have h' : ∀ C, M₁.Circuit C ↔ M₂.Circuit C := by
  exact fun C ↦ (em (C ⊆ M₁.E)).elim (h C)
    (fun hC ↦ iff_of_false (mt Circuit.subset_ground hC)
      (mt Circuit.subset_ground (fun hss ↦ hC (hss.trans_eq hE.symm))))
α : Type u_1
M : Matroid α
C C' I X K C₁ C₂ R : Set α
e f x y : α
M₁ M₂ : Matroid α
hE : M₁.E = M₂.E
h : ∀ C ⊆ M₁.E, M₁.Circuit C ↔ M₂.Circuit C
⊢ M₁ = M₂
α : Type u_1
M : Matroid α
C C' I X K C₁ C₂ R : Set α
e f x y : α
M₁ M₂ : Matroid α
hE : M₁.E = M₂.E
h : ∀ C ⊆ M₁.E, M₁.Circuit C ↔ M₂.Circuit C
h' : ∀ (C : Set α), M₁.Circuit C ↔ M₂.Circuit C
⊢ M₁ = M₂