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/Analysis/Calculus/FDerivAnalytic.lean | HasFPowerSeriesOnBall.hasFDerivAt | [] | [
81,
52
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78,
1
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Mathlib/CategoryTheory/Products/Basic.lean | CategoryTheory.prod_id | [] | [
58,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
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Mathlib/MeasureTheory/Function/ConvergenceInMeasure.lean | MeasureTheory.TendstoInMeasure.aeMeasurable | [
{
"state_after": "case intro\nα : Type u_2\nι : Type u_1\nE : Type u_3\nm : MeasurableSpace α\nμ : Measure α\ninst✝⁴ : MeasurableSpace E\ninst✝³ : NormedAddCommGroup E\ninst✝² : BorelSpace E\nu : Filter ι\ninst✝¹ : NeBot u\ninst✝ : IsCountablyGenerated u\nf : ι → α → E\ng : α → E\nhf : ∀ (n : ι), AEMeasurable (... | [
273,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Logic/IsEmpty.lean | not_nonempty_iff | [] | [
136,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/GroupTheory/Subsemigroup/Centralizer.lean | Set.zero_mem_centralizer | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\nS T : Set M\ninst✝ : MulZeroClass M\n⊢ 0 ∈ centralizer S",
"tactic": "simp [mem_centralizer_iff]"
}
] | [
68,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.ConnectedComponent.ind₂ | [] | [
1995,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1992,
11
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Mathlib/Algebra/Module/LocalizedModule.lean | LocalizedModule.mk_smul_mk | [
{
"state_after": "R : Type u\ninst✝² : CommSemiring R\nS : Submonoid R\nM : Type v\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nr : R\nm : M\ns t : { x // x ∈ S }\n⊢ Localization.liftOn (Localization.mk r s)\n (fun r s =>\n liftOn (mk m t) (fun p => mk (SMul.smul r p.fst) (s * p.snd))\n (... | [
338,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.map_restrict_of_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type u_2\nγ : Type u_1\nδ : Type ?u.809158\ninst✝² : MeasurableSpace α\nK : Type ?u.809164\ninst✝¹ : Zero β\ninst✝ : Zero γ\ng : β → γ\nhg : g 0 = 0\nf : α →ₛ β\ns : Set α\nx : α\nhs : MeasurableSet s\n⊢ ↑(map g (restrict f s)) x = ↑(restrict (... | [
770,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
766,
1
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Mathlib/Data/Multiset/Bind.lean | Multiset.sigma_singleton | [] | [
334,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
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Mathlib/Data/Finset/Image.lean | Finset.subset_image_iff | [
{
"state_after": "case mp\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.140906\ninst✝ : DecidableEq β\ns : Set α\nt : Finset β\nf : α → β\n⊢ ↑t ⊆ f '' s → ∃ s', ↑s' ⊆ s ∧ image f s' = t\n\ncase mpr\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.140906\ninst✝ : DecidableEq β\ns : Set α\nt : Finset β\nf : α → β\n⊢ (∃ s', ↑s... | [
755,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
745,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Fintype.prod_eq_mul_prod_compl | [] | [
1569,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1567,
1
] |
Mathlib/Algebra/Order/Group/OrderIso.lean | OrderIso.mulRight_symm | [
{
"state_after": "case h.h\nα : Type u\ninst✝² : Group α\ninst✝¹ : LE α\ninst✝ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na✝ b c d a x : α\n⊢ ↑(symm (mulRight a)) x = ↑(mulRight a⁻¹) x",
"state_before": "α : Type u\ninst✝² : Group α\ninst✝¹ : LE α\ninst✝ : CovariantClass α α (swa... | [
109,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.ExprCnstr.toPoly_norm_eq | [] | [
557,
6
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
556,
1
] |
Mathlib/Algebra/BigOperators/Associated.lean | Prime.exists_mem_multiset_dvd | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.8870\nγ : Type ?u.8873\nδ : Type ?u.8876\ninst✝ : CommMonoidWithZero α\np : α\nhp : Prime p\ns✝ : Multiset α\na : α\ns : Multiset α\nih : p ∣ Multiset.prod s → ∃ a, a ∈ s ∧ p ∣ a\nh : p ∣ Multiset.prod (a ::ₘ s)\n⊢ p ∣ a * Multiset.prod... | [
41,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/GroupTheory/FreeAbelianGroupFinsupp.lean | Finsupp.toFreeAbelianGroup_comp_singleAddHom | [
{
"state_after": "case h1\nX : Type u_1\nx : X\n⊢ ↑(AddMonoidHom.comp toFreeAbelianGroup (singleAddHom x)) 1 =\n ↑(↑(AddMonoidHom.flip (smulAddHom ℤ (FreeAbelianGroup X))) (of x)) 1",
"state_before": "X : Type u_1\nx : X\n⊢ AddMonoidHom.comp toFreeAbelianGroup (singleAddHom x) =\n ↑(AddMonoidHom.flip ... | [
57,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.toReal_eq_zero_iff | [
{
"state_after": "θ : Angle\n⊢ toReal θ = toReal 0 ↔ θ = 0",
"state_before": "θ : Angle\n⊢ toReal θ = 0 ↔ θ = 0",
"tactic": "nth_rw 1 [← toReal_zero]"
},
{
"state_after": "no goals",
"state_before": "θ : Angle\n⊢ toReal θ = toReal 0 ↔ θ = 0",
"tactic": "exact toReal_inj"
}
] | [
594,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/Algebra/Group/Commute.lean | Commute.refl | [] | [
58,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
11
] |
Mathlib/LinearAlgebra/CrossProduct.lean | cross_dot_cross | [
{
"state_after": "R : Type u_1\ninst✝ : CommRing R\nu v w x : Fin 3 → R\n⊢ vecCons (u 1 * v 2 - u 2 * v 1) ![u 2 * v 0 - u 0 * v 2, u 0 * v 1 - u 1 * v 0] 0 *\n vecCons (w 1 * x 2 - w 2 * x 1) ![w 2 * x 0 - w 0 * x 2, w 0 * x 1 - w 1 * x 0] 0 +\n vecCons (u 1 * v 2 - u 2 * v 1) ![u 2 * v 0 - u 0... | [
132,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | StrictMonoOn.mul_monotone' | [] | [
1530,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1528,
1
] |
Mathlib/Analysis/NormedSpace/QuaternionExponential.lean | Quaternion.hasSum_expSeries_of_imaginary | [
{
"state_after": "q : ℍ\nhq : q.re = 0\nc s : ℝ\nhs : HasSum (fun n => (-1) ^ n * ‖q‖ ^ (2 * n + 1) / ↑(2 * n + 1)!) s\nhc : HasSum (fun a => ↑((-1) ^ a * ‖q‖ ^ (2 * a) / ↑(2 * a)!)) ↑c\n⊢ HasSum (fun n => ↑(expSeries ℝ ℍ n) fun x => q) (↑c + (s / ‖q‖) • q)",
"state_before": "q : ℍ\nhq : q.re = 0\nc s : ℝ\n... | [
92,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Data/Set/Intervals/OrdConnected.lean | Set.ordConnected_Ici | [] | [
136,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/CategoryTheory/NatIso.lean | CategoryTheory.NatIso.cancel_natIso_inv_left | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nE : Type u₃\ninst✝ : Category E\nF G : C ⥤ D\nα : F ≅ G\nX : C\nZ : D\ng g' : F.obj X ⟶ Z\n⊢ α.inv.app X ≫ g = α.inv.app X ≫ g' ↔ g = g'",
"tactic": "simp only [cancel_epi, refl]"
}
] | [
137,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Data/ULift.lean | PLift.exists | [] | [
76,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | NNReal.count_const_le_le_of_tsum_le | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1696412\nγ : Type ?u.1696415\nδ : Type ?u.1696418\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝¹ : MeasurableSpace α\ninst✝ : MeasurableSingletonClass α\na : α → ℝ≥0\na_mble : Measurable a\na_summable : Summable a\nc : ℝ≥0\ntsum_le_c : (∑' (i : α), a i) ≤ c\nε : ℝ≥0\... | [
1432,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1422,
1
] |
Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean | MeasureTheory.ProbabilityMeasure.toFiniteMeasure_continuous | [] | [
227,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | nat_cast_memℓp_infty | [] | [
892,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
891,
1
] |
Mathlib/Data/Nat/Bitwise.lean | Nat.bit_eq_zero | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nb : Bool\n⊢ bit b n = 0 ↔ n = 0 ∧ b = false",
"tactic": "cases b <;> simp [Nat.bit0_eq_zero, Nat.bit1_ne_zero]"
}
] | [
62,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Algebra/Algebra/Unitization.lean | Unitization.snd_add | [] | [
229,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Topology/Maps.lean | openEmbedding_iff_continuous_injective_open | [] | [
606,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
] |
Mathlib/Data/Nat/Set.lean | Nat.range_succ | [
{
"state_after": "no goals",
"state_before": "⊢ range succ = {i | 0 < i}",
"tactic": "ext (_ | i) <;> simp [succ_pos, succ_ne_zero, Set.mem_setOf]"
}
] | [
31,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
11
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.codisjoint_subgroupOf_sup | [
{
"state_after": "case hH\nG : Type u_1\nG' : Type ?u.612020\ninst✝³ : Group G\ninst✝² : Group G'\nA : Type ?u.612029\ninst✝¹ : AddGroup A\nN : Type ?u.612035\ninst✝ : Group N\nf : G →* N\nH K : Subgroup G\n⊢ H ≤ H ⊔ K\n\ncase hK\nG : Type u_1\nG' : Type ?u.612020\ninst✝³ : Group G\ninst✝² : Group G'\nA : Type ... | [
3174,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3171,
1
] |
Mathlib/Data/Set/Finite.lean | Set.finite_image_fst_and_snd_iff | [] | [
1100,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1097,
1
] |
Std/Data/List/Lemmas.lean | List.isInfix.subset | [] | [
1604,
20
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1603,
11
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.uniformity_basis_dist_inv_nat_succ | [] | [
753,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
750,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.one_def | [] | [
242,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.update_piecewise_of_mem | [
{
"state_after": "α : Type u_1\nβ : Type ?u.308183\nγ : Type ?u.308186\nδ : α → Sort u_2\ns : Finset α\nf g : (i : α) → δ i\ninst✝¹ : (j : α) → Decidable (j ∈ s)\ninst✝ : DecidableEq α\ni : α\nhi : i ∈ s\nv : δ i\n⊢ piecewise s (update f i v) (update g i v) = piecewise s (update f i v) g",
"state_before": "... | [
2547,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2543,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.val_eq_toMeasure | [] | [
145,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.lt_mul_of_limit | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.211340\nβ : Type ?u.211343\nγ : Type ?u.211346\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na b c : Ordinal\nh : IsLimit c\n⊢ a < b * c ↔ ∃ c', c' < c ∧ a < b * c'",
"tactic": "simpa only [not_ball, not_le, bex_def] using not_congr (@mu... | [
817,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
815,
1
] |
Mathlib/Data/Finset/Lattice.lean | Multiset.count_finset_sup | [
{
"state_after": "F : Type ?u.410886\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.410895\nι : Type ?u.410898\nκ : Type ?u.410901\ninst✝ : DecidableEq β\ns : Finset α\nf : α → Multiset β\nb : β\nthis : DecidableEq α := Classical.decEq α\n⊢ count b (Finset.sup s f) = Finset.sup s fun a => count b (f a)",
"state_b... | [
1752,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1745,
1
] |
Mathlib/CategoryTheory/Idempotents/FunctorExtension.lean | CategoryTheory.Idempotents.functorExtension₁_comp_whiskeringLeft_toKaroubi | [
{
"state_after": "case refine'_1\nC : Type u_1\nD : Type u_2\nE : Type ?u.30040\ninst✝² : Category C\ninst✝¹ : Category D\ninst✝ : Category E\n⊢ ∀ (X : C ⥤ Karoubi D),\n (functorExtension₁ C D ⋙ (whiskeringLeft C (Karoubi C) (Karoubi D)).obj (toKaroubi C)).obj X =\n (𝟭 (C ⥤ Karoubi D)).obj X\n\ncase re... | [
128,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Algebra/GroupWithZero/Semiconj.lean | SemiconjBy.inv_symm_left_iff₀ | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.637\nM₀ : Type ?u.640\nG₀ : Type u_1\nM₀' : Type ?u.646\nG₀' : Type ?u.649\nF : Type ?u.652\nF' : Type ?u.655\ninst✝ : GroupWithZero G₀\na x y x' y' : G₀\nha : a = 0\n⊢ SemiconjBy a⁻¹ x y ↔ SemiconjBy a y x",
"tactic": "simp only [ha, inv_zero, S... | [
40,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/Data/Set/Function.lean | Set.SurjOn.congr | [
{
"state_after": "no goals",
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785,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
1
] |
Mathlib/Order/Hom/Lattice.lean | BoundedLatticeHom.coe_id | [] | [
1275,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1274,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.tan_add_int_mul_pi | [] | [
1039,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1038,
1
] |
Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean | DifferentiableAt.restrictScalars | [] | [
76,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/GroupTheory/Congruence.lean | Con.quot_mk_eq_coe | [] | [
291,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.toAffineEquiv_symm | [] | [
539,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
] |
Mathlib/Topology/PathConnected.lean | pathConnectedSpace_iff_univ | [
{
"state_after": "case mp\nX : Type u_1\nY : Type ?u.689179\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx y z : X\nι : Type ?u.689194\nF : Set X\n⊢ PathConnectedSpace X → IsPathConnected univ\n\ncase mpr\nX : Type u_1\nY : Type ?u.689179\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx ... | [
1145,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1134,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.abs_sin_eq_of_two_zsmul_eq | [
{
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"state_before": "θ ψ : Angle\nh : 2 • θ = 2 • ψ\n⊢ abs (sin θ) = abs (sin ψ)",
"tactic": "simp_rw [two_zsmul, ← two_nsmul] at h"
},
{
"state_after": "no goals",
"state_before": "θ ψ : Angle\nh : 2 • θ = 2 • ψ\n⊢ ... | [
490,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
1
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Mathlib/CategoryTheory/Conj.lean | CategoryTheory.Iso.conjAut_pow | [] | [
162,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
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Mathlib/Order/Concept.lean | intentClosure_extentClosure_intentClosure | [] | [
150,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
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Mathlib/RingTheory/LaurentSeries.lean | PowerSeries.coe_pow | [] | [
254,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
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Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.coe_trans | [] | [
382,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
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Mathlib/Algebra/Order/Rearrangement.lean | Monovary.sum_comp_perm_mul_lt_sum_mul_iff | [] | [
496,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
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Mathlib/Algebra/Order/Group/Defs.lean | inv_mul_le_iff_le_mul | [
{
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}
] | [
124,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
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Std/Data/Int/Lemmas.lean | Int.max_comm | [
{
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"state_before": "a b : Int\n⊢ max a b = max b a",
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{
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712,
48
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708,
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Mathlib/Topology/Instances/Matrix.lean | Continuous.matrix_conjTranspose | [] | [
97,
49
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Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.angle_midpoint_eq_pi | [
{
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257,
42
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Mathlib/Algebra/GroupRingAction/Invariant.lean | IsInvariantSubring.coe_subtypeHom | [] | [
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70
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60,
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Mathlib/Data/Prod/Basic.lean | Prod_map | [] | [
27,
6
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26,
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Mathlib/Data/Nat/Factorization/Basic.lean | Nat.factorizationEquiv_apply | [
{
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{
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335,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
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Mathlib/CategoryTheory/Sites/Types.lean | CategoryTheory.yoneda'_comp | [] | [
79,
6
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Mathlib/Algebra/Order/Sub/Canonical.lean | tsub_add_tsub_comm | [] | [
230,
91
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Mathlib/Data/Num/Lemmas.lean | ZNum.zneg_neg | [] | [
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Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.IndepSets.indep | [
{
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51
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Mathlib/Order/Hom/Lattice.lean | BoundedLatticeHom.coe_comp | [] | [
1293,
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1291,
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Mathlib/Data/PFun.lean | PFun.comp_id | [
{
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] | [
593,
25
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Mathlib/GroupTheory/Nilpotent.lean | comap_center_subst | [
{
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91
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592,
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Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.measure_inter_add_diff₀ | [
{
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320,
56
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Mathlib/Data/Int/Div.lean | Int.natAbs_le_of_dvd_ne_zero | [] | [
60,
61
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Mathlib/Data/Set/Prod.lean | Set.offDiag_univ | [
{
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}
] | [
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17
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582,
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Mathlib/RingTheory/AlgebraicIndependent.lean | algebraicIndependent_iff | [] | [
83,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/Localization/Integral.lean | isIntegral_localization | [
{
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249,
92
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231,
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Mathlib/Data/Real/Basic.lean | Real.isLUB_sSup | [
{
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"state_before": "x y : ℝ\nS : Set ℝ\nh₁ : Set.Nonempty S\nh₂ : BddAbove S\n⊢ IsLUB S (sSup S)",
"tactic": "simp only [sSup_def, dif_pos (And.intro h₁ h₂)]"
},
{
"state_after": "n... | [
744,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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11
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Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | HomogeneousLocalization.NumDenSameDeg.den_pow | [] | [
254,
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253,
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.integrable_of_forall_fin_meas_le | [
{
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1194,
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1190,
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Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.colimit.post_desc | [
{
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1039,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Intervals/Basic.lean | Set.nonempty_Ioi | [] | [
301,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
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Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.smul_toGerm | [] | [
610,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
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Mathlib/Algebra/Algebra/Operations.lean | Submodule.map_div | [
{
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Mathlib/CategoryTheory/Adjunction/Opposites.lean | CategoryTheory.Adjunction.leftAdjointUniq_refl | [
{
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213,
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206,
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Mathlib/Topology/Algebra/Monoid.lean | continuousOn_list_prod | [
{
"state_after": "ι : Type u_1\nα : Type ?u.175300\nX : Type u_2\nM : Type u_3\nN : Type ?u.175309\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace M\ninst✝¹ : Monoid M\ninst✝ : ContinuousMul M\nf : ι → X → M\nl : List ι\nt : Set X\nh : ∀ (i : ι), i ∈ l → ContinuousOn (f i) t\nx : X\nhx : x ∈ t\n⊢ Contin... | [
555,
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Mathlib/Order/FixedPoints.lean | OrderHom.map_lfp_comp | [] | [
161,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
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Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.mem_adjoin_of_map_mul | [
{
"state_after": "R : Type u\nA : Type v\nB : Type w\ninst✝⁴ : CommSemiring R\ninst✝³ : Semiring A\ninst✝² : Semiring B\ninst✝¹ : Algebra R A\ninst✝ : Algebra R B\ns✝ t s : Set A\nx : A\nf : A →ₗ[R] B\nhf : ∀ (a₁ a₂ : A), ↑f (a₁ * a₂) = ↑f a₁ * ↑f a₂\nh : x ∈ adjoin R s\nr : R\n⊢ (fun a => ↑f a ∈ adjoin R (↑f '... | [
249,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
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Mathlib/Order/LiminfLimsup.lean | Filter.HasBasis.limsInf_eq_iSup_sInf | [] | [
671,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
669,
1
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.HasFiniteIntegral.left_of_add_measure | [] | [
203,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.closure_iUnion | [] | [
1260,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1259,
1
] |
Mathlib/Order/Lattice.lean | max_max_max_comm | [] | [
890,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
889,
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Mathlib/Analysis/Complex/Basic.lean | Complex.dist_self_conj | [
{
"state_after": "no goals",
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"tactic": "rw [dist_comm, dist_conj_self]"
}
] | [
139,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
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Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.measure_univ_of_isMulLeftInvariant | [
{
"state_after": "case intro.intro.intro\n𝕜 : Type ?u.542119\nG : Type u_1\nH : Type ?u.542125\ninst✝¹⁰ : MeasurableSpace G\ninst✝⁹ : MeasurableSpace H\ninst✝⁸ : TopologicalSpace G\ninst✝⁷ : BorelSpace G\nμ✝ : Measure G\ninst✝⁶ : Group G\ninst✝⁵ : TopologicalGroup G\ninst✝⁴ : IsMulLeftInvariant μ✝\ninst✝³ : Lo... | [
655,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
612,
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Mathlib/Data/Int/Cast/Lemmas.lean | map_intCast | [] | [
320,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
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Mathlib/GroupTheory/SchurZassenhaus.lean | Subgroup.exists_right_complement'_of_coprime_aux | [] | [
133,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
9
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | HasFTaylorSeriesUpTo.contDiff | [] | [
1404,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1402,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.dist_eq_card | [] | [
210,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Std/Data/Int/DivMod.lean | Int.ediv_emod_unique | [
{
"state_after": "case mp\na b r q : Int\nh : 0 < b\n⊢ a / b = q ∧ a % b = r → r + b * q = a ∧ 0 ≤ r ∧ r < b\n\ncase mpr\na b r q : Int\nh : 0 < b\n⊢ r + b * q = a ∧ 0 ≤ r ∧ r < b → a / b = q ∧ a % b = r",
"state_before": "a b r q : Int\nh : 0 < b\n⊢ a / b = q ∧ a % b = r ↔ r + b * q = a ∧ 0 ≤ r ∧ r < b",
... | [
510,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
501,
11
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Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.refl_target | [] | [
614,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
1
] |
Mathlib/Topology/SubsetProperties.lean | Filter.cocompact_eq_cofinite | [
{
"state_after": "no goals",
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"tactic": "simp only... | [
547,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.induction₂_neg_left | [] | [
1008,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
997,
1
] |
Mathlib/Analysis/Convex/Hull.lean | Convex.convexHull_subset_iff | [] | [
80,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.coe_toSubmodule_eq_iff | [] | [
146,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
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