Pair Light Prepared42 — sieve eq
ProvedD1Bound5.PairLightPrepared42.sieve_eqdiophantine-tuplesnumber-theory
Auxiliary result PairLightPrepared42.sieve_eq 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 Init import Mathlib.Algebra.Order.Ring.Abs import Mathlib.Algebra.QuadraticAlgebra.Basic import Mathlib.Algebra.Ring.Basic import Mathlib.Algebra.Ring.Equiv import Mathlib.Analysis.Complex.Basic import Mathlib.Analysis.Complex.Norm import Mathlib.Analysis.Complex.Polynomial.Basic import Mathlib.Data.Finset.Card import Mathlib.Data.Finset.Prod import Mathlib.Data.Int.GCD import Mathlib.Data.Int.Interval import Mathlib.Data.Int.Sqrt import Mathlib.Data.List.Basic import Mathlib.Data.List.Range import Mathlib.Data.ZMod.Basic import Mathlib.LinearAlgebra.Dimension.Free import Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex import Mathlib.NumberTheory.NumberField.Norm import Mathlib.Tactic.FieldSimp import Mathlib.Tactic.Linarith import Mathlib.Tactic.LinearCombination import Mathlib.Tactic.Ring import Definitions.Def_D1Bound5_Coordinates_Definitions import Definitions.Def_D1Bound5_SmallPairLightData42_Definitions_001 import Definitions.Def_D1Bound5_SmallPairSieve_1_3_Definitions
Formal statement
section /- Preserved body from D1Bound5.SmallPairGraphInputs42; original SHA256 e751a5007e71d6837bdcdd3b8c93aacd9a20b359f3364e1165d9ae650d464a20. -/ namespace D1Bound5 set_option maxRecDepth 100000 open QuadInt namespace PairGraphPrepared42 end PairGraphPrepared42 end D1Bound5 /- Preserved body from D1Bound5.SmallPairGraphArithmetic42; original SHA256 11d316a549a5c95b93a9ed98fc580dafac8bfeae3a40c435639662a2c047d64e. -/ namespace D1Bound5 set_option maxRecDepth 100000 set_option maxHeartbeats 0 end D1Bound5 /- Preserved body from D1Bound5.SmallPairGraphWitnessData42; original SHA256 709c0bd6914ee1c1181f151840da49be63f2fae2e4de4d163170b17c5dc72c11. -/ namespace D1Bound5.PairGraphPrepared42 set_option maxRecDepth 100000 end D1Bound5.PairGraphPrepared42 /- Preserved body from D1Bound5.SmallPairGraphClosure42; original SHA256 2f7911b205f189a4b5a1cc26fedf3608921021ba95e39dc0344768ee9a21263e. -/ namespace D1Bound5 set_option maxRecDepth 100000 set_option maxHeartbeats 0 open PairGraphPrepared42 end D1Bound5 /- Preserved body from D1Bound5.SmallPairRawSelectedData42; original SHA256 245fb4473f619e3d17a60299f8662a982d483bd8ab8f2abc1366b272dd797def. -/ namespace D1Bound5.PairSelectedPrepared42 set_option maxRecDepth 100000 end D1Bound5.PairSelectedPrepared42 /- Preserved body from D1Bound5.SmallPairLightAssembly42; original SHA256 60c90a5f9d67d181917899dbdbbad52af21334e0b65779e96864677d03075657. -/ namespace D1Bound5.PairLightPrepared42 set_option maxRecDepth 100000 set_option maxHeartbeats 0 theorem _root_.D1Bound5.PairLightPrepared42.sieve_eq : sieve = smallPairSieve_1_3 := by sorry end D1Bound5.PairLightPrepared42 /- Preserved body from D1Bound5.SmallPairGraphTriangle42; original SHA256 91c579c9ca406a72e9bd3b12d424418d47a488728036d60bd1046b2dca9865fe. -/ namespace D1Bound5 set_option maxRecDepth 100000 end D1Bound5 /- Preserved body from D1Bound5.SmallPairGraphData42; original SHA256 fe2f13df896894ce55ebbe0d8a39f9ac40b2578d241debfd77f1b8603357b039. -/ end
Source
D1Bound5/SmallPairGraphData42.lean, lines 3026-3027, SHA-256 1ed8ce699593f8600aa064e65c247cf748c5fb803b6b34d6d288dce915fef4cd. Project: https://github.com/tomislav-math/d1-bound5-lean