`BookProof.NonnegSemigroup.expNeg_add` (A : F →L[ℂ] F) (s t : ℝ) : expNeg A (s + t) = expNeg A s * expNeg A t

Proved

BookProof.NonnegSemigroup.expNeg_add

by leonardopedro · Oct 25, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNonnegSemigroup.

BookProof.NonnegSemigroup.expNeg_add (A : F →L[ℂ] F) (s t : ℝ) : expNeg A (s + t) = expNeg A s * expNeg A t

Formalization note: Lean 4 identifier BookProof.NonnegSemigroup.expNeg_add.

Preamble

-- Generated from ChapterNonnegSemigroup.lean — theorem BookProof.NonnegSemigroup.expNeg_add
import Definitions.Def_ChapterClosureUniqueness
import Definitions.Def_ChapterPositiveSquareRootUnique
import Definitions.Def_ChapterNonnegResolvent
import Definitions.Def_ChapterNonnegUnitaryGroup
import Mathlib
import Definitions.Def_ChapterNonnegSemigroup



open BookProof.ClosureUniqueness
open Filter Topology NormedSpace
open scoped InnerProductSpace

variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F] [CompleteSpace F]

Formal statement

theorem BookProof.NonnegSemigroup.expNeg_add (A : F →L[ℂ] F) (s t : ℝ) :
    expNeg A (s + t) = expNeg A s * expNeg A t := by sorry

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