Theorems · Theorem · combinatorics
Matroid.IsLoop.mem_ground
∀ {α : Type u_1} {M : Matroid α} {e : α}, M.IsLoop e → e ∈ M.E- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 62 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 · cited by 53,352
- Matroidstatement and proof · cited by 1,258
- Matroid.Estatement · cited by 550
- Matroid.IsLoopstatement and proof · cited by 55
- Matroid.closure_subset_groundproof · cited by 23
Cited by4
Results whose statement or proof uses this declaration.
- Matroid.IsColoop.mem_groundproof · cited by 6
- Matroid.isLoop_iff_closure_eq_loops_and_mem_groundproof · cited by 1
- Matroid.loopless_iff_forall_isNonloopproof · cited by 1
- Matroid.loopless_iff_forall_isCircuitproof · cited by 0