Theorems · Definition · combinatorics
Matroid.IsCocircuit
{α : Type u_1} → Matroid α → Set α → PropA cocircuit is a circuit of the dual matroid, or equivalently the complement of a hyperplane.
- Defined in
- Mathlib.Combinatorics.Matroid.Circuit
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.IsCircuitproof · cited by 108
- Matroid.dualproof · cited by 79
Cited by32
Results whose statement or proof uses this declaration.
- Matroid.isCocircuit_defstatement · cited by 7
- Matroid.IsCocircuit.isCircuitstatement and proof · cited by 4
- Matroid.isColoop_tfaestatement and proof · cited by 4
- Matroid.isColoop_iff_forall_mem_isBaseproof · cited by 3
- Matroid.isColoop_iff_sdiff_not_spanningproof · cited by 3
- Matroid.IsCocircuit.subset_groundstatement and proof · cited by 2
- Matroid.fundCocircuit_isCocircuitstatement · cited by 2
- Matroid.isCocircuit_iff_minimal_compl_nonspanningstatement and proof · cited by 2
- Matroid.isColoop_iff_forall_mem_closure_iff_memproof · cited by 2
- Matroid.IsCircuit.inter_isCocircuit_ne_singletonstatement and proof · cited by 2
- Matroid.IsCircuit.isCocircuit_inter_nontrivialstatement and proof · cited by 2
- Matroid.IsCocircuit.delete_sdiff_isCocircuitstatement and proof · cited by 1