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Theorems · Theorem · order theory

Multiset.sum_le_card_nsmul

∀ {α : Type u_2} [inst : AddCommMonoid α] [inst_1 : Preorder α] [AddLeftMono α] (s : Multiset α) (n : α),
  (∀ x ∈ s, x ≤ n) → s.sum ≤ s.card • n
Defined in
Mathlib.Algebra.Order.BigOperators.Group.Multiset
Cited by
3 results in Mathlib
Foundations
Depth 22 from the axioms · uses propext, Quot.sound
Assumes
AddCommMonoidPreorderAddLeftMono
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Finset.sum_le_card_nsmul · cited by 25Finset.sum_le_card_nsmulPolynomial.coeff_le_of_roots_le · cited by 1Polynomial.coeff_le_of_ro…Fin.isAddFreimanIso_Iic · cited by 1Fin.isAddFreimanIso_IicAddCommMonoid · cited by 12281AddCommMonoidPreorder · cited by 7952PreorderMultiset · cited by 2627MultisetAddLeftMono · cited by 687AddLeftMonoMultiset.sum · cited by 388Multiset.sumMultiset.card · cited by 375Multiset.cardList.sum_le_card_nsmul · cited by 3List.sum_le_card_nsmulMultiset.sum_le_card_nsmulCITED BYCITES

Cites7

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Cited by3

Results whose statement or proof uses this declaration.