Half Off Diagonal Inverse norm ge

Proved

D1Bound5.halfOffDiagonalInverse_norm_ge

by tp · Oct 23, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

Auxiliary result halfOffDiagonalInverse_norm_ge in the proof of the bound five for Diophantine D(1) sets in imaginary quadratic integer rings. The formal statement specifies its hypotheses and conclusion; a mathematical prose description remains to be supplied.

Preamble

import Mathlib.Analysis.CStarAlgebra.Matrix
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Complex.Polynomial.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import Mathlib.LinearAlgebra.Matrix.Permutation
import Mathlib.LinearAlgebra.Matrix.SchurComplement
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.FinCases
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_ReferenceMatrixSpectral_Definitions

Formal statement

section
open scoped Matrix.Norms.L2Operator
open Matrix

namespace D1Bound5















theorem _root_.D1Bound5.halfOffDiagonalInverse_norm_ge :
    2 ≤ ‖halfOffDiagonalInverse‖ := by sorry





end D1Bound5
end

Source

D1Bound5/ReferenceInverseNorm.lean, lines 64-82, SHA-256 53050c6b49ff7b7eabf281a545ecf66dea734cd088fd701c36f0829189368aeb. Project: https://github.com/tomislav-math/d1-bound5-lean

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