Theorems · Theorem · combinatorics
Matroid.eRk_submod
∀ {α : Type u_1} (M : Matroid α) (X Y : Set α), M.eRk (X ∩ Y) + M.eRk (X ∪ Y) ≤ M.eRk X + M.eRk YAlias of Matroid.eRk_inter_add_eRk_union_le.
The ℕ∞-valued rank function is submodular.
- Defined in
- Mathlib.Combinatorics.Matroid.Rank.ENat
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- ENatstatement · cited by 4,985
- Matroidstatement · cited by 1,258
- Matroid.eRkstatement · cited by 101
- Matroid.eRk_inter_add_eRk_union_leproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Matroid.eRk_union_le_eRk_add_eRkproof · cited by 6
- Matroid.eRk_compl_union_add_eRk_compl_inter_leproof · cited by 1
- Matroid.eRk_insert_inter_add_eRk_insert_union_leproof · cited by 0