| { |
| "summary": { |
| "total_with_gt": 273, |
| "matched": 43, |
| "accuracy": 0.1575091575091575 |
| }, |
| "details": [ |
| { |
| "id": 0, |
| "match": false, |
| "ground_truth": "· exact mul_le_mul_of_nonneg_left hyu ha", |
| "model_output": "apply mul_le_mul_of_nonneg_left hyu ha" |
| }, |
| { |
| "id": 1, |
| "match": false, |
| "ground_truth": "exact mul_le_mul_of_nonneg_left hyu ha", |
| "model_output": "nlinarith" |
| }, |
| { |
| "id": 2, |
| "match": false, |
| "ground_truth": "· exact mul_le_mul_of_nonneg_left hyv hb", |
| "model_output": "nlinarith" |
| }, |
| { |
| "id": 3, |
| "match": false, |
| "ground_truth": "exact mul_le_mul_of_nonneg_left hyv hb", |
| "model_output": "nlinarith" |
| }, |
| { |
| "id": 4, |
| "match": false, |
| "ground_truth": "rw [lipschitzWith_iff_norm_sub_le] at *", |
| "model_output": "apply (hl.lipschitzWith_of_fderiv_le (by simp)).congr" |
| }, |
| { |
| "id": 5, |
| "match": false, |
| "ground_truth": "by rw [grad_snd_eq h, grad_snd_eq h]", |
| "model_output": "rfl" |
| }, |
| { |
| "id": 6, |
| "match": false, |
| "ground_truth": "rw [grad_snd_eq h, grad_snd_eq h]", |
| "model_output": "rfl" |
| }, |
| { |
| "id": 7, |
| "match": false, |
| "ground_truth": "apply prox_well_define f hc lbdf x", |
| "model_output": "apply LowerSemicontinuous.exists_prox_set ?_ ?_" |
| }, |
| { |
| "id": 8, |
| "match": false, |
| "ground_truth": "refine ⟨x₁, hx₁, x₂, hx₂, hx, ?_⟩", |
| "model_output": "use x₁, hx₁, x₂, hx₂, hx" |
| }, |
| { |
| "id": 9, |
| "match": false, |
| "ground_truth": "exact LinearMap.mem_ker.mp (hker hx₂)", |
| "model_output": "apply hker" |
| }, |
| { |
| "id": 10, |
| "match": false, |
| "ground_truth": "simp [Orthonormal, Pairwise] at *", |
| "model_output": "apply Orthonormal.mk" |
| }, |
| { |
| "id": 11, |
| "match": false, |
| "ground_truth": "by_cases hsf : ProperFunction s f", |
| "model_output": "apply isClosed_closure" |
| }, |
| { |
| "id": 12, |
| "match": false, |
| "ground_truth": "· exact closure_is_closed_of_proper f hs", |
| "model_output": "apply Function.isClosed_closure" |
| }, |
| { |
| "id": 13, |
| "match": false, |
| "ground_truth": "exact closure_is_closed_of_proper f hs", |
| "model_output": "apply isClosed_closure" |
| }, |
| { |
| "id": 14, |
| "match": false, |
| "ground_truth": "apply IsClosed.prod hs isClosed_univ", |
| "model_output": "apply_rules [hs, isClosed_univ, _root_.isClosed_prod]" |
| }, |
| { |
| "id": 15, |
| "match": false, |
| "ground_truth": "simp [w, l, g, AffineMap.decomp']", |
| "model_output": "apply i.h_eq_of_mem" |
| }, |
| { |
| "id": 16, |
| "match": false, |
| "ground_truth": "rw [φ₁_equ fullrank₁ fullrank₂ n]", |
| "model_output": "apply Eq.symm" |
| }, |
| { |
| "id": 17, |
| "match": false, |
| "ground_truth": "exact EReal.coe_le_coe_iff.mp h", |
| "model_output": "norm_cast at *" |
| }, |
| { |
| "id": 18, |
| "match": false, |
| "ground_truth": "rw [← hT.span_range_w_eq_range]", |
| "model_output": "apply Eq.symm" |
| }, |
| { |
| "id": 19, |
| "match": false, |
| "ground_truth": "apply iff_iff_implies_and_implies.mpr", |
| "model_output": "specialize h z" |
| }, |
| { |
| "id": 20, |
| "match": false, |
| "ground_truth": "apply convex_conjugate_ge_bot_univ'", |
| "model_output": "apply lt_of_le_of_ne" |
| }, |
| { |
| "id": 21, |
| "match": false, |
| "ground_truth": "exact HasGradientWithinAt.const_smul h c", |
| "model_output": "apply HasGradientWithinAt.const_smul h c" |
| }, |
| { |
| "id": 22, |
| "match": false, |
| "ground_truth": "exact HasGradientAtFilter.const_add hf c", |
| "model_output": "exact hf.const_add c" |
| }, |
| { |
| "id": 23, |
| "match": false, |
| "ground_truth": "exact HasGradientAtFilter.const_add hf c", |
| "model_output": "exact hf.const_add c" |
| }, |
| { |
| "id": 24, |
| "match": false, |
| "ground_truth": "exact HasGradientAtFilter.const_sub hf c", |
| "model_output": "exact hf.neg.const_sub c" |
| }, |
| { |
| "id": 25, |
| "match": false, |
| "ground_truth": "apply convex_on_p_top\n ext x; exact h x", |
| "model_output": "apply convexOn_of_forall_le_of_forall_le convex_univ" |
| }, |
| { |
| "id": 26, |
| "match": false, |
| "ground_truth": "apply monotone_gradient_convex'", |
| "model_output": "apply ConvexOn.smul" |
| }, |
| { |
| "id": 27, |
| "match": false, |
| "ground_truth": "exact (fun x _ => affine_sq_gradient x)", |
| "model_output": "aesop" |
| }, |
| { |
| "id": 28, |
| "match": false, |
| "ground_truth": "have h_zero_eq := (hS 0).mp h_zero_mem", |
| "model_output": "apply_fun (fun v => B.repr v 0) at h_zero_mem" |
| }, |
| { |
| "id": 29, |
| "match": false, |
| "ground_truth": "have : (0 : 𝕜) < (1 : 𝕜) := one_pos", |
| "model_output": "apply hf' x y" |
| }, |
| { |
| "id": 30, |
| "match": false, |
| "ground_truth": "rw [inner_add_left, real_inner_smul_left, real_inner_smul_left]", |
| "model_output": "rw [inner_add_left,smul_eq_mul,smul_eq_mul]" |
| }, |
| { |
| "id": 31, |
| "match": false, |
| "ground_truth": "rw [← one_mul (-ε * ‖y - x‖), ← hab, add_mul]", |
| "model_output": "apply le_trans" |
| }, |
| { |
| "id": 32, |
| "match": false, |
| "ground_truth": "calc\n _ = ‖(gradient H z).2 - (gradient H z').2‖ := by rw [grad_snd_eq h, grad_snd_eq h]\n _ = ‖(gradient H z - gradient H z').2‖ := rfl\n _ ≤ ‖(gradient H z - gradient H z')‖ := snd_norm_le_prod_L2 _\n _ ≤ _ := hl z z'", |
| "model_output": "apply hl" |
| }, |
| { |
| "id": 33, |
| "match": true, |
| "ground_truth": "by\n intro k\n specialize ck k; rw [ck]\n apply div_pos\n · norm_num\n apply mul_pos\n · linarith [hγ]\n · apply alg.lpos", |
| "model_output": "intro k" |
| }, |
| { |
| "id": 34, |
| "match": true, |
| "ground_truth": "intro k\n specialize ck k; rw [ck]\n apply div_pos\n · norm_num\n apply mul_pos\n · linarith [hγ]\n · apply alg.lpos", |
| "model_output": "intro k" |
| }, |
| { |
| "id": 35, |
| "match": false, |
| "ground_truth": "by\n apply prox_well_define f hc lbdf x", |
| "model_output": "apply LowerSemicontinuous.exists_prox_set ?_ ?_" |
| }, |
| { |
| "id": 36, |
| "match": false, |
| "ground_truth": "by\n unfold colSubmodule\n rw [finrank_span_eq_card]\n simp [h]", |
| "model_output": "apply (LinearMap.finrank_eq_of_range_eq_top _).trans" |
| }, |
| { |
| "id": 37, |
| "match": false, |
| "ground_truth": "unfold colSubmodule\n rw [finrank_span_eq_card]\n simp [h]", |
| "model_output": "apply (LinearMap.finrank_eq_of_range_eq_top _).trans" |
| }, |
| { |
| "id": 38, |
| "match": false, |
| "ground_truth": "let ⟨x₁, hx₁, x₂, hx₂, hx⟩ := exists_orthogonal_decompose s x\n refine ⟨x₁, hx₁, x₂, hx₂, hx, ?_⟩\n rw [hx, LinearMap.map_add]\n suffices T x₂ = 0 from by\n rw [this, add_zero, norm_sq_eq_re_inner (𝕜:=𝕜)]\n exact LinearMap.mem_ker.mp (hker hx₂)", |
| "model_output": "apply exists_add_of_le_ker hker" |
| }, |
| { |
| "id": 39, |
| "match": false, |
| "ground_truth": "suffices T x₂ = 0 from by\n rw [this, add_zero, norm_sq_eq_re_inner (𝕜:=𝕜)]", |
| "model_output": "rw [← LinearMap.map_add]" |
| }, |
| { |
| "id": 40, |
| "match": false, |
| "ground_truth": "by\n rw [this, add_zero, norm_sq_eq_re_inner (𝕜:=𝕜)]", |
| "model_output": "rw [this, add_zero]" |
| }, |
| { |
| "id": 41, |
| "match": false, |
| "ground_truth": "rw [this, add_zero, norm_sq_eq_re_inner (𝕜:=𝕜)]", |
| "model_output": "rw [this, add_zero]" |
| }, |
| { |
| "id": 42, |
| "match": false, |
| "ground_truth": "by\n simp [Orthonormal, Pairwise] at *\n aesop", |
| "model_output": "apply Orthonormal.mk" |
| }, |
| { |
| "id": 43, |
| "match": false, |
| "ground_truth": "simp [Orthonormal, Pairwise] at *\n aesop", |
| "model_output": "apply Orthonormal.mk" |
| }, |
| { |
| "id": 44, |
| "match": false, |
| "ground_truth": "by\n let s := Metric.ball x ε\n have h : ContDiffAt ℝ 1 f x := by\n apply ContDiffOn.contDiffAt hf\n rw [mem_nhds_iff]; use s\n exact ⟨Eq.subset rfl, ⟨Metric.isOpen_ball, Metric.mem_ball_self he⟩⟩\n exact gradient_continuous_of_contdiffat f h", |
| "model_output": "apply ContinuousAt.congr ?_ (fun x hx => ?_)" |
| }, |
| { |
| "id": 45, |
| "match": false, |
| "ground_truth": "let s := Metric.ball x ε\n have h : ContDiffAt ℝ 1 f x := by\n apply ContDiffOn.contDiffAt hf\n rw [mem_nhds_iff]; use s\n exact ⟨Eq.subset rfl, ⟨Metric.isOpen_ball, Metric.mem_ball_self he⟩⟩\n exact gradient_continuous_of_contdiffat f h", |
| "model_output": "apply ContinuousAt.congr ?_ (fun x hx => ?_)" |
| }, |
| { |
| "id": 46, |
| "match": false, |
| "ground_truth": "have h : ContDiffAt ℝ 1 f x := by\n apply ContDiffOn.contDiffAt hf\n rw [mem_nhds_iff]; use s\n exact ⟨Eq.subset rfl, ⟨Metric.isOpen_ball, Metric.mem_ball_self he⟩⟩", |
| "model_output": "apply ContinuousAt.comp" |
| }, |
| { |
| "id": 47, |
| "match": false, |
| "ground_truth": "exact ⟨Eq.subset rfl, ⟨Metric.isOpen_ball, Metric.mem_ball_self he⟩⟩", |
| "model_output": "apply And.intro" |
| }, |
| { |
| "id": 48, |
| "match": false, |
| "ground_truth": "exact gradient_continuous_of_contdiffat f h", |
| "model_output": "apply (contDiffAt_iff_continuousAt_differentiableAt ℝ 1).mp h" |
| }, |
| { |
| "id": 49, |
| "match": false, |
| "ground_truth": "by\n simp [Function.closure]\n intro h; exfalso\n obtain h1 := h.2; simp at h1", |
| "model_output": "apply Function.closure_univ" |
| }, |
| { |
| "id": 50, |
| "match": false, |
| "ground_truth": "simp [Function.closure]\n intro h; exfalso\n obtain h1 := h.2; simp at h1", |
| "model_output": "apply Function.closure_univ" |
| }, |
| { |
| "id": 51, |
| "match": false, |
| "ground_truth": "· simp [hf]; simp [Function.IsClosed]\n have h1 : Epi ⊥ s = s ×ˢ (univ : Set ℝ) := by\n ext ⟨x, _⟩\n simp [Function.Epi]\n rw [h1]\n apply IsClosed.prod hs isClosed_univ", |
| "model_output": "exact isClosed_discrete ⊥" |
| }, |
| { |
| "id": 52, |
| "match": false, |
| "ground_truth": "simp [hf]; simp [Function.IsClosed]\n have h1 : Epi ⊥ s = s ×ˢ (univ : Set ℝ) := by\n ext ⟨x, _⟩\n simp [Function.Epi]\n rw [h1]\n apply IsClosed.prod hs isClosed_univ", |
| "model_output": "aesop" |
| }, |
| { |
| "id": 53, |
| "match": false, |
| "ground_truth": "have h1 : Epi ⊥ s = s ×ˢ (univ : Set ℝ) := by\n ext ⟨x, _⟩\n simp [Function.Epi]", |
| "model_output": "apply epi_of_isClosed_of_frequently_eq (by simpa)" |
| }, |
| { |
| "id": 54, |
| "match": false, |
| "ground_truth": "have h' : Epi ⊤ s = ∅ := by\n ext ⟨x, _⟩; simp [Function.Epi]", |
| "model_output": "simp [epigraph, univ]" |
| }, |
| { |
| "id": 55, |
| "match": false, |
| "ground_truth": "by\n constructor\n · intro h z\n unfold HasSubgradientAt at h\n obtain hz := h z\n simp; linarith\n intro h z\n unfold Banach_HasSubgradientAt at h\n obtain hz := h z; simp at hz\n linarith", |
| "model_output": "rw [HasSubgradientAt, ← hasSubgradientAt_iff_banach_hasSubgradientAt]" |
| }, |
| { |
| "id": 56, |
| "match": false, |
| "ground_truth": "constructor\n · intro h z\n unfold HasSubgradientAt at h\n obtain hz := h z\n simp; linarith\n intro h z\n unfold Banach_HasSubgradientAt at h\n obtain hz := h z; simp at hz\n linarith", |
| "model_output": "rw [HasSubgradientAt, ← hasSubgradientAt_iff_banach_hasSubgradientAt]" |
| }, |
| { |
| "id": 57, |
| "match": true, |
| "ground_truth": "· intro h z\n unfold HasSubgradientAt at h\n obtain hz := h z\n simp; linarith", |
| "model_output": "intro h" |
| }, |
| { |
| "id": 58, |
| "match": true, |
| "ground_truth": "intro h z\n unfold HasSubgradientAt at h\n obtain hz := h z\n simp; linarith", |
| "model_output": "intro h" |
| }, |
| { |
| "id": 59, |
| "match": false, |
| "ground_truth": "· intro x hx\n simpa [w, l, g, AffineMap.decomp', ← EReal.coe_sub, ← EReal.coe_add] using i.hlw x hx", |
| "model_output": "apply i.hg" |
| }, |
| { |
| "id": 60, |
| "match": false, |
| "ground_truth": "intro x hx\n simpa [w, l, g, AffineMap.decomp', ← EReal.coe_sub, ← EReal.coe_add] using i.hlw x hx", |
| "model_output": "norm_cast" |
| }, |
| { |
| "id": 61, |
| "match": false, |
| "ground_truth": "apply Filter.tendsto_iff_seq_tendsto.1 Seq_converge_zero₃", |
| "model_output": "apply tendsto_zero_iff_norm_tendsto_zero.mpr" |
| }, |
| { |
| "id": 62, |
| "match": false, |
| "ground_truth": "have : (fun n => (Int.toNat (φ₁ n))) = (fun n => (φ (n+1))) := by\n ext n; rw [φ₁_equ fullrank₁ fullrank₂ n]; simp", |
| "model_output": "apply strictMono_nat_of_lt_succ" |
| }, |
| { |
| "id": 63, |
| "match": false, |
| "ground_truth": "suffices 0 ≤ (c - a - b).toEReal by exact this", |
| "model_output": "apply le_sub_iff_add_le.2" |
| }, |
| { |
| "id": 64, |
| "match": false, |
| "ground_truth": "have : a + b ≤ c := by exact EReal.coe_le_coe_iff.mp h", |
| "model_output": "norm_cast at *" |
| }, |
| { |
| "id": 65, |
| "match": false, |
| "ground_truth": "refine EReal.coe_nonneg.mpr ?intro.intro.a", |
| "model_output": "norm_cast" |
| }, |
| { |
| "id": 66, |
| "match": false, |
| "ground_truth": "by\n constructor\n · exact hs\n intro x hx y hy a b ha hb hab\n specialize hfun hx hy ha hb hab\n dsimp\n have : m / 2 * a * b * ‖x - y‖ ^ 2 = a * b * (m / 2 * ‖x - y‖ ^ 2) := by ring_nf\n simp at this;\n rw [← this]; exact hfun", |
| "model_output": "apply And.intro hs" |
| }, |
| { |
| "id": 67, |
| "match": false, |
| "ground_truth": "constructor\n · exact hs\n intro x hx y hy a b ha hb hab\n specialize hfun hx hy ha hb hab\n dsimp\n have : m / 2 * a * b * ‖x - y‖ ^ 2 = a * b * (m / 2 * ‖x - y‖ ^ 2) := by ring_nf\n simp at this;\n rw [← this]; exact hfun", |
| "model_output": "apply And.intro hs" |
| }, |
| { |
| "id": 68, |
| "match": false, |
| "ground_truth": "have : m / 2 * a * b * ‖x - y‖ ^ 2 = a * b * (m / 2 * ‖x - y‖ ^ 2) := by ring_nf", |
| "model_output": "linarith [hfun]" |
| }, |
| { |
| "id": 69, |
| "match": false, |
| "ground_truth": "by\n rw [← hT.span_range_w_eq_range]\n simp [finrank_span_eq_card (b:=hT.w) hT.w_orthonormal.linearIndependent]", |
| "model_output": "apply Eq.symm" |
| }, |
| { |
| "id": 70, |
| "match": false, |
| "ground_truth": "rw [← hT.span_range_w_eq_range]\n simp [finrank_span_eq_card (b:=hT.w) hT.w_orthonormal.linearIndependent]", |
| "model_output": "apply Eq.symm" |
| }, |
| { |
| "id": 71, |
| "match": false, |
| "ground_truth": "simp [finrank_span_eq_card (b:=hT.w) hT.w_orthonormal.linearIndependent]", |
| "model_output": "apply Eq.symm" |
| }, |
| { |
| "id": 72, |
| "match": false, |
| "ground_truth": "· exact fun a ↦ set_inclusion_convex_support_eq s t htcv htcl a h", |
| "model_output": "intro hz" |
| }, |
| { |
| "id": 73, |
| "match": false, |
| "ground_truth": "exact fun a ↦ set_inclusion_convex_support_eq s t htcv htcl a h", |
| "model_output": "intro hz" |
| }, |
| { |
| "id": 74, |
| "match": false, |
| "ground_truth": "exact fun a ↦ set_inclusion_convex_support_eq t s hscv hscl a (fun x => (h x).symm)", |
| "model_output": "intro hzt" |
| }, |
| { |
| "id": 75, |
| "match": true, |
| "ground_truth": "by\n intro x _\n simp [convex_support]\n obtain := ConvexIndicator_is_proper_on_univ hs\n apply convex_conjugate_ge_bot_univ'", |
| "model_output": "intro x _" |
| }, |
| { |
| "id": 76, |
| "match": true, |
| "ground_truth": "intro x _\n simp [convex_support]\n obtain := ConvexIndicator_is_proper_on_univ hs\n apply convex_conjugate_ge_bot_univ'", |
| "model_output": "intro x _" |
| }, |
| { |
| "id": 77, |
| "match": false, |
| "ground_truth": "have convex_conjugate_at_zero :\n convex_conjugate univ (convex_indicator s) 0 ≤ 0 := by\n refine (conjugate_le_zero_iff s.convex_indicator).mpr ?_\n simp\n intro y\n simp [convex_indicator]\n split_ifs with hy <;> simp", |
| "model_output": "use 0" |
| }, |
| { |
| "id": 78, |
| "match": false, |
| "ground_truth": "refine (conjugate_le_zero_iff s.convex_indicator).mpr ?_", |
| "model_output": "apply convex_conjugate_indicator_le" |
| }, |
| { |
| "id": 79, |
| "match": false, |
| "ground_truth": "exact lt_of_le_of_lt (convex_conjugate_at_zero) (zero_lt_top)", |
| "model_output": "apply lt_of_le_of_ne convex_conjugate_at_zero" |
| }, |
| { |
| "id": 80, |
| "match": false, |
| "ground_truth": "by\n exact HasGradientWithinAt.const_smul h c", |
| "model_output": "apply HasGradientWithinAt.const_smul h c" |
| }, |
| { |
| "id": 81, |
| "match": false, |
| "ground_truth": "by\n exact HasGradientAtFilter.const_add hf c", |
| "model_output": "exact hf.const_add c" |
| }, |
| { |
| "id": 82, |
| "match": false, |
| "ground_truth": "by\n exact HasGradientAtFilter.const_add hf c", |
| "model_output": "exact hf.const_add c" |
| }, |
| { |
| "id": 83, |
| "match": false, |
| "ground_truth": "by\n simp only [sub_eq_add_neg, gradient_add_const]", |
| "model_output": "apply gradient_sub_const" |
| }, |
| { |
| "id": 84, |
| "match": false, |
| "ground_truth": "simp only [sub_eq_add_neg, gradient_add_const]", |
| "model_output": "apply gradient_sub_const" |
| }, |
| { |
| "id": 85, |
| "match": false, |
| "ground_truth": "by\n exact HasGradientAtFilter.const_sub hf c", |
| "model_output": "exact hf.neg.const_sub c" |
| }, |
| { |
| "id": 86, |
| "match": false, |
| "ground_truth": "by\n obtain h1 := h.2; simp at h1\n rcases h1 with ⟨x, hx⟩; use x; simp [hx]", |
| "model_output": "apply Set.Nonempty.mono (dom_mono (subset_univ _))" |
| }, |
| { |
| "id": 87, |
| "match": false, |
| "ground_truth": "obtain h1 := h.2; simp at h1\n rcases h1 with ⟨x, hx⟩; use x; simp [hx]", |
| "model_output": "apply Set.Nonempty.mono (dom_mono (subset_univ _))" |
| }, |
| { |
| "id": 88, |
| "match": false, |
| "ground_truth": "by\n apply convex_on_p_top\n ext x; exact h x", |
| "model_output": "apply convexOn_of_forall_le_of_forall_le convex_univ" |
| }, |
| { |
| "id": 89, |
| "match": false, |
| "ground_truth": "by\n rw [sub_eq_add_neg u v, mulVec_add, mulVec_neg, sub_eq_add_neg]", |
| "model_output": "apply Matrix.mulVec_sub" |
| }, |
| { |
| "id": 90, |
| "match": false, |
| "ground_truth": "rw [sub_eq_add_neg u v, mulVec_add, mulVec_neg, sub_eq_add_neg]", |
| "model_output": "apply Matrix.mulVec_sub" |
| }, |
| { |
| "id": 91, |
| "match": false, |
| "ground_truth": "· exact (fun x _ => affine_sq_gradient x)", |
| "model_output": "fun x => Aᵀ * (A *ᵥ x - b)" |
| }, |
| { |
| "id": 92, |
| "match": false, |
| "ground_truth": "· intro x _ y _\n rw [Matrix.mulVec_sub, Matrix.mulVec_sub, ← sub_add, sub_add_eq_add_sub, sub_add_cancel,\n ← Matrix.mulVec_sub, real_inner_eq_dot]\n rw [← dot_mul_eq_transpose_mul_dot,← Matrix.mulVec_sub, ← norm2eq_dot]\n apply sq_nonneg", |
| "model_output": "simp [inner, mulVec, transpose]" |
| }, |
| { |
| "id": 93, |
| "match": false, |
| "ground_truth": "intro x _ y _\n rw [Matrix.mulVec_sub, Matrix.mulVec_sub, ← sub_add, sub_add_eq_add_sub, sub_add_cancel,\n ← Matrix.mulVec_sub, real_inner_eq_dot]\n rw [← dot_mul_eq_transpose_mul_dot,← Matrix.mulVec_sub, ← norm2eq_dot]\n apply sq_nonneg", |
| "model_output": "simp [inner, mulVec, transpose]" |
| }, |
| { |
| "id": 94, |
| "match": false, |
| "ground_truth": "rw [Matrix.mulVec_sub, Matrix.mulVec_sub, ← sub_add, sub_add_eq_add_sub, sub_add_cancel,\n ← Matrix.mulVec_sub, real_inner_eq_dot]", |
| "model_output": "apply inner_sub_nonneg" |
| }, |
| { |
| "id": 95, |
| "match": false, |
| "ground_truth": "rw [← dot_mul_eq_transpose_mul_dot,← Matrix.mulVec_sub, ← norm2eq_dot]", |
| "model_output": "apply dotProduct_nonneg_of_angle_le_pi_div_two" |
| }, |
| { |
| "id": 96, |
| "match": false, |
| "ground_truth": "have h_zero_mem : (0 : E) ∈ S := S.zero_mem", |
| "model_output": "have := hS (0 : E)" |
| }, |
| { |
| "id": 97, |
| "match": false, |
| "ground_truth": "have h_repr_zero : B.repr 0 = 0 := LinearEquiv.map_zero B.repr", |
| "model_output": "simp at h_zero_eq" |
| }, |
| { |
| "id": 98, |
| "match": false, |
| "ground_truth": "simp only [map_zero, Finsupp.coe_zero, Pi.zero_apply] at h_zero_eq", |
| "model_output": "simp [h_repr_zero] at h_zero_eq" |
| }, |
| { |
| "id": 99, |
| "match": false, |
| "ground_truth": "simp only [Matrix.mulVec_zero, add_zero] at h_zero_eq", |
| "model_output": "rw [Matrix.mulVec_zero, add_zero] at h_zero_eq" |
| }, |
| { |
| "id": 100, |
| "match": false, |
| "ground_truth": "by\n unfold sup_value\n unfold FeasSet FeasPoint\n simp [hp]", |
| "model_output": "simp [sup_value, hp]" |
| }, |
| { |
| "id": 101, |
| "match": false, |
| "ground_truth": "unfold sup_value\n unfold FeasSet FeasPoint\n simp [hp]", |
| "model_output": "simp [sup_value, hp]" |
| }, |
| { |
| "id": 102, |
| "match": true, |
| "ground_truth": "by\n intro b; rw [polyhedra_iff_cone b]\n exact closed_conic σ b", |
| "model_output": "intro b" |
| }, |
| { |
| "id": 103, |
| "match": true, |
| "ground_truth": "intro b; rw [polyhedra_iff_cone b]\n exact closed_conic σ b", |
| "model_output": "intro b" |
| }, |
| { |
| "id": 104, |
| "match": true, |
| "ground_truth": "by\n rw [h]; apply (local_Minimum_TangentCone' loc hl hf)", |
| "model_output": "rw [h]" |
| }, |
| { |
| "id": 105, |
| "match": true, |
| "ground_truth": "rw [h]; apply (local_Minimum_TangentCone' loc hl hf)", |
| "model_output": "rw [h]" |
| }, |
| { |
| "id": 106, |
| "match": false, |
| "ground_truth": "apply (local_Minimum_TangentCone' loc hl hf)", |
| "model_output": "rw [← h]" |
| }, |
| { |
| "id": 107, |
| "match": false, |
| "ground_truth": "by rw [←ContinuousLinearMap.comp_apply, ←ContinuousLinearMap.adjoint_comp]; simp", |
| "model_output": "apply ContinuousLinearMap.adjoint_apply_eq_of_inner_right" |
| }, |
| { |
| "id": 108, |
| "match": false, |
| "ground_truth": "rw [←ContinuousLinearMap.comp_apply, ←ContinuousLinearMap.adjoint_comp]; simp", |
| "model_output": "apply ContinuousLinearMap.adjoint_apply_eq_of_inner_right" |
| }, |
| { |
| "id": 109, |
| "match": false, |
| "ground_truth": "rw [←ContinuousLinearMap.comp_apply, ←ContinuousLinearMap.adjoint_comp]", |
| "model_output": "apply ContinuousLinearMap.adjoint_apply_eq_of_inner_right" |
| }, |
| { |
| "id": 110, |
| "match": false, |
| "ground_truth": "by rw [←ContinuousLinearMap.comp_apply, ←ContinuousLinearMap.adjoint_comp]; simp", |
| "model_output": "apply ContinuousLinearMap.adjoint_apply_adjoint" |
| }, |
| { |
| "id": 111, |
| "match": false, |
| "ground_truth": "rw [←ContinuousLinearMap.comp_apply, ←ContinuousLinearMap.adjoint_comp]; simp", |
| "model_output": "apply ContinuousLinearMap.adjoint_apply_adjoint" |
| }, |
| { |
| "id": 112, |
| "match": false, |
| "ground_truth": "rw [←ContinuousLinearMap.comp_apply, ←ContinuousLinearMap.adjoint_comp]", |
| "model_output": "apply ContinuousLinearMap.adjoint_apply_adjoint" |
| }, |
| { |
| "id": 113, |
| "match": false, |
| "ground_truth": "by rw [← trace_transpose, ← trace_transpose_mul, transpose_mul]", |
| "model_output": "apply Eq.symm" |
| }, |
| { |
| "id": 114, |
| "match": false, |
| "ground_truth": "rw [← trace_transpose, ← trace_transpose_mul, transpose_mul]", |
| "model_output": "apply Eq.symm" |
| }, |
| { |
| "id": 115, |
| "match": false, |
| "ground_truth": "have : ConvexOn ℝ X fun _ ↦ (0: EReal) := by\n dsimp [ConvexOn]\n constructor\n exact hs\n intro x _ y _ a b _ _ _\n simp", |
| "model_output": "apply ConvexOn.indicator" |
| }, |
| { |
| "id": 116, |
| "match": false, |
| "ground_truth": "have eq : EqOn (fun _ ↦ (0: EReal)) (Set.convex_indicator X) X := by\n dsimp[EqOn]\n intro x hx\n dsimp [Set.convex_indicator]\n rw [if_pos hx]", |
| "model_output": "apply ConvexOn.add this" |
| }, |
| { |
| "id": 117, |
| "match": false, |
| "ground_truth": "by\n apply Subset.antisymm\n · exact iIntersection_closure_sub_closure_iIntersection'' h hinter\n exact closure_iIntersection_sub_iIntersection_closure'", |
| "model_output": "apply Eq.symm" |
| }, |
| { |
| "id": 118, |
| "match": false, |
| "ground_truth": "apply Subset.antisymm\n · exact iIntersection_closure_sub_closure_iIntersection'' h hinter\n exact closure_iIntersection_sub_iIntersection_closure'", |
| "model_output": "apply Eq.symm" |
| }, |
| { |
| "id": 119, |
| "match": false, |
| "ground_truth": "· exact iIntersection_closure_sub_closure_iIntersection'' h hinter", |
| "model_output": "pick_goal 2" |
| }, |
| { |
| "id": 120, |
| "match": false, |
| "ground_truth": "exact iIntersection_closure_sub_closure_iIntersection'' h hinter", |
| "model_output": "apply Set.iInter_subset" |
| }, |
| { |
| "id": 121, |
| "match": false, |
| "ground_truth": "exact closure_iIntersection_sub_iIntersection_closure'", |
| "model_output": "apply intrinsicClosure_iInter_subset_iInter_intrinsicClosure" |
| }, |
| { |
| "id": 122, |
| "match": false, |
| "ground_truth": "have eqone : a + (1 - a) = 1 := add_sub_cancel a 1", |
| "model_output": "apply neq" |
| }, |
| { |
| "id": 123, |
| "match": false, |
| "ground_truth": "have lta' : 0 < 1 - a := sub_pos_of_lt alt", |
| "model_output": "apply neq" |
| }, |
| { |
| "id": 124, |
| "match": false, |
| "ground_truth": "have h : f (a • x + (1 - a) • y) < f y := by\n apply Eq.trans_gt (max_eq_right (hx trivial))\n apply hf' neq lta lta' eqone", |
| "model_output": "apply neq" |
| }, |
| { |
| "id": 125, |
| "match": false, |
| "ground_truth": "apply Eq.trans_gt (max_eq_right (hx trivial))", |
| "model_output": "apply hf'" |
| }, |
| { |
| "id": 126, |
| "match": false, |
| "ground_truth": "intro ε εpos", |
| "model_output": "intro ε hε" |
| }, |
| { |
| "id": 127, |
| "match": false, |
| "ground_truth": "rw [ge_iff_le] at *", |
| "model_output": "apply_rules [ge_iff_le, add_mul]" |
| }, |
| { |
| "id": 128, |
| "match": false, |
| "ground_truth": "apply add_le_add", |
| "model_output": "apply_rules [mul_le_mul_of_nonneg_left, add_le_add] <;> linarith" |
| }, |
| { |
| "id": 129, |
| "match": false, |
| "ground_truth": "apply div_pos", |
| "model_output": "apply div_pos zero_lt_one" |
| }, |
| { |
| "id": 130, |
| "match": false, |
| "ground_truth": "apply mul_pos", |
| "model_output": "apply mul_pos (zero_lt_one.trans hγ) (NNReal.coe_pos.mpr l.property)" |
| }, |
| { |
| "id": 131, |
| "match": false, |
| "ground_truth": "· linarith [hγ]", |
| "model_output": "exact zero_lt_one.trans hγ" |
| }, |
| { |
| "id": 132, |
| "match": true, |
| "ground_truth": "linarith [hγ]", |
| "model_output": "linarith" |
| }, |
| { |
| "id": 133, |
| "match": false, |
| "ground_truth": "· apply alg.lpos", |
| "model_output": "norm_num" |
| }, |
| { |
| "id": 134, |
| "match": false, |
| "ground_truth": "apply alg.lpos", |
| "model_output": "norm_num" |
| }, |
| { |
| "id": 135, |
| "match": false, |
| "ground_truth": "rw [mem_nhds_iff]", |
| "model_output": "apply Metric.ball_mem_nhds" |
| }, |
| { |
| "id": 136, |
| "match": false, |
| "ground_truth": "simp [Function.Epi]", |
| "model_output": "simp [ProperFunction] at hsf" |
| }, |
| { |
| "id": 137, |
| "match": false, |
| "ground_truth": "simp [Function.Epi]", |
| "model_output": "simp [ProperFunction] at hsf" |
| }, |
| { |
| "id": 138, |
| "match": true, |
| "ground_truth": "exact isClosed_empty", |
| "model_output": "exact isClosed_empty" |
| }, |
| { |
| "id": 139, |
| "match": false, |
| "ground_truth": "constructor", |
| "model_output": "rw [HasSubgradientAt, ← hasSubgradientAt_iff_banach_hasSubgradientAt]" |
| }, |
| { |
| "id": 140, |
| "match": true, |
| "ground_truth": "by\n ext g; rw [h]", |
| "model_output": "rw [h]" |
| }, |
| { |
| "id": 141, |
| "match": true, |
| "ground_truth": "ext g; rw [h]", |
| "model_output": "rw [h]" |
| }, |
| { |
| "id": 142, |
| "match": false, |
| "ground_truth": "constructor", |
| "model_output": "apply And.intro" |
| }, |
| { |
| "id": 143, |
| "match": false, |
| "ground_truth": "intro x _hx", |
| "model_output": "intro x hx" |
| }, |
| { |
| "id": 144, |
| "match": false, |
| "ground_truth": "simp at this", |
| "model_output": "rw [this]" |
| }, |
| { |
| "id": 145, |
| "match": false, |
| "ground_truth": "· simp [StrictMono]", |
| "model_output": "exact fun m n hmn => by linarith" |
| }, |
| { |
| "id": 146, |
| "match": false, |
| "ground_truth": "simp [StrictMono]", |
| "model_output": "exact fun m n hmn => by linarith" |
| }, |
| { |
| "id": 147, |
| "match": false, |
| "ground_truth": "by_cases hc2 : c = ⊤", |
| "model_output": "apply le_sub_iff_add_le.2 h" |
| }, |
| { |
| "id": 148, |
| "match": false, |
| "ground_truth": "· rw [hc2]; simp", |
| "model_output": "simp [hc2]" |
| }, |
| { |
| "id": 149, |
| "match": false, |
| "ground_truth": "rw [hc2]; simp", |
| "model_output": "simp [hc2] at h ⊢" |
| }, |
| { |
| "id": 150, |
| "match": false, |
| "ground_truth": "by exact this", |
| "model_output": "norm_cast at *" |
| }, |
| { |
| "id": 151, |
| "match": false, |
| "ground_truth": "constructor", |
| "model_output": "apply And.intro hs" |
| }, |
| { |
| "id": 152, |
| "match": false, |
| "ground_truth": "rw [← this]", |
| "model_output": "rw [this] at hfun" |
| }, |
| { |
| "id": 153, |
| "match": false, |
| "ground_truth": "constructor", |
| "model_output": "apply Iff.intro" |
| }, |
| { |
| "id": 154, |
| "match": false, |
| "ground_truth": "simp [funext_iff]", |
| "model_output": "intro h" |
| }, |
| { |
| "id": 155, |
| "match": false, |
| "ground_truth": "constructor", |
| "model_output": "specialize h z" |
| }, |
| { |
| "id": 156, |
| "match": true, |
| "ground_truth": "· apply convex_univ", |
| "model_output": "apply convex_univ" |
| }, |
| { |
| "id": 157, |
| "match": true, |
| "ground_truth": "apply convex_univ", |
| "model_output": "apply convex_univ" |
| }, |
| { |
| "id": 158, |
| "match": false, |
| "ground_truth": "intro x _ y _", |
| "model_output": "simp [inner, mulVec, transpose]" |
| }, |
| { |
| "id": 159, |
| "match": false, |
| "ground_truth": "apply sq_nonneg", |
| "model_output": "apply pow_two_nonneg" |
| }, |
| { |
| "id": 160, |
| "match": true, |
| "ground_truth": "exact h_zero_eq.symm", |
| "model_output": "symm" |
| }, |
| { |
| "id": 161, |
| "match": false, |
| "ground_truth": "dsimp [ConvexOn]", |
| "model_output": "apply ConvexOn.const" |
| }, |
| { |
| "id": 162, |
| "match": false, |
| "ground_truth": "constructor", |
| "model_output": "aesop" |
| }, |
| { |
| "id": 163, |
| "match": false, |
| "ground_truth": "dsimp[EqOn]", |
| "model_output": "intro x hx" |
| }, |
| { |
| "id": 164, |
| "match": false, |
| "ground_truth": "rw [if_pos hx]", |
| "model_output": "aesop" |
| }, |
| { |
| "id": 165, |
| "match": false, |
| "ground_truth": "by_contra neq", |
| "model_output": "apply eq_of_forall_ge_iff" |
| }, |
| { |
| "id": 166, |
| "match": false, |
| "ground_truth": "intro u hu v hv a b ha hb hab", |
| "model_output": "apply convex_sInter" |
| }, |
| { |
| "id": 167, |
| "match": false, |
| "ground_truth": "rw [has_f_subdiff_iff] at *", |
| "model_output": "apply convex_iff_forall_pos.mpr ?_" |
| }, |
| { |
| "id": 168, |
| "match": false, |
| "ground_truth": "rw [finrank_span_eq_card]", |
| "model_output": "apply (Submodule.finrank_eq_card (finrank_submodule_span_eq_card 𝕜 _)).trans" |
| }, |
| { |
| "id": 169, |
| "match": false, |
| "ground_truth": "rw [hx, LinearMap.map_add]", |
| "model_output": "have : T x₂ = 0" |
| }, |
| { |
| "id": 170, |
| "match": false, |
| "ground_truth": "apply ContDiffOn.contDiffAt hf", |
| "model_output": "apply hf" |
| }, |
| { |
| "id": 171, |
| "match": false, |
| "ground_truth": "simp [Function.closure]", |
| "model_output": "apply Function.closure_univ" |
| }, |
| { |
| "id": 172, |
| "match": false, |
| "ground_truth": "simp [Function.closure, hsf]", |
| "model_output": "apply Function.isClosed_closure" |
| }, |
| { |
| "id": 173, |
| "match": false, |
| "ground_truth": "by_cases hf : ∃ x ∈ s, f x = ⊥", |
| "model_output": "split_ifs with h" |
| }, |
| { |
| "id": 174, |
| "match": false, |
| "ground_truth": "simp [Function.IsClosed]", |
| "model_output": "aesop" |
| }, |
| { |
| "id": 175, |
| "match": false, |
| "ground_truth": "simp [Function.IsClosed]", |
| "model_output": "simp [Function.isClosed_iff]" |
| }, |
| { |
| "id": 176, |
| "match": false, |
| "ground_truth": "apply StrictMono.tendsto_atTop", |
| "model_output": "apply tendsto_atTop_mono'" |
| }, |
| { |
| "id": 177, |
| "match": false, |
| "ground_truth": "apply StrictMono.comp", |
| "model_output": "apply strictMono_nat_of_lt_succ" |
| }, |
| { |
| "id": 178, |
| "match": false, |
| "ground_truth": "· apply hphi_StrictMono", |
| "model_output": "apply strictMono_nat_of_lt_succ" |
| }, |
| { |
| "id": 179, |
| "match": false, |
| "ground_truth": "apply hphi_StrictMono", |
| "model_output": "rw [← this]" |
| }, |
| { |
| "id": 180, |
| "match": false, |
| "ground_truth": "lift a to ℝ using ⟨ha2, ha1⟩", |
| "model_output": "apply le_sub_iff_add_le.mpr" |
| }, |
| { |
| "id": 181, |
| "match": false, |
| "ground_truth": "lift c to ℝ using ⟨hc2, hc1⟩", |
| "model_output": "apply le_sub_iff_add_le'.mpr" |
| }, |
| { |
| "id": 182, |
| "match": false, |
| "ground_truth": "intro x hx y hy a b ha hb hab", |
| "model_output": "intro x hx y hy a b ha hb hab\nspecialize hfun hx hy a ha b hb hab\nsimp at *\nring_nf" |
| }, |
| { |
| "id": 183, |
| "match": false, |
| "ground_truth": "· exact fun h => (by rw [h])", |
| "model_output": "intro h" |
| }, |
| { |
| "id": 184, |
| "match": false, |
| "ground_truth": "exact fun h => (by rw [h])", |
| "model_output": "aesop" |
| }, |
| { |
| "id": 185, |
| "match": false, |
| "ground_truth": "simp [convex_support]", |
| "model_output": "apply hs" |
| }, |
| { |
| "id": 186, |
| "match": false, |
| "ground_truth": "simp [convex_support]", |
| "model_output": "apply hs.exists_mem_interior" |
| }, |
| { |
| "id": 187, |
| "match": false, |
| "ground_truth": "simp [convex_indicator]", |
| "model_output": "apply_rules [nonneg_convex_indicator]" |
| }, |
| { |
| "id": 188, |
| "match": false, |
| "ground_truth": "split_ifs with hy <;> simp", |
| "model_output": "split_ifs <;> simp" |
| }, |
| { |
| "id": 189, |
| "match": false, |
| "ground_truth": "rcases h1 with ⟨x, hx⟩", |
| "model_output": "exact ⟨_, h1⟩" |
| }, |
| { |
| "id": 190, |
| "match": false, |
| "ground_truth": "apply convex_on_p_top", |
| "model_output": "apply convexOn_of_forall_le_of_forall_le convex_univ" |
| }, |
| { |
| "id": 191, |
| "match": false, |
| "ground_truth": "rw [polyhedra_iff_cone b]", |
| "model_output": "apply isClosed_setOf_exists" |
| }, |
| { |
| "id": 192, |
| "match": false, |
| "ground_truth": "exact closed_conic σ b", |
| "model_output": "apply IsClosed.sInter" |
| }, |
| { |
| "id": 193, |
| "match": false, |
| "ground_truth": "intro x _ y _ a b _ _ _", |
| "model_output": "simp" |
| }, |
| { |
| "id": 194, |
| "match": false, |
| "ground_truth": "dsimp [Set.convex_indicator]", |
| "model_output": "rw [convex_indicator_of_mem hx]" |
| }, |
| { |
| "id": 195, |
| "match": false, |
| "ground_truth": "apply ConvexOn.congr this eq", |
| "model_output": "rw [convexOn_indicator_eq]" |
| }, |
| { |
| "id": 196, |
| "match": false, |
| "ground_truth": "apply Subset.antisymm", |
| "model_output": "apply Eq.symm" |
| }, |
| { |
| "id": 197, |
| "match": false, |
| "ground_truth": "apply hf' neq lta lta' eqone", |
| "model_output": "apply lt_of_le_of_ne" |
| }, |
| { |
| "id": 198, |
| "match": false, |
| "ground_truth": "simp only [isMinOn_iff] at hy", |
| "model_output": "apply hy" |
| }, |
| { |
| "id": 199, |
| "match": false, |
| "ground_truth": "apply not_le_of_gt h hy", |
| "model_output": "linarith" |
| }, |
| { |
| "id": 200, |
| "match": false, |
| "ground_truth": "intro u", |
| "model_output": "apply convex_sInter" |
| }, |
| { |
| "id": 201, |
| "match": false, |
| "ground_truth": "intro ε", |
| "model_output": "intro ε hε" |
| }, |
| { |
| "id": 202, |
| "match": false, |
| "ground_truth": "intro z z'", |
| "model_output": "intro x y" |
| }, |
| { |
| "id": 203, |
| "match": false, |
| "ground_truth": "intro z", |
| "model_output": "intro x y" |
| }, |
| { |
| "id": 204, |
| "match": true, |
| "ground_truth": "intro k", |
| "model_output": "intro k" |
| }, |
| { |
| "id": 205, |
| "match": false, |
| "ground_truth": "rw [ck]", |
| "model_output": "rw [ck]; positivity" |
| }, |
| { |
| "id": 206, |
| "match": false, |
| "ground_truth": "· norm_num", |
| "model_output": "exact zero_lt_one" |
| }, |
| { |
| "id": 207, |
| "match": true, |
| "ground_truth": "norm_num", |
| "model_output": "norm_num" |
| }, |
| { |
| "id": 208, |
| "match": false, |
| "ground_truth": "simp [h]", |
| "model_output": "apply rows_linearIndependent_of_orthogonalProjection_eq_self" |
| }, |
| { |
| "id": 209, |
| "match": true, |
| "ground_truth": "aesop", |
| "model_output": "aesop" |
| }, |
| { |
| "id": 210, |
| "match": true, |
| "ground_truth": "intro h", |
| "model_output": "intro h" |
| }, |
| { |
| "id": 211, |
| "match": false, |
| "ground_truth": "exfalso", |
| "model_output": "apply le_antisymm" |
| }, |
| { |
| "id": 212, |
| "match": false, |
| "ground_truth": "simp at h1", |
| "model_output": "cases h1 with\n| inl h1 => exact absurd h1 univ_nonempty\n| inr h1 => exact lt_irrefl _ (h1.choose_spec.2.2)" |
| }, |
| { |
| "id": 213, |
| "match": false, |
| "ground_truth": "simp [hf]", |
| "model_output": "aesop" |
| }, |
| { |
| "id": 214, |
| "match": false, |
| "ground_truth": "ext ⟨x, _⟩", |
| "model_output": "aesop" |
| }, |
| { |
| "id": 215, |
| "match": true, |
| "ground_truth": "rw [h1]", |
| "model_output": "rw [h1]" |
| }, |
| { |
| "id": 216, |
| "match": false, |
| "ground_truth": "simp [hf]", |
| "model_output": "aesop" |
| }, |
| { |
| "id": 217, |
| "match": false, |
| "ground_truth": "ext ⟨x, _⟩", |
| "model_output": "simp [ProperFunction] at hsf" |
| }, |
| { |
| "id": 218, |
| "match": true, |
| "ground_truth": "rw [h']", |
| "model_output": "rw [h']" |
| }, |
| { |
| "id": 219, |
| "match": true, |
| "ground_truth": "intro h z", |
| "model_output": "intro h" |
| }, |
| { |
| "id": 220, |
| "match": true, |
| "ground_truth": "intro h", |
| "model_output": "intro h" |
| }, |
| { |
| "id": 221, |
| "match": false, |
| "ground_truth": "simp", |
| "model_output": "simpa using hz" |
| }, |
| { |
| "id": 222, |
| "match": false, |
| "ground_truth": "linarith", |
| "model_output": "exact hz" |
| }, |
| { |
| "id": 223, |
| "match": true, |
| "ground_truth": "intro h z", |
| "model_output": "intro h" |
| }, |
| { |
| "id": 224, |
| "match": true, |
| "ground_truth": "intro h", |
| "model_output": "intro h" |
| }, |
| { |
| "id": 225, |
| "match": false, |
| "ground_truth": "simp at hz", |
| "model_output": "simpa using hz" |
| }, |
| { |
| "id": 226, |
| "match": false, |
| "ground_truth": "linarith", |
| "model_output": "apply h z" |
| }, |
| { |
| "id": 227, |
| "match": false, |
| "ground_truth": "ext g", |
| "model_output": "rw [h]" |
| }, |
| { |
| "id": 228, |
| "match": true, |
| "ground_truth": "rw [h]", |
| "model_output": "rw [h]" |
| }, |
| { |
| "id": 229, |
| "match": false, |
| "ground_truth": "simp", |
| "model_output": "apply And.intro" |
| }, |
| { |
| "id": 230, |
| "match": false, |
| "ground_truth": "intro x hx", |
| "model_output": "norm_cast" |
| }, |
| { |
| "id": 231, |
| "match": false, |
| "ground_truth": "intro x", |
| "model_output": "norm_cast" |
| }, |
| { |
| "id": 232, |
| "match": false, |
| "ground_truth": "intro x", |
| "model_output": "intro x hx" |
| }, |
| { |
| "id": 233, |
| "match": false, |
| "ground_truth": "ext n", |
| "model_output": "aesop" |
| }, |
| { |
| "id": 234, |
| "match": false, |
| "ground_truth": "simp", |
| "model_output": "apply toNat_of_nonneg" |
| }, |
| { |
| "id": 235, |
| "match": true, |
| "ground_truth": "rw [this]", |
| "model_output": "rw [this]" |
| }, |
| { |
| "id": 236, |
| "match": false, |
| "ground_truth": "rw [hc2]", |
| "model_output": "simp [hc2] at h ⊢" |
| }, |
| { |
| "id": 237, |
| "match": false, |
| "ground_truth": "simp", |
| "model_output": "simp [hc2] at h" |
| }, |
| { |
| "id": 238, |
| "match": false, |
| "ground_truth": "exact this", |
| "model_output": "norm_cast at *" |
| }, |
| { |
| "id": 239, |
| "match": false, |
| "ground_truth": "linarith", |
| "model_output": "rw [← add_zero (c - a - b)]" |
| }, |
| { |
| "id": 240, |
| "match": false, |
| "ground_truth": "· exact hs", |
| "model_output": "apply hs" |
| }, |
| { |
| "id": 241, |
| "match": false, |
| "ground_truth": "exact hs", |
| "model_output": "apply hs" |
| }, |
| { |
| "id": 242, |
| "match": false, |
| "ground_truth": "intro x", |
| "model_output": "intro x hx y hy a b ha hb hab\nspecialize hfun hx hy a ha b hb hab\nsimp at *\nring_nf" |
| }, |
| { |
| "id": 243, |
| "match": false, |
| "ground_truth": "dsimp", |
| "model_output": "simp [← sub_nonneg]" |
| }, |
| { |
| "id": 244, |
| "match": true, |
| "ground_truth": "ring_nf", |
| "model_output": "ring" |
| }, |
| { |
| "id": 245, |
| "match": true, |
| "ground_truth": "exact hfun", |
| "model_output": "exact hfun" |
| }, |
| { |
| "id": 246, |
| "match": true, |
| "ground_truth": "by rw [h]", |
| "model_output": "rw [h]" |
| }, |
| { |
| "id": 247, |
| "match": true, |
| "ground_truth": "rw [h]", |
| "model_output": "rw [h]" |
| }, |
| { |
| "id": 248, |
| "match": true, |
| "ground_truth": "intro h", |
| "model_output": "intro h" |
| }, |
| { |
| "id": 249, |
| "match": false, |
| "ground_truth": "ext z", |
| "model_output": "have h1 := h 0" |
| }, |
| { |
| "id": 250, |
| "match": true, |
| "ground_truth": "intro x _", |
| "model_output": "intro x _" |
| }, |
| { |
| "id": 251, |
| "match": false, |
| "ground_truth": "intro x", |
| "model_output": "intro x _" |
| }, |
| { |
| "id": 252, |
| "match": false, |
| "ground_truth": "right", |
| "model_output": "apply Or.inr" |
| }, |
| { |
| "id": 253, |
| "match": false, |
| "ground_truth": "simp", |
| "model_output": "intro y" |
| }, |
| { |
| "id": 254, |
| "match": true, |
| "ground_truth": "intro y", |
| "model_output": "intro y" |
| }, |
| { |
| "id": 255, |
| "match": false, |
| "ground_truth": "simp", |
| "model_output": "rfl" |
| }, |
| { |
| "id": 256, |
| "match": false, |
| "ground_truth": "simp at h1", |
| "model_output": "cases h1 with\n| inl h1 =>\n rw [h1]\n simp\n| inr h1 =>\n exact h1.2.1" |
| }, |
| { |
| "id": 257, |
| "match": false, |
| "ground_truth": "simp [hx]", |
| "model_output": "apply dom_of_le" |
| }, |
| { |
| "id": 258, |
| "match": true, |
| "ground_truth": "ext x", |
| "model_output": "ext x" |
| }, |
| { |
| "id": 259, |
| "match": true, |
| "ground_truth": "exact h x", |
| "model_output": "exact h x" |
| }, |
| { |
| "id": 260, |
| "match": false, |
| "ground_truth": "intro x", |
| "model_output": "simp [inner, mulVec, transpose]" |
| }, |
| { |
| "id": 261, |
| "match": true, |
| "ground_truth": "simp [hp]", |
| "model_output": "simp [hp]" |
| }, |
| { |
| "id": 262, |
| "match": true, |
| "ground_truth": "intro b", |
| "model_output": "intro b" |
| }, |
| { |
| "id": 263, |
| "match": false, |
| "ground_truth": "by rfl", |
| "model_output": "apply IsLinear_iff'.mpr" |
| }, |
| { |
| "id": 264, |
| "match": false, |
| "ground_truth": "rfl", |
| "model_output": "apply IsLinear_iff'.mpr" |
| }, |
| { |
| "id": 265, |
| "match": true, |
| "ground_truth": "rw [h]", |
| "model_output": "rw [h]" |
| }, |
| { |
| "id": 266, |
| "match": false, |
| "ground_truth": "simp", |
| "model_output": "apply ContinuousLinearMap.adjoint_eq_self_of_self_adjoint" |
| }, |
| { |
| "id": 267, |
| "match": false, |
| "ground_truth": "simp", |
| "model_output": "apply ContinuousLinearMap.adjoint_eq_of_inner_right" |
| }, |
| { |
| "id": 268, |
| "match": false, |
| "ground_truth": "exact hs", |
| "model_output": "apply hs" |
| }, |
| { |
| "id": 269, |
| "match": false, |
| "ground_truth": "intro x", |
| "model_output": "simp" |
| }, |
| { |
| "id": 270, |
| "match": true, |
| "ground_truth": "simp", |
| "model_output": "simp" |
| }, |
| { |
| "id": 271, |
| "match": true, |
| "ground_truth": "intro x hx", |
| "model_output": "intro x hx" |
| }, |
| { |
| "id": 272, |
| "match": false, |
| "ground_truth": "intro x", |
| "model_output": "intro x hx" |
| } |
| ] |
| } |
