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Ordinary height scalar envelope

Proved
D1Bound5.ordinary_height_scalar_envelope

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

diophantine-tuplesnumber-theory

The exact rational-parameter algebra of the ordinary height envelope. Here x,z,d are base-ten logarithms and p,q are the residual rate and coefficient-height logarithms.

Preamble
import Mathlib.Algebra.Order.Floor.Semiring
import Mathlib.Analysis.SpecialFunctions.Log.Basic
import Mathlib.Tactic

Formal statement
section
namespace D1Bound5




theorem _root_.D1Bound5.ordinary_height_scalar_envelope (x z d p q h r u : ℝ)
    (hz : 0 ≤ z) (hq : 0 ≤ q)
    (hp : 2*x+r < p) (hp0 : 0 < 2*x+r)
    (hqh : q < x+h) (hxt : h-r < x)
    (hbound : z*(p-q) < (2*x+u)*p)
    (hd : d < (2/5 : ℝ)-x+2*z) :
    d < 7*x+(4*u+8*h-4*r)+
      (2*u*r+(4*u+8*h-4*r)*(h-r))/(x-(h-r))+(2/5 : ℝ) := by sorry



end D1Bound5
end
Source
D1Bound5/OrdinaryHeightScalar.lean, lines 56-87, SHA-256 0823b901aedbcca1a333b2b988ab8e6173c80406182e7af0372435df321e588d. Project: https://github.com/tomislav-math/d1-bound5-lean

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