Theorem: Matroid.Indep.insert_indep_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
⊢ M.Indep (insert e I) ↔ e ∈ M.E \ M.cl I ∨ e ∈ I
Tactic:
obtain (h | h) := em (e ∈ I)
State after:
case inl
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
h : e ∈ I
⊢ M.Indep (insert e I) ↔ e ∈ M.E \ M.cl I ∨ e ∈ I

case inr
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
h : e ∉ I
⊢ M.Indep (insert e I) ↔ e ∈ M.E \ M.cl I ∨ e ∈ I

State before:
case inr
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
h : e ∉ I
⊢ M.Indep (insert e I) ↔ e ∈ M.E \ M.cl I ∨ e ∈ I
Tactic:
rw [hI.insert_indep_iff_of_not_mem h, or_iff_left h]
State after:
no goals

State before:
case inl
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
h : e ∈ I
⊢ M.Indep (insert e I) ↔ e ∈ M.E \ M.cl I ∨ e ∈ I
Tactic:
simp_rw [insert_eq_of_mem h, iff_true_intro hI, true_iff, iff_true_intro h, or_true]
State after:
no goals