Theorems · Theorem · combinatorics
Matroid.IsCircuit.sdiff_singleton_indep
∀ {α : Type u_1} {M : Matroid α} {C : Set α} {e : α}, M.IsCircuit C → e ∈ C → M.Indep (C \ {e})- Defined in
- Mathlib.Combinatorics.Matroid.Circuit
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.Indepstatement · cited by 367
- Matroid.IsCircuitstatement and proof · cited by 108
- Matroid.IsCircuit.ssubset_indepproof · cited by 4
- Set.sdiff_singleton_ssubsetproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- Matroid.IsCircuit.contract_isCircuitproof · cited by 4
- Matroid.IsCircuit.sdiff_singleton_isBasisproof · cited by 4
- Matroid.IsCircuit.isBasis_iff_eq_sdiff_singletonproof · cited by 2
- Matroid.exists_mem_finite_closure_of_mem_closureproof · cited by 1
- Matroid.IsCircuit.diff_singleton_indepproof · cited by 0