Theorems · Theorem · order theory
List.sum_le_card_nsmul
∀ {M : Type u_3} [inst : AddMonoid M] [inst_1 : Preorder M] [AddRightMono M] [AddLeftMono M] (l : List M) (n : M),
(∀ x ∈ l, x ≤ n) → l.sum ≤ l.length • n- Cited by
- 3 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, 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.
- Preorderstatement and proof · cited by 7,952
- AddMonoidstatement and proof · cited by 2,864
- AddLeftMonostatement and proof · cited by 687
- AddRightMonostatement and proof · cited by 367
- List.sum_replicateproof · cited by 19
- List.sum_le_sumproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- Multiset.sum_le_card_nsmulproof · cited by 3
- Polynomial.coeff_list_prod_of_natDegree_leproof · cited by 1
- List.card_nsmul_le_sumproof · cited by 0