Pair Light Prepared43 — left checked
ProvedD1Bound5.PairLightPrepared43.left_checkeddiophantine-tuplesnumber-theory
Auxiliary result PairLightPrepared43.left_checked 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.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_PairBipartiteCheck_Definitions import Definitions.Def_D1Bound5_SmallPairGraphInputs43_Definitions_003 import Definitions.Def_D1Bound5_SmallPairGraphInputs43_Definitions_004 import Definitions.Def_D1Bound5_SmallPairSieve_1_3_Definitions
Formal statement
section
namespace D1Bound5.PairLightPrepared43
set_option maxRecDepth 100000
set_option maxHeartbeats 0
theorem _root_.D1Bound5.PairLightPrepared43.left_checked :
pairIndependentBool smallPairSieve_1_3 (pairSplitByMask smallPairLarge_43 PairGraphPrepared43.colors).1 = true := by sorry
end D1Bound5.PairLightPrepared43
end
Source
D1Bound5/SmallPairLightAssembly43.lean, lines 24-29, SHA-256 a1f93b85259f267bea1466e442343da00fa48b8f5128ef4939b965627b146f42. Project: https://github.com/tomislav-math/d1-bound5-lean