`BookProof.ChapterWeylSl2.Sl2Rep.cas_apply_eq` {R : Sl2Rep V} (v : V) : R.cas v = 2 • (R.E (R.F v) + R.F (R.E v)) + R.H (R.H v)

Proved

BookProof.ChapterWeylSl2.Sl2Rep.cas_apply_eq

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeylSl2.

BookProof.ChapterWeylSl2.Sl2Rep.cas_apply_eq {R : Sl2Rep V} (v : V) : R.cas v = 2 • (R.E (R.F v) + R.F (R.E v)) + R.H (R.H v)

Formalization note: Lean 4 identifier BookProof.ChapterWeylSl2.Sl2Rep.cas_apply_eq.

Preamble

-- Generated from ChapterWeylSl2.lean — theorem BookProof.ChapterWeylSl2.Sl2Rep.cas_apply_eq
import Mathlib
import Definitions.Def_ChapterWeylSl2
import Definitions.Def_ChapterDoubleSlit
import Definitions.Def_ChapterGleasonPureMixed
open BookProof.ChapterDoubleSlit
open BookProof.ChapterGleasonPureMixed
open BookProof.ChapterWeylSl2
open BookProof.ChapterWeylSl2



universe u

variable {V : Type u} [AddCommGroup V] [Module ℂ V]

variable (R : Sl2Rep V)
variable {R}
variable {R : Sl2Rep V}

Formal statement

theorem BookProof.ChapterWeylSl2.Sl2Rep.cas_apply_eq {R : Sl2Rep V} (v : V) :
    R.cas v = 2 • (R.E (R.F v) + R.F (R.E v)) + R.H (R.H v) := by sorry

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