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Theorems · Theorem · order theory

Multiset.card_nsmul_le_sum

∀ {α : Type u_2} [inst : AddCommMonoid α] [inst_1 : Preorder α] {s : Multiset α} {a : α} [AddLeftMono α],
  (∀ x ∈ s, a ≤ x) → s.card • a ≤ s.sum
Defined in
Mathlib.Algebra.Order.BigOperators.Group.Multiset
Cited by
0 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommMonoidPreorderAddLeftMono
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AddCommMonoid · cited by 12281AddCommMonoidPreorder · cited by 7952PreorderMultiset · cited by 2627MultisetAddLeftMono · cited by 687AddLeftMonoMultiset.sum · cited by 388Multiset.sumMultiset.card · cited by 375Multiset.cardMultiset.sum_replicate · cited by 30Multiset.sum_replicateMultiset.map_const · cited by 9Multiset.map_constMultiset.sum_map_le_sum · cited by 2Multiset.sum_map_le_sumMultiset.card_nsmul_le_sumCITED BYCITES

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