{
  "summary": {
    "total_with_gt": 98,
    "matched": 12,
    "accuracy": 0.12244897959183673
  },
  "details": [
    {
      "id": 0,
      "match": false,
      "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": "cases c <;> simp [ha]"
    },
    {
      "id": 1,
      "match": false,
      "ground_truth": "refine bot_lt_iff_ne_bot.mp ?_",
      "model_output": "a"
    },
    {
      "id": 2,
      "match": false,
      "ground_truth": "simp [botline]",
      "model_output": "intro h"
    },
    {
      "id": 3,
      "match": false,
      "ground_truth": "by\n  by_cases ha1 : a = 0\n  · rw [ha1]; simp\n  rwa [mul_lt_top_iff_lt_top (positivity)]",
      "model_output": "apply mul_lt_top <;> simp_all"
    },
    {
      "id": 4,
      "match": false,
      "ground_truth": "have h := α_inequ' (A:=A) (B:=B)",
      "model_output": "A : real_liminf\nB : real_liminf\ninequ : ∀ n, A.x n ≥ B.x n"
    },
    {
      "id": 5,
      "match": true,
      "ground_truth": "intro h",
      "model_output": "intro h"
    },
    {
      "id": 6,
      "match": false,
      "ground_truth": "refine lowerSemicontinuous_iff_le_liminf.mpr ?_",
      "model_output": "apply LowerSemicontinuous.const_smul hf hm"
    },
    {
      "id": 7,
      "match": false,
      "ground_truth": "simp only [le_top]",
      "model_output": "any_goals\n  first | rfl | apply 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": "apply eq_top_iff.mpr\n  contrapose! hsf\n  exact hf _ hx"
    },
    {
      "id": 10,
      "match": false,
      "ground_truth": "intro h",
      "model_output": "E : Type u_1\ninst"
    },
    {
      "id": 11,
      "match": false,
      "ground_truth": "PiLp.norm_eq_of_nat 1 (norm_num)",
      "model_output": "rw [← sq_eq_sq (by positivity) (by positivity), norm_sq_eq_inner, ← Finset.sum_mul, ←\n  Finset.mul_sum, norm_sq_eq_inner, ← Finset.sum_mul, ← Finset.mul_sum]"
    },
    {
      "id": 12,
      "match": false,
      "ground_truth": "simp [intrinsicInterior]",
      "model_output": "intro x hx"
    },
    {
      "id": 13,
      "match": false,
      "ground_truth": "lift d to ℝ using ⟨hd1, hd2⟩",
      "model_output": "convert h using 1 <;> simp"
    },
    {
      "id": 14,
      "match": false,
      "ground_truth": "simp only [Subtype.preimage_coe_eq_preimage_coe_iff]",
      "model_output": "constructor"
    },
    {
      "id": 15,
      "match": false,
      "ground_truth": "intro x",
      "model_output": "n : ℕ\nm : ℕ\nA : Matrix (Fin m) (Fin n) ℝ\nb : Fin m → ℝ\nμ : ℝ\nμpos : 0 < μ\nAne0 : A ≠ 0\nx₀ : EuclideanSpace ℝ (Fin n)"
    },
    {
      "id": 16,
      "match": false,
      "ground_truth": "· exact general_polyhedra_is_polyhedra_empty τ σ trivial",
      "model_output": "aesop"
    },
    {
      "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 v hv"
    },
    {
      "id": 19,
      "match": false,
      "ground_truth": "have cont_φ := ContDiffOn.continuousOn h₃",
      "model_output": "apply h₄"
    },
    {
      "id": 20,
      "match": false,
      "ground_truth": "have",
      "model_output": "f"
    },
    {
      "id": 21,
      "match": false,
      "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": "case.1 => simp [hctop]"
    },
    {
      "id": 22,
      "match": false,
      "ground_truth": "linarith",
      "model_output": "exact ne_of_gt tpos"
    },
    {
      "id": 23,
      "match": false,
      "ground_truth": "dsimp",
      "model_output": "exact lt_of_le_of_lt (h' ⟨hx, ‹_›⟩) (by assumption)"
    },
    {
      "id": 24,
      "match": false,
      "ground_truth": "constructor",
      "model_output": "symm"
    },
    {
      "id": 25,
      "match": false,
      "ground_truth": "have eq_r : r - r / 2 = r / 2 := linarith",
      "model_output": "apply ball_mem_nhdsWithin"
    },
    {
      "id": 26,
      "match": false,
      "ground_truth": "rw [mem_closure_iff_seq_limit]",
      "model_output": "apply closure_mono (fun x ↦ ?_)"
    },
    {
      "id": 27,
      "match": false,
      "ground_truth": "rw [hasGradientAt_iff_hasFDerivAt] at h",
      "model_output": "exact fun _ => (h _).hasFDerivAt"
    },
    {
      "id": 28,
      "match": false,
      "ground_truth": "intro h",
      "model_output": "intro hv"
    },
    {
      "id": 29,
      "match": false,
      "ground_truth": "field_simp at cond",
      "model_output": "simp [smul_eq_mul]"
    },
    {
      "id": 30,
      "match": false,
      "ground_truth": "field_simp",
      "model_output": "ring"
    },
    {
      "id": 31,
      "match": false,
      "ground_truth": "constructor",
      "model_output": "E : Type u_1\ninst"
    },
    {
      "id": 32,
      "match": false,
      "ground_truth": "intro x",
      "model_output": "intro x hx y hy"
    },
    {
      "id": 33,
      "match": false,
      "ground_truth": "rw [← smul_eq_mul, ← smul_eq_mul]",
      "model_output": "exact hfun yin zin anneg bnneg absum1"
    },
    {
      "id": 34,
      "match": false,
      "ground_truth": "have",
      "model_output": "cases' eq_or_ne x.2 ⊥ with hbot hbot"
    },
    {
      "id": 35,
      "match": true,
      "ground_truth": "exact this",
      "model_output": "exact this"
    },
    {
      "id": 36,
      "match": false,
      "ground_truth": "rw [IsLocalMinOn, IsMinFilter, eventually_iff_exists_mem] at hl",
      "model_output": "f' : E → ℝ"
    },
    {
      "id": 37,
      "match": false,
      "ground_truth": "constructor",
      "model_output": "simp only [mem_setOf_eq, mem_singleton_iff]"
    },
    {
      "id": 38,
      "match": false,
      "ground_truth": "· apply convex_univ",
      "model_output": "exact convex_univ"
    },
    {
      "id": 39,
      "match": false,
      "ground_truth": "right\n    simpa [topline] using ⟨hx1, hx2⟩",
      "model_output": "have : x ∈ closure (Prod.map id (Real.toEReal) '' (Epi f s))"
    },
    {
      "id": 40,
      "match": false,
      "ground_truth": "apply (hxn (n + N)).1",
      "model_output": "exact (hxn (n + N)).1"
    },
    {
      "id": 41,
      "match": false,
      "ground_truth": "exact this",
      "model_output": "convert this"
    },
    {
      "id": 42,
      "match": false,
      "ground_truth": "rcases cn with ⟨lam, mu, ⟨cn1, cn2⟩⟩",
      "model_output": "τ"
    },
    {
      "id": 43,
      "match": false,
      "ground_truth": "simp [mul_comm, mul_left_comm]",
      "model_output": "n : ℕ+\nt : ℝ\nμ : ℝ\nh : EuclideanSpace ℝ (Fin ↑n) → ℝ\nlasso : h = fun y => μ • ∑ i, ‖y i‖\nx : EuclideanSpace ℝ (Fin ↑n)\nxm : EuclideanSpace ℝ (Fin ↑n)\ntpos : 0 < t\nμpos : 0 < μ\nminpoint : ∀ (i : Fin ↑n), xm i = sign (x i) * max (|x i| - t * μ) 0\ng : EuclideanSpace ℝ (Fin ↑n"
    },
    {
      "id": 44,
      "match": false,
      "ground_truth": "simp at hx",
      "model_output": "exact ⟨hx.1.le, hx.2.le⟩"
    },
    {
      "id": 45,
      "match": false,
      "ground_truth": "apply Set.Subset.antisymm",
      "model_output": "n : ℕ\nτ : Finset ℕ\nσ : Finset ℕ\np : Constrained_OptimizationProblem (EuclideanSpace ℝ (Fin n)) τ σ\nx : EuclideanSpace ℝ (Fin n)\nxf : x ∈ FeasSet\nconte : ∀ i ∈ τ, ContDiffAt ℝ (↑1) (p.equality_constraints i) x\nconti : ∀ i ∈ σ, ContDiffAt ℝ (↑1) (p.inequality_sets i) x\nLx : LinearCQ x\nhdomain : p.domain = univ\ndiffable : ∀ i ∈ τ,"
    },
    {
      "id": 46,
      "match": false,
      "ground_truth": "· exact hfx",
      "model_output": "next => exact hfx"
    },
    {
      "id": 47,
      "match": false,
      "ground_truth": "· exact fun a ↦ Real_epi_closed_of_EReal_epi_closed a",
      "model_output": "intro H"
    },
    {
      "id": 48,
      "match": false,
      "ground_truth": "linarith",
      "model_output": "simp only [sub_eq_add_neg, add_assoc, neg_add_eq_sub] at this"
    },
    {
      "id": 49,
      "match": false,
      "ground_truth": "apply Filter.Eventually.of_forall",
      "model_output": "E : Type u_1\ninst"
    },
    {
      "id": 50,
      "match": false,
      "ground_truth": "rfl",
      "model_output": "norm_num"
    },
    {
      "id": 51,
      "match": false,
      "ground_truth": "simp at hab",
      "model_output": "norm_num at *\nlinarith"
    },
    {
      "id": 52,
      "match": false,
      "ground_truth": "exact h_deriv t₀",
      "model_output": "exact (h_deriv t₀).hasDerivAt"
    },
    {
      "id": 53,
      "match": false,
      "ground_truth": "apply div_pos",
      "model_output": "norm_pos_iff.2 (sub_ne_zero.2 (Ne.symm (Ne.intro _)))"
    },
    {
      "id": 54,
      "match": false,
      "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 hy"
    },
    {
      "id": 55,
      "match": false,
      "ground_truth": "have h1 : ‖z.1 - x‖ ≤ ‖z - z'‖ := fst_norm_le_prod_L2 (z - z')",
      "model_output": "norm_sub_rev : ‖z - (x, y)‖ = ‖(z.1 - x, z.2 - y)‖"
    },
    {
      "id": 56,
      "match": false,
      "ground_truth": "simp only [abs_abs]",
      "model_output": "norm_num"
    },
    {
      "id": 57,
      "match": false,
      "ground_truth": "repeat rw [z]; simp; apply norm_prod_left_zero",
      "model_output": "simp only [Prod.norm_def, norm_zero, norm_sub_rev, sub_zero, Prod.snd]"
    },
    {
      "id": 58,
      "match": false,
      "ground_truth": "have",
      "model_output": "k"
    },
    {
      "id": 59,
      "match": false,
      "ground_truth": "have : Inseparable uy vx := Metric.inseparable_iff.mpr this",
      "model_output": "apply h"
    },
    {
      "id": 60,
      "match": false,
      "ground_truth": "have",
      "model_output": "Nonempty"
    },
    {
      "id": 61,
      "match": false,
      "ground_truth": "apply Tendsto.const_mul C this",
      "model_output": "apply Tendsto.const_mul\n  assumption"
    },
    {
      "id": 62,
      "match": false,
      "ground_truth": "linarith",
      "model_output": "τ : Finset ℕ\nσ : Finset ℕ\nn : ℕ\na : ℕ → EuclideanSpace ℝ (Fin n)\nb : ℕ → EuclideanSpace ℝ (Finset ℕ)"
    },
    {
      "id": 63,
      "match": false,
      "ground_truth": "rw [mul_assoc]",
      "model_output": "l2 : a • (f x' + (f' x') (x - x')) + b • (f x' + (f' x') (y - x')) =\n  f x' + b * a * (f' x') (y - x)"
    },
    {
      "id": 64,
      "match": false,
      "ground_truth": "apply hcs.subseq_of_frequently_in (Filter.Frequently.of_forall even)",
      "model_output": "z : ℕ → E × F\nz0 : E × F\nz0_mem : z0 ∈ closure (z ∘ W '' univ)\nz0_lim : z0 ∈ limit_set z\nz0_lim' : z0 ∈ closure (z ∘ W '' univ)"
    },
    {
      "id": 65,
      "match": true,
      "ground_truth": "rfl",
      "model_output": "rfl"
    },
    {
      "id": 66,
      "match": false,
      "ground_truth": "by\n            rw [sub_self ((1 - τ) * ρ * (inner ℝ A₂_x_diff r_n)), zero_add]",
      "model_output": "ring"
    },
    {
      "id": 67,
      "match": false,
      "ground_truth": "linarith",
      "model_output": "nlinarith"
    },
    {
      "id": 68,
      "match": false,
      "ground_truth": "have h1: τ ≥ 0 := rcases admm.htau with ⟨h₁, _⟩; apply le_of_lt h₁",
      "model_output": "abs_nonneg"
    },
    {
      "id": 69,
      "match": false,
      "ground_truth": "norm_num",
      "model_output": "norm_pos_iff.mpr (sub_ne_zero.2 (Ne.symm (Ne.intro _)))"
    },
    {
      "id": 70,
      "match": true,
      "ground_truth": "by\n   intro n\n   rfl",
      "model_output": "intro n"
    },
    {
      "id": 71,
      "match": false,
      "ground_truth": "rw [pow_two]; simp",
      "model_output": "field_simp"
    },
    {
      "id": 72,
      "match": false,
      "ground_truth": "apply div_pos\n            · simp[hx₁]\n            · simp",
      "model_output": "norm_num"
    },
    {
      "id": 73,
      "match": false,
      "ground_truth": "exact Metric.isOpen_ball",
      "model_output": "norm_num"
    },
    {
      "id": 74,
      "match": false,
      "ground_truth": "have",
      "model_output": "E : Type u_1\ninst"
    },
    {
      "id": 75,
      "match": false,
      "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": "linarith"
    },
    {
      "id": 76,
      "match": false,
      "ground_truth": "have : φ_sum = (fun c => ∑ x ∈ ht2.toFinset, φ x c) := ext c; simp [φ_sum]",
      "model_output": "E : Type u_1\ninst1 : NormedAddCommGroup E\ninst2 : InnerProductSpace ℝ E\nf : E → ℝ\nΩ : Set E\nh_compact : IsCompact Ω\nh_Ω1 : ∀ x ∈ Ω, KL_point f x\nh_Ω2 : is_constant_on f Ω\nh_nonempty : Ω.Nonempty\nμ : ℝ\nconstant_value : ∀ x ∈ Ω, f x = μ\nη : E → ℝ\nhη2 : ∀ x ∈ Ω, η x ∈ Ioi 0\nO :"
    },
    {
      "id": 77,
      "match": false,
      "ground_truth": "have",
      "model_output": "rw [hab, hg] at *\nsimp at *\napply le_add_of_nonneg_left\napply xf.2.2 j hj"
    },
    {
      "id": 78,
      "match": false,
      "ground_truth": "rw[h2]",
      "model_output": "rw [h2]"
    },
    {
      "id": 79,
      "match": false,
      "ground_truth": "intro c1 hc1",
      "model_output": "intro c' c'pos"
    },
    {
      "id": 80,
      "match": true,
      "ground_truth": "exact ieq1 b n1leb",
      "model_output": "ieq1 b n1leb"
    },
    {
      "id": 81,
      "match": false,
      "ground_truth": "have",
      "model_output": "simp [← sub_pos]"
    },
    {
      "id": 82,
      "match": false,
      "ground_truth": "simp only [add_le_add_iff_right, ge_iff_le]",
      "model_output": "simp only [inner_add_right, add_le_add_iff_left]"
    },
    {
      "id": 83,
      "match": false,
      "ground_truth": "have",
      "model_output": "mem2 := Nesterov_second_y_mem_univ f h f' x0 k"
    },
    {
      "id": 84,
      "match": true,
      "ground_truth": "rw [norm_sub_rev]; exact ieq1 b n1leb",
      "model_output": "norm_sub_rev"
    },
    {
      "id": 85,
      "match": true,
      "ground_truth": "apply norm_nonneg",
      "model_output": "norm_nonneg"
    },
    {
      "id": 86,
      "match": false,
      "ground_truth": "apply Nat.ne_zero_iff_zero_lt.mpr npos",
      "model_output": "cases n"
    },
    {
      "id": 87,
      "match": true,
      "ground_truth": "linarith",
      "model_output": "linarith"
    },
    {
      "id": 88,
      "match": false,
      "ground_truth": "apply add_pos_of_nonneg_of_pos (Nat.cast_nonneg k) zero_lt_one",
      "model_output": "nlinarith"
    },
    {
      "id": 89,
      "match": true,
      "ground_truth": "by\n      apply reduction",
      "model_output": "apply reduction"
    },
    {
      "id": 90,
      "match": false,
      "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": "q1 : 1 ≤ α q"
    },
    {
      "id": 91,
      "match": false,
      "ground_truth": "by\n          apply mul_div_cancel_left₀\n          linarith",
      "model_output": "norm_num"
    },
    {
      "id": 92,
      "match": false,
      "ground_truth": "rw [rw_rn_1]",
      "model_output": "rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw_rw"
    },
    {
      "id": 93,
      "match": false,
      "ground_truth": "have",
      "model_output": "n : ℕ"
    },
    {
      "id": 94,
      "match": true,
      "ground_truth": "left",
      "model_output": "left"
    },
    {
      "id": 95,
      "match": false,
      "ground_truth": "rw[← sub_zero (A₁ (e₁ n) + A₂ (e₂ n))] at h_n'",
      "model_output": "simp [hr', dist_eq_norm] at *"
    },
    {
      "id": 96,
      "match": false,
      "ground_truth": "simp; apply mul_nonneg; linarith [alg.tpos]; apply sq_nonneg",
      "model_output": "inner_self_nonneg"
    },
    {
      "id": 97,
      "match": false,
      "ground_truth": "rw [← sub_mul, sub_sub_cancel, sub_sub]",
      "model_output": "norm_num"
    }
  ]
}