Theorems · Theorem · combinatorics
Matroid.IsRkFinite.closure_eq_closure_of_subset_of_forall_insert
∀ {α : Type u_1} {M : Matroid α} {X Y : Set α},
M.IsRkFinite X → X ⊆ Y → (∀ e ∈ Y \ X, M.eRk (insert e X) ≤ M.eRk X) → M.closure X = M.closure Y- Defined in
- Mathlib.Combinatorics.Matroid.Rank.ENat
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- ENatstatement and proof · cited by 4,985
- Matroidstatement and proof · cited by 1,258
- LT.lt.neproof · cited by 872
- not_ltproof · cited by 306
- Matroid.closurestatement · cited by 272
- Matroid.eRkstatement and proof · cited by 101
- Matroid.IsRkFinitestatement and proof · cited by 53
- ENat.add_one_le_iffproof · cited by 11
- Matroid.IsRkFinite.eRk_lt_topproof · cited by 3
- Matroid.exists_eRk_insert_eq_add_one_of_ltproof · cited by 1
- Matroid.IsRkFinite.closure_eq_closure_of_subset_of_eRk_ge_eRkproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.eRk_eq_of_eRk_insert_le_forallproof · cited by 0