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Theorems · Theorem · combinatorics

Matroid.IsBasis.cardinalMk_sdiff_comm

∀ {α : Type u} {M : Matroid α} {I J X : Set α} [M.InvariantCardinalRank],
  M.IsBasis I X → M.IsBasis J X → Cardinal.mk ↑(I \ J) = Cardinal.mk ↑(J \ I)
Defined in
Mathlib.Combinatorics.Matroid.Rank.Cardinal
Cited by
4 results in Mathlib
Foundations
Depth 21 from the axioms · uses Quot.sound
Assumes
Matroid.InvariantCardinalRank
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Around this declaration

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

Matroid.IsBasis.cardinalMk_eq · cited by 2IsBasis.cardinalMk_eqMatroid.IsBase.cardinalMk_sdiff_comm · cited by 1IsBase.cardinalMk_sdiff_c…Matroid.IsBasis'.cardinalMk_sdiff_comm · cited by 1IsBasis'.cardinalMk_sdiff…Matroid.IsBasis.cardinalMk_diff_comm · cited by 0IsBasis.cardinalMk_diff_c…Set · cited by 53352SetSet.Elem · cited by 7166Set.ElemCardinal · cited by 2598CardinalMatroid · cited by 1258MatroidCardinal.mk · cited by 942Cardinal.mkMatroid.IsBasis · cited by 219Matroid.IsBasisMatroid.InvariantCardinalRank · cited by 25Matroid.InvariantCardinal…Matroid.InvariantCardinalRank.forall_card_isBasis_diff · cited by 1InvariantCardinalRank.for…IsBasis.cardinalMk_sdiff_commCITED BYCITES

Cites8

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Cited by4

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