Theorems · Theorem · combinatorics
Matroid.IsColoop.isNonloop
∀ {α : Type u_1} {M : Matroid α} {e : α}, M.IsColoop e → M.IsNonloop e- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 1 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Matroidstatement and proof · cited by 1,258
- Matroid.IsBaseproof · cited by 239
- Matroid.IsNonloopstatement and proof · cited by 65
- Matroid.IsColoopstatement and proof · cited by 38
- Matroid.IsBase.indepproof · cited by 22
- Matroid.exists_isBaseproof · cited by 15
- Matroid.Indep.isNonloop_of_memproof · cited by 5
- Matroid.isColoop_iff_forall_mem_isBaseproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.IsLoop.not_isColoopproof · cited by 1