Theorems · Theorem · combinatorics
Matroid.Indep.isBase_of_cRank_le_of_finite
∀ {α : Type u} {M : Matroid α} {I : Set α}, M.Indep I → M.cRank ≤ Cardinal.mk ↑I → I.Finite → M.IsBase I- Cited by
- 0 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
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 and proof · cited by 7,166
- Cardinalstatement · cited by 2,598
- Set.Finitestatement and proof · cited by 1,814
- Matroidstatement and proof · cited by 1,258
- Cardinal.mkstatement and proof · cited by 942
- LE.le.trans_ltproof · cited by 795
- Matroid.Indepstatement and proof · cited by 367
- Matroid.IsBasestatement · cited by 239
- Matroid.RankFiniteproof · cited by 33
- Matroid.cRankstatement and proof · cited by 17
- Cardinal.lt_aleph0_iff_finiteproof · cited by 8
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