Theorems · Theorem · combinatorics
Matroid.isColoop_iff_notMem_closure_compl
∀ {α : Type u_1} {M : Matroid α} {e : α},
autoParam (e ∈ M.E) Matroid.isColoop_iff_notMem_closure_compl._auto_1 → (M.IsColoop e ↔ e ∉ M.closure (M.E \ {e}))- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 1 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.
Cites12
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
- eq_or_neproof · cited by 1,117
- Matroid.Estatement and proof · cited by 550
- LE.le.antisymmproof · cited by 507
- Matroid.closurestatement and proof · cited by 272
- not_iff_notproof · cited by 159
- Set.sdiff_subsetproof · cited by 156
- Matroid.IsColoopstatement · cited by 38
- Matroid.closure_subset_groundproof · cited by 23
- Matroid.subset_closureproof · cited by 23
- Matroid.isColoop_iff_sdiff_closureproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.IsBase.isColoop_iff_forall_notMem_fundCircuitproof · cited by 0