Split (3)

train

The full dataset viewer is not available (click to read why). Only showing a preview of the rows.

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", ...	[ 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", ...	[ 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", ...	[ 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", ...	[ 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", ...	[ 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...	[ 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...	[ 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 : ...	[ 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 : ...	[ 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" ], "...	[ 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" ], "...	[ 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 ...	[ 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)"...	[ 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", ...	[ 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", ...	[ 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", ...	[ 15889, 55623, 55638, 131585, 41371, 118076, 119707, 131585, 134071 ]	[ "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", ...	[ 131585, 119707, 55623, 15889, 55638, 134071, 41371, 118076 ]	[ "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", ...	[ 131585, 119703, 41371, 134071, 119707, 118076 ]	[ "Mathlib/Analysis/Calculus/LineDeriv/Basic.lean" ]
{ "context": [ "E : Type u_1", "inst✝³ : NormedAddCommGroup E", "inst✝² : NormedSpace ℝ E", "F : Type u_2", "inst✝¹ : NormedAddCommGroup F", "inst✝ : NormedSpace ℝ F", "v : ℝ → E → E", "s : ℝ → Set E", "K : ℝ≥0", "f g f' g' : ℝ → E", "a b t₀ εf εg δ : ℝ", "hv : ∀ (t : ℝ...	[ 14316 ]	[ "Mathlib/Analysis/ODE/Gronwall.lean" ]
{ "context": [ "E : Type u_1", "inst✝³ : NormedAddCommGroup E", "inst✝² : NormedSpace ℝ E", "F : Type u_2", "inst✝¹ : NormedAddCommGroup F", "inst✝ : NormedSpace ℝ F", "v : ℝ → E → E", "s : ℝ → Set E", "K : ℝ≥0", "f g f' g' : ℝ → E", "a b t₀ εf εg δ : ℝ", "hv : ∀ (t : ℝ...	[ 14316 ]	[ "Mathlib/Analysis/ODE/Gronwall.lean" ]
{ "context": [ "E : Type u_1", "inst✝³ : NormedAddCommGroup E", "inst✝² : NormedSpace ℝ E", "F : Type u_2", "inst✝¹ : NormedAddCommGroup F", "inst✝ : NormedSpace ℝ F", "v : ℝ → E → E", "s : ℝ → Set E", "K : ℝ≥0", "f g f' g' : ℝ → E", "a b t₀ εf εg δ : ℝ", "hv : ∀ (t : ℝ...	[ 14316 ]	[ "Mathlib/Analysis/ODE/Gronwall.lean" ]
{ "context": [ "C : Type u₁", "inst✝⁸ : Category.{v₁, u₁} C", "inst✝⁷ : MonoidalCategory C", "inst✝⁶ : BraidedCategory C", "D : Type u₂", "inst✝⁵ : Category.{v₂, u₂} D", "inst✝⁴ : MonoidalCategory D", "inst✝³ : BraidedCategory D", "E : Type u₃", "inst✝² : Category.{v₃, u₃} E", ...	[ 107138 ]	[ "Mathlib/CategoryTheory/Monoidal/Braided/Basic.lean" ]
{ "context": [ "C : Type u_1", "inst✝⁸ : Category.{u_3, u_1} C", "inst✝⁷ : Preadditive C", "𝕜 : Type u_2", "inst✝⁶ : Field 𝕜", "inst✝⁵ : IsAlgClosed 𝕜", "inst✝⁴ : Linear 𝕜 C", "inst✝³ : HasKernels C", "X Y : C", "inst✝² : FiniteDimensional 𝕜 (X ⟶ X)", "inst✝¹ : Simple ...	[ 71959 ]	[ "Mathlib/CategoryTheory/Preadditive/Schur.lean" ]
{ "context": [ "C : Type u_1", "inst✝⁸ : Category.{u_3, u_1} C", "inst✝⁷ : Preadditive C", "𝕜 : Type u_2", "inst✝⁶ : Field 𝕜", "inst✝⁵ : IsAlgClosed 𝕜", "inst✝⁴ : Linear 𝕜 C", "inst✝³ : HasKernels C", "X Y : C", "inst✝² : FiniteDimensional 𝕜 (X ⟶ X)", "inst✝¹ : Simple ...	[ 71959 ]	[ "Mathlib/CategoryTheory/Preadditive/Schur.lean" ]
{ "context": [ "C : Type u_1", "inst✝⁸ : Category.{u_3, u_1} C", "inst✝⁷ : Preadditive C", "𝕜 : Type u_2", "inst✝⁶ : Field 𝕜", "inst✝⁵ : IsAlgClosed 𝕜", "inst✝⁴ : Linear 𝕜 C", "inst✝³ : HasKernels C", "X Y : C", "inst✝² : FiniteDimensional 𝕜 (X ⟶ X)", "inst✝¹ : Simple ...	[ 71959 ]	[ "Mathlib/CategoryTheory/Preadditive/Schur.lean" ]
{ "context": [ "n : ℕ", "t : ℝ", "ht' : t ≤ ↑n" ], "goal": "(1 - t / ↑n) ^ n ≤ rexp (-t)" }	[ 70039, 106248, 149344 ]	[ "Mathlib/Data/Complex/Exponential.lean" ]
{ "context": [ "t : ℝ", "ht' : t ≤ ↑0" ], "goal": "(1 - t / ↑0) ^ 0 ≤ rexp (-t)" }	[ 70039, 106248, 149344 ]	[ "Mathlib/Data/Complex/Exponential.lean" ]
{ "context": [ "n : ℕ", "t : ℝ", "ht' : t ≤ ↑n", "hn : n ≠ 0" ], "goal": "(1 - t / ↑n) ^ n ≤ rexp (-t)" }	[ 106248, 149344, 70039 ]	[ "Mathlib/Data/Complex/Exponential.lean" ]
{ "context": [ "n : ℕ", "t : ℝ", "ht' : t ≤ ↑n", "hn : n ≠ 0" ], "goal": "rexp (-t) = rexp (-(t / ↑n)) ^ n" }	[ 106248, 149344 ]	[ "Mathlib/Data/Complex/Exponential.lean" ]
{ "context": [ "n : ℕ", "t : ℝ", "ht' : t ≤ ↑n", "hn : n ≠ 0" ], "goal": "0 ≤ 1 - t / ↑n" }	[ 106248, 149344 ]	[ "Mathlib/Data/Complex/Exponential.lean" ]
{ "context": [ "R : Type u_1", "M : Type u_2", "inst✝² : CommRing R", "inst✝¹ : AddCommGroup M", "inst✝ : Module R M", "Q : QuadraticForm R M", "x : CliffordAlgebra Q" ], "goal": "↑((toEven Q) (reverse (involute x))) = reverse ↑((toEven Q) x)" }	[ 81956, 81967, 81968, 81970, 82298, 82718, 82721, 82723, 82725, 117079, 117080, 117094, 121060, 122047, 122048, 122051, 122054 ]	[ "Mathlib/LinearAlgebra/CliffordAlgebra/EvenEquiv.lean" ]
{ "context": [ "α : Type u_1", "E : Type u_2", "F : Type u_3", "m0 : MeasurableSpace α", "inst✝⁵ : NormedAddCommGroup E", "inst✝⁴ : NormedSpace ℝ E", "inst✝³ : CompleteSpace E", "inst✝² : NormedAddCommGroup F", "inst✝¹ : NormedSpace ℝ F", "inst✝ : CompleteSpace F", "μ ν : M...	[ 26860, 30260 ]	[ "Mathlib/MeasureTheory/Integral/Average.lean" ]
{ "context": [ "C : Type u", "inst✝² : Category.{v, u} C", "inst✝¹ : HasZeroMorphisms C", "S S₁ S₂ S₃ S₄ : ShortComplex C", "φ : S₁ ⟶ S₂", "h₁ : S₁.HomologyData", "h₂ : S₂.HomologyData", "A : C", "inst✝ : S.HasHomology", "h : S.LeftHomologyData" ], "goal": "(S.leftHomologyπ...	[ 88745, 88756, 96173, 115100 ]	[ "Mathlib/Algebra/Homology/ShortComplex/Homology.lean" ]
{ "context": [ "ι : Sort u_1", "V : Type u", "W : Type v", "G : SimpleGraph V", "G' : SimpleGraph W", "v w : V", "hvw : G.Adj v w" ], "goal": "G.subgraphOfAdj ⋯ = G.subgraphOfAdj hvw" }	[ 1723, 1726 ]	[ "Mathlib/Combinatorics/SimpleGraph/Subgraph.lean" ]
{ "context": [ "α : Type u", "β : Type v", "inst✝ : Finite α", "s : Set α", "f : ↑s ↪ β", "h : Nonempty (α ≃ β)" ], "goal": "∃ g, ∀ (x : ↑s), g ↑x = f x" }	[ 49534 ]	[ "Mathlib/SetTheory/Cardinal/Ordinal.lean" ]
{ "context": [ "α : Type u", "β : Type v", "inst✝ : Finite α", "s : Set α", "f : ↑s ↪ β", "h : Nonempty (α ≃ β)" ], "goal": "Nonempty (↑sᶜ ≃ ↑(range ⇑f)ᶜ)" }	[ 49534 ]	[ "Mathlib/SetTheory/Cardinal/Ordinal.lean" ]
{ "context": [ "α : Type u", "β : Type v", "inst✝ : Finite α", "s : Set α", "f : ↑s ↪ β", "h : Nonempty (α ≃ β)", "g : α ≃ β" ], "goal": "Nonempty (↑sᶜ ≃ ↑(range ⇑f)ᶜ)" }	[ 48597, 48597, 49531 ]	[ "Mathlib/SetTheory/Cardinal/Ordinal.lean" ]
{ "context": [ "α : Type u", "β : Type v", "inst✝ : Finite α", "s : Set α", "f : ↑s ↪ β", "h : lift.{max u v, u} #α = lift.{max u v, v} #β", "g : α ≃ β" ], "goal": "Nonempty (↑sᶜ ≃ ↑(range ⇑f)ᶜ)" }	[ 49531, 48597 ]	[ "Mathlib/SetTheory/Cardinal/Ordinal.lean" ]
{ "context": [ "α : Type u", "β : Type v", "inst✝ : Finite α", "s : Set α", "f : ↑s ↪ β", "h : lift.{max u v, u} #α = lift.{max u v, v} #β", "g : α ≃ β" ], "goal": "lift.{max u v, u} #↑s = lift.{max u v, v} #↑(range ⇑f)" }	[ 49531, 48844, 48597 ]	[ "Mathlib/SetTheory/Cardinal/Ordinal.lean" ]
{ "context": [ "α : Type u", "β : Type v", "inst✝ : Finite α", "s : Set α", "f : ↑s ↪ β", "h : lift.{max u v, u} #α = lift.{max u v, v} #β", "g : α ≃ β" ], "goal": "Injective ⇑f" }	[ 48844, 70654 ]	[ "Mathlib/SetTheory/Cardinal/Ordinal.lean" ]
{ "context": [], "goal": "@zipWithLeft' = @zipWithLeft'TR" }	[ 1838 ]	[ ".lake/packages/batteries/Batteries/Data/List/Basic.lean" ]
{ "context": [ "α : Type u_3", "β : Type u_2", "γ : Type u_1", "f : α → Option β → γ", "as : List α", "bs : List β" ], "goal": "zipWithLeft' f as bs = zipWithLeft'TR f as bs" }	[ 1838 ]	[ ".lake/packages/batteries/Batteries/Data/List/Basic.lean" ]
{ "context": [ "α : Type u_3", "β : Type u_2", "γ : Type u_1", "f : α → Option β → γ", "as : List α", "bs : List β", "acc : Array γ", "head✝ : α", "tail✝ : List α" ], "goal": "zipWithLeft'TR.go f (head✝ :: tail✝) [] acc = match zipWithLeft' f (head✝ :: tail✝) [] with \| (l, r) =...	[ 5846 ]	[ ".lake/packages/batteries/Batteries/Data/List/Basic.lean" ]
{ "context": [ "α : Type u_1", "β : Type u_2", "G : Type u_3", "M : Type u_4", "inst✝ : CommGroup G", "a✝ b✝ c d a b : G" ], "goal": "a * (b / a) = b" }	[ 118077, 117806 ]	[ "Mathlib/Algebra/Group/Basic.lean" ]
{ "context": [ "ι : Type u_1", "X : Type u_2", "Y : Type u_3", "inst✝⁵ : EMetricSpace X", "inst✝⁴ : EMetricSpace Y", "inst✝³ : MeasurableSpace X", "inst✝² : BorelSpace X", "inst✝¹ : MeasurableSpace Y", "inst✝ : BorelSpace Y" ], "goal": "μH[1] = volume" }	[ 26594, 30824, 30825, 88683, 141373, 143125 ]	[ "Mathlib/MeasureTheory/Measure/Hausdorff.lean" ]
{ "context": [ "α : Type u_1", "f g h : Perm α", "x : α", "hfx : f x = x", "n : ℕ" ], "goal": "(f ^ Int.negSucc n) x = x" }	[ 7831, 8652, 119787 ]	[ "Mathlib/GroupTheory/Perm/Support.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", ...	[ 48434, 46361, 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", ...	[ 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", ...	[ 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✝ ...	[ 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)...	[ 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), (...	[ 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)", "m : t.pt ⟶ (BinaryFan.assoc Q s).pt", ...	[ 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", "sYZ : BinaryFan Y Z", "Q : IsLimit sYZ", "s : BinaryFan sXY.pt Z", "R : IsLimit s", "t : Cone (pair X sYZ.pt)", "m : t.pt ⟶ (BinaryFan.assoc Q s).pt", ...	[ 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", "inst✝¹ : Group G", "inst✝ : Finite G", "p : ℕ", "hp : Fact (Nat.Prime p)", "this : Fintype G", "hdvd : p ∣ Fintype.card G" ], "goal": "∃ x, orderOf x...	[ 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", "inst✝⁴ : MeasurableSpace α", "μ : Measure α", "inst✝³ : Countable G", "inst✝² : MeasurableSpace G", "s t : Set α", "inst✝¹ :...	[ 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", "inst✝⁵ : MulAction G α", "inst✝⁴ : MeasurableSpace α", "μ : Measure α", "inst✝³ : Countable G", "inst✝² : MeasurableSpace G", "s t : Set α", "inst✝¹ :...	[ 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", "inst✝⁵ : MulAction G α", "inst✝⁴ : MeasurableSpace α", "μ : Measure α", "inst✝³ : Countable G", "inst✝² : MeasurableSpace G", "s t : Set α", "inst✝¹ :...	[ 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", "inst✝⁵ : MulAction G α", "inst✝⁴ : MeasurableSpace α", "μ : Measure α", "inst✝³ : Countable G", "inst✝² : MeasurableSpace G", "s t : Set α", "inst✝¹ :...	[ 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"...	[ 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", ...	[ 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", "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", ...	[ 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 p...	[ 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", "c : Cardinal.{u}", "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 ]	[ "Mathlib/Order/Filter/CardinalInter.lean" ]
{ "context": [ "α : Type u", "a : α", "inst✝² : Group α", "inst✝¹ : DecidableEq α", "inst✝ : Fintype α", "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" ], "goal": "(filter (fun a => orderOf a ...	[ 141401, 1674, 7980 ]	[ "Mathlib/GroupTheory/SpecificGroups/Cyclic.lean" ]
{ "context": [ "α : Type u", "a : α", "inst✝² : Group α", "inst✝¹ : DecidableEq α", "inst✝ : Fintype α", "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" ], "goal": "(filter (...	[ 141401, 1674, 7980 ]	[ "Mathlib/GroupTheory/SpecificGroups/Cyclic.lean" ]
{ "context": [ "α : Type u", "a : α", "inst✝² : Group α", "inst✝¹ : DecidableEq α", "inst✝ : Fintype α", "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" ], "goal": "0 < (filt...	[ 7980, 1734 ]	[ "Mathlib/GroupTheory/SpecificGroups/Cyclic.lean" ]
{ "context": [ "α : Type u", "a : α", "inst✝² : Group α", "inst✝¹ : DecidableEq α", "inst✝ : Fintype α", "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 : ¬0 < (filter (...	[ 137616, 14323, 3806, 1734 ]	[ "Mathlib/GroupTheory/SpecificGroups/Cyclic.lean" ]
{ "context": [ "α : Type u", "a : α", "inst✝² : Group α", "inst✝¹ : DecidableEq α", "inst✝ : Fintype α", "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 ...	[ 137616, 14323, 3806, 14279 ]	[ "Mathlib/GroupTheory/SpecificGroups/Cyclic.lean" ]
{ "context": [ "α : Type u", "a : α", "inst✝² : Group α", "inst✝¹ : DecidableEq α", "inst✝ : Fintype α", "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 ...	[ 14279 ]	[ "Mathlib/GroupTheory/SpecificGroups/Cyclic.lean" ]
{ "context": [ "ι : Type u_1", "α : ι → Type u_2", "β : ι → Type u_3", "s s₁ s₂ : Set ι", "t✝ t₁ t₂ : (i : ι) → Set (α i)", "i : ι", "inst✝ : DecidableEq ι", "hi : i ∈ s", "f : (j : ι) → α j", "a : α i", "t : (j : ι) → α j → Set (β j)" ], "goal": "(s.pi fun j => t j (up...	[ 1674, 133417, 133525, 133678 ]	[ "Mathlib/Data/Set/Prod.lean" ]
{ "context": [ "ι : Type u_1", "α : ι → Type u_2", "β : ι → Type u_3", "s s₁ s₂ : Set ι", "t✝ t₁ t₂ : (i : ι) → Set (α i)", "i : ι", "inst✝ : DecidableEq ι", "hi : i ∈ s", "f : (j : ι) → α j", "a : α i", "t : (j : ι) → α j → Set (β j)" ], "goal": "(({i} ∪ s \\ {i}).pi f...	[ 71464, 134029, 134033, 134036 ]	[ "Mathlib/Data/Set/Prod.lean" ]
{ "context": [ "ι : Type u_1", "α : ι → Type u_2", "β : ι → Type u_3", "s s₁ s₂ : Set ι", "t✝ t₁ t₂ : (i : ι) → Set (α i)", "i : ι", "inst✝ : DecidableEq ι", "hi : i ∈ s", "f : (j : ι) → α j", "a : α i", "t : (j : ι) → α j → Set (β j)" ], "goal": "i ∉ s \\ {i}" }	[ 71464, 134029, 134033, 134036 ]	[ "Mathlib/Data/Set/Prod.lean" ]
{ "context": [ "C : Type u_1", "inst✝ : Category.{u_2, u_1} C", "A✝ B✝ B'✝ X✝ Y✝ Y' : C", "i✝ : A✝ ⟶ B✝", "i'✝ : B✝ ⟶ B'✝", "p✝ : X✝ ⟶ Y✝", "p' : Y✝ ⟶ Y'", "A B A' B' X Y : C", "i : A ⟶ B", "i' : A' ⟶ B'", "e : Arrow.mk i ≅ Arrow.mk i'", "p : X ⟶ Y", "a✝ : HasLiftin...	[ 96641 ]	[ "Mathlib/CategoryTheory/LiftingProperties/Basic.lean" ]
{ "context": [ "C : Type u_1", "inst✝ : Category.{u_2, u_1} C", "A✝ B✝ B'✝ X✝ Y✝ Y' : C", "i✝ : A✝ ⟶ B✝", "i'✝ : B✝ ⟶ B'✝", "p✝ : X✝ ⟶ Y✝", "p' : Y✝ ⟶ Y'", "A B A' B' X Y : C", "i : A ⟶ B", "i' : A' ⟶ B'", "e : Arrow.mk i ≅ Arrow.mk i'", "p : X ⟶ Y", "a✝ : HasLiftin...	[ 96641 ]	[ "Mathlib/CategoryTheory/LiftingProperties/Basic.lean" ]
{ "context": [ "V : Type u_1", "P : Type u_2", "inst✝³ : NormedAddCommGroup V", "inst✝² : InnerProductSpace ℝ V", "inst✝¹ : MetricSpace P", "inst✝ : NormedAddTorsor V P", "s : Set P", "hs : Cospherical s", "p : Fin 3 → P", "hps : Set.range p ⊆ s", "hpi : Function.Injective ...	[ 83636 ]	[ "Mathlib/Geometry/Euclidean/Sphere/Basic.lean" ]
{ "context": [ "V : Type u_1", "P : Type u_2", "inst✝³ : NormedAddCommGroup V", "inst✝² : InnerProductSpace ℝ V", "inst✝¹ : MetricSpace P", "inst✝ : NormedAddTorsor V P", "s : Set P", "hs : Cospherical s", "p : Fin 3 → P", "hps : Set.range p ⊆ s", "hpi : Function.Injective ...	[ 83636 ]	[ "Mathlib/Geometry/Euclidean/Sphere/Basic.lean" ]
{ "context": [ "V : Type u_1", "P : Type u_2", "inst✝³ : NormedAddCommGroup V", "inst✝² : InnerProductSpace ℝ V", "inst✝¹ : MetricSpace P", "inst✝ : NormedAddTorsor V P", "s : Set P", "hs : Cospherical s", "p : Fin 3 → P", "hps : Set.range p ⊆ s", "hpi : Function.Injective ...	[ 83633, 131596 ]	[ "Mathlib/Geometry/Euclidean/Sphere/Basic.lean" ]
{ "context": [ "V : Type u_1", "P : Type u_2", "inst✝³ : NormedAddCommGroup V", "inst✝² : InnerProductSpace ℝ V", "inst✝¹ : MetricSpace P", "inst✝ : NormedAddTorsor V P", "s : Set P", "hs : Cospherical s", "p : Fin 3 → P", "hps : Set.range p ⊆ s", "hpi : Function.Injective ...	[ 83633, 131596 ]	[ "Mathlib/Geometry/Euclidean/Sphere/Basic.lean" ]
{ "context": [ "V : Type u_1", "P : Type u_2", "inst✝³ : NormedAddCommGroup V", "inst✝² : InnerProductSpace ℝ V", "inst✝¹ : MetricSpace P", "inst✝ : NormedAddTorsor V P", "s : Set P", "hs : Cospherical s", "p : Fin 3 → P", "hps : Set.range p ⊆ s", "hpi : Function.Injective ...	[ 134168 ]	[ "Mathlib/Geometry/Euclidean/Sphere/Basic.lean" ]
{ "context": [ "V : Type u_1", "P : Type u_2", "inst✝³ : NormedAddCommGroup V", "inst✝² : InnerProductSpace ℝ V", "inst✝¹ : MetricSpace P", "inst✝ : NormedAddTorsor V P", "s : Set P", "hs : Cospherical s", "p : Fin 3 → P", "hps : Set.range p ⊆ s", "hpi : Function.Injective ...	[ 134168 ]	[ "Mathlib/Geometry/Euclidean/Sphere/Basic.lean" ]
{ "context": [ "V : Type u_1", "P : Type u_2", "inst✝³ : NormedAddCommGroup V", "inst✝² : InnerProductSpace ℝ V", "inst✝¹ : MetricSpace P", "inst✝ : NormedAddTorsor V P", "s : Set P", "p : Fin 3 → P", "hps : Set.range p ⊆ s", "hpi : Function.Injective p", "v : V", "hv :...	[ 131596, 133308 ]	[ "Mathlib/Geometry/Euclidean/Sphere/Basic.lean" ]
{ "context": [ "V : Type u_1", "P : Type u_2", "inst✝³ : NormedAddCommGroup V", "inst✝² : InnerProductSpace ℝ V", "inst✝¹ : MetricSpace P", "inst✝ : NormedAddTorsor V P", "s : Set P", "p : Fin 3 → P", "hps : Set.range p ⊆ s", "hpi : Function.Injective p", "v : V", "hv :...	[ 131596, 133308 ]	[ "Mathlib/Geometry/Euclidean/Sphere/Basic.lean" ]
{ "context": [ "V : Type u_1", "P : Type u_2", "inst✝³ : NormedAddCommGroup V", "inst✝² : InnerProductSpace ℝ V", "inst✝¹ : MetricSpace P", "inst✝ : NormedAddTorsor V P", "s : Set P", "p : Fin 3 → P", "hps : Set.range p ⊆ s", "hpi : Function.Injective p", "v : V", "hv0 ...	[ 1717, 110053, 115870, 115877 ]	[ "Mathlib/Geometry/Euclidean/Sphere/Basic.lean" ]

End of preview.