{b : HilbertBasis ℕ ℂ F} {A : finiteModeDomain b →ₗ[ℂ] finiteModeDomain b} (hpos : ∀ x, 0 ≤ quadForm ((finiteModeDomain b).subtype.comp A) x) : IsPosCol (opCol b A)

Proved

BookProof.FockSecondQuantization.isPosCol_opCol

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

timepiece

Lean 4 theorem BookProof.FockSecondQuantization.isPosCol_opCol (module BookProof.FockSecondQuantization), source chapter BookProof/ChapterFockSecondQuantization.lean.

Preamble

-- Generated from ChapterFockSecondQuantization.lean — theorem BookProof.FockSecondQuantization.isPosCol_opCol
import Mathlib
import Definitions.Def_ChapterFockSecondQuantization
open BookProof.FockSecondQuantization







open BookProof.NavierStokesFlow BookProof.NavierStokesFlow.IkebeKato
open BookProof.FarisLavine BookProof.YangMillsFriedrichs
open BookProof.HermiteGalerkin BookProof.FriedrichsExtension
open BookProof.HashimotoShiftInvert

noncomputable section

















































































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

Formal statement

theorem BookProof.FockSecondQuantization.isPosCol_opCol {b : HilbertBasis ℕ ℂ F}
    {A : finiteModeDomain b →ₗ[ℂ] finiteModeDomain b}
    (hpos : ∀ x, 0 ≤ quadForm ((finiteModeDomain b).subtype.comp A) x) :
    IsPosCol (opCol b A) := by sorry

Source

https://github.com/leonardopedrio/timepiece/blob/61595bc/BookProof/ChapterFockSecondQuantization.lean

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