Theorems · Theorem · combinatorics
Matroid.IsBase.encard_eq_encard_of_isBase
∀ {α : Type u_1} {M : Matroid α} {B₁ B₂ : Set α}, M.IsBase B₁ → M.IsBase B₂ → B₁.encard = B₂.encard- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- ENatstatement and proof · cited by 4,985
- Matroidstatement and proof · cited by 1,258
- Set.encardstatement and proof · cited by 327
- Matroid.IsBasestatement and proof · cited by 239
- Matroid.isBase_exchangeproof · cited by 4
- Matroid.ExchangeProperty.encard_isBase_eqproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Matroid.IsBase.encard_eq_eRankproof · cited by 10
- Matroid.IsBase.finite_of_finiteproof · cited by 2
- Matroid.IsBasis'.encard_eq_encardproof · cited by 1
- Matroid.IsBase.ncard_eq_ncard_of_isBaseproof · cited by 0