putnam-v1 / putnam-1964-b6

putnam-1964-b6

open

difficulty 4

credited

Run this goal:./swarm/run.sh --goal putnam-1964-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-1964-b6.lean

import Mathlib

open Set Function Filter Topology

theorem putnam_1964_b6 (D : Set (EuclideanSpace ℝ (Fin 2)))
    (hD : D = {v : EuclideanSpace ℝ (Fin 2) | dist 0 v ≤ 1})
    (cong : Set (EuclideanSpace ℝ (Fin 2)) → Set (EuclideanSpace ℝ (Fin 2)) → Prop)
    (hcong : ∀ A B, cong A B ↔ ∃ f : (EuclideanSpace ℝ (Fin 2)) → (EuclideanSpace ℝ (Fin 2)), B = f '' A ∧ ∀ v w : EuclideanSpace ℝ (Fin 2), dist v w = dist (f v) (f w))
    : (¬∃ A B : Set (EuclideanSpace ℝ (Fin 2)), cong A B ∧ A ∩ B = ∅ ∧ A ∪ B = D) := by
  sorry

Runs (0)

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