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/Topology/Sets/Compacts.lean | TopologicalSpace.NonemptyCompacts.coe_toCompacts | [] | [
257,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
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Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | Ideal.IsHomogeneous.toIdeal_homogeneousCore_eq_self | [
{
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"stat... | [
212,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
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Mathlib/NumberTheory/Divisors.lean | Nat.properDivisors_eq_singleton_one_iff_prime | [
{
"state_after": "case refine_1\nn : ℕ\n⊢ properDivisors n = {1} → Prime n\n\ncase refine_2\nn : ℕ\n⊢ Prime n → properDivisors n = {1}",
"state_before": "n : ℕ\n⊢ properDivisors n = {1} ↔ Prime n",
"tactic": "refine ⟨?_, ?_⟩"
},
{
"state_after": "case refine_1\nn : ℕ\nh : properDivisors n = {1}\... | [
407,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.erase_single_ne | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.165853\nγ : Type ?u.165856\nι : Type ?u.165859\nM : Type u_2\nM' : Type ?u.165865\nN : Type ?u.165868\nP : Type ?u.165871\nG : Type ?u.165874\nH : Type ?u.165877\nR : Type ?u.165880\nS : Type ?u.165883\ninst✝ : Zero M\na a' : α\nb : M\nh : a ≠ a'\ns : α\n⊢ ↑(e... | [
664,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
661,
1
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.map_add | [] | [
1862,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1861,
1
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Mathlib/Topology/UniformSpace/Completion.lean | UniformSpace.Completion.induction_on₃ | [] | [
516,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
] |
Mathlib/Data/Set/Basic.lean | Set.diff_subset_iff | [] | [
1925,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1924,
1
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csSup_image2_eq_csSup_csSup | [
{
"state_after": "α : Type u_1\nβ : Type u_3\nγ : Type u_2\nι : Sort ?u.111757\ninst✝² : ConditionallyCompleteLattice α\ninst✝¹ : ConditionallyCompleteLattice β\ninst✝ : ConditionallyCompleteLattice γ\nf : α → β → γ\ns : Set α\nt : Set β\nl u : α → β → γ\nl₁ u₁ : β → γ → α\nl₂ u₂ : α → γ → β\nh₁ : ∀ (b : β), Ga... | [
1388,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1381,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.omega_pos | [] | [
182,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
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Std/Data/Nat/Lemmas.lean | Nat.dvd_sub | [
{
"state_after": "no goals",
"state_before": "k m n : Nat\nH : n ≤ m\nh₁ : k ∣ m\nh₂ : k ∣ n\n⊢ k ∣ m - n + n",
"tactic": "rwa [Nat.sub_add_cancel H]"
}
] | [
680,
63
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
679,
1
] |
Mathlib/Data/Finite/Set.lean | Finite.of_injective_finite_range | [] | [
37,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/Topology/Constructions.lean | continuous_uncurry_of_discreteTopology_left | [] | [
681,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
677,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iInter_inter | [] | [
552,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.image_eq_target_inter_inv_preimage | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.32478\nδ : Type ?u.32481\ne : LocalEquiv α β\ne' : LocalEquiv β γ\ns : Set α\nh : s ⊆ e.source\n⊢ ↑e '' s = e.target ∩ ↑(LocalEquiv.symm e) ⁻¹' s",
"tactic": "rw [← e.image_source_inter_eq', inter_eq_self_of_subset_rig... | [
496,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.finite_const_le_of_tsum_ne_top | [
{
"state_after": "α : Type ?u.301039\nβ : Type ?u.301042\nγ : Type ?u.301045\na✝ b c d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε✝ ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\nf g : α → ℝ≥0∞\nι : Type u_1\na : ι → ℝ≥0∞\ntsum_ne_top : (∑' (i : ι), a i) ≠ ⊤\nε : ℝ≥0∞\nε_ne_zero : ε ≠ 0\nh : ¬Set.Finite {i | ε ≤ a i}\n⊢ False",
"state_befor... | [
1047,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1040,
1
] |
Mathlib/Order/CompleteLattice.lean | sSup_empty | [] | [
485,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
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] |
Mathlib/CategoryTheory/Sites/CompatibleSheafification.lean | CategoryTheory.GrothendieckTopology.sheafifyCompIso_inv_eq_sheafifyLift | [
{
"state_after": "case a\nC : Type u\ninst✝¹² : Category C\nJ : GrothendieckTopology C\nD : Type w₁\ninst✝¹¹ : Category D\nE : Type w₂\ninst✝¹⁰ : Category E\nF : D ⥤ E\ninst✝⁹ : ∀ (α β : Type (max v u)) (fst snd : β → α), HasLimitsOfShape (WalkingMulticospan fst snd) D\ninst✝⁸ : ∀ (α β : Type (max v u)) (fst sn... | [
158,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/NumberTheory/Bernoulli.lean | bernoulli_eq_bernoulli'_of_ne_one | [
{
"state_after": "case pos\nA : Type ?u.635032\ninst✝¹ : CommRing A\ninst✝ : Algebra ℚ A\nn : ℕ\nhn : n ≠ 1\nh0 : n = 0\n⊢ bernoulli n = bernoulli' n\n\ncase neg\nA : Type ?u.635032\ninst✝¹ : CommRing A\ninst✝ : Algebra ℚ A\nn : ℕ\nhn : n ≠ 1\nh0 : ¬n = 0\n⊢ bernoulli n = bernoulli' n",
"state_before": "A :... | [
225,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.summable_nnnorm_mul_pow | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.220483\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\np✝ : FormalMultilinea... | [
303,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.integral_integral_sub' | [] | [
418,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/Data/Rat/Cast.lean | Rat.cast_strictMono | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.55640\nι : Type ?u.55643\nα : Type ?u.55646\nβ : Type ?u.55649\nK : Type u_1\ninst✝ : LinearOrderedField K\nm n : ℚ\n⊢ m < n → ↑m < ↑n",
"tactic": "simpa only [sub_pos, cast_sub] using @cast_pos_of_pos K _ (n - m)"
}
] | [
306,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
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Mathlib/Data/Set/Pointwise/BigOperators.lean | Set.image_fintype_prod_pi | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : Type u_2\nβ : Type ?u.90981\nF : Type ?u.90984\ninst✝³ : CommMonoid α\ninst✝² : CommMonoid β\ninst✝¹ : MonoidHomClass F α β\ninst✝ : Fintype ι\nS : ι → Set α\n⊢ (fun f => ∏ i : ι, f i) '' pi univ S = ∏ i : ι, S i",
"tactic": "simpa only [Fi... | [
191,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Iio_filter_lt | [
{
"state_after": "case a\nι : Type ?u.150465\nα✝ : Type ?u.150468\ninst✝³ : LinearOrder α✝\ninst✝² : LocallyFiniteOrder α✝\na✝¹ b✝ : α✝\nα : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : LocallyFiniteOrderBot α\na b a✝ : α\n⊢ a✝ ∈ filter (fun x => x < b) (Iio a) ↔ a✝ ∈ Iio (min a b)",
"state_before": "ι : Type ... | [
811,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
808,
1
] |
Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.leComap_id | [] | [
292,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.HasLimit.isoOfNatIso_inv_π | [] | [
358,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/MeasureTheory/Group/Prod.lean | MeasureTheory.ae_measure_preimage_mul_right_lt_top | [
{
"state_after": "G : Type u_1\ninst✝⁷ : MeasurableSpace G\ninst✝⁶ : Group G\ninst✝⁵ : MeasurableMul₂ G\nμ ν : Measure G\ninst✝⁴ : SigmaFinite ν\ninst✝³ : SigmaFinite μ\ns : Set G\ninst✝² : MeasurableInv G\ninst✝¹ : IsMulLeftInvariant μ\ninst✝ : IsMulLeftInvariant ν\nsm : MeasurableSet s\nhμs : ↑↑μ s ≠ ⊤\n⊢ ∀ (... | [
291,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/GroupTheory/GroupAction/Quotient.lean | Subgroup.quotientCenterEmbedding_apply | [] | [
403,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.vsub_subset_vsub | [] | [
665,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
664,
1
] |
Mathlib/CategoryTheory/Limits/FunctorCategory.lean | CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_inv_colimit_map | [
{
"state_after": "case w\nC : Type u\ninst✝⁴ : Category C\nD : Type u'\ninst✝³ : Category D\nJ : Type u₁\ninst✝² : Category J\nK : Type u₂\ninst✝¹ : Category K\ninst✝ : HasColimitsOfShape J C\nF : J ⥤ K ⥤ C\ni j : K\nf : i ⟶ j\nj✝ : J\n⊢ colimit.ι (F ⋙ (evaluation K C).obj i) j✝ ≫ (colimitObjIsoColimitCompEvalu... | [
306,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/RingTheory/WittVector/Defs.lean | WittVector.one_coeff_zero | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nR : Type u_1\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\n⊢ ↑(aeval (Function.uncurry fun i => ![].coeff)) (wittOne p 0) = 1",
"tactic": "simp only [wittOne_zero_eq_one, AlgHom.map_one]"
}
] | [
342,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/Data/List/Forall2.lean | List.Forall₂.mp | [] | [
50,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/Data/Int/GCD.lean | Int.gcd_one_left | [] | [
285,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.coeff_eq_zero_of_natDegree_lt | [
{
"state_after": "case h\nR : Type u\nS : Type v\na b c d : R\nn✝ m : ℕ\ninst✝ : Semiring R\np✝ q r p : R[X]\nn : ℕ\nh : natDegree p < n\n⊢ degree p < ↑n",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn✝ m : ℕ\ninst✝ : Semiring R\np✝ q r p : R[X]\nn : ℕ\nh : natDegree p < n\n⊢ coeff p n = 0",
"... | [
355,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.updateRow_conjTranspose | [
{
"state_after": "l : Type ?u.1227385\nm : Type u_2\nn : Type u_1\no : Type ?u.1227394\nm' : o → Type ?u.1227399\nn' : o → Type ?u.1227404\nR : Type ?u.1227407\nS : Type ?u.1227410\nα : Type v\nβ : Type w\nγ : Type ?u.1227417\nM : Matrix m n α\ni : m\nj : n\nb : n → α\nc : m → α\ninst✝¹ : DecidableEq n\ninst✝ :... | [
2831,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2827,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | MeasureTheory.Measure.add_haar_smul_of_nonneg | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : MeasurableSpace E\ninst✝⁵ : BorelSpace E\ninst✝⁴ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝³ : IsAddHaarMeasure μ\nF : Type ?u.1940240\ninst✝² : NormedAddCommGroup F\ninst✝¹ : Nor... | [
366,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidWithZeroHom.comp_apply | [] | [
688,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
687,
1
] |
Mathlib/Data/Part.lean | Part.mul_mem_mul | [
{
"state_after": "α : Type u_1\nβ : Type ?u.56876\nγ : Type ?u.56879\ninst✝ : Mul α\na b : Part α\nma mb : α\nha : ma ∈ a\nhb : mb ∈ b\n⊢ get (a * b)\n (_ : ∃ h, ((fun b_1 => (fun y => map y ((fun x => b) ())) (get ((fun x x_1 => x * x_1) <$> a) b_1)) h).Dom) =\n get a (_ : a.Dom) * get b (_ : b.Dom)",
... | [
719,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
718,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.span_singleton_le_span_singleton | [] | [
508,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Std/Data/Int/Lemmas.lean | Int.toNat_add_toNat_neg_eq_natAbs | [] | [
1406,
29
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1403,
9
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.mapQ_pow | [
{
"state_after": "case zero\nR : Type u_1\nM : Type u_2\nr : R\nx y : M\ninst✝⁵ : Ring R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\np p' : Submodule R M\nR₂ : Type ?u.292638\nM₂ : Type ?u.292641\ninst✝² : Ring R₂\ninst✝¹ : AddCommGroup M₂\ninst✝ : Module R₂ M₂\nτ₁₂ : R →+* R₂\nq : Submodule R₂ M₂\nf : M →ₗ[... | [
458,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.hasPullbacks_of_hasLimit_cospan | [] | [
2674,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2672,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | continuousMultilinearCurryRightEquiv_symm_apply | [] | [
1574,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1571,
1
] |
Std/Data/List/Lemmas.lean | List.replaceF_cons | [] | [
1307,
34
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1304,
1
] |
Mathlib/Data/PFunctor/Univariate/M.lean | PFunctor.Approx.cofixA_eq_zero | [] | [
52,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometry.injective | [] | [
164,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
11
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithBot.map_one | [] | [
533,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
11
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.opow_isLimit | [] | [
128,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.IsPartition.existsUnique | [
{
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"state_before": "ι : Type u_1\nI J J₁ J₂ : Box ι\nπ π₁ π₂ : Prepartitio... | [
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83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
745,
11
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.coe_pow | [] | [
607,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
606,
1
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Mathlib/Analysis/NormedSpace/FiniteDimension.lean | Basis.op_nnnorm_le | [
{
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290,
92
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274,
1
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Mathlib/Data/PFunctor/Univariate/Basic.lean | PFunctor.map_eq | [] | [
65,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
11
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Mathlib/Data/Erased.lean | Erased.pure_def | [] | [
146,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
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Mathlib/CategoryTheory/Monoidal/OfHasFiniteProducts.lean | CategoryTheory.monoidalOfHasFiniteProducts.leftUnitor_hom | [] | [
104,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
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Mathlib/Topology/LocallyFinite.lean | LocallyFinite.continuousOn_iUnion | [] | [
109,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
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Mathlib/Data/Finset/Lattice.lean | Finset.iInf_option_toFinset | [] | [
1943,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1942,
1
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Mathlib/Data/Polynomial/Coeff.lean | Polynomial.mul_X_pow_injective | [
{
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303,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.ae_eq_of_ae_le_of_lintegral_le | [
{
"state_after": "α : Type u_1\nβ : Type ?u.967242\nγ : Type ?u.967245\nδ : Type ?u.967248\nm : MeasurableSpace α\nμ ν : Measure α\nf g : α → ℝ≥0∞\nhfg : f ≤ᵐ[μ] g\nhf : (∫⁻ (x : α), f x ∂μ) ≠ ⊤\nhg : AEMeasurable g\nhgf : (∫⁻ (x : α), g x ∂μ) ≤ ∫⁻ (x : α), f x ∂μ\nthis : ∀ (n : ℕ), ∀ᵐ (x : α) ∂μ, g x < f x + (... | [
868,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
855,
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Mathlib/Data/Polynomial/UnitTrinomial.lean | Polynomial.trinomial_support | [] | [
125,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
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Mathlib/Tactic/CancelDenoms.lean | CancelDenoms.derive_trans | [] | [
189,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
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Mathlib/Data/ZMod/Basic.lean | ZMod.lift_comp_castAddHom | [] | [
1222,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1221,
1
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Mathlib/Data/Finset/Slice.lean | Finset.pairwiseDisjoint_slice | [] | [
165,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
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Mathlib/LinearAlgebra/AnnihilatingPolynomial.lean | Polynomial.degree_annIdealGenerator_le_of_mem | [] | [
154,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
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Mathlib/RingTheory/IntegralClosure.lean | IsIntegral.pow_iff | [] | [
673,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
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src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.denote_monomialToExpr | [
{
"state_after": "ctx : Context\nk : Nat\nv : Var\n⊢ Expr.denote ctx (bif v == fixedVar then Expr.num k else bif k == 1 then Expr.var v else Expr.mulL k (Expr.var v)) =\n k * Var.denote ctx v",
"state_before": "ctx : Context\nk : Nat\nv : Var\n⊢ Expr.denote ctx (monomialToExpr k v) = k * Var.denote ctx v... | [
699,
70
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
695,
1
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Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.Measure.prod_eq | [] | [
508,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
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Mathlib/Topology/MetricSpace/GromovHausdorffRealized.lean | GromovHausdorff.candidatesB_nonempty | [] | [
238,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
9
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_X_add_C | [
{
"state_after": "R : Type u\nS : Type v\na✝ b c d : R\nn m : ℕ\ninst✝¹ : Nontrivial R\ninst✝ : Semiring R\na : R\nthis : degree (↑C a) < degree X\n⊢ degree (X + ↑C a) = 1",
"state_before": "R : Type u\nS : Type v\na✝ b c d : R\nn m : ℕ\ninst✝¹ : Nontrivial R\ninst✝ : Semiring R\na : R\n⊢ degree (X + ↑C a) ... | [
1364,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1358,
1
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Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.not_isUnit_X_sub_C | [
{
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507,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
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Mathlib/Algebra/Order/Field/Basic.lean | inv_pos_le_iff_one_le_mul | [
{
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212,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
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Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.eq_zero_or_opow_omega_le_of_mul_eq_right | [
{
"state_after": "case inl\na b : Ordinal\nhab : a * b = b\nha : a = 0\n⊢ b = 0 ∨ a ^ ω ≤ b\n\ncase inr\na b : Ordinal\nhab : a * b = b\nha : 0 < a\n⊢ b = 0 ∨ a ^ ω ≤ b",
"state_before": "a b : Ordinal\nhab : a * b = b\n⊢ b = 0 ∨ a ^ ω ≤ b",
"tactic": "cases' eq_zero_or_pos a with ha ha"
},
{
"s... | [
675,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
666,
1
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Mathlib/Algebra/Order/Interval.lean | NonemptyInterval.length_zero | [] | [
652,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
651,
1
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Mathlib/GroupTheory/Solvable.lean | IsSimpleGroup.comm_iff_isSolvable | [
{
"state_after": "case zero\nG : Type u_1\nG' : Type ?u.84178\ninst✝² : Group G\ninst✝¹ : Group G'\nf : G →* G'\ninst✝ : IsSimpleGroup G\nx✝ : IsSolvable G\nhn : derivedSeries G Nat.zero = ⊥\n⊢ ∀ (a b : G), a * b = b * a\n\ncase succ\nG : Type u_1\nG' : Type ?u.84178\ninst✝² : Group G\ninst✝¹ : Group G'\nf : G ... | [
202,
40
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192,
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src/lean/Init/Core.lean | Eq.substr | [] | [
551,
10
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
550,
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Mathlib/Order/Heyting/Basic.lean | himp_le_himp_himp_himp | [
{
"state_after": "ι : Type ?u.30631\nα : Type u_1\nβ : Type ?u.30637\ninst✝ : GeneralizedHeytingAlgebra α\na b c d : α\n⊢ c ⊓ (b ⊓ a) ≤ c",
"state_before": "ι : Type ?u.30631\nα : Type u_1\nβ : Type ?u.30637\ninst✝ : GeneralizedHeytingAlgebra α\na b c d : α\n⊢ b ⇨ c ≤ (a ⇨ b) ⇨ a ⇨ c",
"tactic": "rw [le... | [
389,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.isUnit_constantCoeff | [] | [
527,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
] |
Mathlib/CategoryTheory/Adjunction/Limits.lean | CategoryTheory.Adjunction.hasColimit_of_comp_equivalence | [] | [
149,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.div_lt_of_lt_mul | [] | [
404,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
11
] |
Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.shortestPrefixDiff_pos | [
{
"state_after": "case intro\nE : ℕ → Type u_1\ninst✝¹ : (n : ℕ) → TopologicalSpace (E n)\ninst✝ : ∀ (n : ℕ), DiscreteTopology (E n)\ns : Set ((n : ℕ) → E n)\nhs : IsClosed s\nx : (n : ℕ) → E n\nhx : ¬x ∈ s\ny : (n : ℕ) → E n\nhy : y ∈ s\n⊢ 0 < shortestPrefixDiff x s",
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528,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
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Mathlib/RepresentationTheory/Basic.lean | Representation.asAlgebraHom_single_one | [
{
"state_after": "no goals",
"state_before": "k : Type u_2\nG : Type u_3\nV : Type u_1\ninst✝³ : CommSemiring k\ninst✝² : Monoid G\ninst✝¹ : AddCommMonoid V\ninst✝ : Module k V\nρ : Representation k G V\ng : G\n⊢ ↑(asAlgebraHom ρ) (Finsupp.single g 1) = ↑ρ g",
"tactic": "simp"
}
] | [
97,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | iteratedFDeriv_add_apply' | [] | [
1252,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1249,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.mem_closedBall_self | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.804396\nR' : Type ?u.804399\n𝕜 : Type u_2\n𝕜₂ : Type ?u.804405\n𝕜₃ : Type ?u.804408\n𝕝 : Type ?u.804411\nE : Type u_1\nE₂ : Type ?u.804417\nE₃ : Type ?u.804420\nF : Type ?u.804423\nG : Type ?u.804426\nι : Type ?u.804429\ninst✝² : SeminormedRing �... | [
659,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
659,
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Mathlib/Algebra/MonoidAlgebra/Degree.lean | AddMonoidAlgebra.le_inf_support_pow | [
{
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130,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
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Mathlib/Data/Polynomial/Coeff.lean | Polynomial.coeff_X_mul_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝ : Semiring R\np✝ q r p : R[X]\n⊢ coeff (X * p) 0 = 0",
"tactic": "simp"
}
] | [
152,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.lsub_eq_blsub | [] | [
1776,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1774,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.const_smul | [] | [
363,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.isIso_limit_cone_parallelPair_of_eq | [] | [
862,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
860,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.iSup_option_toFinset | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.432384\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.432393\nι : Type ?u.432396\nκ : Type ?u.432399\ninst✝ : CompleteLattice β\no : Option α\nf : α → β\n⊢ (⨆ (x : α) (_ : x ∈ Option.toFinset o), f x) = ⨆ (x : α) (_ : x ∈ o), f x",
"tactic": "simp"
}... | [
1939,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1938,
1
] |
Mathlib/Data/Polynomial/Reverse.lean | Polynomial.reverse_trailingCoeff | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nf✝ f : R[X]\n⊢ trailingCoeff (reverse f) = leadingCoeff f",
"tactic": "rw [trailingCoeff, reverse_natTrailingDegree, coeff_zero_reverse]"
}
] | [
313,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | exp_add | [] | [
631,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
629,
1
] |
Mathlib/GroupTheory/GroupAction/ConjAct.lean | ConjAct.units_smul_def | [] | [
165,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mem_iInf | [
{
"state_after": "no goals",
"state_before": "G : Type u_2\nG' : Type ?u.188426\ninst✝² : Group G\ninst✝¹ : Group G'\nA : Type ?u.188435\ninst✝ : AddGroup A\nH K : Subgroup G\nι : Sort u_1\nS : ι → Subgroup G\nx : G\n⊢ (x ∈ ⨅ (i : ι), S i) ↔ ∀ (i : ι), x ∈ S i",
"tactic": "simp only [iInf, mem_sInf, Set... | [
1001,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1000,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | map_extChartAt_nhdsWithin_eq_image | [] | [
1168,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1165,
1
] |
Mathlib/Data/List/Basic.lean | List.enum_cons' | [] | [
3928,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3926,
1
] |
Mathlib/Data/List/Basic.lean | List.map₂Right_cons_cons | [] | [
4153,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4151,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.target_subset_preimage_source | [] | [
546,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
1
] |
Mathlib/RingTheory/Localization/Integral.lean | IsLocalization.integerNormalization_map_to_map | [
{
"state_after": "R : Type u_2\ninst✝⁴ : CommRing R\nM : Submonoid R\nS : Type u_1\ninst✝³ : CommRing S\ninst✝² : Algebra R S\nP : Type ?u.42950\ninst✝¹ : CommRing P\ninst✝ : IsLocalization M S\np : S[X]\nb : { x // x ∈ M }\nhb : ∀ (i : ℕ), ↑(algebraMap R S) (coeff (integerNormalization M p) i) = ↑b • coeff p i... | [
106,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_le_iff | [] | [
715,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
715,
1
] |
Mathlib/Order/Filter/Partial.lean | Filter.rtendsto'_def | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nr : Rel α β\nl₁ : Filter α\nl₂ : Filter β\n⊢ l₁ ≤\n { sets := Rel.image (fun s t => Rel.preimage r s ⊆ t) l₂.sets,\n univ_sets := (_ : ∃ x, x ∈ l₂.sets ∧ (fun s t => Rel.preimage r s ⊆ t) x Set.univ),\n sets_of_superset :=\n (_ :\... | [
195,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean | isLittleO_log_rpow_nhds_zero | [
{
"state_after": "no goals",
"state_before": "r : ℝ\nhr : r < 0\nx : ℝ\nhx : x ∈ Set.Icc 0 1\n⊢ x ∈ {x | (fun x => (fun x => -abs (log x) ^ 1) x = log x) x}",
"tactic": "simp [abs_of_nonpos (log_nonpos hx.1 hx.2)]"
}
] | [
325,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.map_mul_inv | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nM : Type ?u.226815\nN : Type ?u.226818\nP : Type ?u.226821\nG : Type ?u.226824\nH : Type ?u.226827\nF : Type ?u.226830\ninst✝³ : Group G\ninst✝² : CommGroup H\ninst✝¹ : Group α\ninst✝ : DivisionMonoid β\nf : α →* β\ng h : α\n⊢ ↑f (g *... | [
1559,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1558,
11
] |
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