set S := {(insert x I) | x ∈ X \ I}
case neg
α : Type u_1
A B I J X : Set α
x : α
M : RankMatroid α
hI : I ⊆ X
hI_indep : M.Indep I
hI_max : I ∈ maximals (fun x x_1 => x ⊆ x_1) {S | M.Indep S ∧ S ⊆ X}
hXI : ¬X = I
⊢ M.relRank I X = 0
case neg
α : Type u_1
A B I J X : Set α
x : α
M : RankMatroid α
hI : I ⊆ X
hI_indep : M.Indep I
hI_max : I ∈ maximals (fun x x_1 => x ⊆ x_1) {S | M.Indep S ∧ S ⊆ X}
hXI : ¬X = I
S : Set (Set α) := {x | ∃ x_1 ∈ X \ I, insert x_1 I = x}
⊢ M.relRank I X = 0