Theorems · Theorem · combinatorics
Matroid.IsBasis.cardinalMk_diff_comm
Deprecated since 2026-06-03Use Matroid.IsBasis.cardinalMk_sdiff_comm instead.
∀ {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)Alias of Matroid.IsBasis.cardinalMk_sdiff_comm.
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- Foundations
- Depth 22 from the axioms · uses Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.Elemstatement · cited by 7,166
- Cardinalstatement · cited by 2,598
- Matroidstatement · cited by 1,258
- Cardinal.mkstatement · cited by 942
- Matroid.IsBasisstatement · cited by 219
- Matroid.InvariantCardinalRankstatement · cited by 25
- Matroid.IsBasis.cardinalMk_sdiff_commproof · cited by 4
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