Theorems · Inductive type · combinatorics
Matroid.Loopless
{α : Type u_1} → Matroid α → PropA Matroid is Loopless if it has no loop
- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Matroidstatement · cited by 1,258
Cited by18
Results whose statement or proof uses this declaration.
- Matroid.isNonloop_of_looplessstatement and proof · cited by 6
- Matroid.removeLoops_eq_selfstatement and proof · cited by 2
- Matroid.loops_eq_emptystatement and proof · cited by 2
- Matroid.loopless_iffstatement and proof · cited by 1
- Matroid.loopless_iff_forall_isNonloopstatement and proof · cited by 1
- Matroid.loopless_iff_forall_not_isLoopstatement and proof · cited by 1
- Matroid.Loopless.casesOnstatement and proof · cited by 1
- Matroid.Loopless.ground_eqstatement and proof · cited by 1
- Matroid.Loopless.loops_eq_emptystatement and proof · cited by 1
- Matroid.not_isLoopstatement and proof · cited by 1
- Matroid.IsRestriction.isRestriction_removeLoopsstatement and proof · cited by 1
- Matroid.eRk_singleton_eqstatement and proof · cited by 0