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Theorems · Theorem · combinatorics

Matroid.maximality

∀ {α : Type u_1} (self : Matroid α), ∀ X ⊆ self.E, Matroid.ExistsMaximalSubsetProperty self.Indep X

Every independent subset I of a set X for is contained in a maximal independent subset of X.

Defined in
Mathlib.Combinatorics.Matroid.Basic
Cited by
2 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
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Around this declaration

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

Matroid.Indep.subset_isBasis_of_subset · cited by 12Indep.subset_isBasis_of_s…Matroid.existsMaximalSubsetProperty_indep · cited by 0Matroid.existsMaximalSubs…Set · cited by 53352SetMatroid · cited by 1258MatroidMatroid.E · cited by 550Matroid.EMatroid.Indep · cited by 367Matroid.IndepMatroid.ExistsMaximalSubsetProperty · cited by 13Matroid.ExistsMaximalSubs…Matroid.maximalityCITED BYCITES

Cites5

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Cited by2

Results whose statement or proof uses this declaration.