have h₃ : C \ {z} ⊆ M.cl Y := by
  suffices C \ {z} ⊆ C \ insert z (range x) ∪ range x by
    rw [union_diff_distrib] at hY
    convert this.trans (union_subset_union (subset_union_left.trans_eq hY.symm) h₂) using 1
    rw [union_eq_right.mpr]
    exact M.subset_cl Y
  rw [← union_singleton, ← diff_diff, diff_subset_iff, singleton_union, ← insert_union,
    insert_diff_singleton, ← singleton_union, union_assoc, diff_union_self]
  exact subset_union_of_subset_right subset_union_left _
α : Type u_1
M : Matroid α
C C' I X K C₁ C₂ R : Set α
e f x✝ y : α
ι : Type u_2
hC : M.Circuit C
x : ι → α
Cs : ι → Set α
hCs : ∀ (i : ι), M.Circuit (Cs i)
h_mem : ∀ (i : ι), x i ∈ C ∩ Cs i
h_unique : ∀ (i i' : ι), x i ∈ Cs i' → i = i'
z : α
hz : z ∈ C \ ⋃ i, Cs i
Y : Set α := (C ∪ ⋃ x, Cs x) \ insert z (range x)
hY : Y = (C ∪ ⋃ x, Cs x) \ insert z (range x)
hYE : Y ⊆ M.E
h₁ : range x ⊆ M.cl (⋃ i, (Cs i \ {x i}) \ insert z (range x))
h₂ : range x ⊆ M.cl Y
⊢ ∃ C', M.Circuit C' ∧ z ∈ C' ∧ C' ⊆ (C ∪ ⋃ i, Cs i) \ range x
α : Type u_1
M : Matroid α
C C' I X K C₁ C₂ R : Set α
e f x✝ y : α
ι : Type u_2
hC : M.Circuit C
x : ι → α
Cs : ι → Set α
hCs : ∀ (i : ι), M.Circuit (Cs i)
h_mem : ∀ (i : ι), x i ∈ C ∩ Cs i
h_unique : ∀ (i i' : ι), x i ∈ Cs i' → i = i'
z : α
hz : z ∈ C \ ⋃ i, Cs i
Y : Set α := (C ∪ ⋃ x, Cs x) \ insert z (range x)
hY : Y = (C ∪ ⋃ x, Cs x) \ insert z (range x)
hYE : Y ⊆ M.E
h₁ : range x ⊆ M.cl (⋃ i, (Cs i \ {x i}) \ insert z (range x))
h₂ : range x ⊆ M.cl Y
h₃ : C \ {z} ⊆ M.cl Y
⊢ ∃ C', M.Circuit C' ∧ z ∈ C' ∧ C' ⊆ (C ∪ ⋃ i, Cs i) \ range x