Theorems · Theorem · combinatorics
Matroid.dual_isLoop_iff_isColoop
∀ {α : Type u_1} {M : Matroid α} {e : α}, M✶.IsLoop e ↔ M.IsColoop e- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 74 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.
- Matroidstatement and proof · cited by 1,258
- Matroid.dualstatement and proof · cited by 79
- Matroid.IsLoopstatement and proof · cited by 55
- Matroid.IsColoopstatement and proof · cited by 38
- Matroid.dual_dualproof · cited by 22
- Matroid.IsLoop.dual_isColoopproof · cited by 2
- Matroid.IsColoop.dual_isLoopproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Matroid.isColoop_tfaeproof · cited by 4
- Matroid.IsLoop.not_isColoopproof · cited by 1