`BookProof.ChapterG.exists_complete_gaugeFixing` {X Y : Type*} {π : X → Y} (hπ : Function.Surjective π) : ∃ S : Set X, IsCompleteGaugeFixing π S ∧ π '' S = Set.univ

Proved

BookProof.ChapterG.exists_complete_gaugeFixing

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterG.

BookProof.ChapterG.exists_complete_gaugeFixing {X Y : Type*} {π : X → Y} (hπ : Function.Surjective π) : ∃ S : Set X, IsCompleteGaugeFixing π S ∧ π '' S = Set.univ

Formalization note: Lean 4 identifier BookProof.ChapterG.exists_complete_gaugeFixing.

Preamble

-- Generated from ChapterG.lean — theorem BookProof.ChapterG.exists_complete_gaugeFixing
import Mathlib
import Definitions.Def_ChapterG
open BookProof.ChapterG


open scoped ComplexConjugate InnerProductSpace Matrix

Formal statement

theorem BookProof.ChapterG.exists_complete_gaugeFixing {X Y : Type*} {π : X → Y}
    (hπ : Function.Surjective π) :
    ∃ S : Set X, IsCompleteGaugeFixing π S ∧ π '' S = Set.univ := by sorry

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