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{
"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]"
}
]
} |