Theorems · Theorem · commutative algebra
IsSumSq.sum_mul_self
∀ {R : Type u_1} [inst : AddCommMonoid R] [inst_1 : Mul R] {ι : Type u_2} (I : Finset ι) (a : ι → R),
IsSumSq (∑ i ∈ I, a i * a i)In an additive commutative monoid with multiplication,
∑ i ∈ I, a i * a i is a sum of squares.
- Defined in
- Mathlib.Algebra.Ring.SumsOfSquares
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidMul
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 · cited by 5,195
- IsSumSqstatement · cited by 38
- IsSumSq.sumproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- RootPairing.exists_ge_zero_eq_rootFormproof · cited by 1
- RootPairing.rootForm_self_sum_of_squaresproof · cited by 1