Theorems · Theorem · combinatorics
Matroid.eRk_union_le_eRk_add_eRk
∀ {α : Type u_1} (M : Matroid α) (X Y : Set α), M.eRk (X ∪ Y) ≤ M.eRk X + M.eRk Y- Defined in
- Mathlib.Combinatorics.Matroid.Rank.ENat
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 · cited by 4,985
- LE.le.transproof · cited by 3,151
- Matroidstatement and proof · cited by 1,258
- Matroid.eRkstatement · cited by 101
- le_add_selfproof · cited by 51
- Matroid.eRk_submodproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- Matroid.eRk_le_eRk_add_eRk_sdiffproof · cited by 1
- Matroid.eRk_le_eRk_inter_add_eRk_sdiffproof · cited by 1
- Matroid.eRk_union_le_encard_add_eRkproof · cited by 1
- Matroid.eRk_eq_eRk_union_eRk_le_zeroproof · cited by 1
- Matroid.eRk_union_le_eRk_add_encardproof · cited by 0
- Matroid.eRk_insert_le_add_oneproof · cited by 0