Theorems · Theorem · combinatorics
Matroid.loopless_iff_forall_isNonloop
∀ {α : Type u_1} {M : Matroid α}, M.Loopless ↔ ∀ e ∈ M.E, M.IsNonloop e- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement · cited by 53,352
- Matroidstatement and proof · cited by 1,258
- Matroid.Estatement and proof · cited by 550
- Matroid.IsNonloopstatement and proof · cited by 65
- Matroid.IsLoopproof · cited by 55
- Set.subset_empty_iffproof · cited by 40
- Matroid.Looplessstatement and proof · cited by 16
- Matroid.IsNonloop.not_isLoopproof · cited by 8
- Matroid.isNonloop_of_looplessproof · cited by 6
- Matroid.IsLoop.mem_groundproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.loopless_iff_forall_not_isLoopproof · cited by 1