Theorems · Theorem · combinatorics
Matroid.spanning_iff_exists_isBase_subset
∀ {α : Type u_2} {M : Matroid α} {S : Set α},
autoParam (S ⊆ M.E) Matroid.spanning_iff_exists_isBase_subset._auto_1 → (M.Spanning S ↔ ∃ B, M.IsBase B ∧ B ⊆ S)- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.IsBasestatement and proof · cited by 239
- Matroid.Spanningstatement · cited by 63
- Matroid.spanning_iff_exists_isBase_subset'proof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Matroid.Spanning.exists_isBase_subsetproof · cited by 6
- Matroid.coindep_iff_compl_spanningproof · cited by 5
- Matroid.isCocircuit_iff_minimal_compl_nonspanningproof · cited by 2
- isAlgebraic_iff_exists_isTranscendenceBasis_subsetproof · cited by 0