Theorems · Theorem · order theory
List.single_le_sum
∀ {M : Type u_3} [inst : AddCommMonoid M] [inst_1 : Preorder M] [IsOrderedAddMonoid M] {l : List M},
(∀ x ∈ l, 0 ≤ x) → ∀ x ∈ l, x ≤ l.sumSee also List.le_sum_of_mem.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Preorderstatement and proof · cited by 7,952
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- le_add_of_nonneg_rightproof · cited by 69
- IsEmpty.forall_iffproof · cited by 39
- le_add_of_nonneg_of_leproof · cited by 5
- List.sum_nonnegproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- List.all_zero_of_le_zero_le_of_sum_eq_zeroproof · cited by 2
- Multiset.single_le_sumproof · cited by 1
- PseudoMetricSpace.le_two_mul_dist_ofPreNNDistproof · cited by 1