Theorems · Theorem · combinatorics
Matroid.exists_isCircuit
∀ {α : Type u_1} {M : Matroid α} [M✶.RankPos], ∃ C, M.IsCircuit C- Defined in
- Mathlib.Combinatorics.Matroid.Circuit
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Matroid.RankPos
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.dualstatement and proof · cited by 79
- Matroid.RankPosstatement and proof · cited by 22
- Matroid.dual_rankPos_iff_exists_isCircuitproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.isColoop_iff_forall_mem_compl_isCircuitproof · cited by 0