Theorems · Inductive type · combinatorics
Matroid.IsNonloop
{α : Type u_1} → Matroid α → α → PropM.IsNonloop e means that e is an element of M.E but not a loop of M.
- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 65 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 by68
Results whose statement or proof uses this declaration.
- Matroid.removeLoopsproof · cited by 17
- Matroid.indep_singletonstatement · cited by 12
- Matroid.IsNonloop.not_isLoopstatement and proof · cited by 8
- Matroid.IsNonloop.mem_groundstatement and proof · cited by 6
- Matroid.isNonloop_iffstatement and proof · cited by 6
- Matroid.isNonloop_of_looplessstatement · cited by 6
- Matroid.not_isLoop_iffstatement · cited by 5
- Matroid.Indep.isNonloop_of_memstatement · cited by 5
- Matroid.removeLoops_eq_restrictstatement · cited by 4
- Matroid.restrict_isNonloop_iffstatement and proof · cited by 3
- Matroid.IsNonloop.eRk_eqstatement and proof · cited by 3
- Matroid.IsNonloop.indepstatement · cited by 3