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Theorems · Theorem · combinatorics

Matroid.IsBase.cardinalMk_eq

∀ {α : Type u} {M : Matroid α} {B B' : Set α} [M.InvariantCardinalRank],
  M.IsBase B → M.IsBase B' → Cardinal.mk ↑B = Cardinal.mk ↑B'
Defined in
Mathlib.Combinatorics.Matroid.Rank.Cardinal
Cited by
2 results in Mathlib
Foundations
Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Matroid.InvariantCardinalRank
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Around this declaration

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

Matroid.IsBase.cardinalMk_eq_cRank · cited by 6IsBase.cardinalMk_eq_cRankMatroid.Indep.cardinalMk_le_isBase · cited by 0Indep.cardinalMk_le_isBaseSet · cited by 53352SetSet.Elem · cited by 7166Set.ElemCardinal · cited by 2598CardinalMatroid · cited by 1258MatroidCardinal.mk · cited by 942Cardinal.mkMatroid.IsBase · cited by 239Matroid.IsBaseMatroid.InvariantCardinalRank · cited by 25Matroid.InvariantCardinal…Matroid.IsBase.isBasis_ground · cited by 4IsBase.isBasis_groundMatroid.IsBasis.cardinalMk_eq · cited by 2IsBasis.cardinalMk_eqIsBase.cardinalMk_eqCITED BYCITES

Cites9

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Cited by2

Results whose statement or proof uses this declaration.