Theorems · Theorem · combinatorics
Matroid.Dep.superset
∀ {α : Type u_1} {M : Matroid α} {D X : Set α},
M.Dep D → D ⊆ X → autoParam (X ⊆ M.E) Matroid.Dep.superset._auto_1 → M.Dep X- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 61 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.
- Setstatement and proof · cited by 53,352
- Matroidstatement and proof · cited by 1,258
- Matroid.Estatement and proof · cited by 550
- Matroid.Indepproof · cited by 367
- Matroid.Depstatement and proof · cited by 76
- Matroid.Indep.subsetproof · cited by 42
- Matroid.Indep.not_depproof · cited by 7
- Matroid.dep_of_not_indepproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- Matroid.IsBasis.iUnion_isBasis_iUnionproof · cited by 2
- Matroid.IsCircuit.eq_fundCircuit_of_subsetproof · cited by 0
- Matroid.IsLoop.dep_of_memproof · cited by 0
- Matroid.dep_iff_superset_isCircuitproof · cited by 0
- Matroid.dep_iff_superset_isCircuit'proof · cited by 0
- Matroid.IsCircuit.exists_subset_isCircuit_of_contractproof · cited by 0