Theorem: Matroid.er_lt_top_of_finite (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
hX : X.Finite
⊢ 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
hX : X.Finite
I : Set α
hI : M.Basis' I X
⊢ 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
hX : X.Finite
I : Set α
hI : M.Basis' I X
⊢ M.er X < ⊤
Tactic:
rw [hI.er_eq_encard, encard_lt_top_iff]
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
hX : X.Finite
I : Set α
hI : M.Basis' I X
⊢ I.Finite

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
hX : X.Finite
I : Set α
hI : M.Basis' I X
⊢ I.Finite
Tactic:
exact hX.subset hI.subset
State after:
no goals