Theorems · Theorem · combinatorics
Matroid.closure_subset_closure
∀ {α : Type u_2} {X Y : Set α} (M : Matroid α), X ⊆ Y → M.closure X ⊆ M.closure Y- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Matroidstatement and proof · cited by 1,258
- Matroid.Eproof · cited by 550
- Matroid.closurestatement · cited by 272
- subset_transproof · cited by 63
- Set.inter_subset_inter_leftproof · cited by 36
- Set.sInter_subset_of_memproof · cited by 28
- Matroid.IsFlatproof · cited by 27
- Set.subset_sInterproof · cited by 8
Cited by24
Results whose statement or proof uses this declaration.
- Matroid.closure_closureproof · cited by 14
- Matroid.IsBasis.closure_eq_closureproof · cited by 13
- Matroid.closure_subset_closure_of_subset_closureproof · cited by 9
- Matroid.Spanning.supersetproof · cited by 7
- Matroid.closure_monoproof · cited by 4
- Matroid.mem_closure_iff_exists_isCircuitproof · cited by 4
- Matroid.indep_iff_forall_notMem_closure_sdiffproof · cited by 3
- Matroid.Indep.closure_sInter_eq_biInter_closure_of_forall_subsetproof · cited by 3
- Matroid.Indep.closure_ssubset_closureproof · cited by 3
- Matroid.IsBase.isBase_insert_sdiff_of_mem_closureproof · cited by 2
- Matroid.Indep.indep_insert_sdiff_of_mem_closureproof · cited by 2
- IsTranscendenceBasis.of_isAlgebraic_adjoin_insert_sdiffproof · cited by 2