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`BookProof.NonnegSemigroup.isSelfAdjoint_expNeg` {A : F →L[ℂ] F} (hA : IsSelfAdjoint A) (t : ℝ) : IsSelfAdjoint (expNeg A t)

Proved
BookProof.NonnegSemigroup.isSelfAdjoint_expNeg

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNonnegSemigroup.

BookProof.NonnegSemigroup.isSelfAdjoint_expNeg {A : F →L[ℂ] F} (hA : IsSelfAdjoint A) (t : ℝ) : IsSelfAdjoint (expNeg A t)

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

Preamble
-- Generated from ChapterNonnegSemigroup.lean — theorem BookProof.NonnegSemigroup.isSelfAdjoint_expNeg
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.isSelfAdjoint_expNeg {A : F →L[ℂ] F} (hA : IsSelfAdjoint A) (t : ℝ) :
    IsSelfAdjoint (expNeg A t) := by sorry

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