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Theorems · Theorem · combinatorics

Matroid.eq_eRk_iff

∀ {α : Type u_1} {M : Matroid α} {X : Set α} {n : ℕ∞},
  autoParam (X ⊆ M.E) Matroid.eq_eRk_iff._auto_1 → (M.eRk X = n ↔ ∃ I, M.IsBasis I X ∧ I.encard = n)
Defined in
Mathlib.Combinatorics.Matroid.Rank.ENat
Cited by
1 results in Mathlib
Foundations
Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Matroid.Indep.eRk_eq_encard · cited by 15Indep.eRk_eq_encardSet · cited by 53352SetENat · cited by 4985ENatMatroid · cited by 1258MatroidMatroid.E · cited by 550Matroid.ESet.encard · cited by 327Set.encardMatroid.IsBasis · cited by 219Matroid.IsBasisMatroid.eRk · cited by 101Matroid.eRkMatroid.exists_isBasis · cited by 23Matroid.exists_isBasisMatroid.IsBasis.encard_eq_eRk · cited by 9IsBasis.encard_eq_eRkMatroid.eq_eRk_iffCITED BYCITES

Cites9

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Cited by1

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