Theorems · Theorem · combinatorics
Matroid.delete_isCircuit_iff
∀ {α : Type u_1} {M : Matroid α} {D C : Set α}, (M.delete D).IsCircuit C ↔ M.IsCircuit C ∧ Disjoint C D- Cited by
- 4 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Disjointstatement and proof · cited by 2,201
- Matroidstatement and proof · cited by 1,258
- Matroid.IsCircuitstatement and proof · cited by 108
- Matroid.deletestatement · cited by 86
- Set.subset_sdiffproof · cited by 29
- Matroid.IsCircuit.subset_groundproof · cited by 15
- Matroid.delete_eq_restrictproof · cited by 4
- Matroid.restrict_isCircuit_iffproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Matroid.IsCircuit.of_deleteproof · cited by 2
- Matroid.circuit_iff_delete_of_disjointproof · cited by 0
- Matroid.contract_isCocircuit_iffproof · cited by 0
- Matroid.IsCircuit.exists_subset_isCircuit_of_contractproof · cited by 0