putnam-v1 / putnam-1969-a1

putnam-1969-a1

open

difficulty 4

credited

Run this goal:./swarm/run.sh --goal putnam-1969-a1

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-a1.lean

import Mathlib

open Matrix Filter Topology Set Nat
abbrev putnam_1969_a1_solution : Set (Set ℝ) := {{x} | x : ℝ} ∪ {Set.Ici x | x : ℝ} ∪ {Set.Iic x | x : ℝ} ∪ {Set.Iio x | x : ℝ} ∪ {Set.Ioi x | x : ℝ} ∪ {Set.univ}

theorem putnam_1969_a1 : {{z : ℝ | ∃ x : Fin 2 → ℝ, MvPolynomial.eval x f = z} | f : MvPolynomial (Fin 2) ℝ} = putnam_1969_a1_solution := by
  sorry

Runs (0)

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