Theorem: Matroid.Indep.not_mem_cl_iff (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
hI : M.Indep I
he : autoParam (e ∈ M.E) _auto✝
⊢ e ∉ M.cl I ↔ M.Indep (insert e I) ∧ e ∉ I
Tactic:
rw [hI.mem_cl_iff, dep_iff, insert_subset_iff, and_iff_right he,
  and_iff_left hI.subset_ground]
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
hI : M.Indep I
he : autoParam (e ∈ M.E) _auto✝
⊢ ¬(¬M.Indep (insert e I) ∨ e ∈ I) ↔ M.Indep (insert e I) ∧ e ∉ I

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
hI : M.Indep I
he : autoParam (e ∈ M.E) _auto✝
⊢ ¬(¬M.Indep (insert e I) ∨ e ∈ I) ↔ M.Indep (insert e I) ∧ e ∉ I
Tactic:
tauto
State after:
no goals