Theorems · Theorem · combinatorics
Matroid.singleton_isCircuit
∀ {α : Type u_1} {M : Matroid α} {e : α}, M.IsCircuit {e} ↔ M.IsLoop e- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.Eproof · cited by 550
- Matroid.closureproof · cited by 272
- Matroid.IsBaseproof · cited by 239
- List.TFAE.outproof · cited by 177
- Matroid.IsCircuitstatement and proof · cited by 108
- Matroid.Depproof · cited by 76
- Matroid.IsLoopstatement and proof · cited by 55
- Matroid.isLoop_tfaeproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Matroid.IsLoop.isCircuitproof · cited by 3
- Matroid.IsCocircuit.isNonloop_of_memproof · cited by 1
- Matroid.loopless_iff_forall_isCircuitproof · cited by 0