Theorem: Matroid.cl_cl_union_cl_eq_cl_union (Matroid/Closure.lean)

State before:
α : Type u_1
ι : Type u_2
M✝ : Matroid α
F I J X✝ Y✝ B C R : Set α
e f x y : α
M : Matroid α
X Y : Set α
⊢ M.cl (M.cl X ∪ M.cl Y) = M.cl (X ∪ Y)
Tactic:
rw [eq_comm, union_eq_iUnion, ← cl_iUnion_cl_eq_cl_iUnion, union_eq_iUnion]
State after:
α : Type u_1
ι : Type u_2
M✝ : Matroid α
F I J X✝ Y✝ B C R : Set α
e f x y : α
M : Matroid α
X Y : Set α
⊢ M.cl (⋃ i, M.cl (bif i then X else Y)) = M.cl (⋃ b, bif b then M.cl X else M.cl Y)

State before:
α : Type u_1
ι : Type u_2
M✝ : Matroid α
F I J X✝ Y✝ B C R : Set α
e f x y : α
M : Matroid α
X Y : Set α
⊢ M.cl (⋃ i, M.cl (bif i then X else Y)) = M.cl (⋃ b, bif b then M.cl X else M.cl Y)
Tactic:
simp_rw [Bool.cond_eq_ite, apply_ite]
State after:
no goals