`BookProof.QuantumGravityFock.bosOp_ghostOp_comm` (A : BoseAlg →ₗ[ℂ] BoseAlg) (B : FermAlg →ₗ[ℂ] FermAlg) (z : QGGraded) : bosOp A (ghostOp B z) = ghostOp B (bosOp A z)
ProvedBookProof.QuantumGravityFock.bosOp_ghostOp_commtheoremstimepiece
Prove the following Lean 4 theorem from ChapterQuantumGravityFock.
BookProof.QuantumGravityFock.bosOp_ghostOp_comm (A : BoseAlg →ₗ[ℂ] BoseAlg) (B : FermAlg →ₗ[ℂ] FermAlg) (z : QGGraded) : bosOp A (ghostOp B z) = ghostOp B (bosOp A z)
Formalization note: Lean 4 identifier BookProof.QuantumGravityFock.bosOp_ghostOp_comm.
Preamble
-- Generated from ChapterQuantumGravityFock.lean — theorem BookProof.QuantumGravityFock.bosOp_ghostOp_comm import Definitions.Def_ChapterNavierStokesAffineFiberEsa import Definitions.Def_ChapterNavierStokesIkebeKato import Definitions.Def_ChapterNavierStokesFockSpace import Definitions.Def_ChapterNavierStokesFullEsa import Definitions.Def_ChapterFarisLavine import Definitions.Def_ChapterStoneBridge import Definitions.Def_ChapterEsaClosureCore import Definitions.Def_ChapterSirkTrotterKato import Definitions.Def_ChapterYangMillsFriedrichs import Definitions.Def_ChapterHermiteGalerkinFriedrichs import Definitions.Def_ChapterComplexShiftCore import Mathlib import Definitions.Def_ChapterQuantumGravityFock import Definitions.Def_ChapterFockSecondQuantization open BookProof.FockSecondQuantization open BookProof.QuantumGravityFock open BookProof.NavierStokesFlow BookProof.NavierStokesFlow.IkebeKato open BookProof.NavierStokesFlow.FockOfFock BookProof.NavierStokesFlow.FullEsa open BookProof.FarisLavine BookProof.StoneBridge BookProof.EsaClosure open BookProof.ChapterStoneResolvent BookProof.YangMillsFriedrichs open BookProof.HermiteGalerkin BookProof.HashimotoShiftInvert open BookProof.FockSecondQuantization noncomputable section
Formal statement
theorem BookProof.QuantumGravityFock.bosOp_ghostOp_comm (A : BoseAlg →ₗ[ℂ] BoseAlg) (B : FermAlg →ₗ[ℂ] FermAlg)
(z : QGGraded) : bosOp A (ghostOp B z) = ghostOp B (bosOp A z) := by sorry