file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.ext | [] | [
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Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.innerContent_iSup_nat | [
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Mathlib/Data/List/Zip.lean | List.mem_zip | [
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Mathlib/Data/Matrix/Basic.lean | Matrix.row_mulVec | [
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Mathlib/RingTheory/Localization/Basic.lean | Localization.algEquiv_mk' | [] | [
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.comap_isPrime | [
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Mathlib/Analysis/Convex/Basic.lean | convex_iff_pairwise_pos | [
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Mathlib/Topology/Connected.lean | IsConnected.iUnion_of_chain | [
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Mathlib/FieldTheory/RatFunc.lean | RatFunc.map_apply_ofFractionRing_mk | [
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Mathlib/Data/Finset/Basic.lean | Finset.mk_cons | [] | [
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Mathlib/Algebra/Order/Pi.lean | Function.one_lt_const | [] | [
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Mathlib/Data/List/BigOperators/Lemmas.lean | unop_map_list_prod | [
{
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Mathlib/Algebra/Order/ToIntervalMod.lean | Ico_eq_locus_Ioc_eq_iUnion_Ioo | [
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Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoDiv_add_zsmul' | [
{
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"state_before": "Ξ± : Type u_1\ninstβ : LinearOrderedAddCommGroup Ξ±\nhΞ± : Archimedean Ξ±\np : ... | [
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Mathlib/MeasureTheory/Measure/GiryMonad.lean | MeasureTheory.Measure.measurable_lintegral | [
{
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Mathlib/Computability/TuringMachine.lean | Turing.TM2to1.tr_respects_auxβ | [
{
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Mathlib/Analysis/Calculus/ContDiff.lean | contDiff_const_smul | [] | [
1540,
44
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1539,
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Mathlib/LinearAlgebra/Prod.lean | LinearMap.prodMap_comap_prod | [] | [
325,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
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Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | ContDiffOn.exp | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Algebra/Operations.lean | Submodule.bot_mul | [] | [
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Mathlib/Order/LiminfLimsup.lean | Filter.not_isBoundedUnder_of_tendsto_atBot | [] | [
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53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
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Std/Data/Int/Lemmas.lean | Int.zero_sub | [
{
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"tactic": "simp [Int.sub_eq_add_neg]"
}
] | [
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Mathlib/Algebra/Divisibility/Units.lean | IsUnit.dvd | [
{
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},
{
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Mathlib/Analysis/Convex/Function.lean | ConvexOn.add_strictConvexOn | [] | [
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36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/StructuredArrow.lean | CategoryTheory.StructuredArrow.ext_iff | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Basic.lean | Set.union_univ | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/SuccPred/Basic.lean | WithTop.pred_untop | [
{
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"tactic": "induction a using WithTop.recTopCoe <;> simp"
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.Integrable.tendsto_integralSum_toFilteriUnion_single | [] | [
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27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
544,
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Mathlib/Algebra/Algebra/Hom.lean | AlgHom.map_mul | [] | [
254,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_cubic_le | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1233,
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Mathlib/Topology/Algebra/Order/Floor.lean | tendsto_ceil_right_pure_add_one | [
{
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"tactic": "simpa only [floor_intCast] u... | [
112,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Logic/Equiv/List.lean | Denumerable.lower_raise' | [
{
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"tactic": "simp [raise', lower', add_tsub_cancel_right, lower_raise']"
}
] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/NumberTheory/LegendreSymbol/ZModChar.lean | ZMod.Οβ'_eq_Οβ_mul_Οβ | [
{
"state_after": "case head\n\nβ’ βΟβ' { val := 0, isLt := (_ : 0 < 7 + 1) } =\n βΟβ β{ val := 0, isLt := (_ : 0 < 7 + 1) } * βΟβ { val := 0, isLt := (_ : 0 < 7 + 1) }\n\ncase tail.head\n\nβ’ βΟβ' { val := 1, isLt := (_ : (fun a => a < 7 + 1) 1) } =\n βΟβ β{ val := 1, isLt := (_ : (fun a => a < 7 + 1) 1) } ... | [
216,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.isBigO_sub | [] | [
686,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
684,
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Mathlib/Combinatorics/DoubleCounting.lean | Finset.card_mul_le_card_mul | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Ici_prod_Ici | [] | [
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6
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Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biprod.braiding'_eq_braiding | [
{
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"tactic": "aesop_cat"
}
] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Bounds/Basic.lean | IsLUB.of_image | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/FieldTheory/SeparableDegree.lean | Polynomial.HasSeparableContraction.dvd_degree' | [] | [
84,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Convex/Function.lean | ConvexOn.lt_right_of_left_lt | [
{
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Mathlib/FieldTheory/Adjoin.lean | IntermediateField.restrictScalars_bot_eq_self | [
{
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Mathlib/Analysis/Calculus/Deriv/Slope.lean | hasDerivAt_iff_tendsto_slope | [] | [
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.sign_toReal | [
{
"state_after": "case inl\nΞΈ : Angle\nh : ΞΈ β βΟ\nht : toReal ΞΈ < 0\nβ’ βSignType.sign (toReal ΞΈ) = sign ΞΈ\n\ncase inr.inl\nΞΈ : Angle\nh : ΞΈ β βΟ\nht : toReal ΞΈ = 0\nβ’ βSignType.sign (toReal ΞΈ) = sign ΞΈ\n\ncase inr.inr\nΞΈ : Angle\nh : ΞΈ β βΟ\nht : 0 < toReal ΞΈ\nβ’ βSignType.sign (toReal ΞΈ) = sign ΞΈ",
"state_... | [
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Mathlib/MeasureTheory/MeasurableSpace.lean | Measurable.snd | [] | [
660,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
659,
1
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.inter_vsub_subset | [] | [
693,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
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Mathlib/Data/List/Chain.lean | List.chain'_map_of_chain' | [] | [
239,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
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Mathlib/Algebra/Periodic.lean | Function.Periodic.zsmul | [
{
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Mathlib/Data/Polynomial/Splits.lean | Polynomial.roots_ne_zero_of_splits' | [
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193,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.prod_rightl | [] | [
953,
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951,
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Mathlib/Order/Hom/Basic.lean | OrderHom.symm_dual_comp | [] | [
595,
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593,
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Mathlib/GroupTheory/Subsemigroup/Operations.lean | MulHom.mem_srange | [] | [
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Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_neg_Icc | [
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Mathlib/Topology/DenseEmbedding.lean | DenseInducing.mk' | [
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Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | BilinForm.toQuadraticForm_sum | [] | [
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Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.vars_C_mul | [
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Mathlib/Order/OrdContinuous.lean | LeftOrdContinuous.id | [
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Mathlib/Data/Fin/Basic.lean | Fin.mk_one | [] | [
643,
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Mathlib/GroupTheory/Submonoid/Inverses.lean | Submonoid.leftInv_leftInv_le | [
{
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Mathlib/Algebra/DirectLimit.lean | Module.DirectLimit.of.zero_exact | [
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Mathlib/Topology/Algebra/UniformGroup.lean | uniformContinuous_div | [] | [
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Mathlib/RingTheory/IsTensorProduct.lean | IsBaseChange.alg_hom_ext | [
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Mathlib/Order/Filter/Basic.lean | Filter.disjoint_comap_iff | [
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Mathlib/FieldTheory/Adjoin.lean | IntermediateField.subsingleton_of_finrank_adjoin_eq_one | [] | [
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_iff_isBigOWith | [
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Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.coequalizer.Ο_colimMap_desc | [
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Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | AlgHom.coe_codRestrict | [] | [
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Mathlib/RingTheory/HahnSeries.lean | HahnSeries.embDomain_injective | [
{
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Std/Logic.lean | or_iff_right_iff_imp | [
{
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Mathlib/Data/Multiset/Basic.lean | Multiset.erase_add_left_neg | [
{
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Mathlib/Topology/Algebra/ContinuousAffineMap.lean | ContinuousAffineMap.toContinuousMap_coe | [] | [
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76
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Mathlib/Data/Finset/Basic.lean | Finset.attach_nonempty_iff | [
{
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2421,
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Std/Data/Rat/Lemmas.lean | Rat.inv_divInt | [
{
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Mathlib/FieldTheory/Separable.lean | Polynomial.separable_map | [
{
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Mathlib/Topology/Algebra/StarSubalgebra.lean | StarSubalgebra.embedding_inclusion | [] | [
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Mathlib/Order/Heyting/Basic.lean | hnot_hnot_sdiff_distrib | [
{
"state_after": "case refine'_1\nΞΉ : Type ?u.179703\nΞ± : Type u_1\nΞ² : Type ?u.179709\ninstβ : CoheytingAlgebra Ξ±\naβ bβ c a b : Ξ±\nβ’ οΏ’οΏ’(a \\ b) β€ οΏ’οΏ’a \\ οΏ’οΏ’b\n\ncase refine'_2\nΞΉ : Type ?u.179703\nΞ± : Type u_1\nΞ² : Type ?u.179709\ninstβ : CoheytingAlgebra Ξ±\naβ bβ c a b : Ξ±\nβ’ οΏ’οΏ’a \\ οΏ’οΏ’b β€ οΏ’οΏ’(a \\ b)",
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Mathlib/Analysis/Calculus/LHopital.lean | HasDerivAt.lhopital_zero_nhds' | [
{
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Mathlib/Topology/MetricSpace/Basic.lean | dist_eq_zero | [] | [
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Mathlib/Topology/Instances/ENNReal.lean | EMetric.cauchySeq_iff_le_tendsto_0 | [
{
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Std/Data/List/Lemmas.lean | List.forall_mem_append | [
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Mathlib/LinearAlgebra/Basic.lean | Submodule.map_id | [
{
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Mathlib/Dynamics/Ergodic/Ergodic.lean | MeasureTheory.MeasurePreserving.ergodic_conjugate_iff | [
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Mathlib/Analysis/SpecificLimits/Normed.lean | summable_pow_mul_geometric_of_norm_lt_1 | [] | [
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340,
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Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.oreDiv_mul_oreDiv_comm | [
{
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{
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446,
75
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Mathlib/CategoryTheory/Limits/Over.lean | CategoryTheory.Over.epi_iff_epi_left | [] | [
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39
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Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.eventually_mul_left_iff | [
{
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322,
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Mathlib/Analysis/Convex/Basic.lean | convex_iff_openSegment_subset | [] | [
148,
59
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146,
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.support_neg | [] | [
1300,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1295,
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.sumElim_inr | [] | [
1329,
6
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1327,
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Mathlib/Analysis/InnerProductSpace/Adjoint.lean | ContinuousLinearMap.isSelfAdjoint_iff' | [] | [
226,
10
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225,
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Mathlib/LinearAlgebra/Pi.lean | LinearMap.coe_proj | [] | [
92,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Algebra/Group/Opposite.lean | MulOpposite.opAddEquiv_toEquiv | [] | [
280,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.succ_ne_succ | [] | [
180,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Data/Set/Basic.lean | Set.nmem_setOf_iff | [] | [
272,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Topology/Order/Basic.lean | IsLUB.mem_upperBounds_of_tendsto | [
{
"state_after": "case intro.intro\nΞ± : Type u\nΞ² : Type v\nΞ³ : Type w\ninstββΈ : TopologicalSpace Ξ±\ninstββ· : TopologicalSpace Ξ²\ninstββΆ : LinearOrder Ξ±\ninstββ΅ : LinearOrder Ξ²\ninstββ΄ : OrderTopology Ξ±\ninstβΒ³ : OrderTopology Ξ²\ninstβΒ² : Preorder Ξ³\ninstβΒΉ : TopologicalSpace Ξ³\ninstβ : OrderClosedTopology Ξ³\nf... | [
2034,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2027,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | sSupHom.dual_comp | [] | [
807,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
805,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.continuousWithinAt_iff_continuousWithinAt_comp_left | [
{
"state_after": "Ξ± : Type u_2\nΞ² : Type u_3\nΞ³ : Type u_1\nΞ΄ : Type ?u.100825\ninstβΒ³ : TopologicalSpace Ξ±\ninstβΒ² : TopologicalSpace Ξ²\ninstβΒΉ : TopologicalSpace Ξ³\ninstβ : TopologicalSpace Ξ΄\ne : LocalHomeomorph Ξ± Ξ²\ne' : LocalHomeomorph Ξ² Ξ³\nf : Ξ³ β Ξ±\ns : Set Ξ³\nx : Ξ³\nhx : f x β e.source\nh : f β»ΒΉ' e.sour... | [
1177,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1168,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | zero_pow_le_one | [
{
"state_after": "Ξ² : Type ?u.202613\nA : Type ?u.202616\nG : Type ?u.202619\nM : Type ?u.202622\nR : Type u_1\ninstβ : OrderedSemiring R\na x y : R\nnβ m n : β\nβ’ 0 β€ 1",
"state_before": "Ξ² : Type ?u.202613\nA : Type ?u.202616\nG : Type ?u.202619\nM : Type ?u.202622\nR : Type u_1\ninstβ : OrderedSemiring R... | [
400,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.piecewise_le_piecewise | [] | [
2574,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2572,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.surjOn_cos | [
{
"state_after": "no goals",
"state_before": "β’ SurjOn cos (Icc 0 Ο) (Icc (-1) 1)",
"tactic": "simpa only [cos_zero, cos_pi] using intermediate_value_Icc' pi_pos.le continuous_cos.continuousOn"
}
] | [
624,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
] |
Mathlib/Order/Circular.lean | btw_cyclic | [] | [
183,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
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