Finite norm quadratic le

Proved

D1Bound5.finite_norm_quadratic_le

by tp · Oct 24, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

Auxiliary result finite_norm_quadratic_le 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.Elab.Tactic.Omega
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Normed.Ring.Basic
import Mathlib.Tactic.GCongr
import Mathlib.Tactic.Ring

Formal statement

section
namespace D1Bound5





theorem _root_.D1Bound5.finite_norm_quadratic_le (u v w c : ℂ) :
    ‖u+v*c+w*c^2‖ ≤ ‖u‖+‖v‖*‖c‖+‖w‖*‖c‖^2 := by sorry

end D1Bound5
end

Source

D1Bound5/FiniteHomogeneousTwo.lean, lines 36-41, SHA-256 0f528bdfa4bbe6e6461cbf40c954a5b8c6a03faf9be9e291dd140696bc0e3dfa. Project: https://github.com/tomislav-math/d1-bound5-lean

View graph