have h : ∃ i, ¬ M.Indep (C ∩ Xs i) := by
  by_contra! hcon
  refine hC.dep.not_indep ?_
  refine (h.iUnion_indep_subset_indep (fun i ↦ inter_subset_right) hcon).subset ?_
  simp [← inter_iUnion, hCU, Subset.rfl]
case refine_1
ι : Type u_1
α : Type u_2
M : Matroid α
B I J X X' Y Y' F : Set α
Xs Ys Js Is : ι → Set α
i j : ι
e f : α
hXs : ∀ (i : ι), Xs i ⊆ M.E
hdj : Pairwise (Disjoint on Xs)
h : M.SkewFamily Xs
C : Set α
hC : M.Circuit C
hCU : C ⊆ ⋃ i, Xs i
⊢ ∃ i, C ⊆ Xs i
case refine_1
ι : Type u_1
α : Type u_2
M : Matroid α
B I J X X' Y Y' F : Set α
Xs Ys Js Is : ι → Set α
i j : ι
e f : α
hXs : ∀ (i : ι), Xs i ⊆ M.E
hdj : Pairwise (Disjoint on Xs)
h✝ : M.SkewFamily Xs
C : Set α
hC : M.Circuit C
hCU : C ⊆ ⋃ i, Xs i
h : ∃ i, ¬M.Indep (C ∩ Xs i)
⊢ ∃ i, C ⊆ Xs i