Theorem: Matroid.removeLoops_eq_self_iff (Matroid/Loop.lean)

State before:
α : Type u_1
β : Type u_2
M N : Matroid α
e f : α
B L L' I X Y Z F C K : Set α
⊢ M.removeLoops = M ↔ M.Loopless
Tactic:
refine ⟨fun h ↦ ?_, fun h ↦ M.removeLoops_eq_self⟩
State after:
α : Type u_1
β : Type u_2
M N : Matroid α
e f : α
B L L' I X Y Z F C K : Set α
h : M.removeLoops = M
⊢ M.Loopless

State before:
α : Type u_1
β : Type u_2
M N : Matroid α
e f : α
B L L' I X Y Z F C K : Set α
h : M.removeLoops = M
⊢ M.Loopless
Tactic:
rw [← h]
State after:
α : Type u_1
β : Type u_2
M N : Matroid α
e f : α
B L L' I X Y Z F C K : Set α
h : M.removeLoops = M
⊢ M.removeLoops.Loopless

State before:
α : Type u_1
β : Type u_2
M N : Matroid α
e f : α
B L L' I X Y Z F C K : Set α
h : M.removeLoops = M
⊢ M.removeLoops.Loopless
Tactic:
infer_instance
State after:
no goals