Theorem: Matroid.loop_iff_not_mem_base_forall (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
he : autoParam (e ∈ M.E) _auto✝
⊢ M.Loop e ↔ ∀ (B : Set α), M.Base B → e ∉ B
Tactic:
rw [← singleton_dep, ← not_indep_iff, not_iff_comm, not_forall]
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
he : autoParam (e ∈ M.E) _auto✝
⊢ (∃ x, ¬(M.Base x → e ∉ x)) ↔ M.Indep {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
he : autoParam (e ∈ M.E) _auto✝
⊢ (∃ x, ¬(M.Base x → e ∉ x)) ↔ M.Indep {e}
Tactic:
simp_rw [_root_.not_imp, not_not, ← singleton_subset_iff, indep_iff]
State after:
no goals