Theorem: Matroid.Restriction.restrict_delete_of_disjoint (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 D D₁ D₂ R : Set α
h : N ≤r M
hX : Disjoint X N.E
⊢ N ≤r M ＼ X
Tactic:
obtain ⟨D, hD, rfl⟩ := restriction_iff_exists_eq_delete.1 h
State after:
case intro.intro
α : Type u_1
M M' : Matroid α
e f : α
I J R✝ B X Y Z K D✝ D₁ D₂ R D : Set α
hD : D ⊆ M.E
h : M ＼ D ≤r M
hX : Disjoint X (M ＼ D).E
⊢ M ＼ D ≤r M ＼ X

State before:
case intro.intro
α : Type u_1
M M' : Matroid α
e f : α
I J R✝ B X Y Z K D✝ D₁ D₂ R D : Set α
hD : D ⊆ M.E
h : M ＼ D ≤r M
hX : Disjoint X (M ＼ D).E
⊢ M ＼ D ≤r M ＼ X
Tactic:
refine restriction_iff_exists_eq_delete.2 ⟨D \ X, diff_subset_diff_left hD, ?_⟩
State after:
case intro.intro
α : Type u_1
M M' : Matroid α
e f : α
I J R✝ B X Y Z K D✝ D₁ D₂ R D : Set α
hD : D ⊆ M.E
h : M ＼ D ≤r M
hX : Disjoint X (M ＼ D).E
⊢ M ＼ D = M ＼ X ＼ (D \ X)

State before:
case intro.intro
α : Type u_1
M M' : Matroid α
e f : α
I J R✝ B X Y Z K D✝ D₁ D₂ R D : Set α
hD : D ⊆ M.E
h : M ＼ D ≤r M
hX : Disjoint X (M ＼ D).E
⊢ M ＼ D = M ＼ X ＼ (D \ X)
Tactic:
rwa [delete_delete, union_diff_self, union_comm, ← delete_delete, eq_comm,
  delete_eq_self_iff]
State after:
no goals