`BookProof.ChapterE4.wave_succ` (θ : ℕ → ℝ) (s d : ℕ) (i : ℕ) : wave θ s (d + 1) i = Real.cos (θ s) * basisVec s i + Real.sin (θ s) * wave θ (s + 1) d i

Proved

BookProof.ChapterE4.wave_succ

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterE4.

BookProof.ChapterE4.wave_succ (θ : ℕ → ℝ) (s d : ℕ) (i : ℕ) : wave θ s (d + 1) i = Real.cos (θ s) * basisVec s i + Real.sin (θ s) * wave θ (s + 1) d i

Formalization note: Lean 4 identifier BookProof.ChapterE4.wave_succ.

Preamble

-- Generated from ChapterE4.lean — theorem BookProof.ChapterE4.wave_succ
import Mathlib
import Definitions.Def_ChapterE4
open BookProof.ChapterE4


open scoped BigOperators

Formal statement

theorem BookProof.ChapterE4.wave_succ (θ : ℕ → ℝ) (s d : ℕ) (i : ℕ) :
    wave θ s (d + 1) i =
      Real.cos (θ s) * basisVec s i + Real.sin (θ s) * wave θ (s + 1) d i := by sorry

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