`BookProof.ChapterStatementOperator.ModelStatement.truthValue_and_le_left` (S T : ModelStatement H) (hcomm : S.op ∘L T.op = T.op ∘L S.op) : (S.and T hcomm).truthValue ψ ≤ S.truthVa

Proved

BookProof.ChapterStatementOperator.ModelStatement.truthValue_and_le_left

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterStatementOperator.

BookProof.ChapterStatementOperator.ModelStatement.truthValue_and_le_left (S T : ModelStatement H) (hcomm : S.op ∘L T.op = T.op ∘L S.op) : (S.and T hcomm).truthValue ψ ≤ S.truthValue ψ

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

Preamble

-- Generated from ChapterStatementOperator.lean — theorem BookProof.ChapterStatementOperator.ModelStatement.truthValue_and_le_left
import Mathlib
import Definitions.Def_ChapterStatementOperator
import Definitions.Def_ChapterSirkGroupTransfer
open BookProof.ChapterSirkGroupTransfer
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_and_le_left (S T : ModelStatement H)
    (hcomm : S.op ∘L T.op = T.op ∘L S.op) :
    (S.and T hcomm).truthValue ψ ≤ S.truthValue ψ := by sorry

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