Theorems · Theorem · combinatorics
Matroid.IsCircuit.inter_isCocircuit_ne_singleton
∀ {α : Type u_1} {M : Matroid α} {C : Set α} {e : α} {K : Set α}, M.IsCircuit C → M.IsCocircuit K → C ∩ K ≠ {e}A cocircuit and a circuit cannot meet in exactly one element.
- Defined in
- Mathlib.Combinatorics.Matroid.Circuit
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
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
- LE.le.transproof · cited by 3,151
- le_reflproof · cited by 2,061
- Matroidstatement and proof · cited by 1,258
- Matroid.Eproof · cited by 550
- Set.inter_subset_leftproof · cited by 360
- Matroid.closureproof · cited by 272
- Set.subset_union_leftproof · cited by 142
- Eq.subsetproof · cited by 124
- Set.insert_eq_of_memproof · cited by 118
- Matroid.IsCircuitstatement and proof · cited by 108
- Matroid.Spanningproof · cited by 63
Cited by2
Results whose statement or proof uses this declaration.
- Matroid.isColoop_tfaeproof · cited by 4
- Matroid.IsCircuit.isCocircuit_inter_nontrivialproof · cited by 2