Prove2Me

`BookProof.ChapterA.not_isCPseudoreal_and_isCComplex` (M : System ℂ V) : ¬ (IsCPseudoreal M ∧ IsCComplex M)

Proved
BookProof.ChapterA.not_isCPseudoreal_and_isCComplex

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA1c.

BookProof.ChapterA.not_isCPseudoreal_and_isCComplex (M : System ℂ V) : ¬ (IsCPseudoreal M ∧ IsCComplex M)

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

Preamble
-- Generated from ChapterA1c.lean — theorem BookProof.ChapterA.not_isCPseudoreal_and_isCComplex
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.not_isCPseudoreal_and_isCComplex (M : System ℂ V) :
    ¬ (IsCPseudoreal M ∧ IsCComplex M) := by sorry

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