file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/Analysis/MeanInequalitiesPow.lean | Real.arith_mean_le_rpow_mean | [
{
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"state_before": "ι : Type u\ns : Finset ι\nw z : ι → ℝ\nhw : ∀ (i... | [
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105,
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.le_op_norm₂ | [] | [
611,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
1
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.lintegral_coe_eq_integral | [
{
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1173,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Integral/SetIntegral.lean | set_integral_withDensity_eq_set_integral_smul₀ | [
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74
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Mathlib/Topology/Connected.lean | IsPreconnected.closure | [] | [
307,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_const_mul' | [
{
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730,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
719,
1
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Mathlib/Topology/SubsetProperties.lean | CompactExhaustion.subset_succ | [] | [
1455,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1454,
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Mathlib/Order/Filter/AtTopBot.lean | Filter.frequently_atTop | [
{
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"state_before": "ι : Type ?u.27917\nι' : Type ?u.27920\nα : Type u_1\nβ : Type ?u.27926\nγ : Type ?u.27929\ninst✝¹ : SemilatticeSup α\ninst✝ : Nonempty α\np : α → Prop\n⊢ (∀ (i : α), True → ∃ x, x ∈ Ici i ∧ p x) ↔ ∀ (a : α), ∃ b, b ≥ a ∧ p b",
"tactic": "simp"
}
] | [
325,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
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Mathlib/Order/SymmDiff.lean | symmDiff_symmDiff_cancel_left | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.73734\nα : Type u_1\nβ : Type ?u.73740\nπ : ι → Type ?u.73745\ninst✝ : GeneralizedBooleanAlgebra α\na b c d : α\n⊢ a ∆ (a ∆ b) = b",
"tactic": "simp [← symmDiff_assoc]"
}
] | [
497,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
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Mathlib/Data/Set/Intervals/Pi.lean | Set.image_update_Ioo | [
{
"state_after": "no goals",
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"tactic": "rw [← Ico_diff_left, ← Ico_diff_left, image_diff (upda... | [
160,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.algebraMap_eq | [] | [
183,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
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Mathlib/CategoryTheory/Sites/Sheafification.lean | CategoryTheory.GrothendieckTopology.Plus.inj_of_sep | [
{
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336,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.sign_two_nsmul_eq_sign_iff | [
{
"state_after": "case pos\nθ : Angle\nhpi : θ = ↑π\n⊢ sign (2 • θ) = sign θ ↔ θ = ↑π ∨ abs (toReal θ) < π / 2\n\ncase neg\nθ : Angle\nhpi : ¬θ = ↑π\n⊢ sign (2 • θ) = sign θ ↔ θ = ↑π ∨ abs (toReal θ) < π / 2",
"state_before": "θ : Angle\n⊢ sign (2 • θ) = sign θ ↔ θ = ↑π ∨ abs (toReal θ) < π / 2",
"tacti... | [
1030,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
991,
1
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Mathlib/Logic/Equiv/Set.lean | Equiv.Set.insert_apply_left | [] | [
302,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
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Mathlib/Topology/UniformSpace/Separation.lean | separationRel_comap | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : UniformSpace β\ninst✝ : UniformSpace γ\nf : α → β\n⊢ 𝓢 α = Prod.map f f ⁻¹' 𝓢 β",
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184,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
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Mathlib/CategoryTheory/Monoidal/Braided.lean | CategoryTheory.braiding_rightUnitor | [
{
"state_after": "no goals",
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"tactic": "rw [← tensor_left_iff, id_tensor_comp, braiding_rightUnitor_aux₂]"
}
] | [
206,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
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Std/Data/String/Lemmas.lean | String.Iterator.ValidFor.nextn | [
{
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"tactic": "simp [h, Iterator.nextn]"
},
{
"state_after": "l r : List Char\nit : Iterat... | [
611,
59
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
605,
1
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Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.empty | [
{
"state_after": "G : Type w\ninst✝ : TopologicalSpace G\nμ : Content G\nthis : Disjoint ↑⊥ ↑⊥ → toFun μ (⊥ ⊔ ⊥) = toFun μ ⊥ + toFun μ ⊥\n⊢ (fun s => ↑(toFun μ s)) ⊥ = 0",
"state_before": "G : Type w\ninst✝ : TopologicalSpace G\nμ : Content G\n⊢ (fun s => ↑(toFun μ s)) ⊥ = 0",
"tactic": "have := μ.sup_d... | [
119,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
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Mathlib/Data/List/ToFinsupp.lean | List.toFinsupp_apply_le | [] | [
85,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
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Mathlib/Algebra/Module/Submodule/Lattice.lean | Submodule.bot_ext | [
{
"state_after": "case mk\nR : Type u_2\nS : Type ?u.34876\nM : Type u_1\ninst✝⁶ : Semiring R\ninst✝⁵ : Semiring S\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\ninst✝² : Module S M\ninst✝¹ : SMul S R\ninst✝ : IsScalarTower S R M\np q : Submodule R M\ny : { x // x ∈ ⊥ }\nx : M\nxm : x ∈ ⊥\n⊢ { val := x, proper... | [
102,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
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Mathlib/Analysis/Asymptotics/SuperpolynomialDecay.lean | Asymptotics.SuperpolynomialDecay.mul_param_pow | [] | [
128,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
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Mathlib/Analysis/Complex/LocallyUniformLimit.lean | Complex.hasSum_deriv_of_summable_norm | [
{
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198,
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Mathlib/Probability/ProbabilityMassFunction/Basic.lean | Pmf.toOuterMeasure_apply | [] | [
161,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
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Mathlib/CategoryTheory/Monoidal/NaturalTransformation.lean | CategoryTheory.MonoidalNatIso.ofComponents.inv_app | [
{
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173,
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Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.opNorm_zero | [
{
"state_after": "V : Type ?u.313710\nV₁ : Type u_1\nV₂ : Type u_2\nV₃ : Type ?u.313719\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : SeminormedAddCommGroup V₁\ninst✝¹ : SeminormedAddCommGroup V₂\ninst✝ : SeminormedAddCommGroup V₃\nf g : NormedAddGroupHom V₁ V₂\nx✝ : V₁\n⊢ ‖↑0 x✝‖ = 0",
"state_before": "V : ... | [
384,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.BicartesianSq.of_is_biproduct₂ | [] | [
955,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
953,
1
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Mathlib/GroupTheory/Congruence.lean | Con.inf_iff_and | [] | [
501,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
500,
1
] |
Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Presieve.isSheaf_pretopology | [
{
"state_after": "case mp\nC : Type u₁\ninst✝¹ : Category C\nP Q U : Cᵒᵖ ⥤ Type w\nX Y : C\nS : Sieve X\nR : Presieve X\nJ J₂ : GrothendieckTopology C\ninst✝ : HasPullbacks C\nK : Pretopology C\n⊢ IsSheaf (Pretopology.toGrothendieck C K) P →\n ∀ {X : C} (R : Presieve X), R ∈ Pretopology.coverings K X → IsShe... | [
778,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
765,
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Mathlib/Topology/Order/Basic.lean | nhds_bot_basis | [] | [
1146,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1144,
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_erase_mul | [
{
"state_after": "no goals",
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"tactic": "rw [mul_c... | [
1664,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Semiquot.lean | Semiquot.bind_def | [] | [
159,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
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Mathlib/Analysis/Convex/Topology.lean | Convex.closure | [] | [
244,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
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Mathlib/CategoryTheory/Generator.lean | CategoryTheory.hasTerminal_of_isSeparating | [
{
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"state_before": "C : Type u₁\ninst✝⁴ : Category C\nD : Type u₂\ninst✝³ : ... | [
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311,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.zsmul_eq_iff | [] | [
178,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
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Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.f_iUnion | [
{
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"state_before": "α : Type u\nm : OuterMeasure α\ns✝ s₁ s₂ : Set α\ns : ℕ → Set α\nh : ∀ (i : ℕ), IsCarathe... | [
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1023,
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Mathlib/Order/CompleteLattice.lean | iInf_plift_down | [] | [
732,
52
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731,
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.prod_single_index | [
{
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1735,
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Mathlib/Data/Set/Prod.lean | Set.diagonal_subset_iff | [
{
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"tactic": "rw [← range_diag, range_subset_iff]"
}
] | [
501,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
500,
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Mathlib/Data/Set/Basic.lean | Set.diff_univ | [] | [
1912,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1911,
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Mathlib/Analysis/SpecialFunctions/Integrals.lean | intervalIntegral.intervalIntegrable_one_div | [] | [
197,
51
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195,
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Mathlib/Data/Int/Bitwise.lean | Int.bit_decomp | [] | [
139,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
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Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableEquiv.measurable_comp_iff | [
{
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Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.natCoe_mul | [
{
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"state_before": "R : Type u_1\ninst✝ : Semiring R\nf g : ArithmeticFunction ℕ\n⊢ ↑(f * g) = ↑f * ↑g",
"tactic": "ext n"
},
{
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288,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.choose_succ_succ' | [] | [
69,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
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Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.coe_mk | [] | [
134,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Series.lean | Complex.hasSum_sin' | [
{
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"tactic": "rw [Complex.sin, Complex.exp_eq_exp_ℂ]"
},
{
... | [
66,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.hausdorffEdist_self | [
{
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272,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
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Mathlib/Data/Polynomial/Reverse.lean | Polynomial.reverse_natTrailingDegree | [
{
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309,
40
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303,
1
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Mathlib/Analysis/NormedSpace/AddTorsor.lean | dist_lineMap_right | [
{
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122,
66
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118,
1
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Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.of_comp | [
{
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239,
48
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234,
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Mathlib/Data/Complex/Exponential.lean | Real.sinh_two_mul | [
{
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"state_before": "x y : ℝ\n⊢ sinh (2 * x) = 2 * sinh x * cosh x",
"tactic": "rw [← ofReal_inj]"
},
{
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1449,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1448,
8
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Mathlib/Order/GaloisConnection.lean | sInf_image2_eq_sSup_sInf | [] | [
416,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_eq_prod_diff_singleton_mul | [
{
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"tactic": "rw [prod_eq... | [
1562,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1560,
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Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.isRegular_aleph'_succ | [
{
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"tactic": "rw [aleph'_succ]"
},
{
"state_after": "no goals",
"state_b... | [
1008,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1006,
1
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Mathlib/LinearAlgebra/Dfinsupp.lean | CompleteLattice.Independent.dfinsupp_lsum_injective | [
{
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513,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
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Mathlib/Algebra/GCDMonoid/Basic.lean | lcm_one_right | [] | [
802,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
801,
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Mathlib/Topology/GDelta.lean | Set.Subsingleton.isGδ_compl | [] | [
154,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.toNat_finset_prod | [] | [
1819,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1817,
1
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Mathlib/MeasureTheory/Integral/CircleIntegral.lean | hasFPowerSeriesOn_cauchy_integral | [
{
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644,
45
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635,
1
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Mathlib/Order/MinMax.lean | min_le_of_left_le | [] | [
100,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
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Mathlib/AlgebraicTopology/DoldKan/Projections.lean | AlgebraicTopology.DoldKan.P_add_Q_f | [] | [
84,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
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Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | HomogeneousLocalization.pow_val | [
{
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454,
10
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448,
1
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.spanExt_inv_app_zero | [
{
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501,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
500,
1
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Mathlib/Algebra/Order/ToIntervalMod.lean | toIocDiv_add_right' | [
{
"state_after": "no goals",
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"tactic": "simpa only [one_zsmul] using toIocDiv_add_zsmul' hp a b 1"
}
] | [
315,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
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Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.nadd_right_cancel | [] | [
439,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometry.coe_toAffineMap | [
{
"state_after": "no goals",
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83,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
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Mathlib/RingTheory/Ideal/Basic.lean | Ideal.exists_le_maximal | [] | [
335,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/Data/Set/Basic.lean | Set.not_subsingleton_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns s₁ s₂ t t₁ t₂ u : Set α\n⊢ ¬Set.Subsingleton s ↔ Set.Nontrivial s",
"tactic": "simp_rw [Set.Subsingleton, Set.Nontrivial, not_forall]"
}
] | [
2606,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2605,
1
] |
Mathlib/Topology/Algebra/UniformRing.lean | UniformSpace.Completion.coe_one | [] | [
63,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_right | [] | [
644,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
640,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.mul_submatrix_one | [
{
"state_after": "case intro\nl : Type u_4\nm : Type u_3\nn : Type u_1\no : Type u_2\nm' : o → Type ?u.1174423\nn' : o → Type ?u.1174428\nR : Type ?u.1174431\nS : Type ?u.1174434\nα : Type v\nβ : Type w\nγ : Type ?u.1174441\ninst✝³ : Fintype n\ninst✝² : Finite o\ninst✝¹ : NonAssocSemiring α\ninst✝ : DecidableEq... | [
2527,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2518,
1
] |
Mathlib/Topology/Covering.lean | FiberBundle.isCoveringMap | [] | [
194,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
11
] |
Mathlib/Algebra/Homology/Additive.lean | ChainComplex.map_chain_complex_of | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.119211\nV : Type u\ninst✝⁷ : Category V\ninst✝⁶ : Preadditive V\nc : ComplexShape ι\nC D E : HomologicalComplex V c\nf g : C ⟶ D\nh k : D ⟶ E\ni : ι\nW : Type ?u.119566\ninst✝⁵ : Category W\ninst✝⁴ : Preadditive W\nα : Type ?u.119588\ninst✝³ : AddRig... | [
273,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Logic/Basic.lean | or_not | [] | [
201,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Order/Filter/Germ.lean | Filter.Germ.const_compTendsto' | [] | [
288,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | IsClosed.exists_infDist_eq_dist | [
{
"state_after": "case intro\nι : Sort ?u.69127\nα : Type u\nβ : Type v\ninst✝² : PseudoMetricSpace α\ninst✝¹ : PseudoMetricSpace β\ns t u : Set α\nx✝ y : α\nΦ : α → β\ninst✝ : ProperSpace α\nh : IsClosed s\nx z : α\nhz : z ∈ s\n⊢ ∃ y, y ∈ s ∧ infDist x s = dist x y",
"state_before": "ι : Sort ?u.69127\nα :... | [
647,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
639,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.two_zsmul_coe_pi | [
{
"state_after": "no goals",
"state_before": "⊢ 2 • ↑π = 0",
"tactic": "simp [← coe_int_mul_eq_zsmul]"
}
] | [
169,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Topology/CompactOpen.lean | ContinuousMap.tendsto_compactOpen_iff_forall | [
{
"state_after": "α : Type u_2\nβ : Type u_3\nγ : Type ?u.29261\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\nι : Type u_1\nl : Filter ι\nF : ι → C(α, β)\nf : C(α, β)\n⊢ Filter.Tendsto F l (𝓝 f) ↔\n ∀ (s : Set α), IsCompact s → Filter.Tendsto (fun i => restrict s (F ... | [
272,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/Order/Directed.lean | exists_lt_of_directed_ge | [
{
"state_after": "case intro.intro\nα : Type u\nβ : Type v\nι : Sort w\nr r' s : α → α → Prop\ninst✝³ : Preorder α\na✝ : α\ninst✝² : PartialOrder β\ninst✝¹ : IsDirected β fun x x_1 => x ≥ x_1\ninst✝ : Nontrivial β\na b : β\nhne : a ≠ b\n⊢ ∃ a b, a < b",
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303,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.Measure.add_prod | [
{
"state_after": "α : Type u_1\nα' : Type ?u.4497375\nβ : Type u_2\nβ' : Type ?u.4497381\nγ : Type ?u.4497384\nE : Type ?u.4497387\ninst✝⁸ : MeasurableSpace α\ninst✝⁷ : MeasurableSpace α'\ninst✝⁶ : MeasurableSpace β\ninst✝⁵ : MeasurableSpace β'\ninst✝⁴ : MeasurableSpace γ\nμ μ'✝ : Measure α\nν ν' : Measure β\nτ... | [
590,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.compLeft_compRight | [] | [
582,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
1
] |
Mathlib/Analysis/SpecialFunctions/ImproperIntegrals.lean | integral_Ioi_cpow_of_lt | [
{
"state_after": "a : ℂ\nha : a.re < -1\nc : ℝ\nhc : 0 < c\n⊢ Tendsto (fun i => ∫ (x : ℝ) in c..id i, ↑x ^ a) atTop (𝓝 (-↑c ^ (a + 1) / (a + 1)))",
"state_before": "a : ℂ\nha : a.re < -1\nc : ℝ\nhc : 0 < c\n⊢ (∫ (t : ℝ) in Ioi c, ↑t ^ a) = -↑c ^ (a + 1) / (a + 1)",
"tactic": "refine'\n tendsto_nhds_un... | [
125,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Topology/UniformSpace/Completion.lean | CauchyFilter.denseRange_pureCauchy | [
{
"state_after": "α : Type u\ninst✝² : UniformSpace α\nβ : Type v\nγ : Type w\ninst✝¹ : UniformSpace β\ninst✝ : UniformSpace γ\nf : CauchyFilter α\nh_ex : ∀ (s : Set (CauchyFilter α × CauchyFilter α)), s ∈ 𝓤 (CauchyFilter α) → ∃ y, (f, pureCauchy y) ∈ s\n⊢ f ∈ closure (range pureCauchy)",
"state_before": "... | [
201,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.IsSt.map₂ | [
{
"state_after": "case intro\ny : ℝ*\nr s : ℝ\nhys : IsSt y s\nf : ℝ → ℝ → ℝ\nhf : ContinuousAt (Function.uncurry f) (r, s)\nx : ℕ → ℝ\nhxr : IsSt (ofSeq x) r\n⊢ IsSt (Germ.map₂ f (ofSeq x) y) (f r s)",
"state_before": "x y : ℝ*\nr s : ℝ\nhxr : IsSt x r\nhys : IsSt y s\nf : ℝ → ℝ → ℝ\nhf : ContinuousAt (Fun... | [
401,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
] |
Mathlib/Topology/Order/Basic.lean | ContinuousAt.eventually_lt | [] | [
675,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
673,
8
] |
Mathlib/Order/SuccPred/IntervalSucc.lean | Monotone.pairwise_disjoint_on_Ioc_pred | [] | [
82,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Std/Data/Array/Lemmas.lean | Array.get?_eq_getElem? | [] | [
41,
83
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
41,
9
] |
Mathlib/Analysis/Calculus/FormalMultilinearSeries.lean | FormalMultilinearSeries.order_eq_zero_iff' | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\n𝕜' : Type u'\nE : Type v\nF : Type w\nG : Type x\ninst✝¹⁰ : CommRing 𝕜\nn : ℕ\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : Module 𝕜 E\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : TopologicalAddGroup E\ninst✝⁵ : ContinuousConstSMul 𝕜 E\ninst✝⁴ : AddCommGroup F\n... | [
240,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.diag_one | [] | [
652,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
651,
1
] |
Mathlib/CategoryTheory/Preadditive/Biproducts.lean | CategoryTheory.Limits.HasBiproduct.of_hasCoproduct | [
{
"state_after": "case intro\nC : Type u\ninst✝⁴ : Category C\ninst✝³ : Preadditive C\nJ✝ : Type\ninst✝² : Fintype J✝\nJ : Type\ninst✝¹ : Finite J\nf : J → C\ninst✝ : HasCoproduct f\nval✝ : Fintype J\n⊢ HasBiproduct f",
"state_before": "C : Type u\ninst✝⁴ : Category C\ninst✝³ : Preadditive C\nJ✝ : Type\nins... | [
189,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Analysis/Calculus/IteratedDeriv.lean | norm_iteratedFDeriv_eq_norm_iteratedDeriv | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type u_1\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type ?u.109858\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nn : ℕ\nf : 𝕜 → F\ns : Set 𝕜\nx : 𝕜\n⊢ ‖iteratedFDeriv 𝕜 n... | [
248,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Algebra/Order/Ring/WithTop.lean | WithBot.bot_mul_bot | [] | [
250,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigOWith_const_one | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.290943\nE : Type u_2\nF : Type u_3\nG : Type ?u.290952\nE' : Type ?u.290955\nF' : Type ?u.290958\nG' : Type ?u.290961\nE'' : Type ?u.290964\nF'' : Type ?u.290967\nG'' : Type ?u.290970\nR : Type ?u.290973\nR' : Type ?u.290976\n𝕜 : Type ... | [
1309,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1308,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.hasSum_integral_of_dominated_convergence | [
{
"state_after": "α : Type u_2\nE : Type u_3\nF✝ : Type ?u.1002225\n𝕜 : Type ?u.1002228\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace ℝ E\ninst✝⁷ : CompleteSpace E\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedSpace 𝕜 E\ninst✝⁴ : SMulCommClass ℝ 𝕜 E\ninst✝³ : NormedAddCommGroup F✝\ninst✝² : Nor... | [
1039,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1014,
1
] |
Mathlib/Data/Nat/Upto.lean | Nat.Upto.wf | [
{
"state_after": "p : ℕ → Prop\nx : ℕ\nh : p x\n⊢ Upto.GT p = Measure fun y => x - ↑y",
"state_before": "p : ℕ → Prop\nx : ℕ\nh : p x\n⊢ WellFounded (Upto.GT p)",
"tactic": "suffices Upto.GT p = Measure fun y : Nat.Upto p => x - y.val by\n rw [this]\n exact (measure _).wf"
},
{
"state_after": ... | [
63,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
11
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.mem_compl_zeroLocus_iff_not_mem | [
{
"state_after": "R : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nf : R\nI : PrimeSpectrum R\n⊢ ¬f ∈ ↑I.asIdeal ↔ ¬f ∈ I.asIdeal",
"state_before": "R : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nf : R\nI : PrimeSpectrum R\n⊢ I ∈ zeroLocus {f}ᶜ ↔ ¬f ∈ I.asIdeal",
"tacti... | [
401,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/Topology/Perfect.lean | Perfect.small_diam_aux | [
{
"state_after": "α : Type u_1\ninst✝ : MetricSpace α\nC : Set α\nhC : Perfect C\nε : ℝ≥0∞\nε_pos : 0 < ε\nx : α\nxC : x ∈ C\nthis : x ∈ EMetric.ball x (ε / 2)\n⊢ let D := closure (EMetric.ball x (ε / 2) ∩ C);\n Perfect D ∧ Set.Nonempty D ∧ D ⊆ C ∧ EMetric.diam D ≤ ε",
"state_before": "α : Type u_1\ninst✝ ... | [
244,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
9
] |
Mathlib/Dynamics/Ergodic/Ergodic.lean | Ergodic.ae_empty_or_univ_of_preimage_ae_le' | [
{
"state_after": "α : Type u_1\nm : MeasurableSpace α\nf : α → α\ns : Set α\nμ : MeasureTheory.Measure α\nhf : Ergodic f\nhs : MeasurableSet s\nhs' : f ⁻¹' s ≤ᶠ[ae μ] s\nh_fin : ↑↑μ s ≠ ⊤\n⊢ f ⁻¹' s =ᶠ[ae μ] s",
"state_before": "α : Type u_1\nm : MeasurableSpace α\nf : α → α\ns : Set α\nμ : MeasureTheory.Me... | [
143,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Std/Data/Int/Lemmas.lean | Int.ofNat_add | [] | [
35,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
35,
1
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.abs_to_nat | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.659055\np : PosNum\n⊢ natAbs ↑↑p = natAbs (-↑p)",
"tactic": "rw [p.to_nat_to_int, Int.natAbs_neg]"
}
] | [
1100,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1097,
1
] |
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