simp_rw [spanning_iff_superset_base (S := M.E \ K), not_exists, subset_diff, not_and,
  not_disjoint_iff_nonempty_inter, ← and_imp, and_iff_left_of_imp Base.subset_ground,
    inter_comm K]
case h.e'_2.h.e'_5.h.e'_3.h.e'_2.h.a
α : Type u_1
M : Matroid α
C C' I X K✝ C₁ C₂ R : Set α
e f x y : α
B K : Set α
⊢ ¬M.Spanning (M.E \ K) ↔ ∀ (B : Set α), M.Base B → (K ∩ B).Nonempty
no goals