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`BookProof.ChapterGaugeIncompleteFixing.isPhysicalObservable_iff_factors` (f : X → ℝ) : IsPhysicalObservable G f ↔ ∃ F : Quotient (MulAction.orbitRel G X) → ℝ, ∀ x : X, f x = F (Qu

Proved
BookProof.ChapterGaugeIncompleteFixing.isPhysicalObservable_iff_factors

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeIncompleteFixing.

BookProof.ChapterGaugeIncompleteFixing.isPhysicalObservable_iff_factors (f : X → ℝ) : IsPhysicalObservable G f ↔ ∃ F : Quotient (MulAction.orbitRel G X) → ℝ, ∀ x : X, f x = F (Quotient.mk (MulAction.orbitRel G X) x)

Formalization note: Lean 4 identifier BookProof.ChapterGaugeIncompleteFixing.isPhysicalObservable_iff_factors.

Preamble
-- Generated from ChapterGaugeIncompleteFixing.lean — theorem BookProof.ChapterGaugeIncompleteFixing.isPhysicalObservable_iff_factors
import Mathlib
import Definitions.Def_ChapterGaugeIncompleteFixing
open BookProof.ChapterGaugeIncompleteFixing


open scoped InnerProductSpace

variable {X : Type*}
variable (G : Type*) [Group G] [MulAction G X]
Formal statement
theorem BookProof.ChapterGaugeIncompleteFixing.isPhysicalObservable_iff_factors (f : X → ℝ) :
    IsPhysicalObservable G f ↔
      ∃ F : Quotient (MulAction.orbitRel G X) → ℝ,
        ∀ x : X, f x = F (Quotient.mk (MulAction.orbitRel G X) x) := by sorry

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