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Theorems · Theorem · combinatorics

Matroid.InvariantCardinalRank.forall_card_isBasis_diff

∀ {α : Type u} {M : Matroid α} [self : M.InvariantCardinalRank] ⦃I J X : Set α⦄,
  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
1 results in Mathlib
Foundations
Depth 20 from the axioms · uses Quot.sound
Assumes
Matroid.InvariantCardinalRank
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Around this declaration

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Matroid.IsBasis.cardinalMk_sdiff_comm · cited by 4IsBasis.cardinalMk_sdiff_…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…InvariantCardinalRank.forall_…CITED BYCITES

Cites7

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Cited by1

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