file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/Complex/Exponential.lean | Complex.ofReal_sin_ofReal_re | [
{
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}
] | [
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54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Order/SymmDiff.lean | Codisjoint.bihimp_right | [] | [
709,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
707,
11
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Mathlib/Algebra/Star/SelfAdjoint.lean | IsSelfAdjoint.star_mul_self | [
{
"state_after": "no goals",
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}
] | [
89,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
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Mathlib/LinearAlgebra/AffineSpace/Pointwise.lean | AffineSubspace.pointwise_vadd_eq_map | [] | [
54,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
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Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffAt.snd' | [] | [
834,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
832,
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Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSet.congr | [
{
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"tactic": "rwa [← h]"
}
] | [
114,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
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Mathlib/Analysis/Normed/Group/Basic.lean | pow_mem_ball | [
{
"state_after": "𝓕 : Type ?u.915521\n𝕜 : Type ?u.915524\nα : Type ?u.915527\nι : Type ?u.915530\nκ : Type ?u.915533\nE : Type u_1\nF : Type ?u.915539\nG : Type ?u.915542\ninst✝¹ : SeminormedCommGroup E\ninst✝ : SeminormedCommGroup F\na a₁ a₂ b b₁ b₂ : E\nr r₁ r₂ : ℝ\nn : ℕ\nhn : 0 < n\nh : ‖a / b‖ < r\n⊢ ‖(a... | [
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12
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.supp_subset_range | [] | [
203,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
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Mathlib/Analysis/Calculus/Deriv/Basic.lean | HasDerivAtFilter.congr_of_eventuallyEq | [
{
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"state_before": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type w\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL L₁ L₂ : Fi... | [
570,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.type_sum_lex | [] | [
917,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
915,
1
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Mathlib/MeasureTheory/Function/SimpleFuncDense.lean | MeasureTheory.SimpleFunc.nearestPtInd_le | [
{
"state_after": "case zero\nα : Type u_1\nβ : Type ?u.23173\nι : Type ?u.23176\nE : Type ?u.23179\nF : Type ?u.23182\n𝕜 : Type ?u.23185\ninst✝² : MeasurableSpace α\ninst✝¹ : PseudoEMetricSpace α\ninst✝ : OpensMeasurableSpace α\ne : ℕ → α\nx : α\n⊢ ↑(nearestPtInd e Nat.zero) x ≤ Nat.zero\n\ncase succ\nα : Type... | [
101,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Matrix/Basic.lean | Matrix.diag_zero | [] | [
627,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
626,
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Mathlib/Deprecated/Group.lean | Additive.isAddGroupHom | [] | [
467,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_pos_of_pos | [
{
"state_after": "x : ℝ\nhx : 0 < x\ny : ℝ\n⊢ 0 < exp (log x * y)",
"state_before": "x : ℝ\nhx : 0 < x\ny : ℝ\n⊢ 0 < x ^ y",
"tactic": "rw [rpow_def_of_pos hx]"
},
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx : 0 < x\ny : ℝ\n⊢ 0 < exp (log x * y)",
"tactic": "apply exp_pos"
... | [
96,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.Measure.exists_positive_of_not_mutuallySingular | [
{
"state_after": "α : Type u_1\nβ : Type ?u.63219\nm : MeasurableSpace α\nμ✝ ν✝ μ ν : Measure α\ninst✝¹ : IsFiniteMeasure μ\ninst✝ : IsFiniteMeasure ν\nh : ¬μ ⟂ₘ ν\nthis :\n ∀ (n : ℕ),\n ∃ i,\n MeasurableSet i ∧\n VectorMeasure.restrict 0 i ≤\n VectorMeasure.restrict (toSignedMeasure ... | [
452,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
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Mathlib/SetTheory/Game/PGame.lean | PGame.add_comm_le | [] | [
1639,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1638,
1
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Mathlib/AlgebraicTopology/SimplicialObject.lean | CategoryTheory.CosimplicialObject.δ_comp_σ_of_gt' | [
{
"state_after": "no goals",
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"tactic": "simp only [Fin.not_lt_zero, hi] at H"
},
{
"state_after": "C : Type u\ninst✝ : Category C\nX : Cos... | [
569,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
1
] |
Mathlib/Algebra/Order/Group/DenselyOrdered.lean | le_iff_forall_lt_one_mul_le | [] | [
51,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
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Mathlib/FieldTheory/Finite/Basic.lean | card_eq_pow_finrank | [
{
"state_after": "K : Type u_2\nR : Type ?u.998574\nV : Type u_1\ninst✝⁴ : Fintype K\ninst✝³ : DivisionRing K\ninst✝² : AddCommGroup V\ninst✝¹ : Module K V\ninst✝ : Fintype V\nb : Basis { x // x ∈ IsNoetherian.finsetBasisIndex K V } K V := IsNoetherian.finsetBasis K V\n⊢ Fintype.card V = q ^ FiniteDimensional.f... | [
394,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
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Mathlib/Computability/Halting.lean | Nat.Partrec'.of_eq | [] | [
310,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.sinh_sub_cosh | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ sinh x - cosh x = -exp (-x)",
"tactic": "rw [← neg_sub, cosh_sub_sinh]"
}
] | [
1427,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1427,
1
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Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | ContDiffOn.cexp | [] | [
169,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/CategoryTheory/Sites/Sheafification.lean | CategoryTheory.GrothendieckTopology.Plus.isSheaf_of_sep | [
{
"state_after": "C : Type u\ninst✝⁷ : Category C\nJ : GrothendieckTopology C\nD : Type w\ninst✝⁶ : Category D\ninst✝⁵ : ConcreteCategory D\ninst✝⁴ : PreservesLimits (forget D)\ninst✝³ : ∀ (X : C), HasColimitsOfShape (Cover J X)ᵒᵖ D\ninst✝² : ∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : Cover J X), HasMultiequalizer (Cover.ind... | [
446,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
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] |
Mathlib/Data/Nat/Pairing.lean | Nat.unpair_right_le | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ (unpair n).snd ≤ n",
"tactic": "simpa using right_le_pair n.unpair.1 n.unpair.2"
}
] | [
127,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf_attach | [] | [
422,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Data/Finset/Prod.lean | Finset.subset_product | [] | [
90,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Std/Data/Fin/Lemmas.lean | USize.div_toNat | [] | [
34,
17
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
33,
9
] |
Mathlib/NumberTheory/Padics/Hensel.lean | newton_seq_dist_aux | [
{
"state_after": "no goals",
"state_before": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nF : Polynomial ℤ_[p]\na : ℤ_[p]\nhnorm : ‖Polynomial.eval a F‖ < ‖Polynomial.eval a (↑Polynomial.derivative F)‖ ^ 2\nhnsol : Polynomial.eval a F ≠ 0\nn : ℕ\n⊢ ‖newton_seq (n + 0) - newton_seq n‖ ≤ ‖Polynomial.eval a (↑Polynomia... | [
322,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
9
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzOnWith.le_add_mul | [] | [
568,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
566,
11
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.coe_lt_one | [] | [
83,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.vecMul_mulVec | [
{
"state_after": "no goals",
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1945,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1944,
1
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Mathlib/Logic/Equiv/Defs.lean | Equiv.injective_comp | [] | [
367,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.prime_X_sub_C | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np q : R[X]\nr : R\nx✝¹ x✝ : R[X]\n⊢ eval r x✝¹ = 0 ∨ eval r x✝ = 0 → eval r x✝¹ = 0 ∨ eval r x✝ = 0",
"state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝... | [
407,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
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Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.sub_fst | [] | [
281,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
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Mathlib/Algebra/Quaternion.lean | Quaternion.im_star | [] | [
1135,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1134,
1
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Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.spanSingleton_one | [
{
"state_after": "case a\nR : Type u_2\ninst✝⁶ : CommRing R\nS : Submonoid R\nP : Type u_1\ninst✝⁵ : CommRing P\ninst✝⁴ : Algebra R P\nloc : IsLocalization S P\nR₁ : Type ?u.1331786\ninst✝³ : CommRing R₁\nK : Type ?u.1331792\ninst✝² : Field K\ninst✝¹ : Algebra R₁ K\ninst✝ : IsFractionRing R₁ K\nx✝ : P\n⊢ x✝ ∈ s... | [
1363,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1359,
1
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Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.exists_measurable_superset_of_null | [] | [
228,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
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Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_pow_atTop_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.210440\nι' : Type ?u.210443\nα : Type u_1\nβ : Type ?u.210449\nγ : Type ?u.210452\ninst✝ : LinearOrderedSemiring α\nl : Filter β\nf : β → α\nn : ℕ\nh : Tendsto (fun x => x ^ n) atTop atTop\nhn : n = 0\n⊢ False",
"tactic": "simp only [hn, pow_zero... | [
973,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.hasFiniteIntegral_iff_edist | [
{
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127,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
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Std/Data/Int/Lemmas.lean | Int.toNat_sub_toNat_neg | [] | [
1401,
29
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1398,
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Mathlib/Analysis/SpecificLimits/Normed.lean | tendsto_pow_const_div_const_pow_of_one_lt | [] | [
232,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
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Mathlib/Analysis/Convex/Extreme.lean | extremePoints_pi | [
{
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237,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
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Mathlib/Algebra/QuadraticDiscriminant.lean | discrim_lt_zero | [
{
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158,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
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Mathlib/Data/Rat/NNRat.lean | NNRat.coe_le_coe | [] | [
167,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasFDerivWithinAt.congr_of_eventuallyEq | [] | [
894,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
892,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.re_eq_norm_of_mul_conj | [
{
"state_after": "no goals",
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"tactic": "rw [mul_conj, ofReal_re, norm_ofReal, abs_of_nonneg (normSq_nonneg _)]"
}
] | [
762,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
761,
1
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Mathlib/Order/SymmDiff.lean | symmDiff_eq_iff_sdiff_eq | [
{
"state_after": "ι : Type ?u.78168\nα : Type u_1\nβ : Type ?u.78174\nπ : ι → Type ?u.78179\ninst✝ : GeneralizedBooleanAlgebra α\na b c d : α\nha : a ≤ c\n⊢ a ∆ b = c ↔ a ∆ c = b",
"state_before": "ι : Type ?u.78168\nα : Type u_1\nβ : Type ?u.78174\nπ : ι → Type ?u.78179\ninst✝ : GeneralizedBooleanAlgebra α... | [
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567,
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Mathlib/LinearAlgebra/Basis.lean | Basis.prod_apply_inr_fst | [
{
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742,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
1
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | expNegInvGlue.zero_iff_nonpos | [] | [
87,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
9
] |
Mathlib/Order/Bounds/Basic.lean | IsLeast.image2 | [] | [
1396,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1395,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalMax.comp_mono | [] | [
223,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
8
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.preimage_mul_right_one | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.679577\nα : Type u_1\nβ : Type ?u.679583\nγ : Type ?u.679586\ninst✝ : Group α\ns t : Finset α\na b : α\n⊢ preimage 1 (fun x => x * b) (_ : Set.InjOn (fun x => x * b) ((fun x => x * b) ⁻¹' ↑1)) = {b⁻¹}",
"tactic": "classical rw [← image_mul_right'... | [
1233,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1232,
1
] |
Mathlib/Data/Real/Basic.lean | Real.ext_cauchy | [] | [
66,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Data/Int/GCD.lean | Nat.xgcd_aux_P | [
{
"state_after": "no goals",
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"tactic": "induction r, r' using gcd.induction with\n| H0 => simp\n| H1 a b h IH =>\n intro s t s' t' p p'\n rw [xgcd_aux_rec h]; refine'... | [
144,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/RingTheory/NonZeroDivisors.lean | nonZeroDivisors.coe_ne_zero | [] | [
91,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Data/Real/Basic.lean | Real.mk_inf | [] | [
488,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.bit0_comp | [
{
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"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q r : R[X]\n⊢ comp (bit0 p) q = bit0 (comp p q)",
"tactic": "simp only [bit0, add_comp]"
}
] | [
643,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
643,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.isBounded_iff_nndist | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.47942\nι : Type ?u.47945\ninst✝ : PseudoMetricSpace α\nx y z : α\nδ ε ε₁ ε₂ : ℝ\ns✝ s : Set α\n⊢ IsBounded s ↔ ∃ C, ∀ ⦃x : α⦄, x ∈ s → ∀ ⦃y : α⦄, y ∈ s → nndist x y ≤ C",
"tactic": "simp only [isBounded_iff_exists_ge 0, NN... | [
713,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
710,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.sign_coe_nonneg_of_nonneg_of_le_pi | [
{
"state_after": "θ : ℝ\nh0 : 0 ≤ θ\nhpi : θ ≤ π\n⊢ 0 ≤ sin ↑θ",
"state_before": "θ : ℝ\nh0 : 0 ≤ θ\nhpi : θ ≤ π\n⊢ 0 ≤ sign ↑θ",
"tactic": "rw [sign, sign_nonneg_iff]"
},
{
"state_after": "no goals",
"state_before": "θ : ℝ\nh0 : 0 ≤ θ\nhpi : θ ≤ π\n⊢ 0 ≤ sin ↑θ",
"tactic": "exact sin_no... | [
982,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
979,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.boundedBy_zero | [
{
"state_after": "α : Type u_1\nm : Set α → ℝ≥0∞\n⊢ boundedBy 0 ≤ ⊥",
"state_before": "α : Type u_1\nm : Set α → ℝ≥0∞\n⊢ boundedBy 0 = 0",
"tactic": "rw [← coe_bot, eq_bot_iff]"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\nm : Set α → ℝ≥0∞\n⊢ boundedBy 0 ≤ ⊥",
"tactic":... | [
896,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
894,
1
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.add_coe_eq_top_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : Add α\na b c d : WithTop α\nx✝ y✝ : α\nx : WithTop α\ny : α\n⊢ x + ↑y = ⊤ ↔ x = ⊤",
"tactic": "induction x using WithTop.recTopCoe <;> simp [← coe_add]"
}
] | [
177,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Data/List/Basic.lean | List.nthLe_insertNth_self | [
{
"state_after": "no goals",
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"tactic": "rwa [length_insertNth _ _ hn, Nat.lt_succ_iff]"
}
] | [
1730,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1728,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffWithinAt.prod_map | [] | [
1603,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1600,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.AEEqFun.integrable_mk | [
{
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1216,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1212,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.mmap_cons | [] | [
438,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.right_mem_Iic | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.5871\ninst✝ : Preorder α\na a₁ a₂ b b₁ b₂ c x : α\n⊢ a ∈ Iic a",
"tactic": "simp"
}
] | [
226,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Basis.lean | AffineBasis.ext | [] | [
80,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/RingTheory/MvPolynomial/Homogeneous.lean | MvPolynomial.isHomogeneous_monomial | [
{
"state_after": "σ : Type u_1\nτ : Type ?u.126597\nR : Type u_2\nS : Type ?u.126603\ninst✝ : CommSemiring R\nd : σ →₀ ℕ\nr : R\nn : ℕ\nhn : ∑ i in d.support, ↑d i = n\nc : σ →₀ ℕ\nhc : coeff c (↑(monomial d) r) ≠ 0\n⊢ ∑ i in c.support, ↑c i = n",
"state_before": "σ : Type u_1\nτ : Type ?u.126597\nR : Type ... | [
125,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Data/ZMod/Basic.lean | Nat.le_div_two_iff_mul_two_le | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\n⊢ m ≤ n / 2 ↔ ↑m * 2 ≤ ↑n",
"tactic": "rw [Nat.le_div_iff_mul_le zero_lt_two, ← Int.ofNat_le, Int.ofNat_mul, Nat.cast_two]"
}
] | [
932,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
931,
1
] |
Mathlib/Topology/Algebra/Order/MonotoneContinuity.lean | OrderIso.continuous | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝⁵ : PartialOrder α\ninst✝⁴ : PartialOrder β\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : OrderTopology α\ninst✝ : OrderTopology β\ne : α ≃o β\n⊢ Continuous ↑e",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝⁵ : PartialOrder α\nins... | [
315,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
11
] |
Mathlib/Topology/Algebra/UniformGroup.lean | DenseInducing.extend_Z_bilin | [
{
"state_after": "α : Type u_1\nβ : Type u_4\nγ : Type u_2\nδ : Type u_5\nG : Type u_3\ninst✝¹⁶ : TopologicalSpace α\ninst✝¹⁵ : AddCommGroup α\ninst✝¹⁴ : TopologicalAddGroup α\ninst✝¹³ : TopologicalSpace β\ninst✝¹² : AddCommGroup β\ninst✝¹¹ : TopologicalAddGroup β\ninst✝¹⁰ : TopologicalSpace γ\ninst✝⁹ : AddComm... | [
905,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
872,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.pow_atom | [
{
"state_after": "no goals",
"state_before": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na : R\nb : ℕ\n⊢ a ^ b = a ^ b * Nat.rawCast 1 + 0",
"tactic": "simp"
}
] | [
595,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | ciSup_of_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.72243\nγ : Type ?u.72246\nι : Sort u_1\ninst✝¹ : ConditionallyCompleteLinearOrderBot α\ninst✝ : IsEmpty ι\nf : ι → α\n⊢ (⨆ (i : ι), f i) = ⊥",
"tactic": "rw [iSup_of_empty', csSup_empty]"
}
] | [
1020,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1019,
1
] |
Mathlib/Algebra/Group/Conj.lean | ConjClasses.mem_carrier_iff_mk_eq | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝ : Monoid α\na : α\n⊢ ∀ {b : ConjClasses α}, a ∈ carrier b ↔ ConjClasses.mk a = b",
"state_before": "α : Type u\nβ : Type v\ninst✝ : Monoid α\na : α\nb : ConjClasses α\n⊢ a ∈ carrier b ↔ ConjClasses.mk a = b",
"tactic": "revert b"
},
{
"state_after"... | [
326,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/Topology/Category/TopCat/Basic.lean | TopCat.openEmbedding_iff_comp_isIso' | [
{
"state_after": "X Y Z : TopCat\nf : X ⟶ Y\ng : Y ⟶ Z\ninst✝ : IsIso g\n⊢ OpenEmbedding ((forget TopCat).map (f ≫ g)) ↔ OpenEmbedding ((forget TopCat).map f)",
"state_before": "X Y Z : TopCat\nf : X ⟶ Y\ng : Y ⟶ Z\ninst✝ : IsIso g\n⊢ OpenEmbedding ((forget TopCat).map f ≫ (forget TopCat).map g) ↔ OpenEmbed... | [
173,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Topology/MetricSpace/CantorScheme.lean | CantorScheme.VanishingDiam.map_continuous | [
{
"state_after": "β : Type u_1\nα : Type u_2\nA : List β → Set α\ninst✝² : PseudoMetricSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : DiscreteTopology β\nhA : VanishingDiam A\n⊢ ∀ (a : ↑(inducedMap A).fst) (ε : ℝ),\n ε > 0 → ∀ᶠ (x : ↑(inducedMap A).fst) in 𝓝 a, dist (Sigma.snd (inducedMap A) x) (Sigma.snd (i... | [
164,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.and_forall_succ | [] | [
134,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/GroupTheory/SchurZassenhaus.lean | Subgroup.SchurZassenhausInduction.step2 | [
{
"state_after": "G : Type u\ninst✝³ : Group G\ninst✝² : Fintype G\nN : Subgroup G\ninst✝¹ : Normal N\nh1 : Nat.coprime (Fintype.card { x // x ∈ N }) (index N)\nh2 :\n ∀ (G' : Type u) [inst : Group G'] [inst_1 : Fintype G'],\n Fintype.card G' < Fintype.card G →\n ∀ {N' : Subgroup G'} [inst_2 : Normal N... | [
227,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
9
] |
Mathlib/Data/Finsupp/NeLocus.lean | Finsupp.zipWith_neLocus_eq_left | [
{
"state_after": "case a\nα : Type u_4\nM : Type u_2\nN : Type u_1\nP : Type u_3\ninst✝⁵ : DecidableEq α\ninst✝⁴ : DecidableEq N\ninst✝³ : Zero M\ninst✝² : DecidableEq P\ninst✝¹ : Zero P\ninst✝ : Zero N\nF : M → N → P\nF0 : F 0 0 = 0\nf : α →₀ M\ng₁ g₂ : α →₀ N\nhF : ∀ (f : M), Function.Injective fun g => F f g... | [
101,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/MeasureTheory/Function/SpecialFunctions/Basic.lean | Real.measurable_log | [] | [
39,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
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Mathlib/Order/LiminfLimsup.lean | Filter.IsBoundedUnder.sup | [
{
"state_after": "no goals",
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"tactic": "filter_... | [
281,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/LinearAlgebra/TensorPower.lean | TensorPower.one_mul | [
{
"state_after": "R : Type u_1\nM : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nn : ℕ\na : (⨂[R]^n) M\n⊢ ↑(cast R M (_ : 0 + n = n)) (↑mulEquiv (↑(tprod R) Fin.elim0' ⊗ₜ[R] a)) = a",
"state_before": "R : Type u_1\nM : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMo... | [
182,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.image_image | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type u_2\nγ : Type u_1\ninst✝¹ : DecidableEq β\nf g✝ : α → β\ns : Finset α\nt : Finset β\na : α\nb c : β\ninst✝ : DecidableEq γ\ng : β → γ\n⊢ (image g (image f s)).val = (image (g ∘ f) s).val",
"tactic": "simp only [image_val, dedup_map_ded... | [
422,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Algebra/Support.lean | Function.mulSupport_sup | [] | [
159,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_norm_left | [
{
"state_after": "α : Type u_1\nβ : Type ?u.123733\nE : Type ?u.123736\nF : Type u_2\nG : Type ?u.123742\nE' : Type u_3\nF' : Type ?u.123748\nG' : Type ?u.123751\nE'' : Type ?u.123754\nF'' : Type ?u.123757\nG'' : Type ?u.123760\nR : Type ?u.123763\nR' : Type ?u.123766\n𝕜 : Type ?u.123769\n𝕜' : Type ?u.123772\... | [
772,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
770,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.StableUnderBaseChange.respectsIso | [
{
"state_after": "case hP\nC : Type u\ninst✝¹ : Category C\nD : Type ?u.20586\ninst✝ : Category D\nP : MorphismProperty C\nhP : StableUnderBaseChange P\n⊢ ∀ (f g : Arrow C), (f ≅ g) → P f.hom → P g.hom",
"state_before": "C : Type u\ninst✝¹ : Category C\nD : Type ?u.20586\ninst✝ : Category D\nP : MorphismPro... | [
199,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | cardinal_mk_eq_cardinal_mk_field_pow_rank | [
{
"state_after": "K✝ : Type u\nV✝ : Type v\nK V : Type u\ninst✝³ : DivisionRing K\ninst✝² : AddCommGroup V\ninst✝¹ : Module K V\ninst✝ : FiniteDimensional K V\ns : Set V := Basis.ofVectorSpaceIndex K V\n⊢ (#V) = (#K) ^ Module.rank K V",
"state_before": "K✝ : Type u\nV✝ : Type v\nK V : Type u\ninst✝³ : Divis... | [
1546,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1539,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | ContinuousOn.integrableAt_nhdsWithin | [] | [
570,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.closedBall_subset_closedBall' | [] | [
607,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
] |
Mathlib/Topology/Connected.lean | connectedComponentIn_subset | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.51675\nπ : ι → Type ?u.51680\ninst✝ : TopologicalSpace α\ns t u v F : Set α\nx : α\n⊢ (if h : x ∈ F then Subtype.val '' connectedComponent { val := x, property := h } else ∅) ⊆ F",
"state_before": "α : Type u\nβ : Type v\nι : Type ?u.51675\nπ : ι → Type ... | [
616,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
614,
1
] |
Mathlib/Order/SuccPred/Relation.lean | transGen_of_succ_of_reflexive | [
{
"state_after": "case inl\nα : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nr : α → α → Prop\nm : α\nhr : Reflexive r\nh1 : ∀ (i : α), i ∈ Ico m m → r i (succ i)\nh2 : ∀ (i : α), i ∈ Ico m m → r (succ i) i\n⊢ TransGen r m m\n\ncase inr\nα : Type u_1\ninst✝² : LinearOrder... | [
90,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/CategoryTheory/EqToHom.lean | CategoryTheory.eqToHom_unop | [
{
"state_after": "case refl\nC : Type u₁\ninst✝ : Category C\nX : Cᵒᵖ\n⊢ (eqToHom (_ : X = X)).unop = eqToHom (_ : X.unop = X.unop)",
"state_before": "C : Type u₁\ninst✝ : Category C\nX Y : Cᵒᵖ\nh : X = Y\n⊢ (eqToHom h).unop = eqToHom (_ : Y.unop = X.unop)",
"tactic": "cases h"
},
{
"state_after... | [
158,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.WellFoundedOn.induction | [
{
"state_after": "ι : Type ?u.4297\nα : Type u_1\nβ : Type ?u.4303\nr r' : α → α → Prop\ns t : Set α\nx y : α\nhs : WellFoundedOn s r\nhx : x ∈ s\nP : α → Prop\nhP : ∀ (y : α), y ∈ s → (∀ (z : α), z ∈ s → r z y → P z) → P y\nQ : ↑s → Prop := fun y => P ↑y\n⊢ P x",
"state_before": "ι : Type ?u.4297\nα : Type... | [
98,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
11
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.exists_of_liftRel_left | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nR : α → β → Prop\ns : WSeq α\nt : WSeq β\nH : LiftRel R s t\na : α\nh✝ : a ∈ s\nn : ℕ\nh : some a ∈ get? s n\n⊢ ∃ b, b ∈ t ∧ R a b",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : α → β → Prop\ns : WSeq α\nt : WSeq β\nH : LiftRel R s t\na : α\n... | [
1062,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1054,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.map_comap_map | [] | [
318,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_le_pi | [] | [
152,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | NNReal.not_summable_iff_tendsto_nat_atTop | [
{
"state_after": "case mp\nα : Type ?u.312905\nβ : Type ?u.312908\nγ : Type ?u.312911\nf : ℕ → ℝ≥0\n⊢ ¬Summable f → Tendsto (fun n => ∑ i in Finset.range n, f i) atTop atTop\n\ncase mpr\nα : Type ?u.312905\nβ : Type ?u.312908\nγ : Type ?u.312911\nf : ℕ → ℝ≥0\n⊢ Tendsto (fun n => ∑ i in Finset.range n, f i) atTo... | [
1139,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1132,
1
] |
Mathlib/Topology/Algebra/Field.lean | Subfield.topologicalClosure_minimal | [] | [
76,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Tactic/Linarith/Lemmas.lean | Linarith.mul_neg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : StrictOrderedRing α\na b : α\nha : a < 0\nhb : 0 < b\nthis : -b * a > 0\n⊢ 0 < -(b * a)",
"tactic": "simpa"
}
] | [
44,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pullbackConeOfLeftIso_π_app_none | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nW X Y Z : C\nf : X ⟶ Z\ng : Y ⟶ Z\ninst✝ : IsIso f\n⊢ (pullbackConeOfLeftIso f g).π.app none = g",
"tactic": "simp"
}
] | [
1630,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1630,
1
] |
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