Theorems · Theorem · combinatorics
Matroid.eRk_singleton_eq_one_iff
∀ {α : Type u_1} {M : Matroid α} {e : α}, M.eRk {e} = 1 ↔ M.IsNonloop e- Defined in
- Mathlib.Combinatorics.Matroid.Rank.ENat
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- ENatstatement and proof · cited by 4,985
- Matroidstatement and proof · cited by 1,258
- Matroid.eRkstatement and proof · cited by 101
- Matroid.IsNonloopstatement and proof · cited by 65
- Set.encard_singletonproof · cited by 26
- Matroid.indep_singletonproof · cited by 12
- Matroid.indep_iff_eRk_eq_encard_of_finiteproof · cited by 5
- Matroid.IsNonloop.eRk_eqproof · cited by 3
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