simp only [mem_setOf_eq, forall_exists_index, and_imp, not_forall, Classical.not_imp, not_le]
α : Type u_1
M M₁ M₂ : Matroid α
A I X E : Set α
inst✝ : M₁.Finite
hI₁ : M₁.Indep I
hI₂ : M₂.Indep I
⊢ ∀ m < I.ncard, ¬∀ a ∈ {n | ∃ I, M₁.Indep I ∧ M₂.Indep I ∧ I.ncard = n}, a ≤ m
α : Type u_1
M M₁ M₂ : Matroid α
A I X E : Set α
inst✝ : M₁.Finite
hI₁ : M₁.Indep I
hI₂ : M₂.Indep I
⊢ ∀ m < I.ncard, ∃ x x_1, ∃ (_ : M₁.Indep x_1) (_ : M₂.Indep x_1) (_ : x_1.ncard = x), m < x