Theorems · Theorem · combinatorics
Matroid.closure_closure
∀ {α : Type u_2} (M : Matroid α) (X : Set α), M.closure (M.closure X) = M.closure X- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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.ofPredproof · cited by 6,101
- LE.le.transproof · cited by 3,151
- Matroidstatement and proof · cited by 1,258
- Matroid.Eproof · cited by 550
- Matroid.closurestatement and proof · cited by 272
- Eq.subsetproof · cited by 124
- LE.le.antisymm'proof · cited by 104
- Set.sInter_subset_of_memproof · cited by 28
- Matroid.IsFlatproof · cited by 27
- Matroid.closure_subset_closureproof · cited by 24
- Matroid.closure_subset_groundproof · cited by 23
Cited by14
Results whose statement or proof uses this declaration.
- Matroid.IsBasis.closure_eq_closureproof · cited by 13
- Matroid.closure_subset_closure_of_subset_closureproof · cited by 9
- Matroid.closure_union_closure_right_eqproof · cited by 6
- Matroid.closure_union_closure_left_eqproof · cited by 5
- Matroid.closure_sdiff_eq_selfproof · cited by 3
- Matroid.closure_insert_eq_of_mem_closureproof · cited by 2
- Matroid.closure_iUnion_congrproof · cited by 1
- Matroid.IsBasis.closure_eq_rightproof · cited by 1
- Matroid.closure_loopsproof · cited by 1
- Matroid.indep_iff_forall_closure_sdiff_neproof · cited by 1
- Matroid.closure_spanning_iffproof · cited by 1
- Matroid.closure_insert_congrproof · cited by 0