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   "∀ (x : ℝ),\n  0 < x →\n    ∀ (x_2 : ℝ),\n      0 < x_2 →\n        ((0 < x_2 ∧ 0 < x) ∧ (0 < x_2 ∧ 0 < x) ∧ (0 < x_2 ∧ 0 < x) ∧ (0 < x_2 ∧ 0 < x) ∧ ¬A x x_2 = 0) ∧\n          (H x x_2 = GDef x x_2 * (GDef x x_2 / A x x_2) →\n            ((0 < x_2 ∧ 0 < x) ∧ (0 < x_2 ∧ 0 < x) ∧ (0 < x_2 ∧ 0 < x) ∧ ¬A x x_2 = 0) ∧ 0 < x_2 ∧ 0 < x)",
   "lean":
   "∀ (x : ℝ),\n  0 < x →\n    ∀ (x_2 : ℝ),\n      0 < x_2 →\n        H x x_2 = GDef x x_2 * (GDef x x_2 / A x x_2) ∧\n          GDef x x_2 * (GDef x x_2 / A x x_2) ≤ GDef x x_2",
   "justification": "Means.Proofs.proof14",
   "index": 14,
   "cites": []},
  {"status": "companion",
   "sentence": 20,
   "role": "statement",
   "reading":
   "\\forall x\\in \\mathbb{R},\\ 0<x\\Rightarrow (\\forall y\\in \\mathbb{R},\\ 0<y\\Rightarrow \\frac{x+y}{2}\\le Q(x)(y))",
   "rank": 0,
   "premises": [],
   "note": "",
   "module": "Means.Proofs",
   "meaningful": "∀ (x : ℝ), 0 < x → ∀ (x_2 : ℝ), 0 < x_2 → ¬2 = 0 ∧ 0 < x_2 ∧ 0 < x",
   "lean": "∀ (x : ℝ), 0 < x → ∀ (x_2 : ℝ), 0 < x_2 → (x + x_2) / 2 ≤ Q x x_2",
   "justification": "Means.Proofs.proof15",
   "index": 15,
   "cites": []}],
 "axioms": ["propext", "Classical.choice", "Quot.sound"],
 "article": "article.tex"}