Theorems · Theorem · combinatorics
Matroid.mem_closure_of_mem
∀ {α : Type u_2} {X : Set α} {e : α} (M : Matroid α),
e ∈ X → autoParam (X ⊆ M.E) Matroid.mem_closure_of_mem._auto_1 → e ∈ M.closure X- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 63 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 and proof · cited by 53,352
- Matroidstatement and proof · cited by 1,258
- Matroid.Estatement and proof · cited by 550
- Matroid.closurestatement · cited by 272
- Matroid.subset_closureproof · cited by 23
Cited by4
Results whose statement or proof uses this declaration.
- Matroid.mem_closure_of_mem'proof · cited by 8
- Matroid.Indep.closure_sInter_eq_biInter_closure_of_forall_subsetproof · cited by 3
- Matroid.Indep.closure_ssubset_closureproof · cited by 3
- Matroid.indep_iff_forall_closure_sdiff_neproof · cited by 1