Theorems · Definition · combinatorics
Matroid.loopyOn
{α : Type u_1} → Set α → Matroid αThe Matroid α with ground set E whose only base is ∅.
The elements are all 'loops' - see Matroid.IsLoop and Matroid.loopyOn_isLoop_iff.
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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 · cited by 1,258
- Matroid.restrictproof · cited by 111
- Matroid.emptyOnproof · cited by 15
Cited by33
Results whose statement or proof uses this declaration.
- Matroid.freeOnproof · cited by 25
- Matroid.loopyOn_closure_eqstatement · cited by 5
- Matroid.loopyOn_groundstatement · cited by 3
- Matroid.closure_empty_eq_ground_iffstatement and proof · cited by 3
- Matroid.empty_isBase_iffstatement · cited by 2
- Matroid.loopyOn_emptystatement · cited by 2
- Matroid.loopyOn_indep_iffstatement · cited by 2
- Matroid.eRank_eq_zero_iffstatement and proof · cited by 2
- Matroid.eRank_loopyOnstatement and proof · cited by 2
- Matroid.eRk_loopyOnstatement and proof · cited by 1
- Matroid.loopyOn_dual_eqstatement · cited by 1
- Matroid.eq_loopyOn_iffstatement · cited by 1