Theorems · Theorem · combinatorics
Matroid.closure_insert_closure_eq_closure_insert
∀ {α : Type u_2} (M : Matroid α) (e : α) (X : Set α), M.closure (insert e (M.closure X)) = M.closure (insert e X)- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.closurestatement and proof · cited by 272
- Matroid.closure_union_closure_right_eqproof · cited by 6
Cited by6
Results whose statement or proof uses this declaration.
- Matroid.closure_insert_eq_of_mem_closureproof · cited by 2
- Matroid.indep_iff_forall_closure_sdiff_neproof · cited by 1
- Matroid.mem_closure_insertproof · cited by 1
- Matroid.indep_iff_forall_closure_ssubset_of_ssubsetproof · cited by 0
- Matroid.closure_insert_congrproof · cited by 0
- Matroid.IsNonloop.closure_eq_of_mem_closureproof · cited by 0