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The dataset generation failed because of a cast error
Error code: DatasetGenerationCastError
Exception: DatasetGenerationCastError
Message: An error occurred while generating the dataset
All the data files must have the same columns, but at some point there are 1 new columns ({'all_premises'})
This happened while the json dataset builder was generating data using
hf://datasets/ruc-ai4math/mathlib_handler_benchmark_410/random/random_our/train_expand_premise.jsonl (at revision d7eebe1a607c49926b283b5cc129ed8314915c16)
Please either edit the data files to have matching columns, or separate them into different configurations (see docs at https://hf.co/docs/hub/datasets-manual-configuration#multiple-configurations)
Traceback: Traceback (most recent call last):
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 1870, in _prepare_split_single
writer.write_table(table)
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/arrow_writer.py", line 622, in write_table
pa_table = table_cast(pa_table, self._schema)
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/table.py", line 2292, in table_cast
return cast_table_to_schema(table, schema)
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/table.py", line 2240, in cast_table_to_schema
raise CastError(
datasets.table.CastError: Couldn't cast
state: struct<context: list<item: string>, goal: string>
child 0, context: list<item: string>
child 0, item: string
child 1, goal: string
premise: int64
module: list<item: string>
child 0, item: string
all_premises: list<item: int64>
child 0, item: int64
to
{'state': {'context': Sequence(feature=Value(dtype='string', id=None), length=-1, id=None), 'goal': Value(dtype='string', id=None)}, 'premise': Sequence(feature=Value(dtype='int64', id=None), length=-1, id=None), 'module': Sequence(feature=Value(dtype='string', id=None), length=-1, id=None)}
because column names don't match
During handling of the above exception, another exception occurred:
Traceback (most recent call last):
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1438, in compute_config_parquet_and_info_response
parquet_operations = convert_to_parquet(builder)
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1050, in convert_to_parquet
builder.download_and_prepare(
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 924, in download_and_prepare
self._download_and_prepare(
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 1000, in _download_and_prepare
self._prepare_split(split_generator, **prepare_split_kwargs)
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 1741, in _prepare_split
for job_id, done, content in self._prepare_split_single(
File "/src/services/worker/.venv/lib/python3.9/site-packages/datasets/builder.py", line 1872, in _prepare_split_single
raise DatasetGenerationCastError.from_cast_error(
datasets.exceptions.DatasetGenerationCastError: An error occurred while generating the dataset
All the data files must have the same columns, but at some point there are 1 new columns ({'all_premises'})
This happened while the json dataset builder was generating data using
hf://datasets/ruc-ai4math/mathlib_handler_benchmark_410/random/random_our/train_expand_premise.jsonl (at revision d7eebe1a607c49926b283b5cc129ed8314915c16)
Please either edit the data files to have matching columns, or separate them into different configurations (see docs at https://hf.co/docs/hub/datasets-manual-configuration#multiple-configurations)Need help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
state
dict | premise
sequence | module
sequence |
|---|---|---|
{
"context": [
"α : Type u_1",
"inst✝ : LinearOrder α",
"s t : Set α",
"x✝ y z x : α"
],
"goal": "toDual x ∈ (⇑ofDual ⁻¹' s).ordConnectedComponent (toDual x✝) ↔ toDual x ∈ ⇑ofDual ⁻¹' s.ordConnectedComponent x✝"
} | [
17175,
18528,
1713
] | [
"Mathlib/Order/Interval/Set/OrdConnectedComponent.lean"
] |
{
"context": [
"α : Type u_1",
"inst✝ : LinearOrder α",
"s t : Set α",
"x✝ y z x : α"
],
"goal": "⇑ofDual ⁻¹' [[x✝, x]] ⊆ ⇑ofDual ⁻¹' s ↔ toDual x ∈ ⇑ofDual ⁻¹' s.ordConnectedComponent x✝"
} | [
18528,
1713,
17175
] | [
"Mathlib/Order/Interval/Set/OrdConnectedComponent.lean"
] |
{
"context": [
"α : Type u_1",
"G G' : SimpleGraph α",
"inst✝² : DecidableRel G.Adj",
"ε : ℝ",
"s t u : Finset α",
"inst✝¹ : DecidableEq α",
"inst✝ : Fintype α",
"P : Finpartition univ",
"dst : 2 * ε ≤ ↑(G.edgeDensity s t)",
"ust : G.IsUniform ε s t",
"hst : Disjoint s t",
"dsu : 2 * ε ≤ ↑(G.edgeDensity s u)",
"usu : G.IsUniform ε s u",
"hsu : Disjoint s u",
"dtu : 2 * ε ≤ ↑(G.edgeDensity t u)",
"utu : G.IsUniform ε t u",
"htu : Disjoint t u"
],
"goal": "(1 - 2 * ε) * ε ^ 3 * ↑s.card * ↑t.card * ↑u.card ≤ ↑(G.cliqueFinset 3).card"
} | [
52912,
142597
] | [
"Mathlib/Combinatorics/SimpleGraph/Triangle/Counting.lean"
] |
{
"context": [
"α : Type u_1",
"G G' : SimpleGraph α",
"inst✝² : DecidableRel G.Adj",
"ε : ℝ",
"s t u : Finset α",
"inst✝¹ : DecidableEq α",
"inst✝ : Fintype α",
"P : Finpartition univ",
"dst : 2 * ε ≤ ↑(G.edgeDensity s t)",
"ust : G.IsUniform ε s t",
"hst : Disjoint s t",
"dsu : 2 * ε ≤ ↑(G.edgeDensity s u)",
"usu : G.IsUniform ε s u",
"hsu : Disjoint s u",
"dtu : 2 * ε ≤ ↑(G.edgeDensity t u)",
"utu : G.IsUniform ε t u",
"htu : Disjoint t u"
],
"goal": "↑(filter (fun x => match x with | (a, b, c) => G.Adj a b ∧ G.Adj a c ∧ G.Adj b c) (s ×ˢ t ×ˢ u)).card ≤ ↑(G.cliqueFinset 3).card"
} | [
52912,
142597
] | [
"Mathlib/Combinatorics/SimpleGraph/Triangle/Counting.lean"
] |
{
"context": [
"α : Type u_1",
"G G' : SimpleGraph α",
"inst✝² : DecidableRel G.Adj",
"ε : ℝ",
"s t u : Finset α",
"inst✝¹ : DecidableEq α",
"inst✝ : Fintype α",
"P : Finpartition univ",
"dst : 2 * ε ≤ ↑(G.edgeDensity s t)",
"ust : G.IsUniform ε s t",
"hst : Disjoint s t",
"dsu : 2 * ε ≤ ↑(G.edgeDensity s u)",
"usu : G.IsUniform ε s u",
"hsu : Disjoint s u",
"dtu : 2 * ε ≤ ↑(G.edgeDensity t u)",
"utu : G.IsUniform ε t u",
"htu : Disjoint t u"
],
"goal": "(filter (fun x => match x with | (a, b, c) => G.Adj a b ∧ G.Adj a c ∧ G.Adj b c) (s ×ˢ t ×ˢ u)).card ≤ (G.cliqueFinset 3).card"
} | [
137677,
142597
] | [
"Mathlib/Combinatorics/SimpleGraph/Triangle/Counting.lean"
] |
{
"context": [
"α : Type u_1",
"G G' : SimpleGraph α",
"inst✝² : DecidableRel G.Adj",
"ε : ℝ",
"s t u : Finset α",
"inst✝¹ : DecidableEq α",
"inst✝ : Fintype α",
"P : Finpartition univ",
"dst : 2 * ε ≤ ↑(G.edgeDensity s t)",
"ust : G.IsUniform ε s t",
"hst : Disjoint s t",
"dsu : 2 * ε ≤ ↑(G.edgeDensity s u)",
"usu : G.IsUniform ε s u",
"hsu : Disjoint s u",
"dtu : 2 * ε ≤ ↑(G.edgeDensity t u)",
"utu : G.IsUniform ε t u",
"htu : Disjoint t u"
],
"goal": "∀ a ∈ filter (fun x => match x with | (a, b, c) => G.Adj a b ∧ G.Adj a c ∧ G.Adj b c) (s ×ˢ t ×ˢ u), (fun x => match x with | (x, y, z) => {x, y, z}) a ∈ G.cliqueFinset 3"
} | [
137677
] | [
"Mathlib/Combinatorics/SimpleGraph/Triangle/Counting.lean"
] |
{
"context": [
"α : Type u_1",
"G G' : SimpleGraph α",
"inst✝² : DecidableRel G.Adj",
"ε : ℝ",
"s t u : Finset α",
"inst✝¹ : DecidableEq α",
"inst✝ : Fintype α",
"P : Finpartition univ",
"dst : 2 * ε ≤ ↑(G.edgeDensity s t)",
"ust : G.IsUniform ε s t",
"hst : Disjoint s t",
"dsu : 2 * ε ≤ ↑(G.edgeDensity s u)",
"usu : G.IsUniform ε s u",
"hsu : Disjoint s u",
"dtu : 2 * ε ≤ ↑(G.edgeDensity t u)",
"utu : G.IsUniform ε t u",
"htu : Disjoint t u"
],
"goal": "Set.InjOn (fun x => match x with | (x, y, z) => {x, y, z}) ↑(filter (fun x => match x with | (a, b, c) => G.Adj a b ∧ G.Adj a c ∧ G.Adj b c) (s ×ˢ t ×ˢ u))"
} | [
137677
] | [
"Mathlib/Combinatorics/SimpleGraph/Triangle/Counting.lean"
] |
{
"context": [
"α : Type u_1",
"G G' : SimpleGraph α",
"inst✝² : DecidableRel G.Adj",
"ε : ℝ",
"s t✝ u : Finset α",
"inst✝¹ : DecidableEq α",
"inst✝ : Fintype α",
"P : Finpartition univ",
"dst : 2 * ε ≤ ↑(G.edgeDensity s t✝)",
"ust : G.IsUniform ε s t✝",
"hst : Disjoint s t✝",
"dsu : 2 * ε ≤ ↑(G.edgeDensity s u)",
"usu : G.IsUniform ε s u",
"hsu : Disjoint s u",
"dtu : 2 * ε ≤ ↑(G.edgeDensity t✝ u)",
"utu : G.IsUniform ε t✝ u",
"htu : Disjoint t✝ u",
"x₁ y₁ z₁ : α",
"h₁ : (x₁, y₁, z₁) ∈ ↑(filter (fun x => match x with | (a, b, c) => G.Adj a b ∧ G.Adj a c ∧ G.Adj b c) (s ×ˢ t✝ ×ˢ u))",
"x₂ y₂ z₂ : α",
"h₂ : (x₂, y₂, z₂) ∈ ↑(filter (fun x => match x with | (a, b, c) => G.Adj a b ∧ G.Adj a c ∧ G.Adj b c) (s ×ˢ t✝ ×ˢ u))",
"t : (fun x => match x with | (x, y, z) => {x, y, z}) (x₁, y₁, z₁) = (fun x => match x with | (x, y, z) => {x, y, z}) (x₂, y₂, z₂)"
],
"goal": "(x₁, y₁, z₁) = (x₂, y₂, z₂)"
} | [
136829,
138668,
139089,
1101,
1674,
52913
] | [
"Mathlib/Combinatorics/SimpleGraph/Triangle/Counting.lean"
] |
{
"context": [
"α : Type u_1",
"G G' : SimpleGraph α",
"inst✝² : DecidableRel G.Adj",
"ε : ℝ",
"s t✝ u : Finset α",
"inst✝¹ : DecidableEq α",
"inst✝ : Fintype α",
"P : Finpartition univ",
"dst : 2 * ε ≤ ↑(G.edgeDensity s t✝)",
"ust : G.IsUniform ε s t✝",
"hst : Disjoint s t✝",
"dsu : 2 * ε ≤ ↑(G.edgeDensity s u)",
"usu : G.IsUniform ε s u",
"hsu : Disjoint s u",
"dtu : 2 * ε ≤ ↑(G.edgeDensity t✝ u)",
"utu : G.IsUniform ε t✝ u",
"htu : Disjoint t✝ u",
"x₁ y₁ z₁ x₂ y₂ z₂ : α",
"t : (fun x => match x with | (x, y, z) => {x, y, z}) (x₁, y₁, z₁) = (fun x => match x with | (x, y, z) => {x, y, z}) (x₂, y₂, z₂)",
"h₁ : (x₁ ∈ s ∧ y₁ ∈ t✝ ∧ z₁ ∈ u) ∧ G.Adj x₁ y₁ ∧ G.Adj x₁ z₁ ∧ G.Adj y₁ z₁",
"h₂ : (x₂ ∈ s ∧ y₂ ∈ t✝ ∧ z₂ ∈ u) ∧ G.Adj x₂ y₂ ∧ G.Adj x₂ z₂ ∧ G.Adj y₂ z₂"
],
"goal": "(x₁, y₁, z₁) = (x₂, y₂, z₂)"
} | [
1674,
138668,
1101,
139089,
52913,
136829
] | [
"Mathlib/Combinatorics/SimpleGraph/Triangle/Counting.lean"
] |
{
"context": [
"R : Type u_1",
"A : Type u_2",
"p : A → Prop",
"inst✝¹⁸ : OrderedCommRing R",
"inst✝¹⁷ : Nontrivial R",
"inst✝¹⁶ : StarRing R",
"inst✝¹⁵ : StarOrderedRing R",
"inst✝¹⁴ : MetricSpace R",
"inst✝¹³ : TopologicalRing R",
"inst✝¹² : ContinuousStar R",
"inst✝¹¹ : ∀ (α : Type ?u.1282777) [inst : Zero α] [inst_1 : TopologicalSpace α], StarOrderedRing C(α, R)₀",
"inst✝¹⁰ : TopologicalSpace A",
"inst✝⁹ : NonUnitalRing A",
"inst✝⁸ : StarRing A",
"inst✝⁷ : PartialOrder A",
"inst✝⁶ : StarOrderedRing A",
"inst✝⁵ : Module R A",
"inst✝⁴ : IsScalarTower R A A",
"inst✝³ : SMulCommClass R A A",
"inst✝² : StarModule R A",
"inst✝¹ : NonUnitalContinuousFunctionalCalculus R p",
"inst✝ : NonnegSpectrumClass R A",
"f g : R → R",
"a : A",
"hf : autoParam (ContinuousOn f (σₙ R a)) _auto✝",
"hg : autoParam (ContinuousOn g (σₙ R a)) _auto✝",
"hf0 : autoParam (f 0 = 0) _auto✝",
"hg0 : autoParam (g 0 = 0) _auto✝",
"ha : autoParam (p a) _auto✝"
],
"goal": "cfcₙ f a ≤ cfcₙ g a ↔ ∀ x ∈ σₙ R a, f x ≤ g x"
} | [
38025,
38072,
62597
] | [
"Mathlib/Analysis/CstarAlgebra/ContinuousFunctionalCalculus/NonUnital.lean"
] |
{
"context": [
"R : Type u_1",
"A : Type u_2",
"p : A → Prop",
"inst✝¹⁸ : OrderedCommRing R",
"inst✝¹⁷ : Nontrivial R",
"inst✝¹⁶ : StarRing R",
"inst✝¹⁵ : StarOrderedRing R",
"inst✝¹⁴ : MetricSpace R",
"inst✝¹³ : TopologicalRing R",
"inst✝¹² : ContinuousStar R",
"inst✝¹¹ : ∀ (α : Type u_1) [inst : Zero α] [inst_1 : TopologicalSpace α], StarOrderedRing C(α, R)₀",
"inst✝¹⁰ : TopologicalSpace A",
"inst✝⁹ : NonUnitalRing A",
"inst✝⁸ : StarRing A",
"inst✝⁷ : PartialOrder A",
"inst✝⁶ : StarOrderedRing A",
"inst✝⁵ : Module R A",
"inst✝⁴ : IsScalarTower R A A",
"inst✝³ : SMulCommClass R A A",
"inst✝² : StarModule R A",
"inst✝¹ : NonUnitalContinuousFunctionalCalculus R p",
"inst✝ : NonnegSpectrumClass R A",
"f g : R → R",
"a : A",
"hf : autoParam (ContinuousOn f (σₙ R a)) _auto✝",
"hg : autoParam (ContinuousOn g (σₙ R a)) _auto✝",
"hf0 : autoParam (f 0 = 0) _auto✝",
"hg0 : autoParam (g 0 = 0) _auto✝",
"ha : autoParam (p a) _auto✝"
],
"goal": "(∀ (x : ↑(σₙ R a)), { toFun := (σₙ R a).restrict f, continuous_toFun := ⋯, map_zero' := ⋯ } x ≤ { toFun := (σₙ R a).restrict g, continuous_toFun := ⋯, map_zero' := ⋯ } x) ↔ ∀ x ∈ σₙ R a, f x ≤ g x"
} | [
38025,
38072,
62597
] | [
"Mathlib/Analysis/CstarAlgebra/ContinuousFunctionalCalculus/NonUnital.lean"
] |
{
"context": [
"α : Type u_1",
"β : Type u_2",
"γ : Type u_3",
"ι : Type u_4",
"ι' : Type u_5",
"κ : Sort u_6",
"r p q : α → α → Prop",
"s t : Set ι",
"f : ι → Set α",
"h : (s ∪ t).PairwiseDisjoint f"
],
"goal": "(⋃ i ∈ s, f i) \\ ⋃ i ∈ t, f i = ⋃ i ∈ s \\ t, f i"
} | [
1674,
2107,
131589,
135248,
135354,
135582,
135215
] | [
"Mathlib/Data/Set/Pairwise/Lattice.lean"
] |
{
"context": [
"α : Type u_1",
"β : Type u_2",
"γ : Type u_3",
"ι : Type u_4",
"ι' : Type u_5",
"κ : Sort u_6",
"r p q : α → α → Prop",
"s t : Set ι",
"f : ι → Set α",
"h : (s ∪ t).PairwiseDisjoint f",
"i : ι",
"hi : i ∈ s \\ t",
"a : α",
"ha : a ∈ f i"
],
"goal": "a ∉ ⋃ x ∈ t, f x"
} | [
131589,
1674,
135215,
135248,
135354,
2107,
135582
] | [
"Mathlib/Data/Set/Pairwise/Lattice.lean"
] |
{
"context": [
"α : Type u_1",
"β : Type u_2",
"γ : Type u_3",
"ι : Type u_4",
"ι' : Type u_5",
"κ : Sort u_6",
"r p q : α → α → Prop",
"s t : Set ι",
"f : ι → Set α",
"h : (s ∪ t).PairwiseDisjoint f",
"i : ι",
"hi : i ∈ s \\ t",
"a : α",
"ha : a ∈ f i"
],
"goal": "¬∃ i, ∃ (_ : i ∈ t), a ∈ f i"
} | [
135215
] | [
"Mathlib/Data/Set/Pairwise/Lattice.lean"
] |
{
"context": [
"α : Type u_1",
"β : Type u_2",
"γ : Type u_3",
"ι : Type u_4",
"ι' : Type u_5",
"κ : Sort u_6",
"r p q : α → α → Prop",
"s t : Set ι",
"f : ι → Set α",
"h : (s ∪ t).PairwiseDisjoint f",
"i : ι",
"hi : i ∈ s \\ t",
"a : α",
"ha : a ∈ f i",
"j : ι",
"hj : j ∈ t",
"haj : a ∈ f j"
],
"goal": "False"
} | [
35,
1690,
2106,
2107,
13484
] | [
"Mathlib/Data/Set/Pairwise/Lattice.lean"
] |
{
"context": [
"ι : Type u_1",
"α : Type u_2",
"β : Type u_3",
"inst✝² : Preorder α",
"inst✝¹ : LocallyFiniteOrder α",
"inst✝ : Preorder β",
"f : α → β"
],
"goal": "StrictMono f ↔ ∀ (a b : α), a ⋖ b → f a < f b"
} | [
16610,
70476
] | [
"Mathlib/Order/Interval/Finset/Basic.lean"
] |
{
"context": [
"ι : Type u_1",
"α : Type u_2",
"β : Type u_3",
"inst✝² : Preorder α",
"inst✝¹ : LocallyFiniteOrder α",
"inst✝ : Preorder β",
"f : α → β",
"h : ∀ (a b : α), a ⋖ b → f a < f b",
"a b : α",
"hab : a < b"
],
"goal": "f a < f b"
} | [
16610,
70476
] | [
"Mathlib/Order/Interval/Finset/Basic.lean"
] |
{
"context": [
"ι : Type u_1",
"α : Type u_2",
"β : Type u_3",
"inst✝² : Preorder α",
"inst✝¹ : LocallyFiniteOrder α",
"inst✝ : Preorder β",
"f : α → β",
"h : ∀ (a b : α), a ⋖ b → f a < f b",
"a b : α",
"hab : a < b",
"this : TransGen CovBy a b → TransGen LT.lt (f a) (f b)"
],
"goal": "f a < f b"
} | [
70473,
14281,
20706,
70476
] | [
"Mathlib/Order/Interval/Finset/Basic.lean"
] |
{
"context": [
"ι : Type u_1",
"α : Type u_2",
"β : Type u_3",
"inst✝² : Preorder α",
"inst✝¹ : LocallyFiniteOrder α",
"inst✝ : Preorder β",
"f : α → β",
"h : ∀ (a b : α), a ⋖ b → f a < f b",
"a b : α",
"hab : a < b",
"this : a < b → f a < f b"
],
"goal": "f a < f b"
} | [
14281,
20706,
70473
] | [
"Mathlib/Order/Interval/Finset/Basic.lean"
] |
{
"context": [
"𝕜 : Type u_1",
"inst✝⁴ : NontriviallyNormedField 𝕜",
"F : Type u_2",
"inst✝³ : NormedAddCommGroup F",
"inst✝² : NormedSpace 𝕜 F",
"E : Type u_3",
"inst✝¹ : NormedAddCommGroup E",
"inst✝ : NormedSpace 𝕜 E",
"f✝ f₀ f₁ : E → F",
"f' : F",
"s t : Set E",
"x v : E",
"L : E →L[𝕜] F",
"f : E → F",
"x₀ : E",
"C : ℝ",
"hC₀ : 0 ≤ C",
"hlip : ∀ᶠ (x : E) in 𝓝 x₀, ‖f x - f x₀‖ ≤ C * ‖x - x₀‖"
],
"goal": "‖lineDeriv 𝕜 f x₀ v‖ ≤ C * ‖v‖"
} | [
44446
] | [
"Mathlib/Analysis/Calculus/LineDeriv/Basic.lean"
] |
{
"context": [
"𝕜 : Type u_1",
"inst✝⁴ : NontriviallyNormedField 𝕜",
"F : Type u_2",
"inst✝³ : NormedAddCommGroup F",
"inst✝² : NormedSpace 𝕜 F",
"E : Type u_3",
"inst✝¹ : NormedAddCommGroup E",
"inst✝ : NormedSpace 𝕜 E",
"f✝ f₀ f₁ : E → F",
"f' : F",
"s t : Set E",
"x v : E",
"L : E →L[𝕜] F",
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"goal": "∀ᶠ (x : 𝕜) in 𝓝 0, ‖f (x₀ + x • v) - f (x₀ + 0 • v)‖ ≤ C * ‖v‖ * ‖x - 0‖"
} | [
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] | [
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{
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"this : ∀ᶠ (x : E) in 𝓝 (x₀ + 0 • v), ‖f x - f x₀‖ ≤ C * ‖x - x₀‖"
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{
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] | [
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{
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107138
] | [
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{
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],
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{
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{
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71959
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{
"context": [
"n : ℕ",
"t : ℝ",
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"goal": "(1 - t / ↑n) ^ n ≤ rexp (-t)"
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{
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{
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{
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{
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49534
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{
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{
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49531,
48844,
48597
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{
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{
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1838
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1838
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{
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5846
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{
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"inst✝¹ : NormedAddCommGroup X",
"inst✝ : NormedSpace 𝕜 X",
"s s₁ t u : Set E",
"f✝ f₁ : E → F",
"g : F → G",
"x x₀ : E",
"c : F",
"b : E × F → G",
"m n : ℕ∞",
"p : E → FormalMultilinearSeries 𝕜 E F",
"f : E → F",
"hf : ContDiffOn 𝕜 n f univ",
"hmn : m + 1 ≤ n"
],
"goal": "ContDiffOn 𝕜 m (fun p => (fderiv 𝕜 f p.1) p.2) univ"
} | [
46361,
48434,
133914
] | [
"Mathlib/Analysis/Calculus/ContDiff/Basic.lean"
] |
{
"context": [
"𝕜 : Type u_1",
"inst✝¹⁰ : NontriviallyNormedField 𝕜",
"D : Type uD",
"inst✝⁹ : NormedAddCommGroup D",
"inst✝⁸ : NormedSpace 𝕜 D",
"E : Type uE",
"inst✝⁷ : NormedAddCommGroup E",
"inst✝⁶ : NormedSpace 𝕜 E",
"F : Type uF",
"inst✝⁵ : NormedAddCommGroup F",
"inst✝⁴ : NormedSpace 𝕜 F",
"G : Type uG",
"inst✝³ : NormedAddCommGroup G",
"inst✝² : NormedSpace 𝕜 G",
"X : Type u_2",
"inst✝¹ : NormedAddCommGroup X",
"inst✝ : NormedSpace 𝕜 X",
"s s₁ t u : Set E",
"f✝ f₁ : E → F",
"g : F → G",
"x x₀ : E",
"c : F",
"b : E × F → G",
"m n : ℕ∞",
"p : E → FormalMultilinearSeries 𝕜 E F",
"f : E → F",
"hf : ContDiffOn 𝕜 n f univ",
"hmn : m + 1 ≤ n"
],
"goal": "ContDiffOn 𝕜 m (fun p => (fderivWithin 𝕜 f univ p.1) p.2) (univ ×ˢ univ)"
} | [
46361,
133914,
51651,
45679
] | [
"Mathlib/Analysis/Calculus/ContDiff/Basic.lean"
] |
{
"context": [
"n : ℕ",
"c : Char",
"l : List Char"
],
"goal": "{ data := l }.IsSuffix (leftpad n c { data := l })"
} | [
1455
] | [
"Mathlib/Data/String/Lemmas.lean"
] |
{
"context": [
"X : Type u_1",
"Y : Type u_2",
"Z : Type u_3",
"inst✝² : PseudoEMetricSpace X",
"inst✝¹ : PseudoEMetricSpace Y",
"inst✝ : PseudoEMetricSpace Z",
"e : X ≃ᵢ Y"
],
"goal": "ratio e.toDilationEquiv = 1"
} | [
60798,
60825,
61569
] | [
"Mathlib/Topology/MetricSpace/DilationEquiv.lean"
] |
{
"context": [
"n : ℕ"
],
"goal": "χ₈ ↑n = χ₈ ↑(n % 8)"
} | [
138369
] | [
"Mathlib/NumberTheory/LegendreSymbol/ZModChar.lean"
] |
{
"context": [
"α : Type u_1",
"β : Type u_2",
"γ : Type u_3",
"ι : Sort u_4",
"ι' : Sort u_5",
"ι₂ : Sort u_6",
"κ : ι → Sort u_7",
"κ₁ : ι → Sort u_8",
"κ₂ : ι → Sort u_9",
"κ' : ι' → Sort u_10",
"P : ι → α → Prop",
"x✝ : α"
],
"goal": "x✝ ∈ ⋂ i, {x | P i x} ↔ x✝ ∈ {x | ∀ (i : ι), P i x}"
} | [
16574
] | [
"Mathlib/Data/Set/Lattice.lean"
] |
{
"context": [
"α : Type u",
"β : Type v",
"γ : Type w",
"δ : Type u_1",
"ι : Sort x",
"f : Filter α",
"p : α → Prop",
"q : Prop"
],
"goal": "(∀ᶠ (x : α) in f, p x → q) ↔ (∃ᶠ (x : α) in f, p x) → q"
} | [
16036,
16061,
70070
] | [
"Mathlib/Order/Filter/Basic.lean"
] |
{
"context": [
"C : Type u",
"inst✝ : Category.{v, u} C",
"X✝ Y✝ X Y Z : C",
"sXY : BinaryFan X Y",
"P : IsLimit sXY",
"sYZ : BinaryFan Y Z",
"Q : IsLimit sYZ",
"s : BinaryFan sXY.pt Z",
"R : IsLimit s",
"t : Cone (pair X sYZ.pt)"
],
"goal": "R.lift (BinaryFan.assocInv P t) ≫ Q.lift (BinaryFan.mk (s.fst ≫ sXY.snd) s.snd) = BinaryFan.snd t"
} | [
94261
] | [
"Mathlib/CategoryTheory/Monoidal/OfChosenFiniteProducts/Basic.lean"
] |
{
"context": [
"C : Type u",
"inst✝ : Category.{v, u} C",
"X✝ Y✝ X Y Z : C",
"sXY : BinaryFan X Y",
"P : IsLimit sXY",
"sYZ : BinaryFan Y Z",
"Q : IsLimit sYZ",
"s : BinaryFan sXY.pt Z",
"R : IsLimit s",
"t : Cone (pair X sYZ.pt)"
],
"goal": "∀ (j : Discrete WalkingPair), (R.lift (BinaryFan.assocInv P t) ≫ Q.lift (BinaryFan.mk (s.fst ≫ sXY.snd) s.snd)) ≫ sYZ.π.app j = BinaryFan.snd t ≫ sYZ.π.app j"
} | [
94261
] | [
"Mathlib/CategoryTheory/Monoidal/OfChosenFiniteProducts/Basic.lean"
] |
{
"context": [
"C : Type u",
"inst✝ : Category.{v, u} C",
"X✝ Y✝ X Y Z : C",
"sXY : BinaryFan X Y",
"P : IsLimit sXY",
"sYZ : BinaryFan Y Z",
"Q : IsLimit sYZ",
"s : BinaryFan sXY.pt Z",
"R : IsLimit s",
"t : Cone (pair X sYZ.pt)",
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"w : ∀ (j : Discrete WalkingPair), m ≫ (BinaryFan.assoc Q s).π.app j = t.π.app j"
],
"goal": "m = (fun t => R.lift (BinaryFan.assocInv P t)) t"
} | [
94242
] | [
"Mathlib/CategoryTheory/Monoidal/OfChosenFiniteProducts/Basic.lean"
] |
{
"context": [
"C : Type u",
"inst✝ : Category.{v, u} C",
"X✝ Y✝ X Y Z : C",
"sXY : BinaryFan X Y",
"P : IsLimit sXY",
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"Q : IsLimit sYZ",
"s : BinaryFan sXY.pt Z",
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"t : Cone (pair X sYZ.pt)",
"m : t.pt ⟶ (BinaryFan.assoc Q s).pt",
"w : ∀ (j : Discrete WalkingPair), m ≫ (BinaryFan.assoc Q s).π.app j = t.π.app j",
"h : (∀ (j : Discrete WalkingPair), m ≫ s.π.app j = (BinaryFan.assocInv P t).π.app j) → m = R.lift (BinaryFan.assocInv P t)"
],
"goal": "m = (fun t => R.lift (BinaryFan.assocInv P t)) t"
} | [
94242
] | [
"Mathlib/CategoryTheory/Monoidal/OfChosenFiniteProducts/Basic.lean"
] |
{
"context": [
"α : Type u_1",
"inst✝³ : Fintype α",
"G✝ : Type u_2",
"inst✝² : Group G✝",
"n : ℕ",
"G : Type u_3",
"inst✝¹ : Group G",
"inst✝ : Finite G",
"p : ℕ",
"hp : Fact (Nat.Prime p)",
"hdvd : p ∣ Nat.card G",
"this : Fintype G"
],
"goal": "∃ x, orderOf x = p"
} | [
9409,
47564
] | [
"Mathlib/GroupTheory/Perm/Cycle/Type.lean"
] |
{
"context": [
"α : Type u_1",
"inst✝³ : Fintype α",
"G✝ : Type u_2",
"inst✝² : Group G✝",
"n : ℕ",
"G : Type u_3",
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"inst✝ : Finite G",
"p : ℕ",
"hp : Fact (Nat.Prime p)",
"this : Fintype G",
"hdvd : p ∣ Fintype.card G"
],
"goal": "∃ x, orderOf x = p"
} | [
9409,
47564
] | [
"Mathlib/GroupTheory/Perm/Cycle/Type.lean"
] |
{
"context": [
"K : Type u_1",
"inst✝¹ : Field K",
"inst✝ : NumberField K",
"B✝ B : ℝ",
"hB : B ≤ 0"
],
"goal": "volume (convexBodySum K B) = 0"
} | [
14302
] | [
"Mathlib/NumberTheory/NumberField/CanonicalEmbedding/ConvexBody.lean"
] |
{
"context": [
"K : Type u_1",
"inst✝¹ : Field K",
"inst✝ : NumberField K",
"B✝ B : ℝ",
"hB✝ : B ≤ 0",
"hB : B < 0"
],
"goal": "volume (convexBodySum K B) = 0"
} | [
14302
] | [
"Mathlib/NumberTheory/NumberField/CanonicalEmbedding/ConvexBody.lean"
] |
{
"context": [
"K : Type u_1",
"inst✝¹ : Field K",
"inst✝ : NumberField K",
"B✝ B : ℝ",
"hB✝ : B ≤ 0",
"hB : B = 0"
],
"goal": "volume (convexBodySum K B) = 0"
} | [
14302
] | [
"Mathlib/NumberTheory/NumberField/CanonicalEmbedding/ConvexBody.lean"
] |
{
"context": [
"G : Type u_1",
"H : Type u_2",
"α : Type u_3",
"β : Type u_4",
"E : Type u_5",
"inst✝⁶ : Group G",
"inst✝⁵ : MulAction G α",
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"inst✝³ : Countable G",
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"s t : Set α",
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"inst✝ : MeasurableSMul G α",
"fund_dom_s : IsFundamentalDomain G s μ",
"fund_dom_t : IsFundamentalDomain G t μ",
"U : Set (Quotient α_mod_G)",
"meas_U : MeasurableSet U"
],
"goal": "(Measure.map (Quotient.mk α_mod_G) (μ.restrict s)) U = (Measure.map (Quotient.mk α_mod_G) (μ.restrict t)) U"
} | [
33097,
33035
] | [
"Mathlib/MeasureTheory/Group/FundamentalDomain.lean"
] |
{
"context": [
"G : Type u_1",
"H : Type u_2",
"α : Type u_3",
"β : Type u_4",
"E : Type u_5",
"inst✝⁶ : Group G",
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"fund_dom_s : IsFundamentalDomain G s μ",
"fund_dom_t : IsFundamentalDomain G t μ",
"U : Set (Quotient α_mod_G)",
"meas_U : MeasurableSet U"
],
"goal": "μ (Quotient.mk α_mod_G ⁻¹' U ∩ s) = μ (Quotient.mk α_mod_G ⁻¹' U ∩ t)"
} | [
33097,
33035
] | [
"Mathlib/MeasureTheory/Group/FundamentalDomain.lean"
] |
{
"context": [
"G : Type u_1",
"H : Type u_2",
"α : Type u_3",
"β : Type u_4",
"E : Type u_5",
"inst✝⁶ : Group G",
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"fund_dom_s : IsFundamentalDomain G s μ",
"fund_dom_t : IsFundamentalDomain G t μ",
"U : Set (Quotient α_mod_G)",
"meas_U : MeasurableSet U"
],
"goal": "MeasurableSet (Quotient.mk α_mod_G ⁻¹' U)"
} | [
33035
] | [
"Mathlib/MeasureTheory/Group/FundamentalDomain.lean"
] |
{
"context": [
"G : Type u_1",
"H : Type u_2",
"α : Type u_3",
"β : Type u_4",
"E : Type u_5",
"inst✝⁶ : Group G",
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"s t : Set α",
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"inst✝ : MeasurableSMul G α",
"fund_dom_s : IsFundamentalDomain G s μ",
"fund_dom_t : IsFundamentalDomain G t μ",
"U : Set (Quotient α_mod_G)",
"meas_U : MeasurableSet U"
],
"goal": "∀ (g : G), (fun x => g • x) ⁻¹' (Quotient.mk α_mod_G ⁻¹' U) = Quotient.mk α_mod_G ⁻¹' U"
} | [
33035
] | [
"Mathlib/MeasureTheory/Group/FundamentalDomain.lean"
] |
{
"context": [
"R : Type u_1",
"inst✝¹⁶ : CommSemiring R",
"R' : Type u_2",
"inst✝¹⁵ : Monoid R'",
"R'' : Type u_3",
"inst✝¹⁴ : Semiring R''",
"M : Type u_4",
"N : Type u_5",
"P : Type u_6",
"Q : Type u_7",
"S : Type u_8",
"T : Type u_9",
"inst✝¹³ : AddCommMonoid M",
"inst✝¹² : AddCommMonoid N",
"inst✝¹¹ : AddCommMonoid P",
"inst✝¹⁰ : AddCommMonoid Q",
"inst✝⁹ : AddCommMonoid S",
"inst✝⁸ : AddCommMonoid T",
"inst✝⁷ : Module R M",
"inst✝⁶ : Module R N",
"inst✝⁵ : Module R P",
"inst✝⁴ : Module R Q",
"inst✝³ : Module R S",
"inst✝² : Module R T",
"inst✝¹ : DistribMulAction R' M",
"inst✝ : Module R'' M",
"g✝ : P →ₗ[R] Q",
"f✝ : N →ₗ[R] P",
"f : M →ₗ[R] P",
"g : N →ₗ[R] Q"
],
"goal": "lTensor P g ∘ₗ rTensor N f = map f g"
} | [
86898,
109760,
109761
] | [
"Mathlib/LinearAlgebra/TensorProduct/Basic.lean"
] |
{
"context": [
"𝕜 : Type u_1",
"inst✝¹¹ : NontriviallyNormedField 𝕜",
"E : Type u_2",
"inst✝¹⁰ : NormedAddCommGroup E",
"inst✝⁹ : NormedSpace 𝕜 E",
"H : Type u_3",
"inst✝⁸ : TopologicalSpace H",
"I : ModelWithCorners 𝕜 E H",
"M : Type u_4",
"inst✝⁷ : TopologicalSpace M",
"inst✝⁶ : ChartedSpace H M",
"E' : Type u_5",
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"N : Type u_7",
"inst✝² : TopologicalSpace N",
"inst✝¹ : ChartedSpace H' N",
"J : ModelWithCorners 𝕜 E' H'",
"inst✝ : SmoothManifoldWithCorners J N",
"x : M",
"y : N",
"p : M × N"
],
"goal": "p ∈ (I.prod J).interior (M × N) ↔ p ∈ I.interior M ×ˢ J.interior N"
} | [
66448,
67778,
133949
] | [
"Mathlib/Geometry/Manifold/InteriorBoundary.lean"
] |
{
"context": [
"𝕜 : Type u_1",
"inst✝¹¹ : NontriviallyNormedField 𝕜",
"E : Type u_2",
"inst✝¹⁰ : NormedAddCommGroup E",
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"I : ModelWithCorners 𝕜 E H",
"M : Type u_4",
"inst✝⁷ : TopologicalSpace M",
"inst✝⁶ : ChartedSpace H M",
"E' : Type u_5",
"inst✝⁵ : NormedAddCommGroup E'",
"inst✝⁴ : NormedSpace 𝕜 E'",
"H' : Type u_6",
"inst✝³ : TopologicalSpace H'",
"N : Type u_7",
"inst✝² : TopologicalSpace N",
"inst✝¹ : ChartedSpace H' N",
"J : ModelWithCorners 𝕜 E' H'",
"inst✝ : SmoothManifoldWithCorners J N",
"x : M",
"y : N",
"p : M × N",
"aux : interior (range ↑I) ×ˢ interior (range ↑J) = interior (range ↑(I.prod J))"
],
"goal": "p ∈ (I.prod J).interior (M × N) ↔ p ∈ I.interior M ×ˢ J.interior N"
} | [
66448,
67778,
133949
] | [
"Mathlib/Geometry/Manifold/InteriorBoundary.lean"
] |
{
"context": [
"V : Type u_1",
"P : Type u_2",
"inst✝⁴ : NormedAddCommGroup V",
"inst✝³ : InnerProductSpace ℝ V",
"inst✝² : MetricSpace P",
"inst✝¹ : NormedAddTorsor V P",
"hd2 : Fact (finrank ℝ V = 2)",
"inst✝ : Module.Oriented ℝ V (Fin 2)",
"p₁ p₂ p₃ p₄ : P",
"h : Wbtw ℝ p₁ p₂ p₃",
"hne : p₂ ≠ p₃"
],
"goal": "(∡ p₂ p₄ p₃).sign = (∡ p₁ p₄ p₃).sign"
} | [
1690,
38396,
70344,
70410
] | [
"Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean"
] |
{
"context": [
"ι α β : Type u",
"c : Cardinal.{u}",
"l : Filter α",
"inst✝ : CardinalInterFilter l c",
"s : ι → Set α",
"hic : #ι < c"
],
"goal": "⋂ i, s i ∈ l ↔ ∀ (i : ι), s i ∈ l"
} | [
135425,
1715,
12656,
14288,
48841
] | [
"Mathlib/Order/Filter/CardinalInter.lean"
] |
{
"context": [
"ι α β : Type u",
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"l : Filter α",
"inst✝ : CardinalInterFilter l c",
"s : ι → Set α",
"hic : #ι < c"
],
"goal": "⋂₀ range s ∈ l ↔ ∀ (i : ι), s i ∈ l"
} | [
135425,
48841,
12656,
14288,
1715
] | [
"Mathlib/Order/Filter/CardinalInter.lean"
] |
{
"context": [
"ι α β : Type u",
"c : Cardinal.{u}",
"l : Filter α",
"inst✝ : CardinalInterFilter l c",
"s : ι → Set α",
"hic : #ι < c"
],
"goal": "(∀ s_1 ∈ range s, s_1 ∈ l) ↔ ∀ (i : ι), s i ∈ l"
} | [
48841,
12656,
14288,
1715,
134168
] | [
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{
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"a : α",
"inst✝² : Group α",
"inst✝¹ : DecidableEq α",
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"hd : d ∣ Fintype.card α",
"c : ℕ := Fintype.card α"
],
"goal": "(filter (fun a => orderOf a = d) univ).card = φ d"
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141401,
1674,
7980
] | [
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] |
{
"context": [
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"c : ℕ := Fintype.card α",
"hc0 : 0 < c"
],
"goal": "(filter (fun a => orderOf a = d) univ).card = φ d"
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] | [
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{
"context": [
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"d : ℕ",
"hd : d ∣ Fintype.card α",
"c : ℕ := Fintype.card α",
"hc0 : 0 < c"
],
"goal": "0 < (filter (fun a => orderOf a = d) univ).card"
} | [
7980,
1734
] | [
"Mathlib/GroupTheory/SpecificGroups/Cyclic.lean"
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{
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"c : ℕ := Fintype.card α",
"hc0 : 0 < c",
"h0 : ¬0 < (filter (fun a => orderOf a = d) univ).card"
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"goal": "False"
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137616,
14323,
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1734
] | [
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{
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"c : ℕ := Fintype.card α",
"hc0 : 0 < c",
"h0 : filter (fun a => orderOf a = d) univ = ∅"
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"goal": "False"
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{
"context": [
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"hn : ∀ (n : ℕ), 0 < n → (filter (fun a => a ^ n = 1) univ).card ≤ n",
"d : ℕ",
"hd : d ∣ Fintype.card α",
"c : ℕ := Fintype.card α",
"hc0 : 0 < c",
"h0 : filter (fun a => orderOf a = d) univ = ∅"
],
"goal": "c < c"
} | [
14279
] | [
"Mathlib/GroupTheory/SpecificGroups/Cyclic.lean"
] |
{
"context": [
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"t✝ t₁ t₂ : (i : ι) → Set (α i)",
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],
"goal": "(s.pi fun j => t j (update f i a j)) = ({i} ∪ s \\ {i}).pi fun j => t j (update f i a j)"
} | [
1674,
133417,
133525,
133678
] | [
"Mathlib/Data/Set/Prod.lean"
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{
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],
"goal": "(({i} ∪ s \\ {i}).pi fun j => t j (update f i a j)) = {x | x i ∈ t i a} ∩ (s \\ {i}).pi fun j => t j (f j)"
} | [
71464,
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134036
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"Mathlib/Data/Set/Prod.lean"
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{
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],
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} | [
71464,
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] | [
"Mathlib/Data/Set/Prod.lean"
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{
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],
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96641
] | [
"Mathlib/CategoryTheory/LiftingProperties/Basic.lean"
] |
{
"context": [
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],
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} | [
96641
] | [
"Mathlib/CategoryTheory/LiftingProperties/Basic.lean"
] |
{
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"inst✝² : InnerProductSpace ℝ V",
"inst✝¹ : MetricSpace P",
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"hs : Cospherical s",
"p : Fin 3 → P",
"hps : Set.range p ⊆ s",
"hpi : Function.Injective p"
],
"goal": "AffineIndependent ℝ p"
} | [
83636
] | [
"Mathlib/Geometry/Euclidean/Sphere/Basic.lean"
] |
{
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],
"goal": "¬Collinear ℝ (Set.range p)"
} | [
83636
] | [
"Mathlib/Geometry/Euclidean/Sphere/Basic.lean"
] |
{
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],
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} | [
83633,
131596
] | [
"Mathlib/Geometry/Euclidean/Sphere/Basic.lean"
] |
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],
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83633,
131596
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{
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],
"goal": "False"
} | [
134168
] | [
"Mathlib/Geometry/Euclidean/Sphere/Basic.lean"
] |
{
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134168
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{
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],
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} | [
131596,
133308
] | [
"Mathlib/Geometry/Euclidean/Sphere/Basic.lean"
] |
{
"context": [
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"hs' : ∀ (i : Fin 3), dist (p i) c = r"
],
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} | [
131596,
133308
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{
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"f : Fin 3 → ℝ",
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"hsd : ∀ (i : Fin 3), dist (f i • v +ᵥ p 0) c = r"
],
"goal": "False"
} | [
1717,
110053,
115870,
115877
] | [
"Mathlib/Geometry/Euclidean/Sphere/Basic.lean"
] |
End of preview.
This dataset is used in the paper Assisting Mathematical Formalization with A Learning-based Premise Retriever. It contains data for training and evaluating a premise retriever for the Lean theorem prover.
The dataset is described in detail in the GitHub repository. It consists of proof states and corresponding premises from the Mathlib library. The data is designed to train a model to effectively retrieve relevant premises for a given proof state, assisting users in the mathematical formalization process. The dataset is available for download at this link.
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