Theorems · Theorem · combinatorics
Matroid.not_isLoop
∀ {α : Type u_1} (M : Matroid α) [M.Loopless] (e : α), ¬M.IsLoop e- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Quot.sound
- Assumes
- Matroid.Loopless
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Set.ofPredproof · cited by 6,101
- Matroidstatement and proof · cited by 1,258
- Matroid.Eproof · cited by 550
- Matroid.IsLoopstatement and proof · cited by 55
- Set.empty_interproof · cited by 30
- Matroid.IsFlatproof · cited by 27
- Matroid.Looplessstatement and proof · cited by 16
- Matroid.IsNonloop.not_isLoopproof · cited by 8
- Matroid.isNonloop_of_looplessproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.loopless_iff_forall_not_isLoopproof · cited by 1