation
σ' : VarName → VarName
τ : MetaInstantiation
h2 : ↑σ ∘ σ' = id ∧ σ' ∘ ↑σ = id
X : DefName
xs : List VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv [] (def_ X xs)
⊢ Holds D I (V ∘ ↑σ) (fun X' V' => Holds D I (V' ∘ σ') M [] (τ X')) [] (def_ X xs) ↔
    Holds D I V M [] (sub σ τ (def_ X xs))
no goals