The Lean 4 theorem `opNorm_le` in the `ChapterHashimotoShiftInvert` chapter of the timepiece formalization
ProvedBookProof.HashimotoShiftInvert.IsShiftInvert.opNorm_letimepiece
The Lean 4 theorem opNorm_le in the ChapterHashimotoShiftInvert chapter of the timepiece formalization.
Preamble
-- Generated from ChapterHashimotoShiftInvert.lean — theorem BookProof.HashimotoShiftInvert.IsShiftInvert.opNorm_le
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterYangMillsFriedrichs
import Definitions.Def_ChapterYangMillsFriedrichsLimit
import Definitions.Def_ChapterHermiteGalerkinFriedrichs
import Mathlib
import Definitions.Def_ChapterHashimotoShiftInvert
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterComplexShiftCore
open BookProof.HashimotoShiftInvert
variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F] {Dom : Submodule ℂ F}
variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F] [CompleteSpace F]
{Dom : Submodule ℂ F}
open BookProof.FarisLavine BookProof.YangMillsFriedrichs BookProof.YangMillsFriedrichsLimit
open BookProof.HermiteGalerkin
open Filter TopologyFormal statement
theorem BookProof.HashimotoShiftInvert.IsShiftInvert.opNorm_le {A : Dom →ₗ[ℂ] F} {γ : ℝ} {R : F →L[ℂ] F}
(h : IsShiftInvert A γ R) (hpos : ∀ x : Dom, 0 ≤ quadForm A x) (hγ : 0 < γ) :
‖R‖ ≤ γ⁻¹ := by sorrySource