Theorems · Theorem · combinatorics
Matroid.closure_subset_closure_of_subset_closure
∀ {α : Type u_2} {M : Matroid α} {X Y : Set α}, X ⊆ M.closure Y → M.closure X ⊆ M.closure Y- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 65 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
- LE.le.trans_eqproof · cited by 328
- Matroid.closurestatement and proof · cited by 272
- Matroid.closure_subset_closureproof · cited by 24
- Matroid.closure_closureproof · cited by 14
Cited by9
Results whose statement or proof uses this declaration.
- Matroid.closure_union_eq_of_subset_coloopsproof · cited by 4
- Matroid.closure_subset_closure_iff_subset_closureproof · cited by 3
- Matroid.Indep.closure_insert_sdiff_eq_of_mem_closureproof · cited by 2
- Matroid.closure_eq_loops_of_subsetproof · cited by 2
- Matroid.exists_of_closure_ssubsetproof · cited by 0
- Matroid.IsBasis.closure_inter_isBasis_closureproof · cited by 0
- Matroid.IsRkFinite.isBasis_of_subset_closure_of_subset_of_encard_leproof · cited by 0
- Matroid.IsBase.isColoop_iff_forall_notMem_fundCircuitproof · cited by 0
- Matroid.fundCircuit_restrictproof · cited by 0