Theorem: Matroid.Parallel'.loop_or_parallel (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
⊢ M.Loop e ∧ M.Loop f ∨ M.Parallel e f
Tactic:
obtain (he | he) := M.loop_or_nonloop e
State after:
case inl
α : Type u_1
M N : Matroid α
e f g : α
I X P D : Set α
h : M.Parallel' e f
he : M.Loop e
⊢ M.Loop e ∧ M.Loop f ∨ M.Parallel e f

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
he : M.Nonloop e
⊢ M.Loop e ∧ M.Loop f ∨ M.Parallel e f

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
he : M.Nonloop e
⊢ M.Loop e ∧ M.Loop f ∨ M.Parallel e f
Tactic:
exact .inr <| h.parallel_of_nonloop he
State after:
no goals

State before:
case inl
α : Type u_1
M N : Matroid α
e f g : α
I X P D : Set α
h : M.Parallel' e f
he : M.Loop e
⊢ M.Loop e ∧ M.Loop f ∨ M.Parallel e f
Tactic:
exact .inl ⟨he, h.loop_of_loop he⟩
State after:
no goals