unfold sub
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
σ : Instantiation
σ' : VarName → VarName
τ : MetaInstantiation
h2 : ↑σ ∘ σ' = id ∧ σ' ∘ ↑σ = id
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E true_
⊢ Holds D I (V ∘ ↑σ) (fun X' V' => Holds D I (V' ∘ σ') M E (τ X')) E true_ ↔ Holds D I V M E (sub σ τ true_)
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
σ : Instantiation
σ' : VarName → VarName
τ : MetaInstantiation
h2 : ↑σ ∘ σ' = id ∧ σ' ∘ ↑σ = id
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E true_
⊢ Holds D I (V ∘ ↑σ) (fun X' V' => Holds D I (V' ∘ σ') M E (τ X')) E true_ ↔ Holds D I V M E true_