Theorem: Matroid.LoopEquiv.diff_eq_diff (Matroid/Loop.lean)

State before:
α : Type u_1
β : Type u_2
M N : Matroid α
e f : α
B L L' I X Y Z F C K : Set α
h : M.LoopEquiv X Y
⊢ X \ M.cl ∅ = Y \ M.cl ∅
Tactic:
rw [subset_antisymm_iff, diff_subset_iff, union_diff_self, union_comm, ← h.union_eq_union,
  diff_subset_iff, union_diff_self, union_comm _ X, and_iff_right subset_union_left,
  h.union_eq_union]
State after:
α : Type u_1
β : Type u_2
M N : Matroid α
e f : α
B L L' I X Y Z F C K : Set α
h : M.LoopEquiv X Y
⊢ Y ⊆ Y ∪ M.cl ∅

State before:
α : Type u_1
β : Type u_2
M N : Matroid α
e f : α
B L L' I X Y Z F C K : Set α
h : M.LoopEquiv X Y
⊢ Y ⊆ Y ∪ M.cl ∅
Tactic:
apply subset_union_left
State after:
no goals