Theorems · Theorem · combinatorics
Matroid.IsLoop.not_indep_of_mem
∀ {α : Type u_1} {M : Matroid α} {e : α} {X : Set α}, M.IsLoop e → e ∈ X → ¬M.Indep X- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.Indepstatement and proof · cited by 367
- Set.singleton_subset_iffproof · cited by 206
- Matroid.IsLoopstatement and proof · cited by 55
- Matroid.Indep.subsetproof · cited by 42
- Matroid.Dep.not_indepproof · cited by 14
- Matroid.IsLoop.depproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Matroid.IsLoop.notMem_of_indepproof · cited by 3
- Matroid.ext_indep_disjoint_loops_coloopsproof · cited by 0