Theorems · Definition · combinatorics
Matroid.sigma
{ι : Type u_1} → {α : ι → Type u_2} → ((i : ι) → Matroid (α i)) → Matroid ((i : ι) × α i)The sum of an indexed collection of matroids, as a matroid on the sigma-type.
- Defined in
- Mathlib.Combinatorics.Matroid.Sum
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Set.preimageproof · cited by 4,946
- Set.univproof · cited by 3,945
- Matroidstatement and proof · cited by 1,258
- Matroid.Eproof · cited by 550
- Matroid.Indepproof · cited by 367
- Matroid.IsBaseproof · cited by 239
- Set.sigmaproof · cited by 65
Cited by18
Results whose statement or proof uses this declaration.
- Matroid.sumproof · cited by 5
- Matroid.sum'proof · cited by 5
- Matroid.disjointSigmaproof · cited by 4
- Matroid.Finitary.sigmastatement and proof · cited by 1
- Matroid.sum_groundproof · cited by 1
- Matroid.sigma_ground_eqstatement · cited by 0
- Matroid.sigma_indep_iffstatement · cited by 0
- Matroid.sigma_isBase_iffstatement · cited by 0
- Matroid.sigma_isBasis_iffstatement · cited by 0
- Matroid.Finitary.sum'proof · cited by 0
- Matroid.disjointSigma_ground_eqproof · cited by 0
- Matroid.sum'_ground_eqproof · cited by 0