Theorem: Matroid.indep_singleton (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.Indep {e} ↔ M.Nonloop e
Tactic:
rw [Nonloop, ← singleton_dep, dep_iff, not_and, not_imp_not, singleton_subset_iff]
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
⊢ M.Indep {e} ↔ (e ∈ M.E → M.Indep {e}) ∧ e ∈ M.E

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.Indep {e} ↔ (e ∈ M.E → M.Indep {e}) ∧ e ∈ M.E
Tactic:
exact ⟨fun h ↦ ⟨fun _ ↦ h, singleton_subset_iff.mp h.subset_ground⟩, fun h ↦ h.1 h.2⟩
State after:
no goals