Mixed Adj Envelope symmetric

Proved

D1Bound5.mixedAdjEnvelope_symmetric

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

diophantine-tuplesnumber-theory

Auxiliary result mixedAdjEnvelope_symmetric 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 Lean.Util.CollectAxioms
import Mathlib.Algebra.Order.BigOperators.Ring.Finset
import Mathlib.Analysis.CStarAlgebra.Matrix
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Complex.Polynomial.Basic
import Mathlib.Analysis.InnerProductSpace.PiL2
import Mathlib.Analysis.SpecificLimits.Normed
import Mathlib.Data.Complex.Basic
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
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_MixedAdjugateEnvelope_Definitions

Formal statement

section
open scoped Matrix.Norms.L2Operator
open Matrix

namespace D1Bound5





theorem _root_.D1Bound5.mixedAdjEnvelope_symmetric (i j : Fin 4) :
    mixedAdjEnvelope i j = mixedAdjEnvelope j i := by sorry





end D1Bound5
end

Source

D1Bound5/MixedAdjugateEnvelope.lean, lines 19-32, SHA-256 f452ef49f0d5283120370edce69efeffabb48f22241346c2ec9821c339c43131. Project: https://github.com/tomislav-math/d1-bound5-lean

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