simp only [upperBounds, mem_setOf_eq, forall_exists_index, and_imp]
α : Type u_1
M M₁✝ M₂✝ : Matroid α
A I X E : Set α
M₁ M₂ : Matroid α
inst✝ : M₁.Finite
⊢ M₁.E.ncard ∈ upperBounds {n | ∃ I, M₁.Indep I ∧ M₂.Indep I ∧ I.ncard = n}
α : Type u_1
M M₁✝ M₂✝ : Matroid α
A I X E : Set α
M₁ M₂ : Matroid α
inst✝ : M₁.Finite
⊢ ∀ ⦃a : ℕ⦄ (x : Set α), M₁.Indep x → M₂.Indep x → x.ncard = a → a ≤ M₁.E.ncard