Theorems · Theorem · combinatorics
Matroid.IsCircuit.isCocircuit_inter_nontrivial
∀ {α : Type u_1} {M : Matroid α} {C K : Set α}, M.IsCircuit C → M.IsCocircuit K → (C ∩ K).Nonempty → (C ∩ K).Nontrivial- Defined in
- Mathlib.Combinatorics.Matroid.Circuit
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Set.Nonemptystatement and proof · cited by 2,627
- Matroidstatement and proof · cited by 1,258
- Set.Nontrivialstatement · cited by 145
- Matroid.IsCircuitstatement and proof · cited by 108
- Matroid.IsCocircuitstatement and proof · cited by 32
- Matroid.IsCircuit.inter_isCocircuit_ne_singletonproof · cited by 2
- Set.nontrivial_iff_ne_singletonproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Matroid.IsCocircuit.isNonloop_of_memproof · cited by 1
- Matroid.IsCircuit.isCocircuit_disjoint_or_nontrivial_interproof · cited by 0