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Theorems · Theorem · combinatorics

Matroid.IsBase.rankPos_of_nonempty

∀ {α : Type u_1} {M : Matroid α} {B : Set α}, M.IsBase B → B.Nonempty → M.RankPos
Defined in
Mathlib.Combinatorics.Matroid.Basic
Cited by
1 results in Mathlib
Foundations
Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

Matroid.Indep.rankPos_of_nonempty · cited by 1Indep.rankPos_of_nonemptySet · cited by 53352SetSet.Nonempty · cited by 2627Set.NonemptyMatroid · cited by 1258MatroidMatroid.IsBase · cited by 239Matroid.IsBaseSet.empty_subset · cited by 70Set.empty_subsetMatroid.RankPos · cited by 22Matroid.RankPosMatroid.IsBase.eq_of_subset_isBase · cited by 7IsBase.eq_of_subset_isBaseMatroid.rankPos_iff · cited by 6Matroid.rankPos_iffIsBase.rankPos_of_nonemptyCITED BYCITES

Cites8

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Cited by1

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