Finite choose two
ProvedD1Bound5.finite_choose_twodiophantine-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.finite_choose_two (r : F) : Ring.choose r 2 = r*(r-1)/2 := by sorry
end D1Bound5
end
Source
D1Bound5/FiniteN2BennettIdentity.lean, lines 10-16, SHA-256 fcacc869d2713078cd69f64d108df5778a46eb1540584038908ffb1d2b408ba4. Project: https://github.com/tomislav-math/d1-bound5-lean