file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/Topology/Homeomorph.lean | Homeomorph.normalSpace | [] | [
340,
37
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339,
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Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.comp_eq_mk | [
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225,
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Std/Data/String/Lemmas.lean | String.singleton_eq | [] | [
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61
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483,
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Mathlib/LinearAlgebra/Dimension.lean | rank_le_of_submodule | [] | [
187,
59
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184,
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Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.type_eq_one_of_unique | [] | [
251,
54
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250,
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Mathlib/NumberTheory/Padics/PadicNumbers.lean | Padic.AddValuation.map_one | [
{
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1117,
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Mathlib/Data/Sum/Order.lean | Sum.inl_lt_inl_iff | [] | [
143,
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142,
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Mathlib/GroupTheory/Subsemigroup/Operations.lean | MulMemClass.coe_subtype | [] | [
578,
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Mathlib/Algebra/ModEq.lean | AddCommGroup.ModEq.of_nsmul | [
{
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"tactic": "rwa [mul_smul, coe_nat_zsmul]"
}
] | [
156,
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Mathlib/Algebra/Module/LinearMap.lean | DistribMulActionHom.toLinearMap_injective | [
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | ciInf_le | [] | [
818,
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurable_infDist | [] | [
1534,
39
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1533,
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Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.one_mul | [
{
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"state_before": "R : Type u_1\ninst✝¹ : Monoid R\nS : Submonoid R\ninst✝ : OreSet S\nx : OreLocalization R S\n⊢ 1 * x = x",
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Mathlib/Probability/ProbabilityMassFunction/Basic.lean | Pmf.toMeasure_toPmf | [
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388,
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Mathlib/GroupTheory/Subsemigroup/Operations.lean | MulHom.srange_eq_map | [] | [
772,
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Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_zero_of_column_eq | [
{
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Mathlib/Topology/UnitInterval.lean | iccHomeoI_apply_coe | [] | [
236,
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234,
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Mathlib/Data/Matrix/Block.lean | Matrix.fromBlocks_apply₂₂ | [] | [
74,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
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Mathlib/LinearAlgebra/Matrix/ZPow.lean | Matrix.zpow_add_of_nonpos | [
{
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183,
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Mathlib/LinearAlgebra/Finrank.lean | finrank_le_one | [
{
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37
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508,
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Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_ofReal_of_nonneg | [
{
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] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
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Mathlib/Algebra/Order/AbsoluteValue.lean | AbsoluteValue.map_sub_eq_zero_iff | [] | [
161,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
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Mathlib/GroupTheory/GroupAction/FixingSubgroup.lean | fixingSubgroup_antitone | [] | [
136,
49
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Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.exists_of_compat | [
{
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393,
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Mathlib/Topology/Order/Basic.lean | interior_Ici' | [
{
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"tactic": "rw [← compl_Iio, inter... | [
2273,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Finset/Image.lean | Finset.map_erase | [
{
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Mathlib/LinearAlgebra/Basic.lean | Submodule.comap_iInf | [] | [
866,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
864,
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Mathlib/Data/Pi/Algebra.lean | Pi.pow_comp | [] | [
142,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
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Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.roots_of_cyclotomic | [
{
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Mathlib/Data/Int/Order/Basic.lean | Int.pred_self_lt | [] | [
108,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/List/Rdrop.lean | List.rdropWhile_idempotent | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
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Mathlib/GroupTheory/Submonoid/Pointwise.lean | Submonoid.mem_smul_pointwise_iff_exists | [] | [
249,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
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Mathlib/Algebra/Order/Field/Power.lean | Even.zpow_pos_iff | [
{
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"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\na b c d : α\nn : ℤ\nhn : Even n\nh : n ≠ 0\n⊢ 0 < a ^ n ↔ a ≠ 0",
"tactic": "obtain ⟨k, rfl⟩ := hn"
},
... | [
186,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.fromEdgeSet_mono | [
{
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671,
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Mathlib/Init/Algebra/Order.lean | compare_gt_iff_gt | [
{
"state_after": "α : Type u\ninst✝ : LinearOrder α\na b : α\n⊢ (if a < b then Ordering.lt else if a = b then Ordering.eq else Ordering.gt) = Ordering.gt ↔ a > b",
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433,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/NumberTheory/Divisors.lean | Nat.prod_divisorsAntidiagonal | [
{
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469,
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Mathlib/Analysis/MeanInequalities.lean | Real.geom_mean_le_arith_mean3_weighted | [] | [
231,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
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Mathlib/Order/Cover.lean | Set.covby_insert | [] | [
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55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Real/Pi/Bounds.lean | Real.pi_upper_bound_start | [
{
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Std/Data/Option/Lemmas.lean | Option.mem_map_of_mem | [] | [
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Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.mem_boundedContinuousFunction_iff | [] | [
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32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Function/LpSpace.lean | BoundedContinuousFunction.toLp_inj | [
{
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Mathlib/Topology/Constructions.lean | Continuous.subtype_mk | [] | [
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Mathlib/Algebra/Hom/GroupAction.lean | DistribMulActionHom.comp_id | [
{
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Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.LHom.realize_onFormula | [] | [
704,
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702,
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Mathlib/RingTheory/HahnSeries.lean | HahnSeries.SummableFamily.smul_apply | [] | [
1595,
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1594,
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Mathlib/Order/CompleteLattice.lean | sInf_lt_iff | [] | [
594,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
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Mathlib/Algebra/Group/Prod.lean | MonoidHom.snd_comp_inr | [] | [
536,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
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Mathlib/Order/Chain.lean | isChain_of_trichotomous | [] | [
90,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/Basic.lean | LinearMap.smulRightₗ_apply | [] | [
558,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
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Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.angle_eq_zero_iff_eq_and_ne_or_sbtw | [
{
"state_after": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np₁ p₂ p₃ : P\n⊢ p₁ ≠ p₂ ∧ Wbtw ℝ p₂ p₁ p₃ ∨ p₃ ≠ p₂ ∧ Wbtw ℝ p₂ p₃ p₁ ↔ p₁ = p₃ ∧ p₁ ≠ p₂ ∨ Sbtw ℝ p₂ p₁ p₃ ∨ Sbtw ℝ p₂ p₃ p₁",
"state_before": "V... | [
413,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.dfinsupp_sum_apply | [] | [
1158,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1156,
1
] |
Mathlib/Analysis/Normed/Group/Quotient.lean | quotient_norm_mk_le | [] | [
155,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Algebra/Group/Prod.lean | Prod.swap_one | [] | [
122,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
src/lean/Init/Core.lean | dif_pos | [] | [
810,
33
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
807,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Iso.connectedComponentEquiv_symm | [
{
"state_after": "case H.mk\nV : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nφ : G ≃g G'\nx✝ : ConnectedComponent G'\na✝ : V'\n⊢ ↑(connectedComponentEquiv (symm φ)) (Quot.mk (Reachable G') a✝) =\n ↑(connectedComponentEquiv φ).symm (Quot.mk (Reachable G') ... | [
2117,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2114,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.sin_neg | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ sin (-x) = -sin x",
"tactic": "simp [sin, sub_eq_add_neg, exp_neg, (neg_div _ _).symm, add_mul]"
}
] | [
801,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
800,
1
] |
Mathlib/Order/Cover.lean | Covby.Ico_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.36866\ninst✝ : PartialOrder α\na b c : α\nh : a ⋖ b\n⊢ Ico a b = {a}",
"tactic": "rw [← Ioo_union_left h.lt, h.Ioo_eq, empty_union]"
}
] | [
405,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.IsBasis.mem_filterBasis_iff | [] | [
157,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Order/Filter/NAry.lean | Filter.map_map₂_right_comm | [] | [
353,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/MeasureTheory/Decomposition/Jordan.lean | MeasureTheory.SignedMeasure.subset_positive_null_set | [
{
"state_after": "α : Type u_1\nβ : Type ?u.41858\ninst✝² : MeasurableSpace α\ns : SignedMeasure α\nμ ν : Measure α\ninst✝¹ : IsFiniteMeasure μ\ninst✝ : IsFiniteMeasure ν\nu v w : Set α\nhu : MeasurableSet u\nhv : MeasurableSet v\nhw : MeasurableSet w\nhsu : VectorMeasure.restrict 0 u ≤ VectorMeasure.restrict s... | [
293,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.range_comp_le_range | [] | [
1236,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1234,
1
] |
Mathlib/CategoryTheory/Functor/EpiMono.lean | CategoryTheory.Functor.preservesMonomorphisms.of_iso | [
{
"state_after": "C : Type u₁\ninst✝³ : Category C\nD : Type u₂\ninst✝² : Category D\nE : Type u₃\ninst✝¹ : Category E\nF G : C ⥤ D\ninst✝ : PreservesMonomorphisms F\nα : F ≅ G\nX Y : C\nf : X ⟶ Y\nh : Mono f\nthis : Mono (F.map f ≫ (α.app Y).hom)\n⊢ Mono (G.map f)",
"state_before": "C : Type u₁\ninst✝³ : C... | [
129,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.map_iSup | [] | [
1015,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1013,
1
] |
Mathlib/LinearAlgebra/ProjectiveSpace/Basic.lean | Projectivization.map_id | [
{
"state_after": "case h.mk\nK : Type u_2\nV : Type u_1\ninst✝⁵ : DivisionRing K\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module K V\nL : Type ?u.156698\nW : Type ?u.156701\ninst✝² : DivisionRing L\ninst✝¹ : AddCommGroup W\ninst✝ : Module L W\nx✝ : ℙ K V\nv : { v // v ≠ 0 }\n⊢ map LinearMap.id (_ : Function.Injective... | [
223,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Analysis/MeanInequalities.lean | Real.rpow_sum_le_const_mul_sum_rpow_of_nonneg | [
{
"state_after": "no goals",
"state_before": "ι : Type u\ns : Finset ι\nf g : ι → ℝ\np q : ℝ\nhp : 1 ≤ p\nhf : ∀ (i : ι), i ∈ s → 0 ≤ f i\n⊢ (∑ i in s, f i) ^ p ≤ ↑(card s) ^ (p - 1) * ∑ i in s, f i ^ p",
"tactic": "convert rpow_sum_le_const_mul_sum_rpow s f hp using 2 <;> apply sum_congr rfl <;> intro ... | [
655,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
652,
1
] |
Mathlib/RingTheory/Filtration.lean | Ideal.iInf_pow_eq_bot_of_isDomain | [
{
"state_after": "R M : Type u\ninst✝⁴ : CommRing R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\nI : Ideal R\nF F' : Filtration I M\ninst✝¹ : IsNoetherianRing R\ninst✝ : IsDomain R\nh : I ≠ ⊤\n⊢ (⨅ (i : ℕ), I ^ i) ≤ ⊥",
"state_before": "R M : Type u\ninst✝⁴ : CommRing R\ninst✝³ : AddCommGroup M\ninst✝² : ... | [
490,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisConnection.lowerBounds_u_image | [] | [
122,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.mem_nsmul | [
{
"state_after": "α : Type u_1\nβ : Type ?u.47121\nγ : Type ?u.47124\na : α\ns : Multiset α\nn : ℕ\nh0 : n ≠ 0\nh : a ∈ s\n⊢ a ∈ n • s",
"state_before": "α : Type u_1\nβ : Type ?u.47121\nγ : Type ?u.47124\na : α\ns : Multiset α\nn : ℕ\nh0 : n ≠ 0\n⊢ a ∈ n • s ↔ a ∈ s",
"tactic": "refine' ⟨mem_of_mem_nsm... | [
700,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | fderivWithin_const_sub | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.574896\ninst✝³ : NormedAddCommGroup G\ninst✝² : Normed... | [
659,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.union_iInter | [] | [
557,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
1
] |
Mathlib/Data/Finset/Sigma.lean | Finset.disjiUnion_map_sigma_mk | [] | [
91,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Data/List/AList.lean | AList.mk_cons_eq_insert | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\nc : Sigma β\nl : List (Sigma β)\nh : NodupKeys (c :: l)\n⊢ { entries := c :: l, nodupKeys := h } = insert c.fst c.snd { entries := l, nodupKeys := (_ : NodupKeys l) }",
"tactic": "simpa [insert] using (keras... | [
350,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/RingTheory/Filtration.lean | Ideal.Filtration.submodule_eq_span_le_iff_stable_ge | [
{
"state_after": "R M : Type u\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nI : Ideal R\nF F' : Filtration I M\nh : Stable F\nn₀ : ℕ\n⊢ (∀ (i : ℕ),\n ↑(single R i) '' ↑(N F i) ⊆\n ↑(Submodule.span { x // x ∈ reesAlgebra I } (⋃ (i : ℕ) (_ : i ≤ n₀), ↑(single R i) '' ↑(N F i)))) ... | [
366,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/CategoryTheory/Adjunction/Limits.lean | CategoryTheory.Adjunction.hasLimit_comp_equivalence | [] | [
254,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Topology/Separation.lean | TopologicalSpace.subset_trans | [] | [
861,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
857,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | le_of_one_div_le_one_div | [] | [
462,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
] |
Mathlib/Data/Int/ConditionallyCompleteOrder.lean | Int.csSup_of_not_bdd_above | [
{
"state_after": "no goals",
"state_before": "s : Set ℤ\nh : ¬BddAbove s\n⊢ ¬(Set.Nonempty s ∧ BddAbove s)",
"tactic": "simp [h]"
}
] | [
79,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Dynamics/Ergodic/MeasurePreserving.lean | MeasureTheory.MeasurableEquiv.measurePreserving_symm | [] | [
176,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Data/Set/Intervals/Pi.lean | Set.piecewise_mem_Icc | [] | [
54,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Order/SymmDiff.lean | bihimp_left_involutive | [] | [
657,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
1
] |
Mathlib/Analysis/Convex/Segment.lean | segment_subset_uIcc | [
{
"state_after": "case inl\n𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.269436\nG : Type ?u.269439\nι : Type ?u.269442\nπ : ι → Type ?u.269447\ninst✝³ : OrderedSemiring 𝕜\ninst✝² : LinearOrderedAddCommMonoid E\ninst✝¹ : Module 𝕜 E\ninst✝ : OrderedSMul 𝕜 E\na b : 𝕜\nx y : E\nh : x ≤ y\n⊢ [x-[𝕜]y] ⊆ uIcc x y\n\... | [
468,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/Order/WithBot.lean | WithTop.not_top_le_coe | [] | [
853,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
852,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_lt_rpow_left_iff_of_base_lt_one | [
{
"state_after": "no goals",
"state_before": "x y z : ℝ\nhx0 : 0 < x\nhx1 : x < 1\n⊢ x ^ y < x ^ z ↔ z < y",
"tactic": "rw [lt_iff_not_le, rpow_le_rpow_left_iff_of_base_lt_one hx0 hx1, lt_iff_not_le]"
}
] | [
511,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.tendsto_map | [] | [
2936,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2935,
1
] |
Mathlib/Data/Set/Basic.lean | Set.empty_ssubset_singleton | [] | [
1309,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1308,
1
] |
Mathlib/Data/Set/Function.lean | Function.Semiconj.bijOn_image | [] | [
1655,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1652,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion₂_comm | [] | [
796,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
1
] |
Std/Data/RBMap/WF.lean | Std.RBNode.RedRed.setBlack | [] | [
151,
40
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
149,
11
] |
Mathlib/Order/Atoms.lean | IsAtom.le_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.2208\ninst✝¹ : PartialOrder α\ninst✝ : OrderBot α\na b x : α\nh : IsAtom a\n⊢ x ≤ a ↔ x = ⊥ ∨ x = a",
"tactic": "rw [le_iff_lt_or_eq, h.lt_iff]"
}
] | [
92,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.map_vsub | [] | [
625,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
624,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.nat_cast_imJ | [] | [
985,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
985,
1
] |
Mathlib/GroupTheory/Congruence.lean | Con.lift_funext | [
{
"state_after": "M : Type u_1\nN : Type ?u.62273\nP : Type u_2\ninst✝² : MulOneClass M\ninst✝¹ : MulOneClass N\ninst✝ : MulOneClass P\nc : Con M\nx y : M\nf✝ : M →* P\nf g : Con.Quotient c →* P\nh : ∀ (a : M), ↑f ↑a = ↑g ↑a\n⊢ lift c (MonoidHom.comp f (mk' c)) (_ : ∀ (x y : M), ↑c x y → ↑f ↑x = ↑f ↑y) =\n l... | [
967,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
964,
1
] |
Mathlib/Dynamics/Ergodic/MeasurePreserving.lean | MeasureTheory.MeasurePreserving.measure_preimage | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.271396\nδ : Type ?u.271399\ninst✝³ : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\ninst✝ : MeasurableSpace δ\nμa : Measure α\nμb : Measure β\nμc : Measure γ\nμd : Measure δ\nf : α → β\nhf : Mea... | [
125,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.exists_retraction_subtype_of_isClosed | [
{
"state_after": "case intro.intro.intro\nE : ℕ → Type u_1\ninst✝¹ : (n : ℕ) → TopologicalSpace (E n)\ninst✝ : ∀ (n : ℕ), DiscreteTopology (E n)\nf : ((n : ℕ) → E n) → (n : ℕ) → E n\nf_cont : Continuous f\nhs : IsClosed (range f)\nhne : Set.Nonempty (range f)\nfs : ∀ (x : (n : ℕ) → E n), x ∈ range f → f x = x\n... | [
715,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
708,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.map_subgraphOfAdj | [
{
"state_after": "case verts.h\nι : Sort ?u.219034\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' : SimpleGraph W\nf : G →g G'\nv w : V\nhvw : Adj G v w\nx✝ : W\n⊢ x✝ ∈ (Subgraph.map f (subgraphOfAdj G hvw)).verts ↔ x✝ ∈ (subgraphOfAdj G' (_ : Adj G' (↑f v) (↑f w))).verts\n\ncase Adj.h.h.a\nι : Sort ?u.219034\n... | [
933,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
914,
1
] |
Mathlib/Order/Filter/Archimedean.lean | atTop_hasCountableBasis_of_archimedean | [] | [
111,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | isIntegral_of_mem_closure | [] | [
473,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | dist_prod_prod_le_of_le | [
{
"state_after": "𝓕 : Type ?u.739254\n𝕜 : Type ?u.739257\nα : Type ?u.739260\nι : Type u_1\nκ : Type ?u.739266\nE : Type u_2\nF : Type ?u.739272\nG : Type ?u.739275\ninst✝¹ : SeminormedCommGroup E\ninst✝ : SeminormedCommGroup F\na✝ a₁ a₂ b b₁ b₂ : E\nr r₁ r₂ : ℝ\ns : Finset ι\nf a : ι → E\nd : ι → ℝ\nh : ∀ (b... | [
1501,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1497,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_product' | [] | [
676,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
1
] |
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