Theorems · Theorem · combinatorics
Matroid.mem_closure_insert
∀ {α : Type u_2} {M : Matroid α} {X : Set α} {e f : α},
e ∉ M.closure X → e ∈ M.closure (insert f X) → f ∈ M.closure (insert e X)- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
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.Eproof · cited by 550
- Matroid.Indepproof · cited by 367
- Matroid.closurestatement and proof · cited by 272
- Matroid.IsBasisproof · cited by 219
- Set.mem_insertproof · cited by 109
- Set.subset_insertproof · cited by 96
- Matroid.Indep.subset_groundproof · cited by 61
- Matroid.IsBasis.indepproof · cited by 51
- Matroid.Indep.subsetproof · cited by 42
- Set.mem_insert_iffproof · cited by 39
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.closure_exchangeproof · cited by 3