file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.lift_apply' | [] | [
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Mathlib/Data/Real/NNReal.lean | NNReal.coe_ne_zero | [] | [
225,
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225,
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Mathlib/GroupTheory/Subgroup/Finite.lean | Subgroup.eq_bot_of_card_le | [] | [
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Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.zero_def | [] | [
665,
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Mathlib/LinearAlgebra/ProjectiveSpace/Independence.lean | Projectivization.independent_pair_iff_neq | [
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Mathlib/Data/Nat/Factors.lean | Nat.pos_of_mem_factors | [] | [
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Mathlib/Data/Finset/Lattice.lean | Finset.inf'_const | [] | [
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Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.coe_neg | [] | [
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Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.ite_tmul | [
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.ordConnected_setOf_ball_subset | [] | [
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Mathlib/SetTheory/Ordinal/Topology.lean | Ordinal.nhds_eq_pure | [] | [
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Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.unitOfDetInvertible_eq_nonsingInvUnit | [
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Mathlib/Analysis/Convex/Between.lean | sbtw_iff_mem_image_Ioo_and_ne | [
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Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.mem_inverse_graph | [
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Mathlib/Order/Filter/Basic.lean | Filter.sup_join | [
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Mathlib/Computability/TuringMachine.lean | Turing.TM2to1.tr_eval_dom | [] | [
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Mathlib/Analysis/Convex/Gauge.lean | gauge_smul_left | [
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Mathlib/Algebra/Lie/Nilpotent.lean | LieSubmodule.lcs_add_le_iff | [
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Mathlib/RingTheory/PowerSeries/Basic.lean | Polynomial.coe_X | [] | [
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Mathlib/Analysis/SumIntegralComparisons.lean | AntitoneOn.sum_le_integral_Ico | [
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Mathlib/CategoryTheory/Preadditive/FunctorCategory.lean | CategoryTheory.NatTrans.app_neg | [] | [
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Mathlib/LinearAlgebra/Finrank.lean | FiniteDimensional.finrank_fin_fun | [
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.vsub_mem_direction | [] | [
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Mathlib/Algebra/Hom/Equiv/Units/Basic.lean | Equiv.coe_mulRight | [] | [
163,
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Mathlib/Order/Iterate.lean | Monotone.seq_pos_lt_seq_of_lt_of_le | [
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Mathlib/Algebra/Module/LinearMap.lean | LinearMap.isLinear | [] | [
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Mathlib/Analysis/Calculus/ContDiffDef.lean | hasFTaylorSeriesUpToOn_succ_iff_right | [
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasurableEmbedding.stronglyMeasurable_extend | [
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Mathlib/LinearAlgebra/AffineSpace/Ordered.lean | lineMap_mono_right | [
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Mathlib/Algebra/Group/Semiconj.lean | SemiconjBy.mul_left | [
{
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Mathlib/Data/Set/Intervals/OrdConnected.lean | Set.ordConnected_iff_uIcc_subset_right | [
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Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean | HasStrictFDerivAt.restrictScalars | [] | [
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Mathlib/LinearAlgebra/Span.lean | Submodule.span_span | [] | [
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.L1.integral_eq_setToL1 | [
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Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgHom.comp_id | [] | [
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Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.isOrtho_comm | [] | [
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Mathlib/Analysis/Convex/Combination.lean | Set.Finite.convexHull_eq | [
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Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_subtype_disjoint | [
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Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.coe_bot | [] | [
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Mathlib/Data/Finset/Lattice.lean | Finset.set_biInter_singleton | [] | [
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Mathlib/Topology/Maps.lean | IsOpenMap.preimage_closure_subset_closure_preimage | [
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Mathlib/Order/Lattice.lean | inf_le_ite | [] | [
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Mathlib/Algebra/Periodic.lean | Function.Periodic.image_uIcc | [
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Mathlib/Algebra/Ring/Defs.lean | sub_mul_add_eq_of_mul_add_eq_mul_add | [
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Mathlib/Order/Filter/Bases.lean | Filter.le_iff_forall_inf_principal_compl | [] | [
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Mathlib/Analysis/InnerProductSpace/GramSchmidtOrtho.lean | gramSchmidtOrthonormalBasis_inv_triangular' | [
{
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393,
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Mathlib/Topology/Algebra/Group/Basic.lean | IsOpen.leftCoset | [] | [
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Mathlib/Data/Polynomial/IntegralNormalization.lean | Polynomial.integralNormalization_aeval_eq_zero | [] | [
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Mathlib/Algebra/Lie/Submodule.lean | LieHom.le_ker_iff | [
{
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Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.integral_sub | [] | [
313,
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311,
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Mathlib/Combinatorics/SimpleGraph/Clique.lean | SimpleGraph.not_cliqueFree_of_top_embedding | [
{
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180,
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Mathlib/Order/Closure.lean | ClosureOperator.eq_mk₃_closed | [
{
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215,
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Mathlib/Data/Fintype/Basic.lean | Set.toFinset_diff | [
{
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711,
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709,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.OuterMeasure.toMeasure_zero | [
{
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4338,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Int/AbsoluteValue.lean | AbsoluteValue.map_units_int_cast | [
{
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] | [
38,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Algebra/ConstMulAction.lean | set_smul_mem_nhds_smul_iff | [
{
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561,
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557,
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Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.Completion.ofRat_neg | [] | [
153,
29
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152,
1
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Mathlib/Order/Filter/Basic.lean | Filter.sInf_neBot_of_directed' | [] | [
928,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
924,
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Mathlib/Algebra/Hom/GroupInstances.lean | MonoidHom.compl₂_apply | [] | [
261,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
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Mathlib/Topology/Algebra/UniformConvergence.lean | UniformFun.hasBasis_nhds_one_of_basis | [
{
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155,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
11
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Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.neg_le_one_iff | [
{
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}
] | [
221,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
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Mathlib/Data/Finmap.lean | Finmap.insert_insert_of_ne | [
{
"state_after": "no goals",
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"tactic": "simp only [insert_toFinmap, AList.toFinmap_eq, AList.insert_... | [
520,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
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Mathlib/Logic/Equiv/Defs.lean | Equiv.forall₂_congr' | [] | [
895,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
893,
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Mathlib/Algebra/BigOperators/Associated.lean | Finset.prod_primes_dvd | [
{
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"tactic": "classical\n ex... | [
103,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Summable.hasSum_iff | [] | [
487,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
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Mathlib/Topology/Instances/EReal.lean | EReal.nhds_top' | [] | [
142,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
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Mathlib/Data/Pi/Interval.lean | Pi.card_Ioi | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : ι → Type u_2\ninst✝⁴ : DecidableEq ι\ninst✝³ : Fintype ι\ninst✝² : (i : ι) → DecidableEq (α i)\ninst✝¹ : (i : ι) → PartialOrder (α i)\ninst✝ : (i : ι) → LocallyFiniteOrderTop (α i)\na : (i : ι) → α i\n⊢ Finset.card (Ioi a) = ∏ i : ι, Finset.car... | [
98,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
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Mathlib/Data/Finite/Card.lean | Finite.card_image_le | [] | [
176,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
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Mathlib/Algebra/CovariantAndContravariant.lean | Monotone.covariant_of_const' | [] | [
269,
73
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267,
1
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Mathlib/Topology/Algebra/Monoid.lean | Filter.Tendsto.pow | [] | [
599,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.AbsolutelyContinuous.mk | [
{
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2376,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2373,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.lean | Real.continuousOn_tan_Ioo | [
{
"state_after": "x : ℝ\n⊢ x ∈ Ioo (-(π / 2)) (π / 2) → x ∈ {x | cos x ≠ 0}",
"state_before": "⊢ ContinuousOn tan (Ioo (-(π / 2)) (π / 2))",
"tactic": "refine' ContinuousOn.mono continuousOn_tan fun x => _"
},
{
"state_after": "x : ℝ\n⊢ -(π / 2) < x → x < π / 2 → ¬cos x = 0",
"state_before":... | [
92,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/GroupTheory/Submonoid/Centralizer.lean | Submonoid.coe_centralizer | [] | [
45,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
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Mathlib/Order/Filter/Cofinite.lean | Filter.hasBasis_cofinite | [] | [
55,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
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Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.copy_eq | [] | [
143,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | SequentiallyComplete.setSeq_prod_subset | [
{
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672,
37
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668,
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Mathlib/CategoryTheory/Limits/ExactFunctor.lean | CategoryTheory.ExactFunctor.of_fst | [] | [
240,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
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Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSet.tProd | [
{
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969,
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Mathlib/MeasureTheory/Constructions/Polish.lean | MeasureTheory.exists_nat_measurableEquiv_range_coe_fin_of_finite | [
{
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72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
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Mathlib/Data/MvPolynomial/PDeriv.lean | MvPolynomial.pderiv_X_self | [
{
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"tactic": "classical simp"
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{
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"state_before": "R : Type u\nσ : Type v\na a' a₁ a₂ : R\ns : σ →₀ ℕ\ninst✝ : C... | [
101,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_toMeasurable_of_sigmaFinite | [
{
"state_after": "no goals",
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3729,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3725,
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Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.map_comap_le | [] | [
491,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
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Mathlib/Data/Sum/Order.lean | OrderIso.sumLexAssoc_symm_apply_inl | [] | [
677,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
676,
1
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycle.of_zpow | [
{
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578,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
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Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.le_inducedOuterMeasure | [] | [
1451,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1449,
1
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Mathlib/SetTheory/Ordinal/NaturalOps.lean | NatOrdinal.lt_wf | [] | [
94,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Topology/Separation.lean | regularSpace_TFAE | [
{
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1502,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1471,
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Mathlib/CategoryTheory/Monoidal/Rigid/Basic.lean | CategoryTheory.rightDualIso_id | [
{
"state_after": "case w\nC : Type u₁\ninst✝¹ : Category C\ninst✝ : MonoidalCategory C\nX Y : C\np : ExactPairing X Y\n⊢ (rightDualIso p p).hom = (Iso.refl Y).hom",
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657,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
1
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Mathlib/Computability/TuringMachine.lean | Turing.TM2to1.step_run | [
{
"state_after": "K : Type u_1\ninst✝² : DecidableEq K\nΓ : K → Type u_2\nΛ : Type u_3\ninst✝¹ : Inhabited Λ\nσ : Type u_4\ninst✝ : Inhabited σ\nk : K\nq : Stmt₂\nv : σ\nS : (k : K) → List (Γ k)\nf : σ → Option (Γ k) → σ\n⊢ TM2.stepAux (stRun (StAct.peek f) q) v S =\n TM2.stepAux q (stVar v (S k) (StAct.peek... | [
2513,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2509,
1
] |
Mathlib/Data/Fin/VecNotation.lean | Matrix.cons_fin_one | [] | [
217,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Comp.lean | HasStrictFDerivAt.iterate | [
{
"state_after": "case zero\n𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type ?u.151637\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.151732\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' ... | [
253,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
11
] |
Mathlib/Topology/Order/Basic.lean | pi_Ioo_mem_nhds' | [] | [
1527,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1526,
1
] |
Mathlib/Algebra/BigOperators/RingEquiv.lean | RingEquiv.map_list_sum | [] | [
30,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
29,
11
] |
Mathlib/Topology/Algebra/OpenSubgroup.lean | OpenSubgroup.toSubgroup_top | [] | [
156,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.span_insert | [] | [
186,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Topology/Algebra/Order/MonotoneContinuity.lean | continuousWithinAt_right_of_monotoneOn_of_image_mem_nhdsWithin | [] | [
103,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | Dense.eq_zero_of_inner_left | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.899657\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : InnerProductSpace ℝ F\nK : Submodule 𝕜 E\nx y : E\ninst✝ : CompleteSpace E\nhK : Dense ↑... | [
960,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
959,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.ListBlank.map_mk | [] | [
394,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.mem_Iic_of_Iio | [] | [
679,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
678,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | DifferentiableWithinAt.snd | [] | [
303,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
11
] |
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