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Theorems · Theorem · combinatorics

Matroid.IsBasis.cardinalMk_eq_cRk

∀ {α : Type u} {M : Matroid α} {I X : Set α} [M.InvariantCardinalRank], M.IsBasis I X → Cardinal.mk ↑I = M.cRk X
Defined in
Mathlib.Combinatorics.Matroid.Rank.Cardinal
Cited by
1 results in Mathlib
Foundations
Depth 84 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.cRk_closure · cited by 1Matroid.cRk_closureSet · cited by 53352SetSet.Elem · cited by 7166Set.ElemCardinal · cited by 2598CardinalMatroid · cited by 1258MatroidCardinal.mk · cited by 942Cardinal.mkMatroid.IsBasis · cited by 219Matroid.IsBasisMatroid.cRk · cited by 29Matroid.cRkMatroid.InvariantCardinalRank · cited by 25Matroid.InvariantCardinal…Matroid.IsBasis.isBasis' · cited by 18IsBasis.isBasis'Matroid.IsBasis'.cardinalMk_eq_cRk · cited by 3IsBasis'.cardinalMk_eq_cRkIsBasis.cardinalMk_eq_cRkCITED BYCITES

Cites10

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Cited by1

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