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/Order/InitialSeg.lean | PrincipalSeg.irrefl | [
{
"state_after": "α : Type u_1\nβ : Type ?u.37084\nγ : Type ?u.37087\nr✝ : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nr : α → α → Prop\ninst✝ : IsWellOrder α r\nf : r ≺i r\nh : r (↑f.toRelEmbedding f.top) f.top\n⊢ False",
"state_before": "α : Type u_1\nβ : Type ?u.37084\nγ : Type ?u.37087\nr✝ : α → α... | [
291,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | liminf_eq_top | [] | [
301,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Computability/Primrec.lean | Nat.Primrec'.head | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nv : Vector ℕ (Nat.succ n)\n⊢ Vector.get v 0 = Vector.head v",
"tactic": "simp [get_zero]"
}
] | [
1407,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1406,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.Fork.π_comp_hom | [
{
"state_after": "case mk\nC : Type u\ninst✝ : Category C\nX Y : C\nf✝ g : X ⟶ Y\nt : Cofork f✝ g\npt✝ : C\nι✝ : parallelPair f✝ g ⟶ (Functor.const WalkingParallelPair).obj pt✝\nf : { pt := pt✝, ι := ι✝ } ⟶ t\n⊢ Cofork.π { pt := pt✝, ι := ι✝ } ≫ f.Hom = Cofork.π t",
"state_before": "C : Type u\ninst✝ : Cate... | [
720,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
719,
1
] |
Mathlib/Data/Real/GoldenRatio.lean | one_sub_goldConj | [
{
"state_after": "no goals",
"state_before": "⊢ 1 - φ = ψ",
"tactic": "linarith [gold_add_goldConj]"
}
] | [
82,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Algebra/Group/Basic.lean | mul_left_ne_self | [] | [
224,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.find_add | [
{
"state_after": "case refine_1\nm✝ n k l : ℕ\np q : ℕ → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred q\nhₘ : ∃ m, p (m + n)\nhₙ : ∃ n, p n\nhn : n ≤ Nat.find hₙ\nm : ℕ\nhm : m < Nat.find hₘ + n\nhpm : p m\n⊢ Nat.find hₘ + n ≤ m\n\ncase refine_2\nm n k l : ℕ\np q : ℕ → Prop\ninst✝¹ : DecidablePred p\ni... | [
588,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.hasFPowerSeriesOnBall_changeOrigin | [] | [
1277,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1274,
1
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Mathlib/Data/ZMod/Basic.lean | ZMod.nat_cast_self | [] | [
132,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.dual_Ico | [] | [
261,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Algebra/Parity.lean | isSquare_iff_exists_sq | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.5168\nα : Type u_1\nβ : Type ?u.5174\nR : Type ?u.5177\ninst✝ : Monoid α\nn : ℕ\na m : α\n⊢ IsSquare m ↔ ∃ c, m = c ^ 2",
"tactic": "simp [IsSquare, pow_two]"
}
] | [
91,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Init/Data/Nat/Bitwise.lean | Nat.bodd_bit | [
{
"state_after": "b : Bool\nn : ℕ\n⊢ bodd (2 * n + bif b then 1 else 0) = b",
"state_before": "b : Bool\nn : ℕ\n⊢ bodd (bit b n) = b",
"tactic": "rw [bit_val]"
},
{
"state_after": "b : Bool\nn : ℕ\n⊢ bodd (bif b then 1 else 0) = b",
"state_before": "b : Bool\nn : ℕ\n⊢ bodd (2 * n + bif b the... | [
310,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/RingTheory/AlgebraicIndependent.lean | algebraicIndependent_sUnion_of_directed | [
{
"state_after": "ι : Type ?u.873393\nι' : Type ?u.873396\nR : Type u_2\nK : Type ?u.873402\nA : Type u_1\nA' : Type ?u.873408\nA'' : Type ?u.873411\nV : Type u\nV' : Type ?u.873416\nx : ι → A\ninst✝⁶ : CommRing R\ninst✝⁵ : CommRing A\ninst✝⁴ : CommRing A'\ninst✝³ : CommRing A''\ninst✝² : Algebra R A\ninst✝¹ : ... | [
342,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Data/List/Destutter.lean | List.destutter'_is_chain' | [
{
"state_after": "case nil\nα : Type u_1\nl : List α\nR : α → α → Prop\ninst✝ : DecidableRel R\na✝¹ b a✝ a : α\n⊢ Chain' R (destutter' R a [])\n\ncase cons\nα : Type u_1\nl✝ : List α\nR : α → α → Prop\ninst✝ : DecidableRel R\na✝¹ b✝ a✝ b : α\nl : List α\nhl : ∀ (a : α), Chain' R (destutter' R a l)\na : α\n⊢ Cha... | [
101,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Std/Data/Option/Lemmas.lean | Option.to_list_some | [] | [
218,
74
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
218,
9
] |
Mathlib/Data/Dfinsupp/Interval.lean | Dfinsupp.card_Iio | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : ι → Type u_2\ninst✝³ : DecidableEq ι\ninst✝² : (i : ι) → DecidableEq (α i)\ninst✝¹ : (i : ι) → CanonicallyOrderedAddMonoid (α i)\ninst✝ : (i : ι) → LocallyFiniteOrder (α i)\nf : Π₀ (i : ι), α i\n⊢ card (Iio f) = ∏ i in support f, card (Iic (↑f ... | [
213,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.insert | [] | [
685,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
683,
1
] |
Mathlib/Order/Directed.lean | isTop_or_exists_gt | [] | [
283,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Logic/Unique.lean | Fin.eq_zero | [] | [
116,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.filter_mem_image_eq_image | [
{
"state_after": "case a\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.70019\ninst✝ : DecidableEq β\nf✝ g : α → β\ns✝ : Finset α\nt✝ : Finset β\na : α\nb c : β\nf : α → β\ns : Finset α\nt : Finset β\nh : ∀ (x : α), x ∈ s → f x ∈ t\na✝ : β\n⊢ a✝ ∈ filter (fun y => y ∈ image f s) t ↔ a✝ ∈ image f s",
"state_before... | [
377,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.restrict_le_restrict_countable_iUnion | [
{
"state_after": "case intro\nα : Type u_2\nβ : Type u_1\nm : MeasurableSpace α\nM : Type u_3\ninst✝³ : TopologicalSpace M\ninst✝² : OrderedAddCommMonoid M\ninst✝¹ : OrderClosedTopology M\nv w : VectorMeasure α M\ni j : Set α\ninst✝ : Countable β\nf : β → Set α\nhf₁ : ∀ (b : β), MeasurableSet (f b)\nhf₂ : ∀ (b ... | [
978,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
968,
1
] |
Mathlib/Algebra/Group/Prod.lean | MonoidHom.prodMap_def | [] | [
603,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
] |
Mathlib/Data/IsROrC/Lemmas.lean | IsROrC.ofRealClm_norm | [] | [
94,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Algebra/Symmetrized.lean | SymAlg.sym_smul | [] | [
230,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/RingTheory/WittVector/IsPoly.lean | WittVector.IsPoly₂.compRight | [] | [
584,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
582,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_list_count | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.473637\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf g : α → β\ninst✝² : CommMonoid β\ninst✝¹ : DecidableEq α\ninst✝ : CommMonoid α\ns : List α\n⊢ prod s = ∏ m in toFinset s, m ^ count m s",
"tactic": "simpa using prod_list_m... | [
1296,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1295,
1
] |
Mathlib/Data/Real/NNReal.lean | Real.toNNReal_pow | [
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx : 0 ≤ x\nn : ℕ\n⊢ toNNReal (x ^ n) = toNNReal x ^ n",
"tactic": "rw [← NNReal.coe_eq, NNReal.coe_pow, Real.coe_toNNReal _ (pow_nonneg hx _),\n Real.coe_toNNReal x hx]"
}
] | [
699,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
1
] |
Mathlib/Analysis/Convex/SimplicialComplex/Basic.lean | Geometry.SimplicialComplex.facets_subset | [] | [
200,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Algebra/Order/Sub/Basic.lean | le_mul_tsub | [] | [
36,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/Data/Fintype/Basic.lean | Finset.union_compl | [] | [
203,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Order/GameAdd.lean | Prod.rprod_le_transGen_gameAdd | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nrα : α → α → Prop\nrβ : β → β → Prop\nx✝¹ x✝ : α × β\nh : RProd rα rβ x✝¹ x✝\na₁✝ : α\nb₁✝ : β\na₂✝ : α\nb₂✝ : β\nhα : rα a₁✝ a₂✝\nhβ : rβ b₁✝ b₂✝\n⊢ Relation.TransGen (GameAdd rα rβ) (a₁✝, b₁✝) (a₂✝, b₂✝)",
"state_before": "α : Type u_1\nβ : Type u_2\nrα : α → ... | [
95,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Data/Sum/Order.lean | OrderIso.sumAssoc_apply_inl_inl | [] | [
574,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
1
] |
Mathlib/Data/Set/Intervals/Disjoint.lean | Set.Ioc_disjoint_Ioc_same | [] | [
48,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/CategoryTheory/Sums/Associator.lean | CategoryTheory.sum.associator_obj_inr | [] | [
61,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/AlgebraicTopology/DoldKan/GammaCompN.lean | AlgebraicTopology.DoldKan.N₁Γ₀_inv_app | [
{
"state_after": "C : Type u_2\ninst✝² : Category C\ninst✝¹ : Preadditive C\ninst✝ : HasFiniteCoproducts C\nK : ChainComplex C ℕ\n⊢ (N₁Γ₀.app K).inv =\n (toKaroubi (ChainComplex C ℕ)).map (Γ₀NondegComplexIso K).inv ≫\n (Splitting.toKaroubiNondegComplexIsoN₁ (Γ₀.splitting K)).hom",
"state_before": "C... | [
100,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | Left.mul_lt_one_of_le_of_lt | [] | [
614,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
611,
1
] |
Mathlib/Analysis/NormedSpace/Int.lean | Int.nnnorm_coe_nat | [] | [
40,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | IsBoundedBilinearMap.continuous | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E × F → G\nh : IsBounde... | [
412,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/AlgebraicGeometry/RingedSpace.lean | AlgebraicGeometry.RingedSpace.isUnit_of_isUnit_germ | [
{
"state_after": "X : RingedSpace\nU : Opens ↑↑X.toPresheafedSpace\nf : ↑(X.presheaf.obj U.op)\nh : ∀ (x : { x // x ∈ U }), IsUnit (↑(germ X.presheaf x) f)\nV : { x // x ∈ U } → Opens ↑↑X.toPresheafedSpace\niVU : (x : { x // x ∈ U }) → V x ⟶ U\nm : ∀ (x : { x // x ∈ U }), ↑x ∈ V x\nh_unit : ∀ (x : { x // x ∈ U ... | [
140,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Deriv.lean | HasFDerivAt.log | [] | [
146,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/LinearAlgebra/Matrix/Orthogonal.lean | Matrix.HasOrthogonalCols.transpose_hasOrthogonalRows | [] | [
76,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/CategoryTheory/Endofunctor/Algebra.lean | CategoryTheory.Endofunctor.Algebra.comp_eq_comp | [] | [
118,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.completeSpace_lp_of_cauchy_complete_ℒp | [
{
"state_after": "α : Type u_2\nE : Type u_1\nF : Type ?u.8136831\nG : Type ?u.8136834\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nhp : Fact (1 ≤ p)\nH :\n ∀ (f : ℕ → α → E),\n (∀ (n : ℕ), Memℒp (f n... | [
1318,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1284,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.sin_eq | [
{
"state_after": "case h.e'_2.h.e'_1\nx y z : ℂ\n⊢ z = ↑z.re + ↑z.im * I",
"state_before": "x y z : ℂ\n⊢ sin z = sin ↑z.re * cosh ↑z.im + cos ↑z.re * sinh ↑z.im * I",
"tactic": "convert sin_add_mul_I z.re z.im"
},
{
"state_after": "no goals",
"state_before": "case h.e'_2.h.e'_1\nx y z : ℂ\n⊢... | [
882,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
881,
1
] |
Mathlib/Data/Multiset/FinsetOps.lean | Multiset.mem_ndinsert_of_mem | [] | [
73,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Topology/Filter.lean | Filter.isOpen_iff | [] | [
74,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Analysis/Normed/Group/AddTorsor.lean | nndist_vsub_cancel_right | [] | [
169,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.tendsto_id' | [] | [
2909,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2908,
1
] |
Mathlib/Data/Nat/Lattice.lean | Nat.iInf_lt_succ' | [] | [
194,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | InnerProductSpace.Core.norm_eq_sqrt_inner | [] | [
351,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.coe_mk | [] | [
163,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/NumberTheory/LegendreSymbol/MulCharacter.lean | MulChar.sum_one_eq_card_units | [
{
"state_after": "case calc_1\nR : Type u\ninst✝⁴ : CommRing R\nR' : Type v\ninst✝³ : CommRing R'\nR'' : Type w\ninst✝² : CommRing R''\ninst✝¹ : Fintype R\ninst✝ : DecidableEq R\na : R\nx✝ : a ∈ Finset.univ\n⊢ ↑1 a = if IsUnit a then 1 else 0\n\ncase calc_2\nR : Type u\ninst✝⁴ : CommRing R\nR' : Type v\ninst✝³ ... | [
564,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
550,
1
] |
Mathlib/Combinatorics/SimpleGraph/Regularity/Uniform.lean | SimpleGraph.right_nonuniformWitnesses_card | [
{
"state_after": "α : Type u_1\n𝕜 : Type u_2\ninst✝¹ : LinearOrderedField 𝕜\nG : SimpleGraph α\ninst✝ : DecidableRel G.Adj\nε : 𝕜\ns t : Finset α\na b : α\nh : ¬IsUniform G ε s t\n⊢ ↑(card t) * ε ≤\n ↑(card\n (Exists.choose\n (_ :\n ∃ s',\n s' ⊆ s ∧\n ... | [
149,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Order/Bounds/Basic.lean | MonotoneOn.map_bddBelow | [] | [
1192,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1191,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.continuousAt_arg | [
{
"state_after": "x z : ℂ\nh : 0 < x.re ∨ x.im ≠ 0\nh₀ : ↑abs x ≠ 0\n⊢ ContinuousAt arg x",
"state_before": "x z : ℂ\nh : 0 < x.re ∨ x.im ≠ 0\n⊢ ContinuousAt arg x",
"tactic": "have h₀ : abs x ≠ 0 := by\n rw [abs.ne_zero_iff]\n rintro rfl\n simp at h"
},
{
"state_after": "x z : ℂ\nh✝ : 0 < x.... | [
556,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.IsImage.of_symm_image_eq | [] | [
433,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/Deprecated/Subring.lean | IsSubring.iInter | [] | [
88,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.injOn | [] | [
252,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
11
] |
Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.aeval_bind₂ | [] | [
333,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/Order/Heyting/Basic.lean | sdiff_sdiff_left | [] | [
624,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
] |
Mathlib/Order/Heyting/Boundary.lean | Coheyting.boundary_le_hnot | [] | [
57,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Std/Data/Int/Lemmas.lean | Int.lt_add_one_of_le | [] | [
1254,
89
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1254,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.one_re | [] | [
168,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_apply_ite_of_true | [
{
"state_after": "ι : Type ?u.408005\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nf✝ g✝ : α → β\ninst✝ : CommMonoid β\np : α → Prop\nhp : DecidablePred p\nf g : α → γ\nk : γ → β\nh : ∀ (x : α), x ∈ s → p x\n⊢ (∏ x in s, if p x then k (f x) else k (g x)) = ∏ x in s, k (f x)",
"state_before... | [
1030,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1027,
1
] |
Mathlib/CategoryTheory/LiftingProperties/Basic.lean | CategoryTheory.HasLiftingProperty.iff_unop | [] | [
78,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/GroupTheory/DoubleCoset.lean | Doset.doset_union_rightCoset | [
{
"state_after": "case h\nG : Type u_1\ninst✝¹ : Group G\nα : Type ?u.59583\ninst✝ : Mul α\nJ : Subgroup G\ng : G\nH K : Subgroup G\na x : G\n⊢ (x ∈ ⋃ (k : { x // x ∈ K }), rightCoset (↑H) (a * ↑k)) ↔ x ∈ doset a ↑H ↑K",
"state_before": "G : Type u_1\ninst✝¹ : Group G\nα : Type ?u.59583\ninst✝ : Mul α\nJ : ... | [
184,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_union_lt_top_iff | [
{
"state_after": "case refine'_1\nα : Type u_1\nβ : Type ?u.33782\nγ : Type ?u.33785\nδ : Type ?u.33788\nι : Type ?u.33791\ninst✝ : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns s₁ s₂ t : Set α\nh : ↑↑μ (s ∪ t) < ⊤\n⊢ ↑↑μ s < ⊤\n\ncase refine'_2\nα : Type u_1\nβ : Type ?u.33782\nγ : Type ?u.33785\nδ : Type ?u.33788... | [
317,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.id_comp | [] | [
434,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Std/Data/Array/Lemmas.lean | Array.get?_set | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na : Array α\ni : Fin (size a)\nj : Nat\nv : α\n⊢ (set a i v)[j]? = if i.val = j then some v else a[j]?",
"tactic": "if h : i.1 = j then subst j; simp [*] else simp [*]"
},
{
"state_after": "α : Type u_1\na : Array α\ni : Fin (size a)\nv... | [
104,
54
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
102,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.factors_mul | [
{
"state_after": "α : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ninst✝¹ : DecidableEq α\ninst✝ : UniqueFactorizationMonoid α\nx y : α\nhx : x ≠ 0\nhy : y ≠ 0\n⊢ x * y ~ᵤ Multiset.prod (factors x + factors y)",
"state_before": "α : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ninst✝¹ : DecidableEq α\nin... | [
517,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/Data/Option/Basic.lean | Option.map_inj | [] | [
123,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | MonotoneOn.inv | [] | [
1299,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1298,
1
] |
src/lean/Init/Prelude.lean | Nat.le_trans | [] | [
1594,
59
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1592,
11
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.range_reindex | [
{
"state_after": "no goals",
"state_before": "ι : Type u_4\nι' : Type u_2\nR : Type u_3\nR₂ : Type ?u.369229\nK : Type ?u.369232\nM : Type u_1\nM' : Type ?u.369238\nM'' : Type ?u.369241\nV : Type u\nV' : Type ?u.369246\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\ninst✝¹ : AddCommMono... | [
447,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.not_prime_zero | [] | [
58,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Algebra/AddTorsor.lean | neg_vsub_eq_vsub_rev | [
{
"state_after": "G : Type u_1\nP : Type u_2\ninst✝ : AddGroup G\nT : AddTorsor G P\np1 p2 : P\n⊢ p1 -ᵥ p2 + (p2 -ᵥ p1) +ᵥ p1 = 0 +ᵥ p1",
"state_before": "G : Type u_1\nP : Type u_2\ninst✝ : AddGroup G\nT : AddTorsor G P\np1 p2 : P\n⊢ -(p1 -ᵥ p2) = p2 -ᵥ p1",
"tactic": "refine' neg_eq_of_add_eq_zero_rig... | [
159,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Algebra/Opposites.lean | MulOpposite.unop_zero | [] | [
246,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Topology/ContinuousOn.lean | nhdsWithin_le_iff | [] | [
136,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup_himp_left | [] | [
650,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
1
] |
Mathlib/Data/Set/Basic.lean | Set.symmDiff_def | [] | [
2097,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2096,
11
] |
Mathlib/Order/Filter/CountableInter.lean | EventuallyEq.countable_iInter | [] | [
112,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | RingHom.ker_eq_bot_iff_eq_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nF : Type u_1\ninst✝¹ : Ring R\ninst✝ : Semiring S\nrc : RingHomClass F R S\nf : F\n⊢ ker f = ⊥ ↔ ∀ (x : R), ↑f x = 0 → x = 0",
"tactic": "rw [← injective_iff_map_eq_zero f, injective_iff_ker_eq_bot]"
}
] | [
2038,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2037,
1
] |
Mathlib/SetTheory/Cardinal/Finite.lean | Nat.card_congr | [] | [
57,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.map_eq_apply | [] | [
756,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
755,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.ker_coprod_of_disjoint_range | [
{
"state_after": "R : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂✝ : Type w\nV₂ : Type w'\nM₃✝ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nM₅ : Type ?u.249709\nM₆ : Type ?u.249712\ninst✝¹² : Semiring R\ninst✝¹¹ : AddCommMonoid M\ninst✝¹⁰ : AddCommMonoid M₂✝\ninst✝⁹ : AddCommMonoid M₃✝\ninst✝⁸ : AddCom... | [
529,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/AlgebraicGeometry/SheafedSpace.lean | AlgebraicGeometry.SheafedSpace.comp_c_app | [] | [
147,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Analysis/Convex/Jensen.lean | ConvexOn.map_sum_le | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.21381\nβ : Type u_3\nι : Type u_4\ninst✝⁵ : LinearOrderedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : OrderedAddCommGroup β\ninst✝² : Module 𝕜 E\ninst✝¹ : Module 𝕜 β\ninst✝ : OrderedSMul 𝕜 β\ns : Set E\nf : E → β\nt : F... | [
69,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Algebra/Support.lean | Function.mulSupport_binop_subset | [
{
"state_after": "no goals",
"state_before": "α : Type u_4\nβ : Type ?u.9665\nA : Type ?u.9668\nB : Type ?u.9671\nM : Type u_2\nN : Type u_3\nP : Type u_1\nR : Type ?u.9683\nS : Type ?u.9686\nG : Type ?u.9689\nM₀ : Type ?u.9692\nG₀ : Type ?u.9695\nι : Sort ?u.9698\ninst✝² : One M\ninst✝¹ : One N\ninst✝ : On... | [
152,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.mem_divisors | [
{
"state_after": "case inl\nn : ℕ\n⊢ n ∈ divisors 0 ↔ n ∣ 0 ∧ 0 ≠ 0\n\ncase inr\nn m : ℕ\nhm : m ≠ 0\n⊢ n ∈ divisors m ↔ n ∣ m ∧ m ≠ 0",
"state_before": "n m : ℕ\n⊢ n ∈ divisors m ↔ n ∣ m ∧ m ≠ 0",
"tactic": "rcases eq_or_ne m 0 with (rfl | hm)"
},
{
"state_after": "case inr\nn m : ℕ\nhm : m ≠ 0... | [
101,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.eq_pow_of_factorization_eq_single | [
{
"state_after": "n p k : ℕ\nhn : n ≠ 0\nh : factorization n = single p k\n⊢ p ^ 0 = 1",
"state_before": "n p k : ℕ\nhn : n ≠ 0\nh : factorization n = single p k\n⊢ n = p ^ k",
"tactic": "rw [← Nat.factorization_prod_pow_eq_self hn, h, Finsupp.prod_single_index]"
},
{
"state_after": "no goals",
... | [
294,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Equiv.comp_apply | [] | [
885,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
884,
1
] |
Std/Data/List/Init/Lemmas.lean | List.mapM_cons | [
{
"state_after": "no goals",
"state_before": "m : Type u_1 → Type u_2\nα : Type u_3\nβ : Type u_1\na : α\nl : List α\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nf : α → m β\n⊢ mapM f (a :: l) = do\n let __do_lift ← f a\n let __do_lift_1 ← mapM f l\n pure (__do_lift :: __do_lift_1)",
"tactic": "si... | [
221,
84
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
220,
9
] |
Mathlib/Topology/Algebra/Group/Basic.lean | TopologicalGroup.continuous_conj | [] | [
469,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.erase_cons_of_ne | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.210946\nγ : Type ?u.210949\ninst✝ : DecidableEq α\ns✝ t u v : Finset α\na✝ b✝ a b : α\ns : Finset α\nha : ¬a ∈ s\nhb : a ≠ b\n⊢ erase (cons a s ha) b = cons a (erase s b) (_ : a ∈ erase s b → False)",
"tactic": "simp only [cons_eq_i... | [
1926,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1924,
1
] |
Mathlib/Data/Option/Basic.lean | Option.eq_of_mem_of_mem | [] | [
58,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.smul_mk | [] | [
120,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Algebra/Algebra/Unitization.lean | Unitization.lift_symm_apply_apply | [] | [
699,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
1
] |
Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.quotMapOfEquivQuotMapCMapSpanMk_mk | [] | [
743,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
741,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.weightedVSub_congr | [] | [
295,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/CategoryTheory/Monoidal/End.lean | CategoryTheory.μ_hom_inv_app | [] | [
100,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
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