Theorems · Theorem · combinatorics
Fintype.eq_of_subsingleton_of_sum_eq
∀ {M : Type u_4} [inst : AddCommMonoid M] {ι : Type u_5} [Subsingleton ι] {s : Finset ι} {f : ι → M} {b : M},
∑ i ∈ s, f i = b → ∀ i ∈ s, f i = bIf a sum of a Finset of a subsingleton type has a given
value, so do the terms in that sum.
- Defined in
- Mathlib.Data.Fintype.BigOperators
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidSubsingleton
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Finset.sumstatement and proof · cited by 5,195
- Finset.card_le_one_of_subsingletonproof · cited by 3
- Finset.eq_of_card_le_one_of_sum_eqproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- affineIndependent_of_subsingletonproof · cited by 4