refine Nat.sSup_mem (s := {n | ∃ I, M₁.Indep I ∧ M₂.Indep I ∧ I.ncard = n}) ⟨0, ∅, by simp⟩
  ⟨M₁.E.ncard, ?_⟩
α : Type u_1
M M₁✝ M₂✝ : Matroid α
A I X E : Set α
M₁ M₂ : Matroid α
inst✝ : M₁.Finite
⊢ ∃ I, M₁.Indep I ∧ M₂.Indep I ∧ I.ncard = M₁.maxCommonInd M₂
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}