`BookProof.ChapterResidualStream.norm_residual_sub_self` (f : E → E) (x : E) : ‖residual f x - x‖ = ‖f x‖

Proved

BookProof.ChapterResidualStream.norm_residual_sub_self

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterResidualStream.

BookProof.ChapterResidualStream.norm_residual_sub_self (f : E → E) (x : E) : ‖residual f x - x‖ = ‖f x‖

Formalization note: Lean 4 identifier BookProof.ChapterResidualStream.norm_residual_sub_self.

Preamble

-- Generated from ChapterResidualStream.lean — theorem BookProof.ChapterResidualStream.norm_residual_sub_self
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterAttentionOutput
import Mathlib
import Definitions.Def_ChapterResidualStream
open BookProof.ChapterResidualStream


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterAttentionOutput

variable {m : ℕ} {E : Type*} [NormedAddCommGroup E]

Formal statement

theorem BookProof.ChapterResidualStream.norm_residual_sub_self (f : E → E) (x : E) : ‖residual f x - x‖ = ‖f x‖ := by sorry

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