Theorem: Matroid.cl_insert_eq_cl_insert_of_mem (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
he : e ∈ M.cl (insert f X) \ M.cl X
⊢ M.cl (insert e X) = M.cl (insert f X)
Tactic:
have hf := cl_exchange he
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
he : e ∈ M.cl (insert f X) \ M.cl X
hf : f ∈ M.cl (insert e X) \ M.cl X
⊢ M.cl (insert e X) = M.cl (insert f X)

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
he : e ∈ M.cl (insert f X) \ M.cl X
hf : f ∈ M.cl (insert e X) \ M.cl X
⊢ M.cl (insert e X) = M.cl (insert f X)
Tactic:
rw [eq_comm, ← cl_cl, ← insert_eq_of_mem he.1, cl_insert_cl_eq_cl_insert, insert_comm, ← cl_cl,
  ← cl_insert_cl_eq_cl_insert, insert_eq_of_mem hf.1, cl_cl, cl_cl]
State after:
no goals