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Theorems · Theorem · combinatorics

Matroid.singleton_not_indep

∀ {α : Type u_1} {M : Matroid α} {e : α},
  autoParam (e ∈ M.E) Matroid.singleton_not_indep._auto_1 → (¬M.Indep {e} ↔ M.IsLoop e)
Defined in
Mathlib.Combinatorics.Matroid.Loop
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Foundations
Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
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Set · cited by 53352SetMatroid · cited by 1258MatroidMatroid.E · cited by 550Matroid.EMatroid.Indep · cited by 367Matroid.IndepMatroid.IsLoop · cited by 55Matroid.IsLoopMatroid.not_indep_iff · cited by 11Matroid.not_indep_iffMatroid.singleton_dep · cited by 8Matroid.singleton_depMatroid.singleton_not_indepCITED BYCITES

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