Theorems · Theorem · combinatorics
Matroid.IsCircuit.mem_closure_sdiff_singleton_of_mem
∀ {α : Type u_1} {M : Matroid α} {C : Set α} {e : α}, M.IsCircuit C → e ∈ C → e ∈ M.closure (C \ {e})- Defined in
- Mathlib.Combinatorics.Matroid.Circuit
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.closurestatement · cited by 272
- Matroid.IsCircuitstatement and proof · cited by 108
- Matroid.IsCircuit.subset_closure_sdiff_singletonproof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- Matroid.closure_union_eq_of_subset_coloopsproof · cited by 4
- Matroid.isColoop_tfaeproof · cited by 4
- Matroid.mem_closure_iff_exists_isCircuitproof · cited by 4
- Matroid.exists_mem_finite_closure_of_mem_closureproof · cited by 1
- Matroid.IsCircuit.strong_multi_elimination_insertproof · cited by 1
- Matroid.IsCircuit.mem_closure_diff_singleton_of_memproof · cited by 0
- Matroid.IsBase.isColoop_iff_forall_notMem_fundCircuitproof · cited by 0