file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/LinearAlgebra/Basic.lean | LinearMap.pi_apply_eq_sum_univ | [
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Mathlib/Algebra/Order/Ring/Defs.lean | mul_pos_iff | [] | [
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Mathlib/Algebra/Order/Sub/Canonical.lean | tsub_eq_iff_eq_add_of_le | [] | [
213,
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Mathlib/Algebra/MonoidAlgebra/Division.lean | AddMonoidAlgebra.of'_mul_divOf | [
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_inter_ne_empty_iff | [
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.rat_smul_eq_C_mul | [
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] | [
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69
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Mathlib/Analysis/InnerProductSpace/Projection.lean | orthogonalProjection_singleton | [
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Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.pos_div_neg | [
{
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291,
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Mathlib/Data/Polynomial/Mirror.lean | Polynomial.mirror_smul | [
{
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] | [
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Mathlib/Topology/Order/Basic.lean | Filter.tendsto_nhds_max_right | [
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Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.sigmaFinsuppLEquivPiFinsupp_apply | [] | [
988,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.sub | [
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Mathlib/Data/Rat/BigOperators.lean | Rat.cast_prod | [] | [
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31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.nat_cast_def | [] | [
1373,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1372,
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Mathlib/RingTheory/DedekindDomain/Ideal.lean | Ideal.strictAnti_pow | [] | [
736,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Covering/VitaliFamily.lean | VitaliFamily.FineSubfamilyOn.index_countable | [] | [
160,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
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Mathlib/Analysis/Calculus/FDeriv/Comp.lean | HasFDerivAt.comp | [] | [
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49
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113,
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Mathlib/Data/Set/Function.lean | Set.maps_image_to | [] | [
515,
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513,
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Mathlib/RingTheory/Ideal/QuotientOperations.lean | Ideal.Quotient.liftₐ_apply | [] | [
259,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
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Mathlib/Logic/Basic.lean | dec_em' | [] | [
192,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
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Mathlib/Topology/Order/Basic.lean | Monotone.map_iInf_of_continuousAt' | [] | [
2695,
77
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Mathlib/RingTheory/PowerBasis.lean | PowerBasis.equivOfRoot_map | [
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Mathlib/MeasureTheory/Integral/CircleIntegral.lean | deriv_circleMap_eq_zero_iff | [
{
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] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Image.lean | Set.mem_image_elim_on | [] | [
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Mathlib/Topology/Separation.lean | minimal_nonempty_open_eq_singleton | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/UnionFind.lean | UFModel.Models.empty | [] | [
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.balanceL | [
{
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Mathlib/Topology/Inseparable.lean | inseparable_of_nhdsWithin_eq | [] | [
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Mathlib/Data/Sym/Sym2.lean | Sym2.mem_map | [
{
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Mathlib/Algebra/BigOperators/Order.lean | Finset.one_le_prod' | [
{
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Mathlib/Analysis/Normed/Group/Basic.lean | MulOpposite.norm_op | [] | [
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2609,
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src/lean/Init/Classical.lean | Classical.exists_true_of_nonempty | [] | [
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Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.coe_neg | [] | [
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36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/FieldTheory/RatFunc.lean | RatFunc.intDegree_one | [
{
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] | [
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47
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Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.verts_iSup | [
{
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] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_indicator_const_comp | [
{
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1301,
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Mathlib/Data/Nat/Order/Lemmas.lean | Nat.mod_div_self | [
{
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},
{
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229,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | ContDiffOn.ccosh | [] | [
497,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
495,
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Mathlib/CategoryTheory/Limits/Opposites.lean | CategoryTheory.Limits.hasCoproductsOfShape_of_opposite | [] | [
345,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
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Std/Data/Nat/Gcd.lean | Nat.lcm_zero_right | [
{
"state_after": "no goals",
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}
] | [
187,
72
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
187,
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Mathlib/Algebra/Module/Submodule/Lattice.lean | AddSubmonoid.toNatSubmodule_symm | [] | [
358,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
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Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.add_def | [] | [
117,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
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Mathlib/RingTheory/Localization/FractionRing.lean | IsFractionRing.lift_algebraMap | [] | [
213,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
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Mathlib/Geometry/Euclidean/Sphere/Basic.lean | EuclideanGeometry.cospherical_pair | [
{
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205,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
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Mathlib/GroupTheory/Congruence.lean | Con.inv | [
{
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"tactic": "simpa using c.symm (c.mul (c.mul (c.refl x⁻¹) h) (c.refl y⁻¹))"
}
] | [
1225,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/FieldTheory/Subfield.lean | Subfield.zsmul_mem | [] | [
325,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
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Mathlib/LinearAlgebra/Matrix/Charpoly/Eigs.lean | Matrix.trace_eq_sum_roots_charpoly | [] | [
90,
72
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Mathlib/Data/Vector/Basic.lean | Vector.get_tail_succ | [
{
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171,
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170,
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Mathlib/Data/List/Perm.lean | List.nil_subperm | [
{
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26
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403,
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Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.includeLeft_comp_algebraMap | [
{
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Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.sum_ite_self_eq' | [
{
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151,
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Mathlib/NumberTheory/Liouville/Measure.lean | ae_not_liouvilleWith | [
{
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116,
38
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Mathlib/Topology/Algebra/Module/Basic.lean | Submodule.ker_subtypeL | [] | [
1059,
26
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Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.support_map | [
{
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Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.restrict_le_restrict_iUnion | [
{
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Mathlib/Topology/Constructions.lean | frontier_univ_prod_eq | [
{
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775,
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Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | limsInf_nhds | [] | [
173,
26
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Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biproduct.lift_π | [] | [
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Mathlib/Algebra/Algebra/Operations.lean | Submodule.prod_span_singleton | [
{
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44
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Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSpace.generateFrom_induction | [
{
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Mathlib/RepresentationTheory/Basic.lean | Representation.dual_apply | [] | [
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Mathlib/Algebra/Order/Floor.lean | Nat.ceil_pos | [
{
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Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingHom.comp_apply | [] | [
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Mathlib/Order/Filter/Ultrafilter.lean | Filter.forall_neBot_le_iff | [
{
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Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.self_trans_symm | [
{
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_mono_ae | [
{
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Mathlib/Analysis/Calculus/ContDiff.lean | ContDiff.iterate_deriv' | [] | [
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Mathlib/Topology/Bornology/Constructions.lean | Bornology.isBounded_prod_of_nonempty | [] | [
84,
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Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.IndepFun.comp | [
{
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Mathlib/Topology/UniformSpace/Basic.lean | Uniform.tendsto_nhds_right | [
{
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Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.epi_of_target_iso_zero | [
{
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408,
86
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407,
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Mathlib/CategoryTheory/Limits/Shapes/Diagonal.lean | CategoryTheory.Limits.pullback.diagonal_fst | [] | [
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26
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Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesOnBall.neg | [
{
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Mathlib/Order/Hom/Lattice.lean | SupHom.symm_dual_id | [] | [
1389,
6
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1388,
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Mathlib/Data/List/Basic.lean | List.get_drop | [
{
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2203,
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Mathlib/Topology/Algebra/ContinuousAffineMap.lean | ContinuousLinearMap.toContinuousAffineMap_map_zero | [
{
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... | [
287,
98
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287,
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Mathlib/Data/Pi/Algebra.lean | Pi.comp_one | [] | [
75,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.ofReal_bit0 | [] | [
215,
17
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214,
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Mathlib/Data/Vector/Basic.lean | Vector.singleton_tail | [] | [
188,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
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Mathlib/Data/List/Chain.lean | List.chain'_iff_get | [
{
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},
{
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361,
61
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351,
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Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsLimit.OfNatIso.coneOfHom_homOfCone | [
{
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493,
91
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488,
1
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Mathlib/Data/Sum/Basic.lean | Sum.inr_ne_inl | [] | [
168,
7
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167,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_add_pi | [] | [
316,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
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Mathlib/Data/Int/Bitwise.lean | Int.bit0_ne_bit1 | [
{
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"tactic": "simp"
}
] | [
184,
33
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183,
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Mathlib/Data/Real/Irrational.lean | Irrational.nat_mul | [] | [
386,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
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Mathlib/Order/Interval.lean | NonemptyInterval.coe_ssubset_coe | [] | [
259,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
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Mathlib/Algebra/GroupPower/Lemmas.lean | Commute.cast_nat_mul_left | [] | [
1094,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1093,
1
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioo_eq_empty_iff | [
{
"state_after": "no goals",
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"tactic": "rw [← not_nonempty_iff_eq_empty, not_iff_not, nonempty_Ioo]"
}
] | [
695,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
694,
1
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Mathlib/LinearAlgebra/Projection.lean | LinearMap.equivProdOfSurjectiveOfIsCompl_apply | [] | [
339,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
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Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_add_right_eq_add | [
{
"state_after": "no goals",
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"tactic": "simp_rw [toIcoMod, toIcoDiv_sub_eq_toIcoDiv_add', sub_add_eq_add_sub]"
... | [
541,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
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Std/Data/List/Init/Lemmas.lean | List.bind_id | [
{
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93
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109,
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Mathlib/Data/Fin/Basic.lean | Fin.exists_succAbove_eq | [
{
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62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2155,
1
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Mathlib/Data/List/TFAE.lean | List.tfae_cons_cons | [] | [
52,
32
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51,
1
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Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.natTrailingDegree_X_le | [] | [
297,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
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Mathlib/Algebra/Homology/Augment.lean | ChainComplex.augment_d_succ_succ | [
{
"state_after": "no goals",
"state_before": "V : Type u\ninst✝¹ : Category V\ninst✝ : HasZeroMorphisms V\nC : ChainComplex V ℕ\nX : V\nf : HomologicalComplex.X C 0 ⟶ X\nw : d C 1 0 ≫ f = 0\ni j : ℕ\n⊢ d (augment C f w) (i + 1) (j + 1) = d C i j",
"tactic": "cases i <;> rfl"
}
] | [
96,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.pow_dvd_iff_le_multiplicity | [] | [
151,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.enum_cons | [
{
"state_after": "case h.zero\nα : Type u\nβ : Type v\nγ : Type w\ns : Seq α\nx : α\n⊢ get? (enum (cons x s)) Nat.zero = get? (cons (0, x) (map (Prod.map Nat.succ id) (enum s))) Nat.zero\n\ncase h.succ\nα : Type u\nβ : Type v\nγ : Type w\ns : Seq α\nx : α\nn✝ : ℕ\n⊢ get? (enum (cons x s)) (Nat.succ n✝) = get? (... | [
899,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
894,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Filter.lean | BoxIntegral.IntegrationParams.toFilteriUnion_congr | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\ninst✝ : Fintype ι\nI✝ J : Box ι\nc c₁ c₂ : ℝ≥0\nr r₁ r₂ : (ι → ℝ) → ↑(Set.Ioi 0)\nπ π₁✝ π₂✝ : TaggedPrepartition I✝\nl✝ l₁ l₂ : IntegrationParams\nI : Box ι\nl : IntegrationParams\nπ₁ π₂ : Prepartition I\nh : Prepartition.iUnion π₁ = Prepartition.i... | [
467,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/Data/Set/Intervals/OrdConnectedComponent.lean | Set.ordConnectedProj_mem_ordConnectedComponent | [] | [
114,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.coe_powers | [] | [
437,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
] |
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