Prove2Me

`BookProof.ChapterStatementOperator.ModelStatement.truthValue_eq_zero_iff` : S.truthValue ψ = 0 ↔ S.op ψ = 0

Proved
BookProof.ChapterStatementOperator.ModelStatement.truthValue_eq_zero_iff

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterStatementOperator.

BookProof.ChapterStatementOperator.ModelStatement.truthValue_eq_zero_iff : S.truthValue ψ = 0 ↔ S.op ψ = 0

Formalization note: Lean 4 identifier BookProof.ChapterStatementOperator.ModelStatement.truthValue_eq_zero_iff.

Preamble
-- Generated from ChapterStatementOperator.lean — theorem BookProof.ChapterStatementOperator.ModelStatement.truthValue_eq_zero_iff
import Mathlib
import Definitions.Def_ChapterStatementOperator
open BookProof.ChapterStatementOperator
open BookProof.ChapterStatementOperator



open ContinuousLinearMap

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

variable (S : ModelStatement H) (ψ : H)
Formal statement
theorem BookProof.ChapterStatementOperator.ModelStatement.truthValue_eq_zero_iff : S.truthValue ψ = 0 ↔ S.op ψ = 0 := by sorry

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