Theorems · Theorem · order theory
Multiset.abs_sum_le_sum_abs
∀ {α : Type u_2} [inst : AddCommGroup α] [inst_1 : LinearOrder α] [IsOrderedAddMonoid α] {s : Multiset α},
|s.sum| ≤ (Multiset.map abs s).sum- Cited by
- 0 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- Multisetstatement and proof · cited by 2,627
- absstatement and proof · cited by 1,814
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- Multiset.mapstatement · cited by 876
- Eq.leproof · cited by 605
- Multiset.sumstatement · cited by 388
- abs_zeroproof · cited by 88
- abs_add_leproof · cited by 17
- Multiset.le_sum_of_subadditiveproof · cited by 4
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