Theorems · Theorem · combinatorics
Matroid.IsCocircuit.isNonloop_of_mem
∀ {α : Type u_1} {M : Matroid α} {e : α} {K : Set α}, M.IsCocircuit K → e ∈ K → M.IsNonloop e- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.IsCircuitproof · cited by 108
- Matroid.IsNonloopstatement · cited by 65
- Matroid.IsCocircuitstatement and proof · cited by 32
- Set.Nontrivial.exists_neproof · cited by 8
- Matroid.not_isLoop_iffproof · cited by 5
- Set.singleton_inter_of_memproof · cited by 3
- Matroid.singleton_isCircuitproof · cited by 3
- Matroid.IsCircuit.isCocircuit_inter_nontrivialproof · cited by 2
- Matroid.IsCocircuit.subset_groundproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.IsColoop.notMem_isCircuitproof · cited by 3