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Finite N3 choose two

Proved
D1Bound5.finiteN3_choose_two

by tp · Oct 24, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

The second generalized binomial coefficient, derived from the actual choose multiplication identity.

Preamble
import Lean.Elab.Tactic.Omega
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Algebra.BigOperators.NatAntidiagonal
import Mathlib.Algebra.Polynomial.BigOperators
import Mathlib.Algebra.Polynomial.Degree.Operations
import Mathlib.Combinatorics.Enumerative.Catalan.Basic
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
import Mathlib.RingTheory.Binomial
import Mathlib.RingTheory.PowerSeries.Binomial
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.FinCases
import Mathlib.Tactic.LinearCombination
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Ring

Formal statement
section
namespace D1Bound5

variable {F : Type*} [Field F] [CharZero F]


theorem _root_.D1Bound5.finiteN3_choose_two (r : F) : Ring.choose r 2 = r*(r-1)/2 := by sorry





end D1Bound5
end
Source
D1Bound5/FiniteN3BennettIdentity.lean, lines 10-16, SHA-256 9148242701768b71c2b658d39b171d28a071514528febee5c27aae9756a4480e. Project: https://github.com/tomislav-math/d1-bound5-lean

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