Theorem: Matroid.Minor.eq_of_ground_subset (Matroid/Minor/Basic.lean)

State before:
α : Type u_1
M M' N : Matroid α
e f : α
I J R B X Y Z K : Set α
M₀ M₁ M₂ : Matroid α
h : N ≤m M
hE : M.E ⊆ N.E
⊢ M = N
Tactic:
obtain ⟨C, D, -, -, -, rfl⟩ := h
State after:
case intro.intro.intro.intro.intro
α : Type u_1
M M' : Matroid α
e f : α
I J R B X Y Z K : Set α
M₀ M₁ M₂ : Matroid α
C D : Set α
hE : M.E ⊆ (M ／ C ＼ D).E
⊢ M = M ／ C ＼ D

State before:
case intro.intro.intro.intro.intro
α : Type u_1
M M' : Matroid α
e f : α
I J R B X Y Z K : Set α
M₀ M₁ M₂ : Matroid α
C D : Set α
hE : M.E ⊆ (M ／ C ＼ D).E
⊢ M = M ／ C ＼ D
Tactic:
rw [delete_ground, contract_ground, subset_diff, subset_diff] at hE
State after:
case intro.intro.intro.intro.intro
α : Type u_1
M M' : Matroid α
e f : α
I J R B X Y Z K : Set α
M₀ M₁ M₂ : Matroid α
C D : Set α
hE : (M.E ⊆ M.E ∧ Disjoint M.E C) ∧ Disjoint M.E D
⊢ M = M ／ C ＼ D

State before:
case intro.intro.intro.intro.intro
α : Type u_1
M M' : Matroid α
e f : α
I J R B X Y Z K : Set α
M₀ M₁ M₂ : Matroid α
C D : Set α
hE : (M.E ⊆ M.E ∧ Disjoint M.E C) ∧ Disjoint M.E D
⊢ M = M ／ C ＼ D
Tactic:
rw [← contract_inter_ground_eq, hE.1.2.symm.inter_eq, contract_empty, ← delete_inter_ground_eq,
  hE.2.symm.inter_eq, delete_empty]
State after:
no goals