Theorems · Theorem · combinatorics
Matroid.IsLoop.isCircuit
∀ {α : Type u_1} {M : Matroid α} {e : α}, M.IsLoop e → M.IsCircuit {e}Alias of the reverse direction of Matroid.singleton_isCircuit.
- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Matroidstatement and proof · cited by 1,258
- Matroid.IsCircuitstatement · cited by 108
- Matroid.IsLoopstatement · cited by 55
- Matroid.singleton_isCircuitproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Matroid.IsLoop.eq_of_isCircuit_memproof · cited by 2
- Matroid.loopless_iff_forall_isCircuitproof · cited by 0
- Matroid.IsColoop.isCocircuitproof · cited by 0