Theorems · Theorem · functional analysis

LinearEquiv.isometryOfInner.congr_simp

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  {E' : Type u_7} [inst_3 : SeminormedAddCommGroup E'] [inst_4 : InnerProductSpace 𝕜 E'] (f f_1 : E ≃ₗ[𝕜] E')
  (e_f : f = f_1) (h : ∀ (x y : E), inner 𝕜 (f x) (f y) = inner 𝕜 x y), f.isometryOfInner h = f_1.isometryOfInner ⋯

Defined in

Mathlib.Analysis.InnerProductSpace.PiL2

Cited by

0 results in Mathlib

Foundations

Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeSeminormedAddCommGroupInnerProductSpaceSeminormedAddCommGroupInnerProductSpace