Theorems · Theorem · combinatorics
Matroid.Indep.cardinalMk_le_isBasis
∀ {α : Type u} {M : Matroid α} {I J X : Set α} [M.InvariantCardinalRank],
M.Indep I → M.IsBasis J X → I ⊆ X → Cardinal.mk ↑I ≤ Cardinal.mk ↑J- Cited by
- 0 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Elemstatement · cited by 7,166
- Cardinalstatement · cited by 2,598
- Matroidstatement and proof · cited by 1,258
- Cardinal.mkstatement · cited by 942
- Matroid.Indepstatement and proof · cited by 367
- Matroid.IsBasisstatement and proof · cited by 219
- Matroid.InvariantCardinalRankstatement and proof · cited by 25
- Matroid.IsBasis.isBasis'proof · cited by 18
- Matroid.Indep.cardinalMk_le_isBasis'proof · cited by 1
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