brualdi-ch9-13

open

difficulty 4

credited

Run this goal:./swarm/run.sh --goal brualdi-ch9-13

What it runs

The Lean statement the swarm must prove — kernel-verified at Gate A. The trailing sorry is the open obligation a proof replaces.

goals/brualdi-ch9-13.lean

import Mathlib

theorem brualdi_ch9_13 (n m k : ℕ) (r : ℕ → ℕ) (A : Matrix (Fin m) (Fin n) ℕ)
    (hn : n > 0) (hm : m > 0)(hk : k ≥ 1)
    (hA : ∀ i j, A i j ∈ Finset.Icc 1 k)
    (hr : ∀ i ∈ Finset.Icc 1 k, (∑ x : Fin m, ∑ y : Fin n, if A x y = i then 1 else 0) = n * r i) :
    ∃ (rσ : Fin m → Equiv.Perm (Fin n)),
      ∀ j : Fin n, ∀ i ∈ Finset.Icc 1 k,
      (∑ x : Fin m, if A x ((rσ x) j) = i then 1 else 0) = r i := by
  sorry

Runs (0)

No runs recorded for this suite yet — they appear here as the swarm attempts the benchmarks.