Theorems · Theorem · functional analysis

inner_smul_real_left

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  (x y : E) (r : ℝ), inner 𝕜 (↑r • x) y = r • inner 𝕜 x y

Defined in

Mathlib.Analysis.InnerProductSpace.Basic

Cited by

2 results in Mathlib

Foundations

Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeSeminormedAddCommGroupInnerProductSpace