Finite A4 height scaled
ProvedD1Bound5.finiteA4_height_scaleddiophantine-tuplesnumber-theory
Actual integral A4 root-column height. No coefficient table or bound is an input hypothesis: all coefficients and the strict margin are proved.
Preamble
import Lean.Elab.Tactic.Omega import Mathlib.Algebra.BigOperators.Fin import Mathlib.Analysis.Complex.Basic import Mathlib.Analysis.Normed.Ring.Basic import Mathlib.LinearAlgebra.Matrix.Determinant.Basic import Mathlib.LinearAlgebra.Matrix.NonsingularInverse import Mathlib.Tactic import Mathlib.Tactic.Convert import Mathlib.Tactic.GCongr import Mathlib.Tactic.Linarith import Mathlib.Tactic.NormNum import Mathlib.Tactic.Positivity import Mathlib.Tactic.Ring import Definitions.Def_D1Bound5_FiniteA4Matrix_Definitions
Formal statement
section
namespace D1Bound5
theorem _root_.D1Bound5.finiteA4_height_scaled (x y c : ℂ) (hy : y ≠ 0)
(hxy : ‖x‖ ≤ ‖y‖) (hYC : 1000 ≤ ‖y‖*‖c‖) (i : Fin 3) :
(101/100 : ℝ)*(‖finiteA4Left x y c i‖+‖finiteA4Right x y c i‖) <
165763*‖y‖^9*‖c‖^4 := by sorry
end D1Bound5
end
Source
D1Bound5/FiniteA4Height.lean, lines 60-82, SHA-256 9a08f5646dc099fdc32895a9f25b5747a42057d2621384971697b0f7dffad0bf. Project: https://github.com/tomislav-math/d1-bound5-lean