Theorems · Theorem · combinatorics
Matroid.IsCocircuit.delete_sdiff_isCocircuit
∀ {α : Type u_1} {M : Matroid α} {K X : Set α}, M.IsCocircuit K → X ⊆ K → X.Nonempty → (M.delete (K \ X)).IsCocircuit X- Cited by
- 1 results in Mathlib
- Foundations
- Depth 98 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 and proof · cited by 53,352
- Set.Nonemptystatement and proof · cited by 2,627
- Matroidstatement and proof · cited by 1,258
- Matroid.IsCircuitproof · cited by 108
- Matroid.deletestatement · cited by 86
- Matroid.IsCocircuitstatement and proof · cited by 32
- Matroid.isCocircuit_defproof · cited by 7
- Matroid.dual_deleteproof · cited by 5
- Matroid.IsCocircuit.isCircuitproof · cited by 4
- Matroid.IsCircuit.contract_sdiff_isCircuitproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.IsCocircuit.delete_diff_isCocircuitproof · cited by 0