theorem isClosed_convex_constrainedEpigraph_restrict {X : Type u} [TopologicalSpace X] [AddCommMonoid X] [Module ℝ X] {Q Q₁ : Set X} {f : X → WithTop ℝ} (hf_closed : IsClosed (constrainedEpigraph Q f)) (hf_convex : Convex ℝ (constrainedEpigraph Q f)) (hQ₁_subset : Q₁ ⊆ Q) (hQ₁_closed : IsClosed Q₁) (hQ₁_convex : Convex ℝ Q₁) : IsClosed (constrainedEpigraph Q₁ f) ∧ Convex ℝ (constrainedEpigraph Q₁ f)

Lemma 3.2: if the epigraph of f over Q is a closed convex subset of X × ℝ and Q₁ ⊆ Q is closed and convex, then the epigraph of the restriction of f to Q₁ is also closed and convex.