| { | |
| "summary": { | |
| "total_with_gt": 98, | |
| "matched": 42, | |
| "accuracy": 0.42857142857142855 | |
| }, | |
| "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": "have : a > 0 := by\n simp at ha'\n exact Ne.lt_of_le' ha ha'" | |
| }, | |
| { | |
| "id": 1, | |
| "match": false, | |
| "ground_truth": "refine bot_lt_iff_ne_bot.mp ?_", | |
| "model_output": "by_contra h" | |
| }, | |
| { | |
| "id": 2, | |
| "match": true, | |
| "ground_truth": "simp [botline]", | |
| "model_output": "simp [botline]" | |
| }, | |
| { | |
| "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": "by_cases h : b = ⊥" | |
| }, | |
| { | |
| "id": 4, | |
| "match": false, | |
| "ground_truth": "have h := α_inequ' (A:=A) (B:=B)", | |
| "model_output": "simp only [ge_iff_le]" | |
| }, | |
| { | |
| "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": "intro x" | |
| }, | |
| { | |
| "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": "by_contra h" | |
| }, | |
| { | |
| "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": "rw [PiLp.norm_eq_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": "have h1 : a ≥ b + c - d := by exact h" | |
| }, | |
| { | |
| "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": false, | |
| "ground_truth": "· exact general_polyhedra_is_polyhedra_empty τ σ trivial", | |
| "model_output": "intro a b" | |
| }, | |
| { | |
| "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 _" | |
| }, | |
| { | |
| "id": 19, | |
| "match": false, | |
| "ground_truth": "have cont_φ := ContDiffOn.continuousOn h₃", | |
| "model_output": "apply ContinuousAt.mono (h₄)" | |
| }, | |
| { | |
| "id": 20, | |
| "match": false, | |
| "ground_truth": "have", | |
| "model_output": "have g1pos : 0 ≤ g1 := by simp [g1]" | |
| }, | |
| { | |
| "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": "· rw[hctop];simp" | |
| }, | |
| { | |
| "id": 22, | |
| "match": true, | |
| "ground_truth": "linarith", | |
| "model_output": "linarith" | |
| }, | |
| { | |
| "id": 23, | |
| "match": false, | |
| "ground_truth": "dsimp", | |
| "model_output": "simp only [mem_setOf_eq, mem_interior] at hx" | |
| }, | |
| { | |
| "id": 24, | |
| "match": false, | |
| "ground_truth": "constructor", | |
| "model_output": "rw [add_comm]" | |
| }, | |
| { | |
| "id": 25, | |
| "match": false, | |
| "ground_truth": "have eq_r : r - r / 2 = r / 2 := linarith", | |
| "model_output": "apply mem_of_mem_nhds this" | |
| }, | |
| { | |
| "id": 26, | |
| "match": true, | |
| "ground_truth": "rw [mem_closure_iff_seq_limit]", | |
| "model_output": "rw [mem_closure_iff_seq_limit]" | |
| }, | |
| { | |
| "id": 27, | |
| "match": false, | |
| "ground_truth": "rw [hasGradientAt_iff_hasFDerivAt] at h", | |
| "model_output": "intro xin" | |
| }, | |
| { | |
| "id": 28, | |
| "match": false, | |
| "ground_truth": "intro h", | |
| "model_output": "intro hv" | |
| }, | |
| { | |
| "id": 29, | |
| "match": true, | |
| "ground_truth": "field_simp at cond", | |
| "model_output": "simp" | |
| }, | |
| { | |
| "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 xs y ys" | |
| }, | |
| { | |
| "id": 33, | |
| "match": false, | |
| "ground_truth": "rw [← smul_eq_mul, ← smul_eq_mul]", | |
| "model_output": "have" | |
| }, | |
| { | |
| "id": 34, | |
| "match": false, | |
| "ground_truth": "have", | |
| "model_output": "simp at hx" | |
| }, | |
| { | |
| "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": "have" | |
| }, | |
| { | |
| "id": 37, | |
| "match": false, | |
| "ground_truth": "constructor", | |
| "model_output": "simp" | |
| }, | |
| { | |
| "id": 38, | |
| "match": false, | |
| "ground_truth": "· apply convex_univ", | |
| "model_output": "· exact convex_univ" | |
| }, | |
| { | |
| "id": 39, | |
| "match": true, | |
| "ground_truth": "right\n simpa [topline] using ⟨hx1, hx2⟩", | |
| "model_output": "right" | |
| }, | |
| { | |
| "id": 40, | |
| "match": false, | |
| "ground_truth": "apply (hxn (n + N)).1", | |
| "model_output": "exact (hxn (n + N)).1" | |
| }, | |
| { | |
| "id": 41, | |
| "match": true, | |
| "ground_truth": "exact this", | |
| "model_output": "exact this" | |
| }, | |
| { | |
| "id": 42, | |
| "match": false, | |
| "ground_truth": "rcases cn with ⟨lam, mu, ⟨cn1, cn2⟩⟩", | |
| "model_output": "rcases cn with ⟨lam, mu, mu_nonneg, cn⟩" | |
| }, | |
| { | |
| "id": 43, | |
| "match": false, | |
| "ground_truth": "simp [mul_comm, mul_left_comm]", | |
| "model_output": "simp only [PiLp.smul_apply, mul_sub]" | |
| }, | |
| { | |
| "id": 44, | |
| "match": true, | |
| "ground_truth": "simp at hx", | |
| "model_output": "simp at hx" | |
| }, | |
| { | |
| "id": 45, | |
| "match": false, | |
| "ground_truth": "apply Set.Subset.antisymm", | |
| "model_output": "ext d" | |
| }, | |
| { | |
| "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 ↦ a" | |
| }, | |
| { | |
| "id": 48, | |
| "match": true, | |
| "ground_truth": "linarith", | |
| "model_output": "linarith" | |
| }, | |
| { | |
| "id": 49, | |
| "match": false, | |
| "ground_truth": "apply Filter.Eventually.of_forall", | |
| "model_output": "rw [Filter.eventually_atTop]" | |
| }, | |
| { | |
| "id": 50, | |
| "match": true, | |
| "ground_truth": "rfl", | |
| "model_output": "rfl" | |
| }, | |
| { | |
| "id": 51, | |
| "match": false, | |
| "ground_truth": "simp at hab", | |
| "model_output": "rw [hab, inner_zero_left, zero_add] at hsl" | |
| }, | |
| { | |
| "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": false, | |
| "ground_truth": "have h1 : ‖z.1 - x‖ ≤ ‖z - z'‖ := fst_norm_le_prod_L2 (z - z')", | |
| "model_output": "have h1 : ‖z.1 - x‖ ≤ ‖z - (x, y)‖ := fst_norm_le_prod_L2 (z - (x, y))" | |
| }, | |
| { | |
| "id": 56, | |
| "match": false, | |
| "ground_truth": "simp only [abs_abs]", | |
| "model_output": "rw[abs_abs]" | |
| }, | |
| { | |
| "id": 57, | |
| "match": false, | |
| "ground_truth": "repeat rw [z]; simp; apply norm_prod_left_zero", | |
| "model_output": "simp [z]" | |
| }, | |
| { | |
| "id": 58, | |
| "match": false, | |
| "ground_truth": "have", | |
| "model_output": "intro k" | |
| }, | |
| { | |
| "id": 59, | |
| "match": false, | |
| "ground_truth": "have : Inseparable uy vx := Metric.inseparable_iff.mpr this", | |
| "model_output": "have : dist uy vx > 0 := by\n apply dist_pos_of_ne h\n exact h" | |
| }, | |
| { | |
| "id": 60, | |
| "match": true, | |
| "ground_truth": "have", | |
| "model_output": "have" | |
| }, | |
| { | |
| "id": 61, | |
| "match": false, | |
| "ground_truth": "apply Tendsto.const_mul C this", | |
| "model_output": "apply Filter.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": false, | |
| "ground_truth": "apply hcs.subseq_of_frequently_in (Filter.Frequently.of_forall even)", | |
| "model_output": "rcases IsSeqCompact.tendsto_subseq hcs even with ⟨z', _, α, _, con1, con2⟩" | |
| }, | |
| { | |
| "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": true, | |
| "ground_truth": "linarith", | |
| "model_output": "linarith" | |
| }, | |
| { | |
| "id": 68, | |
| "match": false, | |
| "ground_truth": "have h1: τ ≥ 0 := rcases admm.htau with ⟨h₁, _⟩; apply le_of_lt h₁", | |
| "model_output": "rw [abs_of_pos admm.hrho, abs_of_pos admm.hrho]" | |
| }, | |
| { | |
| "id": 69, | |
| "match": false, | |
| "ground_truth": "norm_num", | |
| "model_output": "linarith" | |
| }, | |
| { | |
| "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": "apply div_self this" | |
| }, | |
| { | |
| "id": 72, | |
| "match": true, | |
| "ground_truth": "apply div_pos\n · simp[hx₁]\n · simp", | |
| "model_output": "apply div_pos" | |
| }, | |
| { | |
| "id": 73, | |
| "match": false, | |
| "ground_truth": "exact Metric.isOpen_ball", | |
| "model_output": "· apply Metric.isOpen_ball" | |
| }, | |
| { | |
| "id": 74, | |
| "match": true, | |
| "ground_truth": "have", | |
| "model_output": "have" | |
| }, | |
| { | |
| "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": "apply add_lt_add_right (lt_of_le_of_lt (le_abs_self x₁) hx₁)" | |
| }, | |
| { | |
| "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 at xf" | |
| }, | |
| { | |
| "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": false, | |
| "ground_truth": "exact ieq1 b n1leb", | |
| "model_output": "apply ieq1 b n1leb" | |
| }, | |
| { | |
| "id": 81, | |
| "match": false, | |
| "ground_truth": "have", | |
| "model_output": "have h3 : Φ k = Φ k := by simp only [id_eq]" | |
| }, | |
| { | |
| "id": 82, | |
| "match": true, | |
| "ground_truth": "simp only [add_le_add_iff_right, ge_iff_le]", | |
| "model_output": "simp" | |
| }, | |
| { | |
| "id": 83, | |
| "match": false, | |
| "ground_truth": "have", | |
| "model_output": "have mem2 : alg.x 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": false, | |
| "ground_truth": "apply Nat.ne_zero_iff_zero_lt.mpr npos", | |
| "model_output": "· linarith" | |
| }, | |
| { | |
| "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": "linarith" | |
| }, | |
| { | |
| "id": 89, | |
| "match": false, | |
| "ground_truth": "by\n apply reduction", | |
| "model_output": "apply reduction q" | |
| }, | |
| { | |
| "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": false, | |
| "ground_truth": "by\n apply mul_div_cancel_left₀\n linarith", | |
| "model_output": "by field_simp" | |
| }, | |
| { | |
| "id": 92, | |
| "match": true, | |
| "ground_truth": "rw [rw_rn_1]", | |
| "model_output": "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": false, | |
| "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": false, | |
| "ground_truth": "simp; apply mul_nonneg; linarith [alg.tpos]; apply sq_nonneg", | |
| "model_output": "rw [sub_self, inner_zero_right, add_zero]" | |
| }, | |
| { | |
| "id": 97, | |
| "match": false, | |
| "ground_truth": "rw [← sub_mul, sub_sub_cancel, sub_sub]", | |
| "model_output": "ring" | |
| } | |
| ] | |
| } |