The Lean 4 theorem `re_formInner_sq_le` in the `ChapterYangMillsFriedrichs` chapter of the timepiece formalization

-- Generated from ChapterYangMillsFriedrichs.lean — theorem BookProof.YangMillsFriedrichs.re_formInner_sq_le
import Mathlib
import Definitions.Def_ChapterYangMillsFriedrichs
open BookProof.YangMillsFriedrichs


















open BookProof.FarisLavine




variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F] {D : Submodule ℂ F}

theorem BookProof.YangMillsFriedrichs.re_formInner_sq_le {H : D →ₗ[ℂ] F} (hsym : SymmetricOn D H)
    (hpos : ∀ x : D, 0 ≤ quadForm H x) (x y : D) :
    (formInner H x y).re ^ 2 ≤ formNormSq H x * formNormSq H y := by sorry