Theorem: Matroid.eq_loopyOn_iff_cl (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
h : M = loopyOn E
⊢ M.cl ∅ = E ∧ M.E = E
Tactic:
rw [h]
State after:
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
h : M = loopyOn E
⊢ (loopyOn E).cl ∅ = E ∧ (loopyOn E).E = E

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
h : M = loopyOn E
⊢ (loopyOn E).cl ∅ = E ∧ (loopyOn E).E = E
Tactic:
simp
State after:
no goals

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
x✝ : M.cl ∅ = E ∧ M.E = E
h : M.cl ∅ = E
h' : M.E = E
⊢ M = loopyOn E
Tactic:
rw [← h', ← cl_empty_eq_ground_iff, h, h']
State after:
no goals