Theorems · Theorem · combinatorics
Matroid.IsColoop.mem_ground
∀ {α : Type u_1} {M : Matroid α} {e : α}, M.IsColoop e → e ∈ M.E- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 70 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.IsColoopstatement and proof · cited by 38
- Matroid.IsLoop.mem_groundproof · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- Matroid.isColoop_tfaeproof · cited by 4
- Matroid.restrict_isColoop_iffproof · cited by 1
- Matroid.coloops_subset_groundproof · cited by 1
- Matroid.isColoop_iff_forall_mem_closure_iff_mem'proof · cited by 0
- Matroid.isColoop_iff_forall_mem_compl_isCircuitproof · cited by 0
- Matroid.IsColoop.insert_indep_of_indepproof · cited by 0