Theorems · Theorem · combinatorics
Matroid.IsNonloop.eRk_eq
∀ {α : Type u_1} {M : Matroid α} {e : α}, M.IsNonloop e → M.eRk {e} = 1- Defined in
- Mathlib.Combinatorics.Matroid.Rank.ENat
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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 · cited by 101
- Matroid.IsNonloopstatement and proof · cited by 65
- Set.encard_singletonproof · cited by 26
- Matroid.Indep.isBasis_selfproof · cited by 12
- Matroid.IsBasis.encard_eq_eRkproof · cited by 9
- Matroid.IsNonloop.indepproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Matroid.eRk_eq_one_iffproof · cited by 0
- Matroid.eRk_singleton_eqproof · cited by 0
- Matroid.eRk_singleton_eq_one_iffproof · cited by 0