Theorems · Theorem · combinatorics
Matroid.Spanning.isBase_of_le_cRank_of_finite
∀ {α : Type u} {M : Matroid α} {X : Set α}, M.Spanning X → Cardinal.mk ↑X ≤ M.cRank → X.Finite → M.IsBase X- Cited by
- 1 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Set.Finite.subsetproof · cited by 285
- Matroid.IsBasestatement and proof · cited by 239
- Matroid.Spanningstatement and proof · cited by 63
- Matroid.RankFiniteproof · cited by 33
- 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.isTranscendenceBasis_of_lift_le_trdeg_of_finiteproof · cited by 2