putnam-v1 / putnam-1969-a5

putnam-1969-a5

open

difficulty 4

credited

Run this goal:./swarm/run.sh --goal putnam-1969-a5

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-a5.lean

import Mathlib

open Matrix Filter Topology Set Nat

theorem putnam_1969_a5 (x0 y0 t : ℝ)
    (ht : 0 < t) :
    x0 = y0 ↔ ∃ x y u : ℝ → ℝ,
      Differentiable ℝ x ∧
      Differentiable ℝ y ∧
      Continuous u ∧
      deriv x = - 2 • y + u ∧
      deriv y = - 2 • x + u ∧
      x 0 = x0 ∧
      y 0 = y0 ∧
      x t = 0 ∧
      y t = 0 := by
  sorry

Runs (0)

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