| { | |
| "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" | |
| } | |
| ] | |
| } |