Theorems · Theorem · combinatorics
Matroid.restrict_isColoop_iff
∀ {α : Type u_1} {M : Matroid α} {e : α} {R : Set α},
R ⊆ M.E → ((M.restrict R).IsColoop e ↔ e ∉ M.closure (R \ {e}) ∧ e ∈ R)- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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.Estatement and proof · cited by 550
- Matroid.closurestatement and proof · cited by 272
- Set.insert_eq_of_memproof · cited by 118
- Matroid.restrictstatement and proof · cited by 111
- Matroid.IsCircuitproof · cited by 108
- Matroid.IsColoopstatement and proof · cited by 38
- Set.insert_sdiff_singletonproof · cited by 28
- Matroid.IsColoop.mem_groundproof · cited by 6
- Matroid.mem_closure_iff_exists_isCircuitproof · cited by 4
- Matroid.restrict_isCircuit_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.delete_isColoop_iffproof · cited by 0