`BookProof.ChapterG.dampedFlow_add` (M : Matrix (Fin 4) (Fin 4) ℝ) (s t : ℝ) : NormedSpace.exp ((s + t) • M) = NormedSpace.exp (s • M) * NormedSpace.exp (t • M)
ProvedBookProof.ChapterG.dampedFlow_addtheoremstimepiece
Prove the following Lean 4 theorem from ChapterG.
BookProof.ChapterG.dampedFlow_add (M : Matrix (Fin 4) (Fin 4) ℝ) (s t : ℝ) : NormedSpace.exp ((s + t) • M) = NormedSpace.exp (s • M) * NormedSpace.exp (t • M)
Formalization note: Lean 4 identifier BookProof.ChapterG.dampedFlow_add.
Preamble
-- Generated from ChapterG.lean — theorem BookProof.ChapterG.dampedFlow_add
import Mathlib
import Definitions.Def_ChapterG
open BookProof.ChapterG
open scoped ComplexConjugate InnerProductSpace Matrix
open MeasureTheory
variable {G : Type*} [Group G] [MeasurableSpace G]
variable {μG : Measure G} [IsProbabilityMeasure μG] [μG.IsMulLeftInvariant]
variable {X : Type*} [MulAction G X]
variable {A : Type*} [Ring A]Formal statement
theorem BookProof.ChapterG.dampedFlow_add (M : Matrix (Fin 4) (Fin 4) ℝ) (s t : ℝ) :
NormedSpace.exp ((s + t) • M) = NormedSpace.exp (s • M) * NormedSpace.exp (t • M) := by sorry