Theorems · Theorem · combinatorics
Matroid.loopless_iff_forall_isCircuit
∀ {α : Type u_1} {M : Matroid α}, M.Loopless ↔ ∀ (C : Set α), M.IsCircuit C → C.Nontrivial- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Matroidstatement and proof · cited by 1,258
- Matroid.Eproof · cited by 550
- Set.Subsingletonproof · cited by 276
- Set.Nontrivialstatement and proof · cited by 145
- Matroid.IsCircuitstatement and proof · cited by 108
- Matroid.IsLoopproof · cited by 55
- Set.Subsingleton.eq_empty_or_singletonproof · cited by 16
- Matroid.Looplessstatement · cited by 16
- Matroid.IsLoop.mem_groundproof · cited by 4
- Matroid.IsCircuit.nonemptyproof · cited by 3
- Matroid.singleton_isCircuitproof · cited by 3
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