Theorems · Definition · combinatorics
Matroid.removeLoops
{α : Type u_1} → Matroid α → Matroid αThe loopless matroid obtained from M by deleting all its loops.
- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 17 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.
- Set.ofPredproof · cited by 6,101
- Matroidstatement and proof · cited by 1,258
- Matroid.restrictproof · cited by 111
- Matroid.IsNonloopproof · cited by 65
Cited by17
Results whose statement or proof uses this declaration.
- Matroid.removeLoops_eq_restrictstatement · cited by 4
- Matroid.removeLoops_eq_selfstatement · cited by 2
- Matroid.removeLoops_indep_eqstatement · cited by 2
- Matroid.removeLoops_isNonloop_eqstatement · cited by 1
- Matroid.removeLoops_isRestrictionstatement · cited by 1
- Matroid.IsRestriction.isRestriction_removeLoopsstatement · cited by 1
- Matroid.restrict_univ_removeLoops_eqstatement and proof · cited by 0
- Matroid.removeLoops_eq_self_iffstatement and proof · cited by 0
- Matroid.removeLoops_ground_eqstatement · cited by 0
- Matroid.removeLoops_idemstatement and proof · cited by 0
- Matroid.removeLoops_isBase_eqstatement · cited by 0
- Matroid.removeLoops_isBasis'_eqstatement · cited by 0