One Small Thirds 14 complete
ProvedD1Bound5.oneSmallThirds_14_completediophantine-tuplesnumber-theory
Auxiliary result oneSmallThirds_14_complete 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.Algebra.Ring.Basic import Mathlib.Algebra.Ring.Equiv import Mathlib.Data.Finset.Card import Mathlib.Data.Finset.Prod import Mathlib.Data.Int.Interval import Mathlib.Data.Int.Sqrt import Mathlib.Data.List.Range import Mathlib.Tactic.IntervalCases import Mathlib.Tactic.Linarith import Mathlib.Tactic.LinearCombination import Definitions.Def_D1Bound5_Coordinates_Definitions import Definitions.Def_D1Bound5_OneSmallThirdData_Definitions_001 import Definitions.Def_D1Bound5_PairExtensionCore_Definitions
Formal statement
section
namespace D1Bound5
open QuadInt
set_option maxRecDepth 32768
set_option maxHeartbeats 12000000
theorem _root_.D1Bound5.oneSmallThirds_14_complete (s : QuadInt 1 1) (hbound : s.norm ≤ 224)
(horder : oneSmallPairB_14.norm ≤ s.norm)
(ha : s ≠ oneSmallPairA_14) (hb : s ≠ oneSmallPairB_14)
(hpair : PairExtension oneSmallPairA_14 oneSmallPairB_14 s) : s ∈ oneSmallThirds_14 := by sorry
end D1Bound5
end
Source
D1Bound5/OneSmallThirdData.lean, lines 255-261, SHA-256 1a99812615576213a57446af3223d15f39986fed5a03e5b58ab6c3210a77a7c2. Project: https://github.com/tomislav-math/d1-bound5-lean