`BookProof.ChapterA.cType_exhaustive` (M : System ℂ V) : IsCReal M ∨ IsCPseudoreal M ∨ IsCComplex M

Proved

BookProof.ChapterA.cType_exhaustive

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA1c.

BookProof.ChapterA.cType_exhaustive (M : System ℂ V) : IsCReal M ∨ IsCPseudoreal M ∨ IsCComplex M

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

Preamble

-- Generated from ChapterA1c.lean — theorem BookProof.ChapterA.cType_exhaustive
import Mathlib
import Definitions.Def_ChapterA1c
import Definitions.Def_ChapterA
open BookProof.ChapterA
open BookProof.ChapterA


open scoped ComplexConjugate InnerProductSpace RealInnerProductSpace

variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℂ V] [CompleteSpace V]

Formal statement

theorem BookProof.ChapterA.cType_exhaustive (M : System ℂ V) :
    IsCReal M ∨ IsCPseudoreal M ∨ IsCComplex M := by sorry

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