Theorems · Theorem · functional analysis
parallelogram_law
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{x y : E}, inner 𝕜 (x + y) (x + y) + inner 𝕜 (x - y) (x - y) = 2 * (inner 𝕜 x x + inner 𝕜 y y)Parallelogram law
- Defined in
- Mathlib.Analysis.InnerProductSpace.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Inner.innerstatement and proof · cited by 1,089
- inner_sub_sub_selfproof · cited by 3
- inner_add_add_selfproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- parallelogram_law_with_norm_mulproof · cited by 4