putnam-v1 / putnam-1969-b6

putnam-1969-b6

open

difficulty 4

credited

Run this goal:./swarm/run.sh --goal putnam-1969-b6

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/putnam-1969-b6.lean

import Mathlib

open Matrix Filter Topology Set Nat

theorem putnam_1969_b6 (A : Matrix (Fin 3) (Fin 2) ℝ)
(B : Matrix (Fin 2) (Fin 3) ℝ)
(p : Fin 3 → Fin 3 → ℝ)
(hp : p 0 0 = 8 ∧ p 0 1 = 2 ∧ p 0 2 = -2 ∧
p 1 0 = 2 ∧ p 1 1 = 5 ∧ p 1 2 = 4 ∧
p 2 0 = -2 ∧ p 2 1 = 4 ∧ p 2 2 = 5)
(hAB : A * B = Matrix.of p)
: B * A = 9 * (1 : Matrix (Fin 2) (Fin 2) ℝ) := by
  sorry

Runs (0)

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