The Lean 4 theorem `sub_resolvent_apply` in the `ChapterHermiteGalerkinFriedrichs` chapter of the timepiece formalization

-- Generated from ChapterHermiteGalerkinFriedrichs.lean — theorem BookProof.HermiteGalerkin.sub_resolvent_apply
import Mathlib
import Definitions.Def_ChapterHermiteGalerkinFriedrichs
open BookProof.HermiteGalerkin












open BookProof.FarisLavine BookProof.YangMillsFriedrichs BookProof.YangMillsFriedrichsLimit
open Filter Topology



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






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


















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



variable {D : Submodule ℂ F}












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

theorem BookProof.HermiteGalerkin.sub_resolvent_apply (T : F →L[ℂ] F) (hT : IsSelfAdjoint T) {z : ℂ} (hz : z.im ≠ 0)
    (w : F) : (algebraMap ℂ (F →L[ℂ] F) z - T) (resolvent T z w) = w := by sorry