Theorems · Theorem · combinatorics
Matroid.isColoop_iff_sdiff_not_spanning
∀ {α : Type u_1} {M : Matroid α} {e : α}, M.IsColoop e ↔ ¬M.Spanning (M.E \ {e})- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 3 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.
Cites12
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.closureproof · cited by 272
- Matroid.IsBaseproof · cited by 239
- List.TFAE.outproof · cited by 177
- Matroid.IsCircuitproof · cited by 108
- Matroid.Spanningstatement and proof · cited by 63
- Matroid.IsColoopstatement and proof · cited by 38
- Matroid.coloopsproof · cited by 34
- Matroid.IsCocircuitproof · cited by 32
- Matroid.isColoop_tfaeproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Matroid.isColoop_iff_sdiff_closureproof · cited by 2
- Matroid.isColoop_iff_diff_not_spanningproof · cited by 0
- Matroid.IsColoop.sdiff_not_spanningproof · cited by 0