`BookProof.ChapterGaugeParametrization.isPhysicalObservable_iff_factors_through` (π : X → Y) (f : X → ℝ) : IsPhysicalObservable (fiberGauge π) f ↔ ∃ F : Y → ℝ, ∀ x, f x = F (π x)

Proved

BookProof.ChapterGaugeParametrization.isPhysicalObservable_iff_factors_through

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeParametrization.

BookProof.ChapterGaugeParametrization.isPhysicalObservable_iff_factors_through (π : X → Y) (f : X → ℝ) : IsPhysicalObservable (fiberGauge π) f ↔ ∃ F : Y → ℝ, ∀ x, f x = F (π x)

Formalization note: Lean 4 identifier BookProof.ChapterGaugeParametrization.isPhysicalObservable_iff_factors_through.

Preamble

-- Generated from ChapterGaugeParametrization.lean — theorem BookProof.ChapterGaugeParametrization.isPhysicalObservable_iff_factors_through
import Mathlib
import Definitions.Def_ChapterGaugeParametrization
import Definitions.Def_ChapterGaugeIncompleteFixing
open BookProof.ChapterGaugeIncompleteFixing
open BookProof.ChapterGaugeParametrization



open BookProof.ChapterGaugeIncompleteFixing

variable {X Y : Type*}

Formal statement

theorem BookProof.ChapterGaugeParametrization.isPhysicalObservable_iff_factors_through (π : X → Y) (f : X → ℝ) :
    IsPhysicalObservable (fiberGauge π) f ↔ ∃ F : Y → ℝ, ∀ x, f x = F (π x) := by sorry

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