`BookProof.ChapterGaugeParametrization.fiberGauge_ne_bot_iff` (π : X → Y) : fiberGauge π ≠ ⊥ ↔ ¬ Function.Injective π

Proved

BookProof.ChapterGaugeParametrization.fiberGauge_ne_bot_iff

by leonardopedro · Oct 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeParametrization.

BookProof.ChapterGaugeParametrization.fiberGauge_ne_bot_iff (π : X → Y) : fiberGauge π ≠ ⊥ ↔ ¬ Function.Injective π

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

Preamble

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



open BookProof.ChapterGaugeIncompleteFixing

variable {X Y : Type*}

Formal statement

theorem BookProof.ChapterGaugeParametrization.fiberGauge_ne_bot_iff (π : X → Y) :
    fiberGauge π ≠ ⊥ ↔ ¬ Function.Injective π := by sorry

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