nonempty_innerProductSpace

theorem nonempty_innerProductSpace : ∀ (𝕜 : Type u_1) [inst : RCLike 𝕜] (E : Type u_2) [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : InnerProductSpaceable E], Nonempty (InnerProductSpace 𝕜 E)

**Fréchet–von Neumann–Jordan Theorem**. This theorem asserts that for any given normed space `E`, provided the norm adheres to the parallelogram identity, it is possible to construct a corresponding, compatible inner product. To apply this theorem locally, taking `InnerProductSpaceable E` to `InnerProductSpace 𝕜 E`, use `casesI nonempty_innerProductSpace 𝕜 E`.

More concisely: Given a normed space `E` satisfying the parallelogram identity, there exists a compatible inner product defining the given norm.