Theorem: Matroid.LoopEquiv.inter_eq_of_indep (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
hI : M.Indep I
⊢ X ∩ I = Y ∩ I
Tactic:
rw [show X ∩ I = (X ∪ M.cl ∅) ∩ I
  by rw [union_inter_distrib_right, hI.disjoint_loops.symm.inter_eq, union_empty],
  h.union_eq_union, union_inter_distrib_right, hI.disjoint_loops.symm.inter_eq, union_empty]
State after:
no goals

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
hI : M.Indep I
⊢ X ∩ I = (X ∪ M.cl ∅) ∩ I
Tactic:
rw [union_inter_distrib_right, hI.disjoint_loops.symm.inter_eq, union_empty]
State after:
no goals