minif2f-v1 / algebra-amgm-sqrtxymulxmyeqxpy-xpygeq4

algebra-amgm-sqrtxymulxmyeqxpy-xpygeq4

open

difficulty 4

credited

Run this goal:./swarm/run.sh --goal algebra-amgm-sqrtxymulxmyeqxpy-xpygeq4

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/algebra-amgm-sqrtxymulxmyeqxpy-xpygeq4.lean

import Mathlib

set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat

theorem algebra_amgm_sqrtxymulxmyeqxpy_xpygeq4 (x y : ℝ) (h₀ : 0 < x ∧ 0 < y) (h₁ : y ≤ x)
  (h₂ : Real.sqrt (x * y) * (x - y) = x + y) : x + y ≥ 4 := by
  sorry

Runs (0)

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