Theorem: Matroid.Parallel'.mem_cl_iff_mem_cl (Matroid/Parallel.lean)

State before:
α : Type u_1
M N : Matroid α
e f g : α
I X✝ P D : Set α
h : M.Parallel' e f
X : Set α
⊢ e ∈ M.cl X ↔ f ∈ M.cl X
Tactic:
obtain (⟨he, hf⟩ | h) := h.loop_or_parallel
State after:
case inl.intro
α : Type u_1
M N : Matroid α
e f g : α
I X✝ P D : Set α
h : M.Parallel' e f
X : Set α
he : M.Loop e
hf : M.Loop f
⊢ e ∈ M.cl X ↔ f ∈ M.cl X

case inr
α : Type u_1
M N : Matroid α
e f g : α
I X✝ P D : Set α
h✝ : M.Parallel' e f
X : Set α
h : M.Parallel e f
⊢ e ∈ M.cl X ↔ f ∈ M.cl X

State before:
case inr
α : Type u_1
M N : Matroid α
e f g : α
I X✝ P D : Set α
h✝ : M.Parallel' e f
X : Set α
h : M.Parallel e f
⊢ e ∈ M.cl X ↔ f ∈ M.cl X
Tactic:
exact h.mem_cl_iff_mem_cl
State after:
no goals

State before:
case inl.intro
α : Type u_1
M N : Matroid α
e f g : α
I X✝ P D : Set α
h : M.Parallel' e f
X : Set α
he : M.Loop e
hf : M.Loop f
⊢ e ∈ M.cl X ↔ f ∈ M.cl X
Tactic:
simp [he.mem_cl, hf.mem_cl]
State after:
no goals