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/Algebra/Order/Ring/Lemmas.lean | le_mul_of_le_of_one_le_of_nonneg | [] | [
765,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
763,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.iUnion_ball_nat | [] | [
468,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.snd_mk | [] | [
106,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Data/List/Perm.lean | List.Subperm.exists_of_length_lt | [
{
"state_after": "α : Type uu\nβ : Type vv\nl₁✝ l₂✝ l₁ l₂ l : List α\np : l ~ l₁\ns : l <+ l₂\nh : length l₁ < length l₂\n⊢ length l < length l₂ → ∃ a, a :: l <+~ l₂",
"state_before": "α : Type uu\nβ : Type vv\nl₁✝ l₂✝ l₁ l₂ l : List α\np : l ~ l₁\ns : l <+ l₂\nh : length l₁ < length l₂\n⊢ ∃ a, a :: l₁ <+~ ... | [
732,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
720,
1
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Mathlib/Analysis/ODE/PicardLindelof.lean | PicardLindelof.FunSpace.lipschitz | [] | [
181,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
11
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Mathlib/Algebra/Divisibility/Basic.lean | map_dvd | [] | [
99,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
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Mathlib/Data/Fin/Tuple/Basic.lean | Fin.tuple0_le | [] | [
54,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.EqOnSource.restr | [] | [
980,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
978,
1
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Mathlib/LinearAlgebra/Span.lean | Submodule.apply_mem_span_image_of_mem_span | [
{
"state_after": "R : Type u_1\nR₂ : Type u_2\nK : Type ?u.203558\nM : Type u_3\nM₂ : Type u_4\nV : Type ?u.203567\nS : Type ?u.203570\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\nx✝ : M\np p' : Submodule R M\ninst✝³ : Semiring R₂\nσ₁₂ : R →+* R₂\ninst✝² : AddCommMonoid M₂\ninst✝¹ : Modu... | [
583,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
1
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Mathlib/Control/Functor.lean | Functor.Comp.run_map | [] | [
203,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
11
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Mathlib/Analysis/Calculus/BumpFunctionInner.lean | ContDiffBump.rOut_pos | [] | [
345,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
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Mathlib/RingTheory/Artinian.lean | isArtinian_of_fg_of_artinian | [
{
"state_after": "R : Type u_1\nM : Type u_2\ninst✝³ : Ring R\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\nN : Submodule R M\ninst✝ : IsArtinianRing R\nhN : FG N\ns : Finset M\nhs : span R ↑s = N\n⊢ IsArtinian R { x // x ∈ N }",
"state_before": "R : Type u_1\nM : Type u_2\ninst✝³ : Ring R\ninst✝² : AddCom... | [
355,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Algebra/QuadraticDiscriminant.lean | quadratic_eq_zero_iff_discrim_eq_sq | [
{
"state_after": "R : Type u_1\ninst✝² : CommRing R\na b c : R\ninst✝¹ : NeZero 2\ninst✝ : NoZeroDivisors R\nha : a ≠ 0\nx : R\nh : discrim a b c = (2 * a * x + b) ^ 2\n⊢ a * x * x + b * x + c = 0",
"state_before": "R : Type u_1\ninst✝² : CommRing R\na b c : R\ninst✝¹ : NeZero 2\ninst✝ : NoZeroDivisors R\nh... | [
73,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.normSq_apply | [] | [
584,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
] |
Std/Data/List/Lemmas.lean | List.forall_mem_map_iff | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nf : α → β\nl : List α\nP : β → Prop\n⊢ (∀ (i : β) (x : α), x ∈ l → f x = i → P i) ↔ ∀ (j : α), j ∈ l → P (f j)",
"state_before": "α : Type u_1\nβ : Type u_2\nf : α → β\nl : List α\nP : β → Prop\n⊢ (∀ (i : β), i ∈ map f l → P i) ↔ ∀ (j : α), j ∈ l → P (f j)",
... | [
166,
69
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
164,
1
] |
Mathlib/Data/Vector3.lean | vectorAllP_iff_forall | [
{
"state_after": "case refine'_1\nα : Type u_1\nm n : ℕ\np : α → Prop\nv : Vector3 α n\n⊢ VectorAllP p [] ↔ ∀ (i : Fin2 0), p []\n\ncase refine'_2\nα : Type u_1\nm n : ℕ\np : α → Prop\nv : Vector3 α n\n⊢ ∀ {n : ℕ} (a : α) (w : Vector3 α n),\n (VectorAllP p w ↔ ∀ (i : Fin2 n), p (w i)) → (VectorAllP p (a :: w... | [
296,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.set_biInter_insert_update | [] | [
2074,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2072,
1
] |
Mathlib/Combinatorics/SimpleGraph/Hasse.lean | SimpleGraph.hasseDualIso_symm_apply | [] | [
64,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.up_left_mem | [] | [
99,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.mul_div_cancel | [
{
"state_after": "R : Type u\ninst✝ : EuclideanDomain R\na b : R\nb0 : b ≠ 0\n⊢ b * a / b = a",
"state_before": "R : Type u\ninst✝ : EuclideanDomain R\na b : R\nb0 : b ≠ 0\n⊢ a * b / b = a",
"tactic": "rw [mul_comm]"
},
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : Euclid... | [
49,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
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Mathlib/Data/Finset/Sigma.lean | Finset.coe_sigma | [] | [
59,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Std/Data/String/Lemmas.lean | String.data_append | [] | [
28,
76
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
28,
9
] |
Mathlib/Data/Polynomial/Splits.lean | Polynomial.mem_lift_of_splits_of_roots_mem_range | [
{
"state_after": "F : Type u\nK : Type v\nL : Type w\ninst✝⁴ : Field K\ninst✝³ : Field L\ninst✝² : Field F\ni : K →+* L\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : Algebra R K\nf : K[X]\nhs : Splits (RingHom.id K) f\nhm : Monic f\nhr : ∀ (a : K), a ∈ roots f → a ∈ RingHom.range (algebraMap R K)\n⊢ Multiset.prod... | [
383,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/MeasureTheory/CardMeasurableSpace.lean | MeasurableSpace.self_subset_generateMeasurableRec | [
{
"state_after": "α : Type u\ns : Set (Set α)\ni : (Quotient.out (ord (aleph 1))).α\n⊢ s ⊆\n let i := i;\n let S := ⋃ (j : ↑(Iio i)), generateMeasurableRec s ↑j;\n s ∪ {∅} ∪ compl '' S ∪ range fun f => ⋃ (n : ℕ), ↑(f n)",
"state_before": "α : Type u\ns : Set (Set α)\ni : (Quotient.out (ord (aleph 1... | [
62,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | CompleteLattice.Independent.subtype_ne_bot_le_finrank | [
{
"state_after": "no goals",
"state_before": "K : Type u\nV : Type v\ninst✝⁶ : DivisionRing K\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module K V\nV₂ : Type v'\ninst✝³ : AddCommGroup V₂\ninst✝² : Module K V₂\ninst✝¹ : FiniteDimensional K V\nι : Type w\np : ι → Submodule K V\nhp : CompleteLattice.Independent p\nin... | [
438,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.t1Space | [] | [
290,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
11
] |
Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.funCongrLeft_symm | [] | [
2675,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2674,
1
] |
Mathlib/Topology/UrysohnsLemma.lean | Urysohns.CU.lim_of_mem_C | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : NormalSpace X\nc : CU X\nx : X\nh : x ∈ c.C\n⊢ CU.lim c x = 0",
"tactic": "simp only [CU.lim, approx_of_mem_C, h, ciSup_const]"
}
] | [
227,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/RingTheory/Coprime/Lemmas.lean | IsCoprime.of_prod_left | [] | [
75,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.equivOfEq_rfl | [
{
"state_after": "case h.a\nF : Type u_1\ninst✝² : Field F\nE : Type u_2\ninst✝¹ : Field E\ninst✝ : Algebra F E\nS : IntermediateField F E\na✝ : { x // x ∈ S }\n⊢ ↑(↑(equivOfEq (_ : S = S)) a✝) = ↑(↑AlgEquiv.refl a✝)",
"state_before": "F : Type u_1\ninst✝² : Field F\nE : Type u_2\ninst✝¹ : Field E\ninst✝ : ... | [
202,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Algebra/Polynomial/BigOperators.lean | Polynomial.natDegree_multiset_prod_of_monic | [
{
"state_after": "R : Type u\nι : Type w\ns : Finset ι\ninst✝ : CommSemiring R\nf : ι → R[X]\nt : Multiset R[X]\nh : ∀ (f : R[X]), f ∈ t → Monic f\n✝ : Nontrivial R\n⊢ natDegree (prod t) = Multiset.sum (Multiset.map natDegree t)",
"state_before": "R : Type u\nι : Type w\ns : Finset ι\ninst✝ : CommSemiring R... | [
206,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Data/Set/Basic.lean | Set.compl_singleton_eq | [] | [
1700,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1699,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.nth_zero_iterate | [] | [
291,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.toList_singleton | [] | [
488,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
1
] |
Mathlib/LinearAlgebra/Basis.lean | VectorSpace.card_fintype | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.1163482\nι' : Type ?u.1163485\nR : Type ?u.1163488\nR₂ : Type ?u.1163491\nK : Type u_1\nM : Type ?u.1163497\nM' : Type ?u.1163500\nM'' : Type ?u.1163503\nV : Type u\nV' : Type ?u.1163508\ninst✝⁶ : DivisionRing K\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Add... | [
1512,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1510,
1
] |
Mathlib/Algebra/Free.lean | FreeMagma.toFreeSemigroup_comp_of | [] | [
726,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
726,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.invFun_as_coe | [] | [
206,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.sum_affineCombinationSingleWeights | [
{
"state_after": "k : Type u_2\nV : Type ?u.415884\nP : Type ?u.415887\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\nS : AffineSpace V P\nι : Type u_1\ns : Finset ι\nι₂ : Type ?u.416543\ns₂ : Finset ι₂\ninst✝ : DecidableEq ι\ni : ι\nh : i ∈ s\n⊢ ∑ j in s, affineCombinationSingleWeights k i j =... | [
671,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
668,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Units.mem_posSubgroup | [] | [
1521,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1519,
1
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | finrank_vectorSpan_range_le | [
{
"state_after": "k : Type u_2\nV : Type u_3\nP : Type u_4\nι : Type u_1\ninst✝⁴ : DivisionRing k\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AffineSpace V P\ninst✝ : Fintype ι\np : ι → P\nn : ℕ\nhc : Fintype.card ι = n + 1\n⊢ finrank k { x // x ∈ vectorSpan k ↑(Finset.image p Finset.univ) } ≤ n",
... | [
163,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Data/Set/Intervals/OrdConnectedComponent.lean | Set.ordConnectedSection_subset | [] | [
153,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Data/Set/Intervals/Disjoint.lean | IsGLB.biUnion_Ioi_eq | [
{
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189,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/CategoryTheory/Bicategory/Strict.lean | CategoryTheory.Bicategory.eqToHom_whiskerRight | [
{
"state_after": "case refl\nB : Type u\ninst✝ : Bicategory B\na b c : B\nf : a ⟶ b\nh : b ⟶ c\n⊢ eqToHom (_ : f = f) ▷ h = eqToHom (_ : f ≫ h = f ≫ h)",
"state_before": "B : Type u\ninst✝ : Bicategory B\na b c : B\nf g : a ⟶ b\nη : f = g\nh : b ⟶ c\n⊢ eqToHom η ▷ h = eqToHom (_ : f ≫ h = g ≫ h)",
"tact... | [
92,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Algebra/Lie/Nilpotent.lean | LieModule.isNilpotent_iff | [] | [
192,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Algebra/Lie/Semisimple.lean | LieAlgebra.abelian_radical_of_semisimple | [
{
"state_after": "R : Type u\nL : Type v\ninst✝³ : CommRing R\ninst✝² : LieRing L\ninst✝¹ : LieAlgebra R L\ninst✝ : IsSemisimple R L\n⊢ IsLieAbelian { x // x ∈ ↑⊥ }",
"state_before": "R : Type u\nL : Type v\ninst✝³ : CommRing R\ninst✝² : LieRing L\ninst✝¹ : LieAlgebra R L\ninst✝ : IsSemisimple R L\n⊢ IsLieA... | [
104,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.restrict_withDensity | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.1771367\nγ : Type ?u.1771370\nδ : Type ?u.1771373\nm : MeasurableSpace α\nμ ν : Measure α\ns : Set α\nhs : MeasurableSet s\nf : α → ℝ≥0∞\nt : Set α\nht : MeasurableSet t\n⊢ ↑↑(Measure.restrict (withDensity μ f) s) t = ↑↑(withDensity (Measure.restrict μ s) f) t... | [
1666,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1662,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | sup_eq_prod_inf_factors | [
{
"state_after": "R : Type ?u.906300\nA : Type ?u.906303\nK : Type ?u.906306\ninst✝⁶ : CommRing R\ninst✝⁵ : CommRing A\ninst✝⁴ : Field K\ninst✝³ : IsDomain A\nT : Type u_1\ninst✝² : CommRing T\ninst✝¹ : IsDomain T\ninst✝ : IsDedekindDomain T\nI J : Ideal T\nhI : I ≠ ⊥\nhJ : J ≠ ⊥\nH :\n normalizedFactors (Mult... | [
937,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | exists_square_le | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.59597\ninst✝² : MulOneClass α\ninst✝¹ : LinearOrder α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x < x_1\na : α\nh : a < 1\n⊢ ∃ b, b * b ≤ a\n\ncase neg\nα : Type u_1\nβ : Type ?u.59597\ninst✝² : MulOneClass α\ninst✝¹ : LinearOrder α\nin... | [
1200,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1192,
1
] |
Mathlib/Init/Data/Nat/Bitwise.lean | Nat.bodd_two | [] | [
65,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/GroupTheory/SpecificGroups/Quaternion.lean | QuaternionGroup.orderOf_a | [
{
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"state_before": "n : ℕ\ninst✝ : NeZero n\ni : ZMod (2 * n)\n⊢ orderOf (a i) = 2 * n / Nat.gcd (2 * n) (ZMod.val i)",
"tactic": "conv_lhs => rw [← ZMod.nat_cast_zmod_val i]"
... | [
263,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Nat.cast_multiset_prod | [] | [
2206,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2205,
1
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Mathlib/Order/Filter/Pointwise.lean | Filter.mul_bot | [] | [
318,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Data/Fintype/BigOperators.lean | Fintype.prod_eq_single | [] | [
83,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Antiperiodic.neg_eq | [
{
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"tactic": "simpa only [zero_add] using h.neg 0"
}
] | [
420,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
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Std/Data/Nat/Lemmas.lean | Nat.div_zero | [
{
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"state_before": "n : Nat\n⊢ n / 0 = 0",
"tactic": "rw [div_eq]"
},
{
"state_after": "no goals",
"state_before": "n : Nat\n⊢ (if 0 < 0 ∧ 0 ≤ n then (n - 0) / 0 + 1 else 0) = 0",
"tactic": "simp [Nat.lt_irref... | [
262,
36
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
261,
19
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.nhds_coe_coe | [] | [
104,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
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Mathlib/Analysis/Convex/Segment.lean | Convex.mem_Icc | [
{
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"state_before": "𝕜 : Type u_1\nE : Type ?u.... | [
538,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
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Mathlib/Topology/Bases.lean | TopologicalSpace.IsTopologicalBasis.prod | [
{
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254,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
11
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Mathlib/Order/Hom/Lattice.lean | SupBotHom.id_apply | [] | [
784,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
783,
1
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Mathlib/Data/ZMod/Quotient.lean | IsOfFinOrder.finite_zpowers | [
{
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"state_before": "n : ℕ\nA : Type ?u.324794\nR : Type ?u.324797\ninst✝² : AddGroup A\ninst✝¹ ... | [
206,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
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Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_mulIndicator | [
{
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"state_before": "α : Typ... | [
240,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
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Mathlib/Algebra/Order/Group/Defs.lean | Left.self_le_inv | [] | [
453,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.succ_ne_self | [] | [
16,
50
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
14,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPushout.flip_iff | [] | [
671,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
670,
1
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Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | ContinuousLinearEquiv.differentiableWithinAt | [] | [
79,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
11
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Mathlib/Data/Nat/Factorial/Basic.lean | Nat.succ_descFactorial | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ (n + 1 - 0) * descFactorial (n + 1) 0 = (n + 1) * descFactorial n 0",
"tactic": "rw [tsub_zero, descFactorial_zero, descFactorial_zero]"
},
{
"state_after": "no goals",
"state_before": "n k : ℕ\n⊢ (n + 1 - (k + 1)) * descFactorial (n + 1... | [
388,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
1
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Mathlib/Computability/Primrec.lean | PrimrecRel.comp₂ | [] | [
505,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
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] |
Mathlib/MeasureTheory/Function/AEEqOfIntegral.lean | MeasureTheory.ae_const_le_iff_forall_lt_measure_zero | [
{
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161,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasurableEquiv.map_measurableEquiv_injective | [
{
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4309,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4306,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mul_lt_aleph0_iff_of_ne_zero | [
{
"state_after": "no goals",
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"tactic": "simp [mul_lt_aleph0_iff, ha, hb]"
}
] | [
1590,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1589,
1
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Mathlib/Algebra/Invertible.lean | map_invOf | [
{
"state_after": "α : Type u\nR : Type u_1\nS : Type u_2\nF : Type u_3\ninst✝³ : MulOneClass R\ninst✝² : Monoid S\ninst✝¹ : MonoidHomClass F R S\nf : F\nr : R\ninst✝ : Invertible r\n⊢ ↑f ⅟r = ⅟(↑f r)",
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445,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
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Mathlib/Data/Seq/Seq.lean | Stream'.Seq.coinduction2 | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ns : Seq α\nf g : Seq α → Seq β\nH : ∀ (s : Seq α), BisimO (fun s1 s2 => ∃ s, s1 = f s ∧ s2 = g s) (destruct (f s)) (destruct (g s))\n⊢ IsBisimulation fun s1 s2 => ∃ s, s1 = f s ∧ s2 = g s",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : Seq α\n... | [
433,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.ofReal_mul_re | [
{
"state_after": "no goals",
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"tactic": "simp only [mul_re, ofReal_im, zero_mul, ofReal_re, sub_zero]"
}
] | [
275,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
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Mathlib/Data/Nat/Sqrt.lean | Nat.le_sqrt | [] | [
89,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | nhds_eq_uniformity' | [] | [
793,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
792,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.limsSup_le_limsSup | [] | [
501,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.restrict_biInf | [
{
"state_after": "α : Type u_2\nι : Type u_1\nI : Set ι\nhI : Set.Nonempty I\ns : Set α\nm : ι → OuterMeasure α\nthis : Nonempty ↑I\n⊢ ↑(restrict s) (⨅ (i : ι) (_ : i ∈ I), m i) = ⨅ (i : ι) (_ : i ∈ I), ↑(restrict s) (m i)",
"state_before": "α : Type u_2\nι : Type u_1\nI : Set ι\nhI : Set.Nonempty I\ns : Se... | [
1282,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1278,
1
] |
src/lean/Init/Classical.lean | Classical.byContradiction | [] | [
124,
55
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
123,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_le_snorm_mul_snorm'_of_norm | [] | [
1450,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1446,
1
] |
Mathlib/Order/Antisymmetrization.lean | OrderHom.antisymmetrization_apply_mk | [] | [
238,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.lift_spec_mul | [
{
"state_after": "no goals",
"state_before": "M : Type u_3\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type u_2\ninst✝¹ : CommMonoid N\nP : Type u_1\ninst✝ : CommMonoid P\nf : LocalizationMap S N\ng : M →* P\nhg : ∀ (y : { x // x ∈ S }), IsUnit (↑g ↑y)\nz : N\nw v : (fun x => P) z\n⊢ ↑(lift f hg) z * w = v... | [
975,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
974,
1
] |
Mathlib/Data/Polynomial/Splits.lean | Polynomial.splits_zero | [] | [
63,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoDiv_apply_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b c : α\nn : ℤ\na : α\n⊢ a - 0 • p ∈ Set.Ico a (a + p)",
"tactic": "simp [hp]"
}
] | [
196,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Algebra/Group/Basic.lean | div_right_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.34821\nG : Type ?u.34824\ninst✝ : DivisionCommMonoid α\na b c d : α\n⊢ a / b / c = a / c / b",
"tactic": "simp"
}
] | [
535,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.of_mul | [] | [
422,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.toLinearEquiv_injective | [] | [
564,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
563,
1
] |
Mathlib/Order/Minimal.lean | IsAntichain.minimals_eq | [] | [
184,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Std/Data/List/Lemmas.lean | List.mem_append_right | [] | [
150,
26
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
149,
1
] |
Mathlib/Data/Int/Cast/Prod.lean | Prod.fst_intCast | [] | [
31,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Mathlib/FieldTheory/Fixed.lean | FixedPoints.minpoly.irreducible_aux | [
{
"state_after": "M : Type u\ninst✝⁵ : Monoid M\nG : Type u\ninst✝⁴ : Group G\nF : Type v\ninst✝³ : Field F\ninst✝² : MulSemiringAction M F\ninst✝¹ : MulSemiringAction G F\nm : M\ninst✝ : Fintype G\nx : F\nf g : Polynomial { x // x ∈ subfield G F }\nhf : Polynomial.Monic f\nhg : Polynomial.Monic g\nhfg : f * g ... | [
249,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.Semiconj.mapsTo_periodicPts | [] | [
264,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.ConnectedComponent.map_mk | [] | [
2057,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2055,
1
] |
Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | GeneralizedContinuedFraction.of_correctness_of_terminatedAt | [] | [
253,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.eq_C_of_degree_le_zero | [
{
"state_after": "case a.zero\nR : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.469754\nh : degree p ≤ 0\n⊢ coeff p Nat.zero = coeff (↑C (coeff p 0)) Nat.zero\n\ncase a.succ\nR : Type u\nS : Type v\na b c d : R\nn✝ m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.46975... | [
623,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
620,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.commute_add_nat | [
{
"state_after": "no goals",
"state_before": "f g : CircleDeg1Lift\nn : ℕ\n⊢ Function.Commute ↑f fun x => x + ↑n",
"tactic": "simp only [add_comm _ (n : ℝ), f.commute_nat_add n]"
}
] | [
339,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.subset_union_left | [] | [
1374,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1374,
1
] |
Mathlib/Topology/Basic.lean | closure_empty | [] | [
490,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/Data/Finset/PImage.lean | Finset.mem_pimage | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\ninst✝² : DecidableEq β\nf g : α →. β\ninst✝¹ : (x : α) → Decidable (f x).Dom\ninst✝ : (x : α) → Decidable (g x).Dom\ns t : Finset α\nb : β\n⊢ b ∈ pimage f s ↔ ∃ a, a ∈ s ∧ b ∈ f a",
"tactic": "simp [pimage]"
}
] | [
70,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Std/Data/Nat/Gcd.lean | Nat.coprime_div_gcd_div_gcd | [
{
"state_after": "no goals",
"state_before": "m n : Nat\nH : 0 < gcd m n\n⊢ coprime (m / gcd m n) (n / gcd m n)",
"tactic": "rw [coprime_iff_gcd_eq_one, gcd_div (gcd_dvd_left m n) (gcd_dvd_right m n), Nat.div_self H]"
}
] | [
275,
94
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
273,
1
] |
src/lean/Init/Data/Nat/SOM.lean | Nat.SOM.Expr.eq_of_toPoly_eq | [
{
"state_after": "ctx : Context\na b : Expr\nh✝ : (toPoly a == toPoly b) = true\nh : Poly.denote ctx (toPoly a) = Poly.denote ctx (toPoly b)\n⊢ denote ctx a = denote ctx b",
"state_before": "ctx : Context\na b : Expr\nh : (toPoly a == toPoly b) = true\n⊢ denote ctx a = denote ctx b",
"tactic": "have h :... | [
183,
13
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
180,
1
] |
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