Theorems · Theorem · combinatorics
Matroid.Indep.closure_eq_setOfPred_isBasis_insert
∀ {α : Type u_2} {M : Matroid α} {I : Set α}, M.Indep I → M.closure I = {x | M.IsBasis I (insert x I)}- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
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
- Set.ofPredstatement and proof · cited by 6,101
- LE.le.transproof · cited by 3,151
- Matroidstatement and proof · cited by 1,258
- Matroid.Eproof · cited by 550
- Matroid.Indepstatement and proof · cited by 367
- Set.inter_subset_leftproof · cited by 360
- Matroid.closurestatement and proof · cited by 272
- Set.sInterproof · cited by 225
- Matroid.IsBasisstatement and proof · cited by 219
- Set.subset_union_rightproof · cited by 123
- Set.mem_insertproof · cited by 109
Cited by6
Results whose statement or proof uses this declaration.
- Matroid.IsBasis.closure_eq_closureproof · cited by 13
- Matroid.Indep.mem_closure_iffproof · cited by 6
- Matroid.Indep.isBasis_closureproof · cited by 5
- AlgebraicIndependent.matroid_closure_eqproof · cited by 3
- Matroid.Indep.insert_isBasis_iff_mem_closureproof · cited by 1
- Matroid.Indep.closure_eq_setOf_isBasis_insertproof · cited by 0