simp only [Holds]
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_x : VarName
h2_phi h2_phi' : Formula
a✝ : IsConv E h2_phi h2_phi'
h2_ih : ∀ (V : Valuation D), Holds D I V M E h2_phi ↔ Holds D I V M E h2_phi'
V : Valuation D
⊢ Holds D I V M E (forall_ h2_x h2_phi) ↔ Holds D I V M E (forall_ h2_x h2_phi')
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_x : VarName
h2_phi h2_phi' : Formula
a✝ : IsConv E h2_phi h2_phi'
h2_ih : ∀ (V : Valuation D), Holds D I V M E h2_phi ↔ Holds D I V M E h2_phi'
V : Valuation D
⊢ (∀ (d : D), Holds D I (Function.updateITE V h2_x d) M E h2_phi) ↔
    ∀ (d : D), Holds D I (Function.updateITE V h2_x d) M E h2_phi'