Map finite QRow Form
ProvedD1Bound5.map_finiteQRowFormdiophantine-tuplesnumber-theory
Auxiliary result map_finiteQRowForm 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.BigOperators.Fin import Mathlib.Algebra.QuadraticAlgebra.Basic import Mathlib.Algebra.Ring.Basic import Mathlib.Algebra.Ring.Equiv import Mathlib.Analysis.Complex.Norm import Mathlib.Data.Finset.Card import Mathlib.Data.Int.GCD import Mathlib.LinearAlgebra.Dimension.Free import Mathlib.LinearAlgebra.Matrix.Determinant.Basic import Mathlib.LinearAlgebra.Matrix.NonsingularInverse import Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex import Mathlib.NumberTheory.NumberField.Norm import Mathlib.Tactic.FinCases import Mathlib.Tactic.Linarith import Mathlib.Tactic.LinearCombination import Mathlib.Tactic.NormNum import Mathlib.Tactic.Ring import Definitions.Def_D1Bound5_FiniteQIntegralRows_Definitions
Formal statement
section
open scoped NumberField
open Module
namespace D1Bound5
variable {R S : Type*} [CommRing R] [CommRing S]
@[simp] theorem _root_.D1Bound5.map_finiteQRowForm (f : R →+* S)
(a b s t c z rA rB rS rT : R) (i : Fin 5) :
f (finiteQRowForm a b s t c z rA rB rS rT i) =
finiteQRowForm (f a) (f b) (f s) (f t) (f c)
(f z) (f rA) (f rB) (f rS) (f rT) i := by sorry
end D1Bound5
end
Source
D1Bound5/FiniteQIntegralRows.lean, lines 36-46, SHA-256 13dbc71d3f13cc35a26b1a62808a9ec3ba2232668209833fc8f21e0bdba9f6ad. Project: https://github.com/tomislav-math/d1-bound5-lean