refine eq_of_base_iff_base_forall (by simp) (fun B hBE ↦ ?_)
case inr.intro.inr
α : Type u_1
M : Matroid α
E I B X C : Set α
hE : E.Finite
k : ℕ
hlt : ↑k < E.encard
⊢ (unifOn E ↑k)✶ = unifOn E (E.encard - ↑k)
case inr.intro.inr
α : Type u_1
M : Matroid α
E I B✝ X C : Set α
hE : E.Finite
k : ℕ
hlt : ↑k < E.encard
B : Set α
hBE : B ⊆ (unifOn E ↑k)✶.E
⊢ (unifOn E ↑k)✶.Base B ↔ (unifOn E (E.encard - ↑k)).Base B