Theorems · Theorem · combinatorics
Matroid.isColoop_iff_forall_mem_compl_isCircuit
∀ {α : Type u_1} {M : Matroid α} {e : α} [M✶.RankPos], M.IsColoop e ↔ ∀ (C : Set α), M.IsCircuit C → e ∈ M.E \ C- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Matroid.RankPos
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Cites9
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.Estatement and proof · cited by 550
- Matroid.IsCircuitstatement and proof · cited by 108
- Matroid.dualstatement and proof · cited by 79
- Matroid.IsColoopstatement and proof · cited by 38
- Matroid.RankPosstatement and proof · cited by 22
- Matroid.IsColoop.mem_groundproof · cited by 6
- Matroid.exists_isCircuitproof · cited by 1
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