`BookProof.ChapterMackeyImprimitivity.mackeyMap_surjective` (hs : ∀ x, s x • x₀ = x) {f : X → E} (hf : f ∈ InducedSpace S x₀) : ∃ ψ : E, mackeyMap S s ψ = f
ProvedBookProof.ChapterMackeyImprimitivity.mackeyMap_surjectivetheoremstimepiece
Prove the following Lean 4 theorem from ChapterMackeyImprimitivity.
BookProof.ChapterMackeyImprimitivity.mackeyMap_surjective (hs : ∀ x, s x • x₀ = x) {f : X → E} (hf : f ∈ InducedSpace S x₀) : ∃ ψ : E, mackeyMap S s ψ = f
Formalization note: Lean 4 identifier BookProof.ChapterMackeyImprimitivity.mackeyMap_surjective.
Preamble
-- Generated from ChapterMackeyImprimitivity.lean — theorem BookProof.ChapterMackeyImprimitivity.mackeyMap_surjective
import Mathlib
import Definitions.Def_ChapterMackeyImprimitivity
open BookProof.ChapterMackeyImprimitivity
open scoped InnerProductSpace
open Finset
variable {G : Type*} [Group G] {X : Type*} [Fintype X] [MulAction G X]
variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℂ E]
variable (S : ImprimitivitySystem G X E)
variable (S : ImprimitivitySystem G X E) (x₀ : X) (s : X → G)
variable {S x₀ s}Formal statement
theorem BookProof.ChapterMackeyImprimitivity.mackeyMap_surjective (hs : ∀ x, s x • x₀ = x) {f : X → E}
(hf : f ∈ InducedSpace S x₀) : ∃ ψ : E, mackeyMap S s ψ = f := by sorry