Small Pair Sieve 1 8 valid

Proved

D1Bound5.smallPairSieve_1_8_valid

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

diophantine-tuplesnumber-theory

Auxiliary result smallPairSieve_1_8_valid 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.Algebra.QuadraticAlgebra.Basic
import Mathlib.Data.Int.Sqrt
import Mathlib.Data.ZMod.Basic
import Mathlib.Tactic.Linarith
import Definitions.Def_D1Bound5_FastSquareTest_Definitions
import Definitions.Def_D1Bound5_SmallPairSieve_1_8_Definitions

Formal statement

section
namespace D1Bound5
set_option maxRecDepth 100000
set_option maxHeartbeats 0














































































theorem _root_.D1Bound5.smallPairSieve_1_8_valid : CoordinateSquareSieveValid 1 8 smallPairSieve_1_8 := by sorry

end D1Bound5
end

Source

D1Bound5/SmallPairSieve_1_8.lean, lines 160-187, SHA-256 380989e40c875e6a4f2db650c09a50e5c724b19eff67f6343cbe03358ae7c4b3. Project: https://github.com/tomislav-math/d1-bound5-lean

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