Theorems · Theorem · order theory
Finset.sum_le_one_iff
∀ {α : Type u_2} {s : Finset α} {f : α → ℕ},
∑ x ∈ s, f x ≤ 1 ↔ ∀ (x y : α), x ∈ s → y ∈ s → f x ≠ 0 → f y ≠ 0 → x = y ∧ f x = 1- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- AddCommMonoidproof · cited by 12,281
- Finset.sumstatement and proof · cited by 5,195
- LE.le.transproof · cited by 3,151
- zero_addproof · cited by 2,366
- Finset.sum_congrproof · cited by 2,323
- Finset.sum_singletonproof · cited by 251
- Finset.sum_const_zeroproof · cited by 219
- Finset.singleton_subset_iffproof · cited by 38
- Finset.sum_sdiffproof · cited by 16
- Finset.sum_mono_setproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Multiset.card_le_card_toFinset_add_one_iffproof · cited by 0