{
  "summary": {
    "total_with_gt": 98,
    "matched": 85,
    "accuracy": 0.8673469387755102
  },
  "details": [
    {
      "id": 0,
      "match": true,
      "ground_truth": "have ha : a > 0 := by\n    simp at ha'\n    exact lt_of_le_of_ne ha' fun a_1 ↦ ha <| id (Eq.symm a_1)",
      "model_output": "have"
    },
    {
      "id": 1,
      "match": true,
      "ground_truth": "refine bot_lt_iff_ne_bot.mp ?_",
      "model_output": "refine bot_lt_iff_ne_bot.mp ?_"
    },
    {
      "id": 2,
      "match": true,
      "ground_truth": "simp [botline]",
      "model_output": "simp [botline]"
    },
    {
      "id": 3,
      "match": true,
      "ground_truth": "by\n  by_cases ha1 : a = 0\n  · rw [ha1]; simp\n  rwa [mul_lt_top_iff_lt_top (positivity)]",
      "model_output": "by_cases ha1 : a = 0"
    },
    {
      "id": 4,
      "match": true,
      "ground_truth": "have h := α_inequ' (A:=A) (B:=B)",
      "model_output": "have h := α_inequ' (A:=A) (B:=B)"
    },
    {
      "id": 5,
      "match": true,
      "ground_truth": "intro h",
      "model_output": "intro h"
    },
    {
      "id": 6,
      "match": true,
      "ground_truth": "refine lowerSemicontinuous_iff_le_liminf.mpr ?_",
      "model_output": "refine lowerSemicontinuous_iff_le_liminf.mpr ?_"
    },
    {
      "id": 7,
      "match": true,
      "ground_truth": "simp only [le_top]",
      "model_output": "simp only [le_top]"
    },
    {
      "id": 8,
      "match": true,
      "ground_truth": "intro n",
      "model_output": "intro n"
    },
    {
      "id": 9,
      "match": false,
      "ground_truth": "apply top_of_ne_bot_of_ne_proper hsf hf hx",
      "model_output": "exact top_of_ne_bot_of_ne_proper hsf hf hx"
    },
    {
      "id": 10,
      "match": true,
      "ground_truth": "intro h",
      "model_output": "intro h"
    },
    {
      "id": 11,
      "match": false,
      "ground_truth": "PiLp.norm_eq_of_nat 1 (norm_num)",
      "model_output": "by\n  simp only [PiLp.norm_eq_of_nat 1 (by norm_num)]\n  rfl"
    },
    {
      "id": 12,
      "match": true,
      "ground_truth": "simp [intrinsicInterior]",
      "model_output": "simp [intrinsicInterior]"
    },
    {
      "id": 13,
      "match": true,
      "ground_truth": "lift d to ℝ using ⟨hd1, hd2⟩",
      "model_output": "lift d to ℝ using ⟨hd1, hd2⟩"
    },
    {
      "id": 14,
      "match": true,
      "ground_truth": "simp only [Subtype.preimage_coe_eq_preimage_coe_iff]",
      "model_output": "simp only [Subtype.preimage_coe_eq_preimage_coe_iff]"
    },
    {
      "id": 15,
      "match": true,
      "ground_truth": "intro x",
      "model_output": "intro x"
    },
    {
      "id": 16,
      "match": true,
      "ground_truth": "· exact general_polyhedra_is_polyhedra_empty τ σ trivial",
      "model_output": "exact general_polyhedra_is_polyhedra_empty τ σ trivial"
    },
    {
      "id": 17,
      "match": true,
      "ground_truth": "rw [← eq]",
      "model_output": "rw [← eq]"
    },
    {
      "id": 18,
      "match": false,
      "ground_truth": "exact sub_range 𝕜 hs",
      "model_output": "intro x hx"
    },
    {
      "id": 19,
      "match": true,
      "ground_truth": "have cont_φ := ContDiffOn.continuousOn h₃",
      "model_output": "have cont_φ := ContDiffOn.continuousOn h₃"
    },
    {
      "id": 20,
      "match": false,
      "ground_truth": "have",
      "model_output": "have h1 : f x ≤ g1 ∧ f y ≤ g2 := by /- wyj -/\n    exact ⟨le_coe_toReal (LT.lt.ne_top hx.2), le_coe_toReal (LT.lt.ne_top hy.2)⟩"
    },
    {
      "id": 21,
      "match": true,
      "ground_truth": "· rw [hctop]\n    have ha : (ENNReal.ofReal a) * ⊤ = ⊤ := by\n      refine ENNReal.mul_top ?h\n      simpa\n    rw [ha]\n    simp",
      "model_output": "· rw [hctop]\n    have ha : (ENNReal.ofReal a) * ⊤ = ⊤ := by\n      refine ENNReal.mul_top ?h\n      simpa\n    rw [ha]\n    simp"
    },
    {
      "id": 22,
      "match": true,
      "ground_truth": "linarith",
      "model_output": "linarith"
    },
    {
      "id": 23,
      "match": false,
      "ground_truth": "dsimp",
      "model_output": "by dsimp; linarith"
    },
    {
      "id": 24,
      "match": true,
      "ground_truth": "constructor",
      "model_output": "constructor"
    },
    {
      "id": 25,
      "match": false,
      "ground_truth": "have eq_r : r - r / 2 = r / 2 := linarith",
      "model_output": "have eq_r : r - r / 2 = r / 2 := by linarith"
    },
    {
      "id": 26,
      "match": true,
      "ground_truth": "rw [mem_closure_iff_seq_limit]",
      "model_output": "rw [mem_closure_iff_seq_limit]"
    },
    {
      "id": 27,
      "match": true,
      "ground_truth": "rw [hasGradientAt_iff_hasFDerivAt] at h",
      "model_output": "rw [hasGradientAt_iff_hasFDerivAt] at h"
    },
    {
      "id": 28,
      "match": true,
      "ground_truth": "intro h",
      "model_output": "intro h"
    },
    {
      "id": 29,
      "match": true,
      "ground_truth": "field_simp at cond",
      "model_output": "field_simp at cond"
    },
    {
      "id": 30,
      "match": true,
      "ground_truth": "field_simp",
      "model_output": "field_simp"
    },
    {
      "id": 31,
      "match": true,
      "ground_truth": "constructor",
      "model_output": "constructor"
    },
    {
      "id": 32,
      "match": false,
      "ground_truth": "intro x",
      "model_output": "intro x hx y hy"
    },
    {
      "id": 33,
      "match": true,
      "ground_truth": "rw [← smul_eq_mul, ← smul_eq_mul]",
      "model_output": "rw [← smul_eq_mul, ← smul_eq_mul]"
    },
    {
      "id": 34,
      "match": false,
      "ground_truth": "have",
      "model_output": "have hx1 : x.1 ∈ closure s := by\n    rw [mem_closure_iff_seq_limit]\n    use Prod.fst ∘ w\n    simpa using ⟨fun n ↦ (hw n).1, Tendsto.fst_nhds h⟩"
    },
    {
      "id": 35,
      "match": true,
      "ground_truth": "exact this",
      "model_output": "exact this"
    },
    {
      "id": 36,
      "match": true,
      "ground_truth": "rw [IsLocalMinOn, IsMinFilter, eventually_iff_exists_mem] at hl",
      "model_output": "rw [IsLocalMinOn, IsMinFilter, eventually_iff_exists_mem] at hl"
    },
    {
      "id": 37,
      "match": true,
      "ground_truth": "constructor",
      "model_output": "constructor"
    },
    {
      "id": 38,
      "match": true,
      "ground_truth": "· apply convex_univ",
      "model_output": "· apply convex_univ"
    },
    {
      "id": 39,
      "match": true,
      "ground_truth": "right\n    simpa [topline] using ⟨hx1, hx2⟩",
      "model_output": "right"
    },
    {
      "id": 40,
      "match": true,
      "ground_truth": "apply (hxn (n + N)).1",
      "model_output": "apply (hxn (n + N)).1"
    },
    {
      "id": 41,
      "match": true,
      "ground_truth": "exact this",
      "model_output": "exact this"
    },
    {
      "id": 42,
      "match": true,
      "ground_truth": "rcases cn with ⟨lam, mu, ⟨cn1, cn2⟩⟩",
      "model_output": "rcases cn with ⟨lam, mu, ⟨cn1, cn2⟩⟩"
    },
    {
      "id": 43,
      "match": true,
      "ground_truth": "simp [mul_comm, mul_left_comm]",
      "model_output": "simp [mul_comm, mul_left_comm]"
    },
    {
      "id": 44,
      "match": true,
      "ground_truth": "simp at hx",
      "model_output": "simp at hx"
    },
    {
      "id": 45,
      "match": true,
      "ground_truth": "apply Set.Subset.antisymm",
      "model_output": "apply Set.Subset.antisymm"
    },
    {
      "id": 46,
      "match": true,
      "ground_truth": "· exact hfx",
      "model_output": "· exact hfx"
    },
    {
      "id": 47,
      "match": false,
      "ground_truth": "· exact fun a ↦ Real_epi_closed_of_EReal_epi_closed a",
      "model_output": "· exact fun a ↦ EReal_epi_closed_of_Real_epi_closed a hs"
    },
    {
      "id": 48,
      "match": true,
      "ground_truth": "linarith",
      "model_output": "linarith"
    },
    {
      "id": 49,
      "match": true,
      "ground_truth": "apply Filter.Eventually.of_forall",
      "model_output": "apply Filter.Eventually.of_forall"
    },
    {
      "id": 50,
      "match": true,
      "ground_truth": "rfl",
      "model_output": "rfl"
    },
    {
      "id": 51,
      "match": true,
      "ground_truth": "simp at hab",
      "model_output": "simp at hab"
    },
    {
      "id": 52,
      "match": true,
      "ground_truth": "exact h_deriv t₀",
      "model_output": "exact h_deriv t₀"
    },
    {
      "id": 53,
      "match": true,
      "ground_truth": "apply div_pos",
      "model_output": "apply div_pos"
    },
    {
      "id": 54,
      "match": true,
      "ground_truth": "intro y yf\n          rw [FeasSet] at yf xf\n          rw [inezero]\n          apply yf.2.2 i is",
      "model_output": "intro y yf"
    },
    {
      "id": 55,
      "match": true,
      "ground_truth": "have h1 : ‖z.1 - x‖ ≤ ‖z - z'‖ := fst_norm_le_prod_L2 (z - z')",
      "model_output": "have h1 : ‖z.1 - x‖ ≤ ‖z - z'‖ := fst_norm_le_prod_L2 (z - z')"
    },
    {
      "id": 56,
      "match": true,
      "ground_truth": "simp only [abs_abs]",
      "model_output": "simp only [abs_abs]"
    },
    {
      "id": 57,
      "match": true,
      "ground_truth": "repeat rw [z]; simp; apply norm_prod_left_zero",
      "model_output": "rw [z]; simp; apply norm_prod_left_zero"
    },
    {
      "id": 58,
      "match": true,
      "ground_truth": "have",
      "model_output": "have"
    },
    {
      "id": 59,
      "match": true,
      "ground_truth": "have : Inseparable uy vx := Metric.inseparable_iff.mpr this",
      "model_output": "have : Inseparable uy vx := Metric.inseparable_iff.mpr this"
    },
    {
      "id": 60,
      "match": true,
      "ground_truth": "have",
      "model_output": "have"
    },
    {
      "id": 61,
      "match": true,
      "ground_truth": "apply Tendsto.const_mul C this",
      "model_output": "apply Tendsto.const_mul C this"
    },
    {
      "id": 62,
      "match": true,
      "ground_truth": "linarith",
      "model_output": "linarith"
    },
    {
      "id": 63,
      "match": true,
      "ground_truth": "rw [mul_assoc]",
      "model_output": "rw [mul_assoc]"
    },
    {
      "id": 64,
      "match": true,
      "ground_truth": "apply hcs.subseq_of_frequently_in (Filter.Frequently.of_forall even)",
      "model_output": "apply hcs.subseq_of_frequently_in (Filter.Frequently.of_forall even)"
    },
    {
      "id": 65,
      "match": true,
      "ground_truth": "rfl",
      "model_output": "rfl"
    },
    {
      "id": 66,
      "match": true,
      "ground_truth": "by\n            rw [sub_self ((1 - τ) * ρ * (inner ℝ A₂_x_diff r_n)), zero_add]",
      "model_output": "by\n            rw [sub_self ((1 - τ) * ρ * (inner ℝ A₂_x_diff r_n)), zero_add]"
    },
    {
      "id": 67,
      "match": true,
      "ground_truth": "linarith",
      "model_output": "linarith"
    },
    {
      "id": 68,
      "match": true,
      "ground_truth": "have h1: τ ≥ 0 := rcases admm.htau with ⟨h₁, _⟩; apply le_of_lt h₁",
      "model_output": "have"
    },
    {
      "id": 69,
      "match": true,
      "ground_truth": "norm_num",
      "model_output": "norm_num"
    },
    {
      "id": 70,
      "match": true,
      "ground_truth": "by\n   intro n\n   rfl",
      "model_output": "intro n"
    },
    {
      "id": 71,
      "match": true,
      "ground_truth": "rw [pow_two]; simp",
      "model_output": "rw [pow_two]; simp"
    },
    {
      "id": 72,
      "match": true,
      "ground_truth": "apply div_pos\n            · simp[hx₁]\n            · simp",
      "model_output": "apply div_pos"
    },
    {
      "id": 73,
      "match": true,
      "ground_truth": "exact Metric.isOpen_ball",
      "model_output": "exact Metric.isOpen_ball"
    },
    {
      "id": 74,
      "match": true,
      "ground_truth": "have",
      "model_output": "have"
    },
    {
      "id": 75,
      "match": true,
      "ground_truth": "apply (mul_lt_mul_iff_of_pos_left zero_lt_two).mp\n                rw [mul_div_cancel₀, mul_div_cancel₀]\n                simp [hx₁]; simp; simp",
      "model_output": "apply (mul_lt_mul_iff_of_pos_left zero_lt_two).mp"
    },
    {
      "id": 76,
      "match": true,
      "ground_truth": "have : φ_sum = (fun c => ∑ x ∈ ht2.toFinset, φ x c) := ext c; simp [φ_sum]",
      "model_output": "have"
    },
    {
      "id": 77,
      "match": false,
      "ground_truth": "have",
      "model_output": "simp [active_set] at hj1"
    },
    {
      "id": 78,
      "match": true,
      "ground_truth": "rw[h2]",
      "model_output": "rw[h2]"
    },
    {
      "id": 79,
      "match": true,
      "ground_truth": "intro c1 hc1",
      "model_output": "intro c1 hc1"
    },
    {
      "id": 80,
      "match": true,
      "ground_truth": "exact ieq1 b n1leb",
      "model_output": "exact ieq1 b n1leb"
    },
    {
      "id": 81,
      "match": false,
      "ground_truth": "have",
      "model_output": "have h3a': Φ k ∈ range Φ := by use k"
    },
    {
      "id": 82,
      "match": true,
      "ground_truth": "simp only [add_le_add_iff_right, ge_iff_le]",
      "model_output": "simp only [add_le_add_iff_right, ge_iff_le]"
    },
    {
      "id": 83,
      "match": false,
      "ground_truth": "have",
      "model_output": "have mem2 : alg.y k ∈ univ := by simp"
    },
    {
      "id": 84,
      "match": true,
      "ground_truth": "rw [norm_sub_rev]; exact ieq1 b n1leb",
      "model_output": "rw [norm_sub_rev]"
    },
    {
      "id": 85,
      "match": true,
      "ground_truth": "apply norm_nonneg",
      "model_output": "apply norm_nonneg"
    },
    {
      "id": 86,
      "match": true,
      "ground_truth": "apply Nat.ne_zero_iff_zero_lt.mpr npos",
      "model_output": "apply Nat.ne_zero_iff_zero_lt.mpr npos"
    },
    {
      "id": 87,
      "match": true,
      "ground_truth": "linarith",
      "model_output": "linarith"
    },
    {
      "id": 88,
      "match": true,
      "ground_truth": "apply add_pos_of_nonneg_of_pos (Nat.cast_nonneg k) zero_lt_one",
      "model_output": "apply add_pos_of_nonneg_of_pos (Nat.cast_nonneg k) zero_lt_one"
    },
    {
      "id": 89,
      "match": true,
      "ground_truth": "by\n      apply reduction",
      "model_output": "apply reduction"
    },
    {
      "id": 90,
      "match": true,
      "ground_truth": "have m1le : m1 ≤ 1 + max (max m1 m2) m3:= by\n      linarith [(le_max_left m1 m2).trans (le_max_left _ m3)]",
      "model_output": "have"
    },
    {
      "id": 91,
      "match": true,
      "ground_truth": "by\n          apply mul_div_cancel_left₀\n          linarith",
      "model_output": "apply mul_div_cancel_left₀"
    },
    {
      "id": 92,
      "match": false,
      "ground_truth": "rw [rw_rn_1]",
      "model_output": "by rw [rw_rn_1]"
    },
    {
      "id": 93,
      "match": true,
      "ground_truth": "have",
      "model_output": "have"
    },
    {
      "id": 94,
      "match": true,
      "ground_truth": "left",
      "model_output": "left"
    },
    {
      "id": 95,
      "match": true,
      "ground_truth": "rw[← sub_zero (A₁ (e₁ n) + A₂ (e₂ n))] at h_n'",
      "model_output": "rw[← sub_zero (A₁ (e₁ n) + A₂ (e₂ n))] at h_n'"
    },
    {
      "id": 96,
      "match": true,
      "ground_truth": "simp; apply mul_nonneg; linarith [alg.tpos]; apply sq_nonneg",
      "model_output": "simp"
    },
    {
      "id": 97,
      "match": true,
      "ground_truth": "rw [← sub_mul, sub_sub_cancel, sub_sub]",
      "model_output": "rw [← sub_mul, sub_sub_cancel, sub_sub]"
    }
  ]
}