file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/NumberTheory/VonMangoldt.lean | Nat.ArithmeticFunction.vonMangoldt_pos_iff | [] | [
103,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
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Mathlib/Analysis/NormedSpace/Banach.lean | ContinuousLinearMap.closure_preimage | [] | [
286,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
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Mathlib/Data/Finset/Pointwise.lean | Finset.Nonempty.zero_div | [
{
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"tactic": "simpa [mem_div] using hs"
}
] | [
1200,
60
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Mathlib/Computability/EpsilonNFA.lean | εNFA.evalFrom_empty | [
{
"state_after": "case H0\nα : Type u\nσ σ' : Type v\nM : εNFA α σ\nS : Set σ\nx : List α\ns : σ\na : α\n⊢ evalFrom M ∅ [] = ∅\n\ncase H1\nα : Type u\nσ σ' : Type v\nM : εNFA α σ\nS : Set σ\nx✝ : List α\ns : σ\na✝ : α\nx : List α\na : α\nih : evalFrom M ∅ x = ∅\n⊢ evalFrom M ∅ (x ++ [a]) = ∅",
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_range | [
{
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633,
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630,
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Mathlib/Analysis/Complex/UnitDisc/Basic.lean | Complex.UnitDisc.mk_coe | [] | [
93,
18
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Mathlib/Data/Nat/Cast/Basic.lean | Nat.cast_lt | [] | [
138,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
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Mathlib/Order/Hom/CompleteLattice.lean | Set.image_sSup | [
{
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"state_before": "F : Type ?u.92960\nα : Type u_1\nβ : Type u_2\nγ : Type ?... | [
952,
34
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Mathlib/RingTheory/ZMod.lean | isReduced_zmod | [
{
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31,
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src/lean/Init/Data/Array/Basic.lean | Array.size_mkArray | [] | [
25,
27
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
24,
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Mathlib/Algebra/Support.lean | Function.mulSupport_one | [] | [
138,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_restrict_mem₀ | [
{
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2830,
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Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.coe_zeta_mul_moebius | [
{
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"state_before": "R : Type ?u.604756\n⊢ ↑ζ * μ = 1",
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}
] | [
1046,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1045,
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Mathlib/Algebra/Support.lean | Function.mulSupport_int_cast | [] | [
343,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Iio_insert | [] | [
897,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
896,
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Mathlib/Data/Set/Lattice.lean | Set.surjOn_iUnion₂_iUnion₂ | [] | [
1605,
59
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.IsAdjointPair.smul | [
{
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Mathlib/Algebra/Order/Rearrangement.lean | MonovaryOn.sum_mul_comp_perm_lt_sum_mul_iff | [] | [
373,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/DiscreteValuationRing/Basic.lean | DiscreteValuationRing.of_ufd_of_unique_irreducible | [
{
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"state_before": "R✝ : Type ?u.1056... | [
307,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
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Mathlib/Order/BoundedOrder.lean | Ne.lt_top' | [] | [
192,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
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Mathlib/Topology/MetricSpace/IsometricSMul.lean | Metric.preimage_smul_closedBall | [
{
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"tactic": "rw [preimage_smul,... | [
450,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
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src/lean/Init/Data/Nat/Basic.lean | Nat.add_right_cancel | [
{
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"state_before": "n m k : Nat\nh : n + m = k + m\n⊢ n = k",
"tactic": "rw [Nat.add_comm n m, Nat.add_comm k m] at h"
},
{
"state_after": "no goals",
"state_before": "n m k : Nat\nh : m + n = m + k\n⊢ n = k",
"tactic": "apply Nat.... | [
155,
30
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
153,
11
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Mathlib/Algebra/GCDMonoid/Finset.lean | Finset.lcm_dvd | [] | [
72,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
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Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atBot_atBot_of_monotone' | [] | [
1688,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1686,
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Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Term.realize_constants | [] | [
109,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
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Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.WalkingParallelPairHom.id.sizeOf_spec' | [
{
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"state_before": "X : WalkingParallelPair\n⊢ sizeOf (𝟙 X) = 1 + sizeOf X",
"tactic": "cases X <;> rfl"
}
] | [
128,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
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Mathlib/Algebra/Algebra/Operations.lean | Submodule.one_mul | [
{
"state_after": "ι : Sort uι\nR : Type u\ninst✝² : CommSemiring R\nA : Type v\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\nS T : Set A\nM N P Q : Submodule R A\nm n : A\n⊢ span R {1} * span R ↑M = M",
"state_before": "ι : Sort uι\nR : Type u\ninst✝² : CommSemiring R\nA : Type v\ninst✝¹ : Semiring A\ninst✝ : ... | [
222,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
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Mathlib/Order/RelIso/Basic.lean | RelEmbedding.isTrans | [] | [
359,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
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Mathlib/Order/Hom/CompleteLattice.lean | CompleteLatticeHom.setPreimage_apply | [] | [
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6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.tendsto_inv_smul_nhds_zero | [
{
"state_after": "no goals",
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1824,
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Mathlib/Topology/Algebra/Order/IntermediateValue.lean | mem_range_of_exists_le_of_exists_ge | [] | [
197,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
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Mathlib/LinearAlgebra/Matrix/Reindex.lean | Matrix.reindexLinearEquiv_mul | [] | [
106,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
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Mathlib/LinearAlgebra/Prod.lean | LinearMap.range_prod_le | [
{
"state_after": "R : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nM₅ : Type ?u.230981\nM₆ : Type ?u.230984\ninst✝⁸ : Semiring R\ninst✝⁷ : AddCommMonoid M\ninst✝⁶ : AddCommMonoid M₂\ninst✝⁵ : AddCommMonoid M₃\ninst✝⁴ : AddCommMonoid... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
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Mathlib/Data/Finset/Card.lean | Finset.fiber_card_ne_zero_iff_mem_image | [
{
"state_after": "no goals",
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"tactic": "rw [← pos_iff_ne_zero, card_pos, fiber_nonempty_iff_mem_image]"
}
] | [
248,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
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Mathlib/Data/Finset/Image.lean | Finset.filter_map | [] | [
184,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
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Mathlib/CategoryTheory/Extensive.lean | CategoryTheory.BinaryCofan.isVanKampen_iff | [
{
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23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
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Mathlib/Data/Polynomial/Expand.lean | Polynomial.expand_zero | [
{
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"tactic": "simp [expand]"
}
] | [
81,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/Basic.lean | Submodule.comap_comp | [] | [
808,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Image.lean | Set.image_singleton | [
{
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342,
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | left_mem_affineSpan_pair | [] | [
1299,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Groupoid/Basic.lean | CategoryTheory.Groupoid.isThin_iff | [
{
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"tactic": "refine' ⟨fun h c => h c c, fun h c d => Subsingleton.intro fun f g ... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Covering/Differentiation.lean | VitaliFamily.ae_tendsto_lintegral_div' | [
{
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779,
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Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integral_indicator_const | [
{
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454,
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Mathlib/Analysis/Calculus/FDerivMeasurable.lean | FDerivMeasurableAux.mem_a_of_differentiable | [
{
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183,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
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Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.mul_def | [
{
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"tactic": "simp only [... | [
551,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
550,
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Mathlib/Algebra/Homology/Homology.lean | HomologicalComplex.boundaries_eq_bot | [
{
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Mathlib/Analysis/Asymptotics/SuperpolynomialDecay.lean | Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_abs | [
{
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175,
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Mathlib/Data/Prod/PProd.lean | PProd.exists' | [] | [
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Mathlib/Data/Real/NNReal.lean | Real.toNNReal_coe | [] | [
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Mathlib/CategoryTheory/Extensive.lean | CategoryTheory.IsVanKampenColimit.isUniversal | [] | [
101,
43
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Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.count_factors_eq_find_of_dvd_pow | [
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.normalClosure_eq_iInf | [
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Mathlib/Computability/Primrec.lean | Primrec.option_get | [
{
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Mathlib/Topology/Order/Basic.lean | frontier_Ioc | [
{
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2379,
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Mathlib/Data/List/Cycle.lean | List.nextOr_self_cons_cons | [] | [
55,
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | uniformity_basis_edist_nnreal | [] | [
241,
47
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Mathlib/Topology/Order.lean | TopologicalSpace.generateFrom_surjective | [] | [
229,
35
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Mathlib/Order/UpperLower/Basic.lean | isLowerSet_univ | [] | [
82,
71
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Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.coprod.map_comp_inl_inr_codiag | [
{
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951,
97
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Mathlib/Data/Finset/Image.lean | Finset.mem_map' | [] | [
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27
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Mathlib/Logic/Equiv/Defs.lean | Equiv.rightInverse_symm | [] | [
363,
90
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363,
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.finStronglyMeasurable_zero | [
{
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990,
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Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.coeFn_zpow | [] | [
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19
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Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.isPrimitive_iff_content_eq_one | [
{
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239,
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236,
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Mathlib/Topology/Algebra/Order/LeftRight.lean | nhds_left'_sup_nhds_right' | [
{
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] | [
74,
41
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Mathlib/CategoryTheory/ConcreteCategory/Basic.lean | CategoryTheory.ConcreteCategory.mono_of_injective | [] | [
160,
59
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158,
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Mathlib/Order/Filter/Lift.lean | Filter.lift_lift'_assoc | [
{
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348,
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344,
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Mathlib/Data/Set/Ncard.lean | Set.ncard_def | [] | [
66,
60
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Mathlib/Analysis/Convex/Caratheodory.lean | Caratheodory.mem_minCardFinsetOfMemConvexHull | [] | [
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91
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Mathlib/Order/GaloisConnection.lean | GaloisConnection.u_sInf | [] | [
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17
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310,
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Mathlib/Data/List/Sigma.lean | List.kerase_append_right | [
{
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532,
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529,
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Mathlib/CategoryTheory/Bicategory/Basic.lean | CategoryTheory.Bicategory.pentagon_inv_inv_hom_hom_inv | [
{
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268,
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Mathlib/Data/Finset/Sups.lean | Finset.sups_right_comm | [] | [
212,
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Mathlib/FieldTheory/Separable.lean | AlgHom.card_of_powerBasis | [
{
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.zipWith_def | [
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Mathlib/MeasureTheory/Group/Arithmetic.lean | AEMeasurable.mul' | [] | [
153,
51
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151,
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Mathlib/Analysis/Convex/Join.lean | convexHull_union | [
{
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204,
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Mathlib/Topology/Order/Basic.lean | closure_Ioi | [] | [
2224,
28
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2223,
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Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.map_id | [] | [
68,
14
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Mathlib/Topology/MetricSpace/Polish.lean | PolishSpace.IsClopenable.iUnion | [
{
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Mathlib/CategoryTheory/Sites/Sheafification.lean | CategoryTheory.GrothendieckTopology.isoSheafify_hom | [] | [
551,
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Mathlib/CategoryTheory/Category/Preorder.lean | CategoryTheory.Iso.to_eq | [] | [
168,
32
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167,
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.comp_id_right | [
{
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Mathlib/Analysis/InnerProductSpace/Projection.lean | orthogonalProjection_orthogonalComplement_singleton_eq_zero | [] | [
984,
42
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Mathlib/Algebra/ModEq.lean | AddCommGroup.ModEq.sub_right_cancel' | [] | [
259,
29
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258,
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ico_subset_Ico_right | [] | [
199,
26
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198,
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Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.pow_le | [
{
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Mathlib/LinearAlgebra/Determinant.lean | LinearEquiv.isUnit_det | [
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433,
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Mathlib/Computability/RegularExpressions.lean | RegularExpression.deriv_char_of_ne | [] | [
198,
11
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Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.monotone_distinctConstantsTheory | [] | [
1128,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1126,
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Mathlib/Data/PFun.lean | PFun.comp_assoc | [
{
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624,
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Mathlib/Topology/Algebra/WithZeroTopology.lean | WithZeroTopology.isOpen_Iio | [] | [
151,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
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Mathlib/Data/Nat/Factorization/Basic.lean | Nat.Prime.factorization_self | [
{
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281,
96
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281,
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Mathlib/Algebra/BigOperators/Finprod.lean | MonoidHom.map_finprod_mem | [] | [
713,
42
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711,
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Mathlib/Data/Rat/NNRat.lean | Rat.toNNRat_div' | [
{
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}
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430,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.mem_toSet | [] | [
731,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
730,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_nat_cast | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q r : R[X]\nx : R\nn : ℕ\n⊢ eval x ↑n = ↑n",
"tactic": "simp only [← C_eq_nat_cast, eval_C]"
}
] | [
357,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/Data/Polynomial/Reverse.lean | Polynomial.reflect_monomial | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nf : R[X]\nN n : ℕ\n⊢ reflect N (X ^ n) = X ^ ↑(revAt N) n",
"tactic": "rw [← one_mul (X ^ n), ← one_mul (X ^ revAt N n), ← C_1, reflect_C_mul_X_pow]"
}
] | [
169,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.ofReal_toReal_ae_eq | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.1005086\nγ : Type ?u.1005089\nδ : Type ?u.1005092\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\nf : α → ℝ≥0∞\nhf : ∀ᵐ (x : α) ∂μ, f x < ⊤\n⊢ ∀ (a : α), f a < ⊤ → ENNReal.ofReal... | [
835,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
831,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Submodule.mem_iSup_iff_exists_finset | [] | [
1170,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1167,
1
] |
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