Theorems · Theorem · combinatorics
Matroid.IsCircuit.contract_sdiff_isCircuit
∀ {α : Type u_1} {M : Matroid α} {K C : Set α}, M.IsCircuit C → K.Nonempty → K ⊆ C → (M.contract (C \ K)).IsCircuit K- Cited by
- 2 results in Mathlib
- Foundations
- Depth 97 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
- Set.Nonemptystatement and proof · cited by 2,627
- Matroidstatement and proof · cited by 1,258
- Matroid.IsCircuitstatement and proof · cited by 108
- Matroid.contractstatement and proof · cited by 103
- Set.inter_eq_self_of_subset_rightproof · cited by 39
- sdiff_sdiff_right_selfproof · cited by 20
- Matroid.IsCircuit.contract_isCircuitproof · cited by 4
- Set.sdiff_ssubset_left_iffproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Matroid.IsCocircuit.delete_sdiff_isCocircuitproof · cited by 1
- Matroid.IsCircuit.contract_diff_isCircuitproof · cited by 0