Theorems · Theorem · combinatorics
Matroid.closure_insert_eq_of_mem_closure
∀ {α : Type u_2} {M : Matroid α} {X : Set α} {e : α}, e ∈ M.closure X → M.closure (insert e X) = M.closure X- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Set.insert_eq_of_memproof · cited by 118
- Matroid.closure_closureproof · cited by 14
- Matroid.closure_insert_closure_eq_closure_insertproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Matroid.closure_exchangeproof · cited by 3
- Matroid.Indep.indep_insert_sdiff_of_mem_closureproof · cited by 2