Theorem: Matroid.Minor.trans (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✝ M₁ M₂ M₃ : Matroid α
h : M₁ ≤m M₂
h' : M₂ ≤m M₃
⊢ M₁ ≤m M₃
Tactic:
obtain ⟨C₁, D₁, -, -, -, rfl⟩ := h
State after:
case intro.intro.intro.intro.intro
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✝ M₂ M₃ : Matroid α
h' : M₂ ≤m M₃
C₁ D₁ : Set α
⊢ M₂ ／ C₁ ＼ D₁ ≤m M₃

State before:
case intro.intro.intro.intro.intro
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✝ M₂ M₃ : Matroid α
h' : M₂ ≤m M₃
C₁ D₁ : Set α
⊢ M₂ ／ C₁ ＼ D₁ ≤m M₃
Tactic:
obtain ⟨C₂, D₂, -, -, -, rfl⟩ := h'
State after:
case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
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 M₃ : Matroid α
C₁ D₁ C₂ D₂ : Set α
⊢ M₃ ／ C₂ ＼ D₂ ／ C₁ ＼ D₁ ≤m M₃

State before:
case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
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 M₃ : Matroid α
C₁ D₁ C₂ D₂ : Set α
⊢ M₃ ／ C₂ ＼ D₂ ／ C₁ ＼ D₁ ≤m M₃
Tactic:
rw [contract_delete_contract_delete']
State after:
case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
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 M₃ : Matroid α
C₁ D₁ C₂ D₂ : Set α
⊢ M₃ ／ (C₂ ∪ C₁ \ D₂) ＼ (D₂ ∪ D₁) ≤m M₃

State before:
case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
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 M₃ : Matroid α
C₁ D₁ C₂ D₂ : Set α
⊢ M₃ ／ (C₂ ∪ C₁ \ D₂) ＼ (D₂ ∪ D₁) ≤m M₃
Tactic:
apply contract_delete_minor
State after:
no goals