Theorems · Theorem · combinatorics
Matroid.isColoop_iff_forall_mem_closure_iff_mem
∀ {α : Type u_1} {M : Matroid α} {e : α}, M.IsColoop e ↔ ∀ (X : Set α), e ∈ M.closure X ↔ e ∈ X- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 95 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
- Matroid.Eproof · cited by 550
- Matroid.closurestatement and proof · cited by 272
- Matroid.IsBaseproof · cited by 239
- List.TFAE.outproof · cited by 177
- Matroid.IsCircuitproof · cited by 108
- Matroid.Spanningproof · cited by 63
- Matroid.IsColoopstatement and proof · cited by 38
- Matroid.coloopsproof · cited by 34
- Matroid.IsCocircuitproof · cited by 32
- Matroid.isColoop_tfaeproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Matroid.IsColoop.mem_closure_iff_memproof · cited by 5
- Matroid.isColoop_iff_forall_mem_closure_iff_mem'proof · cited by 0