brualdi-ch10-60

open

difficulty 4

credited

Run this goal:./swarm/run.sh --goal brualdi-ch10-60

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-ch10-60.lean

import Mathlib

structure LatinSquare (n : ℕ) where
  carrier : Matrix (Fin n) (Fin n) (ZMod n)
  pairwise_1 : ∀ i j1 j2, j1 ≠ j2 → carrier i j1 ≠ carrier i j2
  pairwise_2 : ∀ j i1 i2, i1 ≠ i2 → carrier i1 j ≠ carrier i2 j
def IsIdempotent {n : ℕ} (L : LatinSquare n) : Prop :=
  ∀ i, L.carrier i i = i

theorem brualdi_ch10_60 {n : ℕ} (hn : n > 0) (L : LatinSquare n) :
    IsIdempotent L ∧ L.1.IsSymm → Odd n := by
  sorry

Runs (0)

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