Theorems · Theorem · combinatorics
Matroid.IsCircuit.sdiff_singleton_isBasis
∀ {α : Type u_1} {M : Matroid α} {C : Set α} {e : α}, M.IsCircuit C → e ∈ C → M.IsBasis (C \ {e}) C- Defined in
- Mathlib.Combinatorics.Matroid.Circuit
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 63 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
- Matroidstatement and proof · cited by 1,258
- Matroid.IsBasisstatement and proof · cited by 219
- Set.insert_eq_of_memproof · cited by 118
- Matroid.IsCircuitstatement and proof · cited by 108
- Matroid.Depproof · cited by 76
- Set.insert_sdiff_singletonproof · cited by 28
- Matroid.IsCircuit.depproof · cited by 15
- Matroid.IsCircuit.sdiff_singleton_indepproof · cited by 5
- Matroid.Indep.isBasis_insert_iffproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Matroid.IsCircuit.closure_sdiff_singleton_eqproof · cited by 5
- Matroid.IsCircuit.isBasis_iff_eq_sdiff_singletonproof · cited by 2
- Matroid.IsCircuit.eq_fundCircuit_of_subsetproof · cited by 0
- Matroid.IsCircuit.diff_singleton_isBasisproof · cited by 0