putnam-v1 / putnam-1968-b4

putnam-1968-b4

open

difficulty 4

credited

Run this goal:./swarm/run.sh --goal putnam-1968-b4

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-1968-b4.lean

import Mathlib

open Finset Polynomial Topology Filter Metric

theorem putnam_1968_b4 (f : ℝ → ℝ)
(hf : Continuous f ∧ ∃ r : ℝ, Tendsto (fun y => ∫ x in ball 0 y, f x) atTop (𝓝 r))
: ∃ r : ℝ, Tendsto (fun y => ∫ x in (ball 0 y \ ball 0 (1 / y)), f (x - 1/x)) atTop (𝓝 r) ∧ Tendsto (fun y => ∫ x in ball 0 y, f x) atTop (𝓝 r) := by
  sorry

Runs (0)

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