Theorems · Theorem · combinatorics
Matroid.Spanning.superset
∀ {α : Type u_2} {M : Matroid α} {S T : Set α},
M.Spanning S → S ⊆ T → autoParam (T ⊆ M.E) Matroid.Spanning.superset._auto_1 → M.Spanning T- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- LE.le.antisymmproof · cited by 507
- Matroid.closureproof · cited by 272
- Matroid.Spanningstatement and proof · cited by 63
- Matroid.closure_subset_closureproof · cited by 24
- Matroid.closure_subset_groundproof · cited by 23
- Matroid.Spanning.closure_eqproof · cited by 4
Cited by7
Results whose statement or proof uses this declaration.
- Matroid.IsBase.spanning_of_supersetproof · cited by 1
- Matroid.spanning_iff_exists_isBase_subset'proof · cited by 1
- Matroid.IsBase.compl_closure_sdiff_singleton_isCocircuitproof · cited by 1
- Matroid.Spanning.closure_eq_of_supersetproof · cited by 0
- Matroid.Spanning.union_leftproof · cited by 0
- Matroid.Spanning.union_rightproof · cited by 0
- Matroid.Spanning.contractproof · cited by 0