First Pair Geometry Matches — pair invariants
ProvedD1Bound5.FirstPairGeometryMatches.pair_invariantsdiophantine-tuplesnumber-theory
Matching coordinate pairs have identical exact squared norms and separation, even though the unused third coordinate differs.
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_FirstPairGeometryData_Definitions_001 import Definitions.Def_D1Bound5_FirstPairGeometryFixedRows_Definitions import Definitions.Def_D1Bound5_OneSmallCutoffArithmetic_Definitions_001
Formal statement
section
namespace D1Bound5
theorem _root_.D1Bound5.FirstPairGeometryMatches.pair_invariants
(g : FirstPairGeometryRow) (r : OneSmallCutoffRow)
(h : FirstPairGeometryMatches g r) :
g.a0 = r.a0 ∧ g.b0 = r.b0 ∧ g.dab = r.dab := by sorry
end D1Bound5
end
Source
D1Bound5/FirstPairFixedTransfer.lean, lines 5-16, SHA-256 3faa8c267acd6dc418ad7dfd9d428a018612986ed715dc34ae106ea4a4b160f1. Project: https://github.com/tomislav-math/d1-bound5-lean