Prove2Me

`BookProof.ChapterA.rType_exhaustive` (M : System ℝ W) : IsRRealType M ∨ IsRComplexType M ∨ IsRPseudorealType M

Proved
BookProof.ChapterA.rType_exhaustive

by leonardopedro · Oct 16, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA1h.

BookProof.ChapterA.rType_exhaustive (M : System ℝ W) : IsRRealType M ∨ IsRComplexType M ∨ IsRPseudorealType M

Formalization note: Lean 4 identifier BookProof.ChapterA.rType_exhaustive.

Preamble
-- Generated from ChapterA1h.lean — theorem BookProof.ChapterA.rType_exhaustive
import Definitions.Def_Complexification
import Mathlib
import Definitions.Def_ChapterA1h
import Definitions.Def_ChapterA
open BookProof.ChapterA
open BookProof.ChapterA


open scoped ComplexConjugate InnerProductSpace RealInnerProductSpace


open BookProof.Complexification

variable {W : Type*} [NormedAddCommGroup W] [InnerProductSpace ℝ W] [CompleteSpace W]
Formal statement
theorem BookProof.ChapterA.rType_exhaustive (M : System ℝ W) :
    IsRRealType M ∨ IsRComplexType M ∨ IsRPseudorealType M := by sorry

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