`BookProof.ChapterIPin.ipin_left` (Λ : P →* Multiplicative (AddAut V)) (x y : IPin Λ) : toAdd (x * y).left = toAdd x.left + Multiplicative.toAdd (Λ x.right) (toAdd y.left)

Proved

BookProof.ChapterIPin.ipin_left

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterIPin.

BookProof.ChapterIPin.ipin_left (Λ : P →* Multiplicative (AddAut V)) (x y : IPin Λ) : toAdd (x * y).left = toAdd x.left + Multiplicative.toAdd (Λ x.right) (toAdd y.left)

Formalization note: Lean 4 identifier BookProof.ChapterIPin.ipin_left.

Preamble

-- Generated from ChapterIPin.lean — theorem BookProof.ChapterIPin.ipin_left
import Mathlib
import Definitions.Def_ChapterIPin
open BookProof.ChapterIPin



open Multiplicative

variable {P V : Type*} [Group P] [AddCommGroup V] (Λ : P →* Multiplicative (AddAut V))

Formal statement

theorem BookProof.ChapterIPin.ipin_left (Λ : P →* Multiplicative (AddAut V)) (x y : IPin Λ) :
    toAdd (x * y).left = toAdd x.left + Multiplicative.toAdd (Λ x.right) (toAdd y.left) := by sorry

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