file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/Finset/Image.lean | Finset.mem_map_equiv | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.3584\nf✝ : α ↪ β\ns : Finset α\nf : α ≃ β\nb : β\n⊢ (∃ a, a ∈ s ∧ ↑(Equiv.toEmbedding f) a = b) ↔ ↑f.symm b ∈ s",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.3584\nf✝ : α ↪ β\ns : Finset α\nf : α ≃ β\nb : β\n⊢ b ∈ map (Equiv.toEmbedding ... | [
80,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Topology/Order/Basic.lean | nhdsWithin_Ioi_neBot | [] | [
2388,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2387,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.disjoint_atTop_atBot | [] | [
129,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Data/List/Lattice.lean | List.inter_subset_left | [] | [
171,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Topology/LocallyConstant/Basic.lean | LocallyConstant.coe_mk | [] | [
270,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_subtype | [] | [
1198,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1196,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.toFinset_eq_univ | [] | [
288,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
11
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.isOpen_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.209202\ninst✝ : PseudoEMetricSpace α\nx y z : α\nε ε₁ ε₂ : ℝ≥0∞\ns t : Set α\n⊢ IsOpen s ↔ ∀ (x : α), x ∈ s → ∃ ε, ε > 0 ∧ ball x ε ⊆ s",
"tactic": "simp [isOpen_iff_nhds, mem_nhds_iff]"
}
] | [
687,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
686,
1
] |
Mathlib/Data/Polynomial/Degree/Lemmas.lean | Polynomial.natDegree_bit1 | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nι : Type w\na✝ b : R\nm n : ℕ\ninst✝ : Semiring R\np q r a : R[X]\n⊢ max (natDegree (bit0 a)) (natDegree 1) ≤ natDegree a",
"tactic": "simp [natDegree_bit0]"
}
] | [
263,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Analysis/SpecialFunctions/CompareExp.lean | Complex.IsExpCmpFilter.isLittleO_log_abs_re | [
{
"state_after": "l : Filter ℂ\nhl : IsExpCmpFilter l\nz : ℂ\nhz : 1 ≤ z.re\nh2 : 0 < Real.sqrt 2\n⊢ ‖Real.log (↑abs z)‖ ≤ 1 * ‖Real.log (Real.sqrt 2) + Real.log (max z.re (Abs.abs z.im))‖",
"state_before": "l : Filter ℂ\nhl : IsExpCmpFilter l\nz : ℂ\nhz : 1 ≤ z.re\n⊢ ‖Real.log (↑abs z)‖ ≤ 1 * ‖Real.log (Re... | [
163,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Data/Fintype/Lattice.lean | Finite.exists_max | [
{
"state_after": "case intro\nα : Type u_1\nβ : Type u_2\ninst✝² : Finite α\ninst✝¹ : Nonempty α\ninst✝ : LinearOrder β\nf : α → β\nval✝ : Fintype α\n⊢ ∃ x₀, ∀ (x : α), f x ≤ f x₀",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝² : Finite α\ninst✝¹ : Nonempty α\ninst✝ : LinearOrder β\nf : α → β\n⊢ ∃ x₀,... | [
65,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Images.lean | CategoryTheory.Limits.image.map_id | [
{
"state_after": "case e_self\nC : Type u\ninst✝⁴ : Category C\nf g : Arrow C\ninst✝³ : HasImage f.hom\ninst✝² : HasImage g.hom\nsq : f ⟶ g\ninst✝¹ : HasImageMap sq\ninst✝ : HasImageMap (𝟙 f)\n⊢ HasImageMap.imageMap (𝟙 f) = imageMapId f",
"state_before": "C : Type u\ninst✝⁴ : Category C\nf g : Arrow C\nin... | [
843,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.tensorTensorTensorAssoc_symm_tmul | [] | [
966,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
964,
1
] |
Mathlib/Analysis/Calculus/Deriv/Add.lean | deriv_neg | [] | [
263,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Order/Filter/Archimedean.lean | tendsto_int_cast_atTop_iff | [
{
"state_after": "α : Type u_2\nR : Type u_1\ninst✝¹ : StrictOrderedRing R\ninst✝ : Archimedean R\nf : α → ℤ\nl : Filter α\n⊢ Tendsto (fun n => ↑(f n)) l atTop ↔ Tendsto (Int.cast ∘ f) l atTop",
"state_before": "α : Type u_2\nR : Type u_1\ninst✝¹ : StrictOrderedRing R\ninst✝ : Archimedean R\nf : α → ℤ\nl : ... | [
61,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.limZero_congr | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝² : LinearOrderedField α\ninst✝¹ : Ring β\nabv : β → α\ninst✝ : IsAbsoluteValue abv\nf g : CauSeq β abv\nh : f ≈ g\nl : LimZero f\n⊢ LimZero g",
"tactic": "simpa using add_limZero (Setoid.symm h) l"
},
{
"state_after"... | [
495,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_smul | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝³ : Semiring R\np✝ q r : R[X]\nx✝ : R\ninst✝² : Monoid S\ninst✝¹ : DistribMulAction S R\ninst✝ : IsScalarTower S R R\ns : S\np : R[X]\nx : R\n⊢ eval x (s • p) = s • eval x p",
"tactic": "... | [
400,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/Data/Matrix/Basis.lean | Matrix.StdBasisMatrix.diag_zero | [] | [
153,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Std/Logic.lean | exists_congr | [] | [
377,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
376,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurable_limsup | [] | [
1341,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1339,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.bijOn_cos | [] | [
646,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
645,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.symm_map_nhds_eq | [] | [
1973,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1972,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | Padic.AddValuation.map_add | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nx y : ℚ_[p]\n⊢ min (if x = 0 then ⊤ else ↑(valuation x)) (if y = 0 then ⊤ else ↑(valuation y)) ≤\n if x + y = 0 then ⊤ else ↑(valuation (x + y))",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nx y : ℚ_[p]\n⊢ min (addValuationDef x) (addValuationDef y) ... | [
1144,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1131,
1
] |
Mathlib/Topology/Algebra/Order/MonotoneContinuity.lean | StrictMonoOn.continuousWithinAt_left_of_closure_image_mem_nhdsWithin | [] | [
192,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Deriv.lean | Real.contDiffOn_log | [
{
"state_after": "x : ℝ\nn : ℕ∞\nthis : ContDiffOn ℝ ⊤ log ({0}ᶜ)\n⊢ ContDiffOn ℝ n log ({0}ᶜ)\n\ncase this\nx : ℝ\nn : ℕ∞\n⊢ ContDiffOn ℝ ⊤ log ({0}ᶜ)",
"state_before": "x : ℝ\nn : ℕ∞\n⊢ ContDiffOn ℝ n log ({0}ᶜ)",
"tactic": "suffices : ContDiffOn ℝ ⊤ log ({0}ᶜ)"
},
{
"state_after": "case this\... | [
84,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.primPart_zero | [] | [
264,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csSup_Ioc | [] | [
771,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
770,
1
] |
Std/Data/Int/DivMod.lean | Int.zero_fmod | [
{
"state_after": "no goals",
"state_before": "b : Int\n⊢ fmod 0 b = 0",
"tactic": "cases b <;> rfl"
}
] | [
250,
73
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
250,
9
] |
Mathlib/Topology/LocalAtTarget.lean | isOpen_iff_coe_preimage_of_iSup_eq_top | [
{
"state_after": "α : Type ?u.17624\nβ : Type u_1\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α → β\ns✝ : Set β\nι : Type ?u.17643\nU : ι → Opens β\nhU : iSup U = ⊤\ns : Set β\n⊢ (∀ (i : ι), IsOpen (s ∩ ↑(U i))) ↔ ∀ (i : ι), IsOpen (Subtype.val ⁻¹' s)",
"state_before": "α : Type ?u.17624\n... | [
100,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.map_fract | [
{
"state_after": "no goals",
"state_before": "F : Type u_3\nα : Type u_1\nβ : Type u_2\ninst✝⁴ : LinearOrderedRing α\ninst✝³ : LinearOrderedRing β\ninst✝² : FloorRing α\ninst✝¹ : FloorRing β\ninst✝ : RingHomClass F α β\na✝ : α\nb : β\nf : F\nhf : StrictMono ↑f\na : α\n⊢ fract (↑f a) = ↑f (fract a)",
"ta... | [
1543,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1542,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.mem_sets | [] | [
118,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
11
] |
Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.haarContent_apply | [] | [
560,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.inits_eq | [
{
"state_after": "case a\nα : Type u\nβ : Type v\nδ : Type w\ns : Stream' α\n⊢ ∀ (n : ℕ), nth (inits s) n = nth ([head s] :: map (List.cons (head s)) (inits (tail s))) n",
"state_before": "α : Type u\nβ : Type v\nδ : Type w\ns : Stream' α\n⊢ inits s = [head s] :: map (List.cons (head s)) (inits (tail s))",
... | [
728,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
722,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_range_eq_sUnion | [
{
"state_after": "case h\nα✝ : Type ?u.180126\nβ✝ : Type ?u.180129\nγ : Type ?u.180132\nι : Sort ?u.180135\nι' : Sort ?u.180138\nι₂ : Sort ?u.180141\nκ : ι → Sort ?u.180146\nκ₁ : ι → Sort ?u.180151\nκ₂ : ι → Sort ?u.180156\nκ' : ι' → Sort ?u.180161\nα : Type u_1\nβ : Type u_2\nC : Set (Set α)\nf : (s : ↑C) → β ... | [
1384,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1375,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | InnerProductGeometry.norm_div_cos_angle_add_of_inner_eq_zero | [
{
"state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : inner x y = 0\nh0 : x ≠ 0 ∨ y = 0\n⊢ ‖x‖ / (‖x‖ / ‖x + y‖) = ‖x + y‖",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : inner x y = 0\nh0 : x ≠ ... | [
209,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Order/LocallyFinite.lean | Finset.coe_Ici | [] | [
394,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
Mathlib/Data/MvPolynomial/Supported.lean | MvPolynomial.supported_eq_range_rename | [
{
"state_after": "σ : Type u_1\nτ : Type ?u.560\nR : Type u\nS : Type v\nr : R\ne : ℕ\nn m : σ\ninst✝ : CommSemiring R\np q : MvPolynomial σ R\ns : Set σ\n⊢ AlgHom.range (aeval fun x => X ↑x) = AlgHom.range (aeval (X ∘ Subtype.val))",
"state_before": "σ : Type u_1\nτ : Type ?u.560\nR : Type u\nS : Type v\nr... | [
52,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.normSq_div | [] | [
1397,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1396,
1
] |
Mathlib/Topology/Separation.lean | nhds_inter_eq_singleton_of_mem_discrete | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : TopologicalSpace α\ns : Set α\ninst✝ : DiscreteTopology ↑s\nx : α\nhx : x ∈ s\n⊢ ∃ U, U ∈ 𝓝 x ∧ U ∩ s = {x}",
"tactic": "simpa using (𝓝 x).basis_sets.exists_inter_eq_singleton_of_mem_discrete hx"
}
] | [
838,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
836,
1
] |
Mathlib/Logic/Equiv/Option.lean | Equiv.coe_optionSubtype_apply_apply | [] | [
228,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.sub_eq_of_eq_add_rev | [] | [
1132,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1131,
11
] |
Mathlib/Order/Heyting/Boundary.lean | Coheyting.boundary_le_boundary_sup_sup_boundary_inf_right | [
{
"state_after": "α : Type u_1\ninst✝ : CoheytingAlgebra α\na b : α\n⊢ ∂ b ≤ ∂ (b ⊔ a) ⊔ ∂ (b ⊓ a)",
"state_before": "α : Type u_1\ninst✝ : CoheytingAlgebra α\na b : α\n⊢ ∂ b ≤ ∂ (a ⊔ b) ⊔ ∂ (a ⊓ b)",
"tactic": "rw [@sup_comm _ _ a, inf_comm]"
},
{
"state_after": "no goals",
"state_before": ... | [
125,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.count_normalizedFactors_eq' | [
{
"state_after": "case inl\nα : Type ?u.1182347\nR : Type u_1\ninst✝⁴ : CancelCommMonoidWithZero R\ninst✝³ : UniqueFactorizationMonoid R\ninst✝² : Nontrivial R\ninst✝¹ : NormalizationMonoid R\ndec_dvd : DecidableRel Dvd.dvd\ninst✝ : DecidableEq R\nx : R\nn : ℕ\nhnorm : ↑normalize 0 = 0\nhle : 0 ^ n ∣ x\nhlt : ¬... | [
1024,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1016,
1
] |
Mathlib/Algebra/Module/Opposites.lean | MulOpposite.opLinearEquiv_toAddEquiv | [] | [
62,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Combinatorics/SimpleGraph/DegreeSum.lean | SimpleGraph.dart_edge_fiber_card | [
{
"state_after": "V : Type u\nG : SimpleGraph V\ninst✝³ : Fintype V\ninst✝² : DecidableRel G.Adj\ninst✝¹ : Fintype (Sym2 V)\ninst✝ : DecidableEq V\ne : Sym2 V\nh✝ : e ∈ edgeSet G\nv w : V\nh : Quotient.mk (Sym2.Rel.setoid V) (v, w) ∈ edgeSet G\n⊢ card (filter (fun d => Dart.edge d = Quotient.mk (Sym2.Rel.setoid... | [
100,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Std/Data/List/Init/Lemmas.lean | List.append_inj' | [
{
"state_after": "α✝ : Type u_1\ns₁ t₁ s₂ t₂ : List α✝\nh : s₁ ++ t₁ = s₂ ++ t₂\nhl : length t₁ = length t₂\nhap : length (s₁ ++ t₁) = length (s₂ ++ t₂) := congrArg length h\n⊢ length s₁ + length t₁ = length s₂ + length t₁",
"state_before": "α✝ : Type u_1\ns₁ t₁ s₂ t₂ : List α✝\nh : s₁ ++ t₁ = s₂ ++ t₂\nhl ... | [
70,
82
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
68,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.lift_umax | [] | [
694,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/Data/Finset/Basic.lean | Multiset.toFinset_dedup | [
{
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}
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3198,
39
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3197,
1
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Mathlib/Data/Quot.lean | Quotient.inductionOn₃' | [] | [
689,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
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Mathlib/Algebra/Order/ToIntervalMod.lean | toIocDiv_add_zsmul | [
{
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251,
92
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249,
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Mathlib/Data/Finset/Lattice.lean | Finset.min'_image | [
{
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1512,
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Mathlib/Analysis/LocallyConvex/Basic.lean | balanced_iUnion | [] | [
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190,
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Mathlib/Order/Partition/Finpartition.lean | Finpartition.default_eq_empty | [] | [
141,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
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Mathlib/CategoryTheory/Sites/Grothendieck.lean | CategoryTheory.GrothendieckTopology.isGLB_sInf | [
{
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30
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.update_self | [
{
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573,
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570,
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.integrable_finset_sum' | [] | [
671,
31
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668,
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Mathlib/Data/Finset/Basic.lean | Finset.inter_eq_inter_iff_right | [] | [
1815,
23
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1814,
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.map_pow | [] | [
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29
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911,
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Mathlib/Topology/ContinuousOn.lean | continuousAt_update_same | [
{
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804,
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802,
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_le_of_surjective | [] | [
281,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.left_inv | [] | [
158,
16
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157,
1
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Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.adjoin_empty | [
{
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154,
21
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151,
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Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.comap_iInf | [] | [
349,
63
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347,
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Mathlib/Data/Multiset/Basic.lean | Multiset.count_inter | [
{
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2473,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2471,
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Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.refl_restr_source | [
{
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}
] | [
629,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
629,
1
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Mathlib/Data/List/Basic.lean | List.reduceOption_cons_of_none | [
{
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}
] | [
3425,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3424,
1
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Mathlib/Data/Nat/Multiplicity.lean | Nat.Prime.pow_dvd_factorial_iff | [
{
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}
] | [
166,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
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src/lean/Init/Data/Nat/Basic.lean | Nat.add_le_add_left | [] | [
388,
28
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
383,
11
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Mathlib/Order/Interval.lean | NonemptyInterval.coe_dual | [] | [
287,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
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Mathlib/RingTheory/Ideal/Basic.lean | Ideal.span_singleton_le_iff_mem | [] | [
176,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
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Mathlib/Topology/PartitionOfUnity.lean | BumpCovering.sum_toPartitionOfUnity_eq | [] | [
484,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
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Mathlib/Order/LiminfLimsup.lean | Filter.bliminf_antitone | [
{
"state_after": "no goals",
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862,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
861,
1
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Mathlib/Algebra/Associated.lean | DvdNotUnit.not_associated | [
{
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1197,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1192,
1
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Mathlib/Deprecated/Submonoid.lean | IsSubmonoid.finset_prod_mem | [
{
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265,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
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Mathlib/CategoryTheory/Limits/Pi.lean | CategoryTheory.pi.hasLimit_of_hasLimit_comp_eval | [] | [
121,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
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Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.associator_conjugation | [
{
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... | [
330,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/Data/Set/Intervals/OrderIso.lean | OrderIso.image_Ioc | [
{
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"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ne : α ≃o β\na b : α\n⊢ ↑e '' Ioc a b = Ioc (↑e a) (↑e b)",
"tactic": "rw [e.image_eq_preimage, e.symm.preimage_Ioc, e.symm_symm]"
}
] | [
96,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
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Mathlib/Order/Interval.lean | Interval.coe_bot | [] | [
498,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_biUnion | [
{
"state_after": "no goals",
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519,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
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Mathlib/RingTheory/PowerBasis.lean | PowerBasis.dim_le_degree_of_root | [
{
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188,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
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Mathlib/Data/Nat/Prime.lean | Int.prime_two | [] | [
809,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
808,
1
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Mathlib/Logic/Equiv/Set.lean | Equiv.image_eq_preimage | [] | [
44,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
11
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Mathlib/Algebra/Opposites.lean | AddOpposite.unop_eq_one_iff | [] | [
388,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoDiv_sub' | [
{
"state_after": "no goals",
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"tactic": "simpa only [one_zsmul] using toIcoDiv_sub_zsmul' hp a b 1"
}
] | [
345,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
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Mathlib/Algebra/Group/Basic.lean | inv_eq_of_mul_eq_one_left | [
{
"state_after": "no goals",
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"tactic": "rw [← inv_eq_of_mul_eq_one_right h, inv_inv]"
}
] | [
361,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
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Mathlib/Analysis/Convex/Side.lean | AffineSubspace.wOppSide_comm | [
{
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212,
94
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205,
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Mathlib/Order/Interval.lean | NonemptyInterval.subset_coe_map | [] | [
291,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
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Mathlib/Algebra/Homology/Augment.lean | CochainComplex.cochainComplex_d_succ_succ_zero | [
{
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"state_before": "V : Type u\ninst✝¹ : Category V\ninst✝ : HasZeroMorphisms V\nC : CochainComplex V ℕ\ni : ℕ\n⊢ d C 0 (i + 2) = 0",
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327,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
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Mathlib/Topology/Separation.lean | t2_separation_nhds | [] | [
937,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
934,
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.C_mul | [] | [
507,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
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] |
Mathlib/CategoryTheory/Sites/Closed.lean | CategoryTheory.GrothendieckTopology.close_eq_top_iff_mem | [
{
"state_after": "case mp\nC : Type u\ninst✝ : Category C\nJ₁ J₂ : GrothendieckTopology C\nX : C\nS : Sieve X\n⊢ close J₁ S = ⊤ → S ∈ sieves J₁ X\n\ncase mpr\nC : Type u\ninst✝ : Category C\nJ₁ J₂ : GrothendieckTopology C\nX : C\nS : Sieve X\n⊢ S ∈ sieves J₁ X → close J₁ S = ⊤",
"state_before": "C : Type u\... | [
165,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.two_lt_ncard_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.157357\ns t : Set α\na b x y : α\nf : α → β\nhs : autoParam (Set.Finite s) _auto✝\n⊢ 2 < ncard s ↔ ∃ a b c, a ∈ s ∧ b ∈ s ∧ c ∈ s ∧ a ≠ b ∧ a ≠ c ∧ b ≠ c",
"tactic": "simp_rw [ncard_eq_toFinset_card _ hs, Finset.two_lt_card_iff, Fin... | [
710,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
708,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.cospan_one | [] | [
222,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
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Mathlib/Order/Bounded.lean | Set.bounded_gt_inter_ge | [] | [
440,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/Data/List/Func.lean | List.Func.get_nil | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\na : α\nas as1 as2 as3 : List α\ninst✝¹ : Inhabited α\ninst✝ : Inhabited β\nk : ℕ\n⊢ get k [] = default",
"tactic": "cases k <;> rfl"
}
] | [
119,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Data/Analysis/Filter.lean | Filter.Realizer.top_σ | [] | [
187,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Data/Set/Basic.lean | Set.antitoneOn_singleton | [] | [
2699,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2698,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atTop_pure | [] | [
305,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMapClass.ker_eq_bot | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nR₁ : Type ?u.1427240\nR₂ : Type u_3\nR₃ : Type ?u.1427246\nR₄ : Type ?u.1427249\nS : Type ?u.1427252\nK : Type ?u.1427255\nK₂ : Type ?u.1427258\nM : Type u_1\nM' : Type ?u.1427264\nM₁ : Type ?u.1427267\nM₂ : Type u_4\nM₃ : Type ?u.1427273\nM₄ : Typ... | [
1506,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1505,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.dvd_to_nat | [
{
"state_after": "m n : Num\nx✝ : ↑m ∣ ↑n\nk : ℕ\ne : ↑n = ↑m * k\n⊢ ↑(↑m * k) = m * ↑k",
"state_before": "m n : Num\nx✝ : ↑m ∣ ↑n\nk : ℕ\ne : ↑n = ↑m * k\n⊢ n = m * ↑k",
"tactic": "rw [← of_to_nat n, e]"
},
{
"state_after": "no goals",
"state_before": "m n : Num\nx✝ : ↑m ∣ ↑n\nk : ℕ\ne : ↑n... | [
513,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
1
] |
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