Theorem: Matroid.er_inter_ground_eq (Matroid/Rank.lean)

State before:
α : Type u_1
ι : Type u_2
M✝ N : Matroid α
I B X✝ X' Y Y' Z R : Set α
n : ℕ∞
e f : α
M : Matroid α
X : Set α
⊢ M.er (X ∩ M.E) = M.er X
Tactic:
obtain ⟨I, hI⟩ := M.exists_basis' X
State after:
case intro
α : Type u_1
ι : Type u_2
M✝ N : Matroid α
I✝ B X✝ X' Y Y' Z R : Set α
n : ℕ∞
e f : α
M : Matroid α
X I : Set α
hI : M.Basis' I X
⊢ M.er (X ∩ M.E) = M.er X

State before:
case intro
α : Type u_1
ι : Type u_2
M✝ N : Matroid α
I✝ B X✝ X' Y Y' Z R : Set α
n : ℕ∞
e f : α
M : Matroid α
X I : Set α
hI : M.Basis' I X
⊢ M.er (X ∩ M.E) = M.er X
Tactic:
rw [← hI.basis_inter_ground.encard, ← hI.encard]
State after:
no goals