Theorems · Theorem · order theory
Finset.sum_le_sum_of_ne_zero
∀ {ι : Type u_1} {M : Type u_4} [inst : AddCommMonoid M] [inst_1 : Preorder M] [CanonicallyOrderedAdd M] {f : ι → M}
{s t : Finset ι}, (∀ x ∈ s, f x ≠ 0 → x ∈ t) → ∑ x ∈ s, f x ≤ ∑ x ∈ t, f x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Preorderstatement and proof · cited by 7,952
- Finset.sumstatement and proof · cited by 5,195
- IsOrderedAddMonoidproof · cited by 1,659
- le_of_eqproof · cited by 366
- CanonicallyOrderedAddstatement and proof · cited by 229
- Finset.mem_filterproof · cited by 185
- Finset.sum_unionproof · cited by 40
- Finset.filter_union_filter_not_eqproof · cited by 16
- Finset.sum_le_sum_of_subsetproof · cited by 14
- Finset.disjoint_filterproof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- Finset.card_sq_le_card_mul_mulEnergyproof · cited by 1
- Finset.card_sq_le_card_mul_addEnergyproof · cited by 1