Theorems · Theorem · combinatorics
Matroid.isColoop_iff_sdiff_closure
∀ {α : Type u_1} {M : Matroid α} {e : α}, M.IsColoop e ↔ M.closure (M.E \ {e}) ≠ M.E- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.Estatement and proof · cited by 550
- Matroid.closurestatement and proof · cited by 272
- Matroid.IsColoopstatement · cited by 38
- Matroid.spanning_iff_closure_eqproof · cited by 7
- Matroid.isColoop_iff_sdiff_not_spanningproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Matroid.isColoop_iff_notMem_closure_complproof · cited by 1
- Matroid.isColoop_iff_diff_closureproof · cited by 0