file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSet.of_compl | [] | [
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26
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94,
11
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Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.IsNormal.apply_lt_nfp | [
{
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"tactic": "unfo... | [
475,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
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Mathlib/Data/Set/Image.lean | Set.preimage_inr_range_inl | [
{
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"tactic": "rw [← image_univ, preimage_inr_image_inl]"
}
] | [
936,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.nonempty_ball | [] | [
434,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
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Mathlib/Data/Set/Lattice.lean | Set.biInter_and' | [
{
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831,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Order/AbsoluteValue.lean | AbsoluteValue.map_one_of_isLeftRegular | [
{
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"tactic": "simp [← map_mul]"
}
] | [
140,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
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Mathlib/Computability/Language.lean | Language.map_map | [
{
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"tactic": "simp [map, image_image]"
}
] | [
176,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
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Mathlib/Analysis/Complex/Arg.lean | Complex.sameRay_iff_arg_div_eq_zero | [
{
"state_after": "x y : ℂ\n⊢ x = 0 ∨ y = 0 ∨ arg x = arg y ↔ ↑(arg (x / y)) = 0",
"state_before": "x y : ℂ\n⊢ SameRay ℝ x y ↔ arg (x / y) = 0",
"tactic": "rw [← Real.Angle.toReal_zero, ← arg_coe_angle_eq_iff_eq_toReal, sameRay_iff]"
},
{
"state_after": "case pos\nx y : ℂ\nhx : x = 0\n⊢ x = 0 ∨ y... | [
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48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
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Mathlib/LinearAlgebra/Dimension.lean | rank_fun | [
{
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1019,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1017,
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Mathlib/Data/Rat/Lemmas.lean | Rat.mul_den_eq_num | [
{
"state_after": "q : ℚ\n⊢ q.num /. ↑q.den * (↑q.den /. 1) = q.num /. 1",
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"tactic": "suffices (q.num /. ↑q.den) * (↑q.den /. 1) = q.num /. 1 by\n conv => pattern (occs := 1)q ; (rw [← @num_den q])\n simp only [coe_int_eq_divInt, coe_nat_eq_divInt, num_de... | [
194,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/UniformSpace/Cauchy.lean | totallyBounded_iff_ultrafilter | [
{
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"state_before": "α : Type u\nβ : Type v\ninst✝ : UniformSpace α\ns : Set α\n⊢ TotallyBounded s ↔ ∀ (f : Ultrafilter ... | [
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87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/PFunctor/Univariate/M.lean | PFunctor.M.children_mk | [
{
"state_after": "no goals",
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"tactic": "rw [head_mk]"
},
{
"state_after": "case H\nF : PFunctor\nX : Typ... | [
547,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
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Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.symm_trans_apply | [] | [
393,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
] |
Mathlib/Data/List/Basic.lean | List.zipLeft_nil_right | [
{
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}
] | [
4176,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4175,
1
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Mathlib/Order/Filter/Pointwise.lean | Filter.vsub_le_vsub_left | [] | [
1148,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1147,
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Mathlib/Data/Set/Intervals/ProjIcc.lean | Set.projIcc_eq_left | [
{
"state_after": "α : Type u_1\nβ : Type ?u.3590\ninst✝ : LinearOrder α\na b : α\nh✝ : a ≤ b\nx : α\nh : a < b\nh' : projIcc a b (_ : a ≤ b) x = { val := a, property := (_ : a ∈ Icc a b) }\n⊢ x ≤ a",
"state_before": "α : Type u_1\nβ : Type ?u.3590\ninst✝ : LinearOrder α\na b : α\nh✝ : a ≤ b\nx : α\nh : a < ... | [
62,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Semicontinuous.lean | UpperSemicontinuous.upperSemicontinuousWithinAt | [] | [
705,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
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] |
Mathlib/Order/Filter/Pi.lean | Filter.map_pi_map_coprodᵢ_le | [
{
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265,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
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Mathlib/RingTheory/Ideal/Operations.lean | RingHom.ker_eq | [] | [
2005,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2004,
1
] |
Mathlib/Topology/Order.lean | continuous_id_iff_le | [] | [
819,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
818,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.map_copy | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nf : G →g G'\nf' : G' →g G''\nu' v' : V\np : Walk G u' v'\n⊢ Walk.map f (Walk.copy p (_ : u' = u') (_ : v' = v')) =\n Walk.copy (Walk.map f p) (_ : ↑f u' = ↑f u') (_ : ↑f v' = ↑f v')",
"... | [
1469,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1466,
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Mathlib/Control/Traversable/Lemmas.lean | Traversable.traverse_map' | [
{
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137,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
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] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mk'_spec | [
{
"state_after": "no goals",
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743,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
742,
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Mathlib/RingTheory/FreeCommRing.lean | FreeCommRing.lift_of | [] | [
146,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
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] |
Mathlib/Data/Finset/Sum.lean | Finset.inr_mem_disjSum | [] | [
82,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
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] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | ContDiff.rpow | [] | [
517,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
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] |
Mathlib/Order/WellFounded.lean | Function.not_lt_argmin | [] | [
194,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Topology/MetricSpace/Gluing.lean | Metric.eq_of_glueDist_eq_zero | [
{
"state_after": "no goals",
"state_before": "X : Type u\nY : Type v\nZ : Type w\ninst✝² : MetricSpace X\ninst✝¹ : MetricSpace Y\nΦ✝ : Z → X\nΨ✝ : Z → Y\nε✝ : ℝ\ninst✝ : Nonempty Z\nΦ : Z → X\nΨ : Z → Y\nε : ℝ\nε0 : 0 < ε\nx y : X\nh : glueDist Φ Ψ ε (Sum.inl x) (Sum.inl y) = 0\n⊢ Sum.inl x = Sum.inl y",
... | [
162,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
9
] |
Mathlib/Algebra/Order/Floor.lean | Int.preimage_Ico | [
{
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"state_before": "F : Type ?u.238645\nα : Type u_1\nβ : Type ?u.238651\ninst✝¹ : LinearOrderedRing α\n... | [
1275,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1273,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_ennreal_zero | [] | [
467,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/Data/Multiset/Dedup.lean | Multiset.dedup_zero | [] | [
39,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
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] |
Mathlib/Analysis/InnerProductSpace/Calculus.lean | hasFDerivWithinAt_euclidean | [
{
"state_after": "𝕜 : Type u_1\nι : Type u_3\nH : Type u_2\ninst✝³ : IsROrC 𝕜\ninst✝² : NormedAddCommGroup H\ninst✝¹ : NormedSpace 𝕜 H\ninst✝ : Fintype ι\nf : H → EuclideanSpace 𝕜 ι\nf' : H →L[𝕜] EuclideanSpace 𝕜 ι\nt : Set H\ny : H\n⊢ (∀ (i : ι),\n HasFDerivWithinAt (fun x => (↑(EuclideanSpace.equiv... | [
333,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
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Mathlib/Data/Finset/Sym.lean | Finset.sym_inter | [
{
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"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns✝ t✝ : Finset α\na b : α\nn✝ : ℕ\nm :... | [
220,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.comp_mk | [] | [
220,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/NumberTheory/LSeries.lean | Nat.ArithmeticFunction.LSeries_eq_zero_of_not_LSeriesSummable | [] | [
56,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
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Mathlib/RingTheory/Adjoin/FG.lean | Subalgebra.fg_def | [] | [
105,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.factors_prod | [
{
"state_after": "α : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ninst✝¹ : DecidableEq α\ninst✝ : UniqueFactorizationMonoid α\na : α\nane0 : a ≠ 0\n⊢ Multiset.prod (Classical.choose (_ : ∃ f, (∀ (b : α), b ∈ f → Prime b) ∧ Multiset.prod f ~ᵤ a)) ~ᵤ a",
"state_before": "α : Type u_1\ninst✝² : CancelCommMo... | [
450,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
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Mathlib/Order/MinMax.lean | max_min_distrib_left | [] | [
116,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.mem_map_iff_exists_image | [] | [
1852,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1850,
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.map_top | [] | [
1385,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1384,
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Mathlib/Topology/Sheaves/Stalks.lean | TopCat.Presheaf.stalkSpecializes_comp | [
{
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353,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
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Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.to_hasBasis | [] | [
358,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
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Mathlib/Analysis/Normed/Group/Seminorm.lean | GroupSeminorm.comp_assoc | [] | [
367,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
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Mathlib/Analysis/Quaternion.lean | Quaternion.coe_ofComplex | [] | [
173,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iio_union_Ioo | [
{
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1447,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1443,
1
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Mathlib/Data/Set/Function.lean | Function.Semiconj.injOn_image | [
{
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1643,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1639,
1
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Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.measure_preimage_mul | [
{
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284,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
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Mathlib/LinearAlgebra/TensorAlgebra/Basic.lean | TensorAlgebra.ι_leftInverse | [
{
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"tactic": "simp [ιInv, (AlgHom.toLinearMap_apply), toTrivSqZeroExt_ι _]"
}
] | [
248,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
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Mathlib/Deprecated/Subfield.lean | Field.closure_subset | [
{
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139,
46
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136,
1
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Mathlib/Algebra/Periodic.lean | Function.Antiperiodic.funext' | [] | [
374,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
11
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Mathlib/Data/Set/Basic.lean | Set.disjoint_iff_inter_eq_empty | [] | [
1522,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1521,
1
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Mathlib/ModelTheory/LanguageMap.lean | FirstOrder.Language.lhomWithConstants_injective | [] | [
473,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
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Mathlib/Data/Set/Intervals/Basic.lean | IsMin.Iio_eq | [] | [
711,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
710,
1
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Mathlib/Data/Fin/Basic.lean | Fin.monotone_iff_le_succ | [] | [
1891,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1889,
1
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Mathlib/LinearAlgebra/Basic.lean | LinearMap.iterate_succ | [
{
"state_after": "no goals",
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371,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
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Mathlib/RingTheory/Localization/Module.lean | LinearIndependent.localization | [
{
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57,
73
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47,
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Mathlib/SetTheory/Game/PGame.lean | PGame.fuzzy_congr_imp | [] | [
963,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
962,
1
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Mathlib/Algebra/Algebra/Hom.lean | AlgHom.coe_mks | [] | [
163,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
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Mathlib/ModelTheory/ElementaryMaps.lean | FirstOrder.Language.Equiv.coe_toElementaryEmbedding | [] | [
346,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
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Mathlib/Analysis/Calculus/ContDiffDef.lean | iteratedFDerivWithin_succ_eq_comp_right | [
{
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860,
66
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855,
1
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Mathlib/LinearAlgebra/Quotient.lean | Submodule.mapQ_comp | [
{
"state_after": "case h.h\nR : Type u_5\nM : Type u_6\nr : R\nx y : M\ninst✝⁹ : Ring R\ninst✝⁸ : AddCommGroup M\ninst✝⁷ : Module R M\np p' : Submodule R M\nR₂ : Type u_3\nM₂ : Type u_4\ninst✝⁶ : Ring R₂\ninst✝⁵ : AddCommGroup M₂\ninst✝⁴ : Module R₂ M₂\nτ₁₂ : R →+* R₂\nq : Submodule R₂ M₂\nR₃ : Type u_1\nM₃ : T... | [
438,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.norm_le_pow_iff_norm_lt_pow_add_one | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nx : ℤ_[p]\nn : ℤ\n⊢ ‖↑x‖ ≤ ↑p ^ n ↔ ‖↑x‖ < ↑p ^ (n + 1)",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nx : ℤ_[p]\nn : ℤ\n⊢ ‖x‖ ≤ ↑p ^ n ↔ ‖x‖ < ↑p ^ (n + 1)",
"tactic": "rw [norm_def]"
},
{
"state_after": "no goals",
"state_before": "p : ... | [
563,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
561,
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Mathlib/Topology/MetricSpace/Antilipschitz.lean | AntilipschitzWith.edist_lt_top | [] | [
42,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
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Mathlib/CategoryTheory/CofilteredSystem.lean | nonempty_sections_of_finite_cofiltered_system | [
{
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102,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
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Mathlib/Data/Finset/Card.lean | Finset.card_cons | [] | [
100,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.weightedSMul_congr | [
{
"state_after": "case h\nα : Type u_1\nE : Type ?u.42851\nF : Type u_2\n𝕜 : Type ?u.42857\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nm : MeasurableSpace α\nμ : Measure α\ns t : Set α\nhst : ↑↑μ s = ↑↑μ t\nx : F\n⊢ ↑(weightedSMul μ s) x = ↑(weightedSMul μ t) x",
"state_before": "α : Type u_1\... | [
208,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
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Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.map_div_right_eq_self | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.311574\nG : Type u_1\nH : Type ?u.311580\ninst✝³ : MeasurableSpace G\ninst✝² : MeasurableSpace H\ninst✝¹ : DivInvMonoid G\nμ : Measure G\ninst✝ : IsMulRightInvariant μ\ng : G\n⊢ Measure.map (fun x => x / g) μ = μ",
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258,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
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Mathlib/Data/Set/Lattice.lean | Function.Surjective.iUnion_comp | [] | [
2051,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2050,
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Mathlib/GroupTheory/NoncommPiCoprod.lean | Subgroup.eq_one_of_noncommProd_eq_one_of_independent | [
{
"state_after": "G : Type u_2\ninst✝ : Group G\nι : Type u_1\ns : Finset ι\nf : ι → G\ncomm : Set.Pairwise ↑s fun a b => Commute (f a) (f b)\nK : ι → Subgroup G\nhind : CompleteLattice.Independent K\nhmem : ∀ (x : ι), x ∈ s → f x ∈ K x\n⊢ Finset.noncommProd s f comm = 1 → ∀ (i : ι), i ∈ s → f i = 1",
"stat... | [
83,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
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Mathlib/Order/UpperLower/Hom.lean | UpperSet.coe_icisSupHom | [] | [
59,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
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Mathlib/Data/Rel.lean | Rel.core_mono | [] | [
223,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.sub_def'' | [] | [
174,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/WideEqualizers.lean | CategoryTheory.Limits.WalkingParallelFamily.hom_id | [] | [
117,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.Integrable.to_subbox | [] | [
539,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
] |
Std/Classes/Order.lean | Std.TransCmp.cmp_congr_right | [
{
"state_after": "no goals",
"state_before": "cmp✝ : ?m.3864 → ?m.3864 → Ordering\ninst✝² : TransCmp cmp✝\nx✝ : Sort u_1\ncmp : x✝ → x✝ → Ordering\ninst✝¹ : TransCmp cmp\ny z x : x✝\ninst✝ : TransCmp cmp\nyz : cmp y z = Ordering.eq\n⊢ cmp x y = cmp x z",
"tactic": "rw [← Ordering.swap_inj, symm, symm, c... | [
86,
58
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
85,
1
] |
Mathlib/RingTheory/Int/Basic.lean | induction_on_primes | [
{
"state_after": "case h₁\nP : ℕ → Prop\nh₀ : P 0\nh₁ : P 1\nh : ∀ (p a : ℕ), Nat.Prime p → P a → P (p * a)\nn : ℕ\n⊢ P 0\n\ncase h₂\nP : ℕ → Prop\nh₀ : P 0\nh₁ : P 1\nh : ∀ (p a : ℕ), Nat.Prime p → P a → P (p * a)\nn : ℕ\n⊢ ∀ (x : ℕ), IsUnit x → P x\n\ncase h₃\nP : ℕ → Prop\nh₀ : P 0\nh₁ : P 1\nh : ∀ (p a : ℕ)... | [
362,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/MeasureTheory/Function/ContinuousMapDense.lean | MeasureTheory.Integrable.exists_hasCompactSupport_lintegral_sub_le | [
{
"state_after": "α : Type u_1\ninst✝⁷ : MeasurableSpace α\ninst✝⁶ : TopologicalSpace α\ninst✝⁵ : NormalSpace α\ninst✝⁴ : BorelSpace α\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\nμ : Measure α\np : ℝ≥0∞\ninst✝² : NormedSpace ℝ E\ninst✝¹ : LocallyCompactSpace α\ninst✝ : Measure.Regular μ\nf : α → E\nε : ℝ≥0∞\n... | [
224,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Order/InitialSeg.lean | RelEmbedding.collapseF.not_lt | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.71243\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\ninst✝ : IsWellOrder β s\nf : r ↪r s\na : α\nb : β\nh : ∀ (a' : α), r a' a → s (↑(collapseF f a')) b\n⊢ ¬s b\n ↑(WellFounded.fix (_ : WellFounded r)\n (fun a IH =>\n let... | [
527,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
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Mathlib/Data/Stream/Init.lean | Stream'.drop_const | [] | [
265,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.le_restrict_empty | [
{
"state_after": "α : Type u_1\nβ : Type ?u.545966\nm : MeasurableSpace α\nM : Type u_2\ninst✝² : TopologicalSpace M\ninst✝¹ : AddCommMonoid M\ninst✝ : PartialOrder M\nv w : VectorMeasure α M\nj : Set α\na✝ : MeasurableSet j\n⊢ ↑(restrict v ∅) j ≤ ↑(restrict w ∅) j",
"state_before": "α : Type u_1\nβ : Type ... | [
902,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
900,
1
] |
Mathlib/Data/Rat/Cast.lean | Rat.cast_mul | [] | [
230,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Analysis/Convex/Join.lean | Convex.convexHull_union | [] | [
198,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
11
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_sub_eq_right_of_natDegree_lt | [] | [
1344,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1342,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coeToSubmodule_injective | [] | [
205,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.isIrreducible_iff_vanishingIdeal_isPrime | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\ns : Set (PrimeSpectrum R)\n⊢ IsIrreducible s ↔ Ideal.IsPrime (vanishingIdeal s)",
"tactic": "rw [← isIrreducible_iff_closure, ← zeroLocus_vanishingIdeal_eq_closure,\n isIrreducible_zeroLocus_i... | [
561,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
] |
Mathlib/Data/Set/Pointwise/Finite.lean | Set.Finite.smul | [] | [
96,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Data/Dfinsupp/Interval.lean | Dfinsupp.card_Ioo | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : ι → Type u_2\ninst✝⁴ : DecidableEq ι\ninst✝³ : (i : ι) → DecidableEq (α i)\ninst✝² : (i : ι) → PartialOrder (α i)\ninst✝¹ : (i : ι) → Zero (α i)\ninst✝ : (i : ι) → LocallyFiniteOrder (α i)\nf g : Π₀ (i : ι), α i\n⊢ card (Ioo f g) = ∏ i in suppo... | [
194,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.Quotient.restrictScalarsEquiv_symm_mk | [] | [
246,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.sub_self_add | [
{
"state_after": "n m : Nat\n⊢ n + 0 - (n + m) = 0",
"state_before": "n m : Nat\n⊢ n - (n + m) = 0",
"tactic": "show (n + 0) - (n + m) = 0"
},
{
"state_after": "no goals",
"state_before": "n m : Nat\n⊢ n + 0 - (n + m) = 0",
"tactic": "rw [Nat.add_sub_add_left, Nat.zero_sub]"
}
] | [
636,
42
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
634,
11
] |
Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.IsPrimitive.dvd_primPart_iff_dvd | [
{
"state_after": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\np q : R[X]\nhp : IsPrimitive p\nhq : q ≠ 0\nh : p ∣ q\n⊢ p ∣ primPart q",
"state_before": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\np q : R[X]\nhp : IsPrimit... | [
433,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/Topology/MetricSpace/Closeds.lean | EMetric.isClosed_subsets_of_isClosed | [
{
"state_after": "α : Type u\ninst✝ : EMetricSpace α\ns : Set α\nhs : IsClosed s\nt : Closeds α\nht : t ∈ closure {t | ↑t ⊆ s}\nx : α\nhx : x ∈ ↑t\n⊢ x ∈ s",
"state_before": "α : Type u\ninst✝ : EMetricSpace α\ns : Set α\nhs : IsClosed s\n⊢ IsClosed {t | ↑t ⊆ s}",
"tactic": "refine' isClosed_of_closure_... | [
88,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Order/UpperLower/Basic.lean | IsLowerSet.ordConnected | [] | [
242,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/CategoryTheory/Over.lean | CategoryTheory.Under.under_left | [
{
"state_after": "no goals",
"state_before": "T : Type u₁\ninst✝ : Category T\nX : T\nU : Under X\n⊢ U.left = { as := PUnit.unit }",
"tactic": "simp only"
}
] | [
336,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/Data/PNat/Prime.lean | PNat.gcd_mul_lcm | [] | [
103,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Topology/Semicontinuous.lean | lowerSemicontinuous_iSup | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝³ : TopologicalSpace α\nβ : Type ?u.128024\ninst✝² : Preorder β\nf✝ g : α → β\nx : α\ns t : Set α\ny z : β\nι : Sort u_3\nδ : Type u_2\nδ' : Type ?u.128056\ninst✝¹ : CompleteLinearOrder δ\ninst✝ : ConditionallyCompleteLinearOrder δ'\nf : ι → α... | [
619,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
617,
1
] |
Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingIso.coe_mk | [] | [
400,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/GroupTheory/GroupAction/Group.lean | MulAction.injective | [] | [
154,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
11
] |
Mathlib/Topology/Bases.lean | TopologicalSpace.IsTopologicalBasis.open_eq_sUnion' | [] | [
191,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Data/Int/Bitwise.lean | Int.bitwise_and | [
{
"state_after": "case h.h\nm n : ℤ\n⊢ bitwise and m n = land m n",
"state_before": "⊢ bitwise and = land",
"tactic": "funext m n"
},
{
"state_after": "case h.h.negSucc.ofNat\nm n : ℕ\n⊢ ↑(Nat.bitwise' (fun x y => !x && y) m n) = land -[m+1] (ofNat n)\n\ncase h.h.negSucc.negSucc\nm n : ℕ\n⊢ -[Na... | [
255,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Order/Hom/Bounded.lean | BotHom.id_comp | [] | [
473,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
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