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Theorems · Theorem · combinatorics

Matroid.IsBase.nonempty

∀ {α : Type u_1} {M : Matroid α} {B : Set α} [M.RankPos], M.IsBase B → B.Nonempty
Defined in
Mathlib.Combinatorics.Matroid.Basic
Cited by
2 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Matroid.RankPos
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Matroid.exists_isNonloop · cited by 0Matroid.exists_isNonloopMatroid.one_le_eRank · cited by 0Matroid.one_le_eRankSet · cited by 53352SetSet.Nonempty · cited by 2627Set.NonemptyMatroid · cited by 1258MatroidMatroid.IsBase · cited by 239Matroid.IsBaseSet.nonempty_iff_ne_empty · cited by 96Set.nonempty_iff_ne_emptyMatroid.RankPos · cited by 22Matroid.RankPosMatroid.empty_not_isBase · cited by 2Matroid.empty_not_isBaseIsBase.nonemptyCITED BYCITES

Cites7

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Cited by2

Results whose statement or proof uses this declaration.