Finite A choose four

Proved

D1Bound5.finiteA_choose_four

by tp · Oct 23, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

Auxiliary result finiteA_choose_four 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.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.RingTheory.Binomial
import Mathlib.RingTheory.PowerSeries.Binomial
import Mathlib.Tactic
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.finiteA_choose_four (r : F) : Ring.choose r 4 = r*(r-1)*(r-2)*(r-3)/24 := by sorry



end D1Bound5
end

Source

D1Bound5/FiniteChooseFive.lean, lines 19-23, SHA-256 bde24ed91fa3925db41d2480e279480d17f11937e1a240043403eb90798427c3. Project: https://github.com/tomislav-math/d1-bound5-lean

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