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Theorems · Theorem · combinatorics

Matroid.Indep.cardinalMk_le_isBase

∀ {α : Type u} {M : Matroid α} {I B : Set α} [M.InvariantCardinalRank],
  M.Indep I → M.IsBase B → Cardinal.mk ↑I ≤ Cardinal.mk ↑B
Defined in
Mathlib.Combinatorics.Matroid.Rank.Cardinal
Cited by
0 results in Mathlib
Foundations
Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Matroid.InvariantCardinalRank
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Around this declaration

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Set · cited by 53352SetSet.Elem · cited by 7166Set.ElemCardinal · cited by 2598CardinalMatroid · cited by 1258MatroidCardinal.mk · cited by 942Cardinal.mkMatroid.Indep · cited by 367Matroid.IndepMatroid.IsBase · cited by 239Matroid.IsBaseCardinal.mk_le_mk_of_subset · cited by 37Cardinal.mk_le_mk_of_subs…Matroid.InvariantCardinalRank · cited by 25Matroid.InvariantCardinal…Matroid.Indep.exists_isBase_superset · cited by 18Indep.exists_isBase_super…Matroid.IsBase.cardinalMk_eq · cited by 2IsBase.cardinalMk_eqIndep.cardinalMk_le_isBaseCITED BYCITES

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