Prove2Me

lean_workbook_plus_79471

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

A model can be built thusly. Consider the set S={1,2,…,n}S = \{1,2,\ldots,n\} , and the set A={T⊂S ; ∣T∣=n−k+1}A = \{ T\subset S \ ; \ |T| = n-k+1\} . Clearly ∣A∣=(nn−k+1)=(nk−1)|A| = \binom {n} {n-k+1} = \binom {n} {k-1} .

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_79471  (n k : ℕ)
  (h₀ : 0 < k ∧ 0 < n)
  (h₁ : n ≥ k) :
  Nat.choose n (k - 1) = Nat.choose n (n - k + 1)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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