Theorem: Matroid.freeOn_er_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
E : Set α
hXE : X ⊆ E
⊢ (freeOn E).er X = X.encard
Tactic:
obtain ⟨I, hI⟩ := (freeOn E).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
E : Set α
hXE : X ⊆ E
I : Set α
hI : (freeOn E).Basis I X
⊢ (freeOn E).er X = X.encard

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
E : Set α
hXE : X ⊆ E
I : Set α
hI : (freeOn E).Basis I X
⊢ (freeOn E).er X = X.encard
Tactic:
rw [hI.er_eq_encard, (freeOn_indep hXE).eq_of_basis hI]
State after:
no goals