Theorems · Theorem · combinatorics
Matroid.Spanning.cRank_le_cardinalMk
∀ {α : Type u} {M : Matroid α} {X : Set α} [M.InvariantCardinalRank], M.Spanning X → M.cRank ≤ Cardinal.mk ↑X- Cited by
- 1 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Matroidstatement and proof · cited by 1,258
- Cardinal.mkstatement and proof · cited by 942
- Matroid.IsBaseproof · cited by 239
- Eq.trans_leproof · cited by 155
- Matroid.Spanningstatement and proof · cited by 63
- Cardinal.mk_le_mk_of_subsetproof · cited by 37
- Matroid.InvariantCardinalRankstatement and proof · cited by 25
- Matroid.cRankstatement and proof · cited by 17
- Matroid.Spanning.exists_isBase_subsetproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.IsAlgebraic.trdeg_le_cardinalMkproof · cited by 1