Bennett Repeated Nodes card
ProvedD1Bound5.bennettRepeatedNodes_carddiophantine-tuplesnumber-theory
Auxiliary result bennettRepeatedNodes_card 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 Lean.Elab.Tactic.Omega import Mathlib.Algebra.BigOperators.Group.Finset.Sigma import Mathlib.Algebra.Polynomial.BigOperators import Mathlib.Algebra.Polynomial.PartialFractions import Mathlib.Algebra.Polynomial.Reverse import Mathlib.Algebra.Polynomial.RingDivision import Mathlib.Data.Finset.Insert import Mathlib.Data.Sym.Basic import Mathlib.LinearAlgebra.Lagrange import Mathlib.RingTheory.MvPolynomial.Symmetric.Defs import Mathlib.RingTheory.PowerSeries.Binomial import Mathlib.Tactic.Ring import Definitions.Def_D1Bound5_BennettRepeatedHsymm_Definitions
Formal statement
section
open Finset
namespace D1Bound5
section Homogeneous
variable {R ι : Type*} [CommRing R] [DecidableEq ι]
end Homogeneous
section Repeated
variable {F ι : Type*} [Field F] [CharZero F]
variable [Fintype ι] [DecidableEq ι]
theorem _root_.D1Bound5.bennettRepeatedNodes_card (e : ι → ℕ) :
Fintype.card (BennettRepeatedNodes e) = ∑ i, (e i + 1) := by sorry
end Repeated
end D1Bound5
end
Source
D1Bound5/BennettRepeatedHsymm.lean, lines 84-86, SHA-256 2c35125785b6ff0c9b69a4236b7a718a4b75a5a68706b7a3ada2c46efaddc905. Project: https://github.com/tomislav-math/d1-bound5-lean