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/Set/Lattice.lean | Set.sUnion_subset | [] | [
1053,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1052,
1
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mem_iSup_of_mem | [] | [
1046,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1044,
1
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Mathlib/Data/Finsupp/NeLocus.lean | Finsupp.coe_neLocus | [
{
"state_after": "case h\nα : Type u_1\nM : Type ?u.2198\nN : Type u_2\nP : Type ?u.2204\ninst✝² : DecidableEq α\ninst✝¹ : DecidableEq N\ninst✝ : Zero N\nf g : α →₀ N\nx✝ : α\n⊢ x✝ ∈ ↑(neLocus f g) ↔ x✝ ∈ {x | ↑f x ≠ ↑g x}",
"state_before": "α : Type u_1\nM : Type ?u.2198\nN : Type u_2\nP : Type ?u.2204\nin... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
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Mathlib/Analysis/NormedSpace/ContinuousAffineMap.lean | ContinuousAffineMap.add_contLinear | [] | [
138,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
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Mathlib/Algebra/Divisibility/Units.lean | IsUnit.dvd_mul_right | [
{
"state_after": "case intro\nα : Type u_1\ninst✝ : Monoid α\na b : α\nu : αˣ\n⊢ a ∣ b * ↑u ↔ a ∣ b",
"state_before": "α : Type u_1\ninst✝ : Monoid α\na b u : α\nhu : IsUnit u\n⊢ a ∣ b * u ↔ a ∣ b",
"tactic": "rcases hu with ⟨u, rfl⟩"
},
{
"state_after": "no goals",
"state_before": "case int... | [
87,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Data/Int/Parity.lean | Int.even_or_odd | [] | [
68,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arccos_pos | [
{
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"state_before": "x : ℝ\n⊢ 0 < arccos x ↔ x < 1",
"tactic": "simp [arccos]"
}
] | [
358,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/Analysis/Complex/Arg.lean | Complex.abs_add_eq | [] | [
65,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
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Std/Data/Rat/Lemmas.lean | Rat.mkRat_eq_zero | [
{
"state_after": "no goals",
"state_before": "d : Nat\nn : Int\nd0 : d ≠ 0\n⊢ mkRat n d = 0 ↔ n = 0",
"tactic": "simp [mkRat_def, d0]"
}
] | [
101,
86
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
101,
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Mathlib/Logic/Embedding/Basic.lean | Function.Embedding.setValue_eq | [
{
"state_after": "no goals",
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"tactic": "simp [setValue]"
}
] | [
208,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
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Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean | TopCat.fst_embedding_of_right_embedding | [
{
"state_after": "case h.e'_5.h\nJ : Type v\ninst✝ : SmallCategory J\nX✝ Y✝ Z : TopCat\nX Y S : TopCat\nf : X ⟶ S\ng : Y ⟶ S\nH : Embedding ((forget TopCat).map g)\ne_2✝ : (forget TopCat).obj X = ↑X\n⊢ (forget TopCat).map pullback.fst =\n ↑(homeoOfIso (asIso pullback.fst)) ∘\n (forget TopCat).map (pullb... | [
305,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.ext_iff | [] | [
159,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Order/WithBot.lean | WithBot.coe_sup | [] | [
416,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
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Mathlib/RingTheory/Artinian.lean | isArtinian_of_linearEquiv | [] | [
100,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
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Mathlib/Topology/PathConnected.lean | pathConnectedSpace_iff_connectedSpace | [
{
"state_after": "case mp\nX : Type u_1\nY : Type ?u.703689\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\nx y z : X\nι : Type ?u.703704\nF : Set X\ninst✝ : LocPathConnectedSpace X\n⊢ PathConnectedSpace X → ConnectedSpace X\n\ncase mpr\nX : Type u_1\nY : Type ?u.703689\ninst✝² : TopologicalSpace X\n... | [
1232,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1213,
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Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.mkPiField_apply | [] | [
897,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
895,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.smul_eq_C_smul | [
{
"state_after": "case ofFractionRing\nK : Type u\ninst✝ : CommRing K\nR : Type ?u.178730\nr : K\nx : FractionRing K[X]\n⊢ r • { toFractionRing := x } = ↑Polynomial.C r • { toFractionRing := x }",
"state_before": "K : Type u\ninst✝ : CommRing K\nR : Type ?u.178730\nx : RatFunc K\nr : K\n⊢ r • x = ↑Polynomia... | [
463,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | FG_adjoin_singleton_of_integral | [
{
"state_after": "case intro.intro\nR : Type u_1\nA : Type u_2\nB : Type ?u.290022\nS : Type ?u.290025\ninst✝⁵ : CommRing R\ninst✝⁴ : CommRing A\ninst✝³ : CommRing B\ninst✝² : CommRing S\ninst✝¹ : Algebra R A\ninst✝ : Algebra R B\nf✝ : R →+* S\nx : A\nf : R[X]\nhfm : Monic f\nhfx : eval₂ (algebraMap R A) x f = ... | [
227,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
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Mathlib/Data/Set/Image.lean | Set.rightInverse_rangeSplitting | [] | [
1176,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1173,
1
] |
Mathlib/GroupTheory/Complement.lean | Subgroup.MemRightTransversals.mul_inv_toFun_mem | [] | [
426,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.empty_sdiff | [] | [
2172,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2171,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycle.pow_iff | [
{
"state_after": "case intro\nι : Type ?u.1194880\nα : Type ?u.1194883\nβ : Type u_1\nf✝ g : Perm α\nx y : α\ninst✝² : DecidableEq α\ninst✝¹ : Fintype α\ninst✝ : Finite β\nf : Perm β\nhf : IsCycle f\nn : ℕ\nval✝ : Fintype β\n⊢ IsCycle (f ^ n) ↔ Nat.coprime n (orderOf f)",
"state_before": "ι : Type ?u.119488... | [
667,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
646,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.IsPath.transfer | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V\np : Walk G u v\nH : SimpleGraph V\nhp : ∀ (e : Sym2 V), e ∈ edges p → e ∈ edgeSet H\npp : IsPath p\n⊢ IsPath (Walk.transfer p H hp)",
"tactic": "in... | [
1719,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1713,
11
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.exists_nat_pos_mul_gt | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.339781\nβ : Type ?u.339784\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nha : a ≠ 0\nhb : b ≠ ⊤\nn : ℕ\nhn : b / a < ↑n\n⊢ b < ↑n * a",
"tactic": "rwa [← ENNReal.div_lt_iff (Or.inl ha) (Or.inr hb)]"
}
] | [
1825,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1822,
1
] |
Mathlib/Topology/Instances/AddCircle.lean | AddCircle.equivAddCircle_apply_mk | [] | [
334,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_iUnion_eq_or_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.94012\nι : Sort ?u.94015\nι' : Sort ?u.94018\nι₂ : Sort ?u.94021\nκ : ι → Sort ?u.94026\nκ₁ : ι → Sort ?u.94031\nκ₂ : ι → Sort ?u.94036\nκ' : ι' → Sort ?u.94041\nb : β\np : β → Prop\ns : (x : β) → x = b ∨ p x → Set α\n⊢ (⋃... | [
838,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
836,
1
] |
Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.continuous_coe | [] | [
179,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Analysis/NormedSpace/CompactOperator.lean | isCompactOperator_zero | [] | [
71,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/CategoryTheory/Limits/ColimitLimit.lean | CategoryTheory.Limits.map_id_right_eq_curry_swap_map | [] | [
52,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.const_max | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝ : PseudoEMetricSpace α\nf g : α → ℝ\nKf Kg : ℝ≥0\nhf : LipschitzWith Kf f\na : ℝ\n⊢ LipschitzWith Kf fun x => max a (f x)",
"tactic": "simpa only [max_comm] using hf.max_const a"
}
] | [
456,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
] |
Mathlib/Logic/Relation.lean | Acc.of_downward_closed | [] | [
204,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
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] |
Mathlib/Analysis/Convex/Independent.lean | Subsingleton.convexIndependent | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_3\nι : Type u_1\ninst✝³ : OrderedSemiring 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ns✝ t : Set E\ninst✝ : Subsingleton ι\np : ι → E\ns : Set ι\nx : ι\nhx : p x ∈ ↑(convexHull 𝕜).toOrderHom (p '' s)\n⊢ x ∈ s",
"state_before": "𝕜 : Type u_2\nE : Type u_3\... | [
71,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.cast_zneg | [] | [
1064,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1061,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.one_mem_div_iff | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.114914\nα : Type u_1\nβ : Type ?u.114920\nγ : Type ?u.114923\ninst✝ : Group α\ns t : Set α\na b : α\n⊢ 1 ∈ s / t ↔ ¬Disjoint s t",
"tactic": "simp [not_disjoint_iff_nonempty_inter, mem_div, div_eq_one, Set.Nonempty]"
}
] | [
1163,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1162,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.aestronglyMeasurable | [] | [
230,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
11
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.comp_equiv_symm_dotProduct | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.146320\nm : Type u_1\nn : Type u_2\no : Type ?u.146329\nm' : o → Type ?u.146334\nn' : o → Type ?u.146339\nR : Type ?u.146342\nS : Type ?u.146345\nα : Type v\nβ : Type w\nγ : Type ?u.146352\ninst✝² : Fintype m\ninst✝¹ : Fintype n\ninst✝ : NonUnitalNon... | [
785,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
783,
1
] |
Mathlib/Topology/UniformSpace/AbstractCompletion.lean | AbstractCompletion.extend_def | [] | [
136,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | Part.ωSup_eq_none | [] | [
341,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Data/Nat/GCD/BigOperators.lean | Nat.coprime_prod_left | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nx : ℕ\ns : ι → ℕ\nt : Finset ι\n⊢ (fun y => coprime y x) 1",
"tactic": "simp"
}
] | [
27,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
25,
1
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Mathlib/MeasureTheory/Constructions/Polish.lean | IsClosed.measurableSet_image_of_continuousOn_injOn | [
{
"state_after": "α : Type ?u.320629\ninst✝⁵ : TopologicalSpace α\nι : Type ?u.320635\nγ : Type u_2\ntγ : TopologicalSpace γ\ninst✝⁴ : PolishSpace γ\nβ : Type u_1\ninst✝³ : TopologicalSpace β\ninst✝² : T2Space β\ninst✝¹ : MeasurableSpace β\ninst✝ : BorelSpace β\ns : Set γ\nhs : IsClosed s\nf : γ → β\nf_cont : C... | [
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39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
574,
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Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.nadd_one | [
{
"state_after": "case h\na✝ b c a : Ordinal\nIH : ∀ (k : Ordinal), k < a → k ♯ 1 = succ k\n⊢ a ♯ 1 = succ a",
"state_before": "a b c : Ordinal\n⊢ a ♯ 1 = succ a",
"tactic": "induction' a using Ordinal.induction with a IH"
},
{
"state_after": "case h\na✝ b c a : Ordinal\nIH : ∀ (k : Ordinal), k ... | [
302,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
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Mathlib/Analysis/SpecialFunctions/Exp.lean | Filter.Tendsto.cexp | [] | [
94,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
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src/lean/Init/Control/ExceptCps.lean | ExceptCpsT.runCatch_pure | [] | [
62,
95
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
62,
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Mathlib/Algebra/Order/WithZero.lean | one_le_inv₀ | [] | [
155,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.currySum_apply | [] | [
1786,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1784,
1
] |
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | IsBoundedLinearMap.isBigO_sub | [] | [
203,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.opow_lt_opow_iff_right | [] | [
116,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Algebra/Field/Basic.lean | div_sub_one | [] | [
169,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Order/Minimal.lean | eq_of_mem_minimals | [] | [
93,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Algebra/Category/GroupCat/EpiMono.lean | GroupCat.SurjectiveOfEpiAuxs.one_smul | [
{
"state_after": "A B : GroupCat\nf : A ⟶ B\nx : X'\ny : ↑(Set.range (Function.swap leftCoset (MonoidHom.range f).toSubmonoid.toSubsemigroup.carrier))\n⊢ fromCoset\n { val := 1 *l ↑y,\n property :=\n (_ : 1 *l ↑y ∈ Set.range (Function.swap leftCoset (MonoidHom.range f).toSubmonoid.toSubsemi... | [
144,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.zero_lf | [
{
"state_after": "x : PGame\n⊢ ((∃ i,\n (∀ (i' : LeftMoves 0), moveLeft 0 i' ⧏ moveLeft x i) ∧\n ∀ (j : RightMoves (moveLeft x i)), 0 ⧏ moveRight (moveLeft x i) j) ∨\n ∃ j,\n (∀ (i : LeftMoves (moveRight 0 j)), moveLeft (moveRight 0 j) i ⧏ x) ∧\n ∀ (j' : RightMoves x), moveR... | [
681,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
679,
1
] |
Mathlib/Analysis/Calculus/IteratedDeriv.lean | ContDiffWithinAt.differentiableWithinAt_iteratedDerivWithin | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type ?u.53911\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nn✝ : ℕ\nf : 𝕜 → F\ns : Set 𝕜\nx : 𝕜\nn : ℕ∞\nm : ℕ\nh : Con... | [
167,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | MulLECancellable.mul_le_mul_iff_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.86235\ninst✝² : LE α\ninst✝¹ : CommSemigroup α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b c : α\nha : MulLECancellable a\n⊢ b * a ≤ c * a ↔ b ≤ c",
"tactic": "rw [mul_comm b, mul_comm c, ha.mul_le_m... | [
1642,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1640,
11
] |
Mathlib/Data/Nat/Cast/WithTop.lean | Nat.cast_withTop | [] | [
23,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
22,
1
] |
Mathlib/Analysis/Normed/Field/UnitBall.lean | coe_mul_unitBall | [] | [
54,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/CategoryTheory/Monoidal/Mon_.lean | Mon_.comp_hom' | [] | [
133,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.functorPushforward_comp | [
{
"state_after": "case h\nC : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nF : C ⥤ D\nX Y Z : C\nf : Y ⟶ X\nS R✝ : Sieve X\nE : Type u₃\ninst✝ : Category E\nG : D ⥤ E\nR : Sieve X\nY✝ : E\nf✝ : Y✝ ⟶ (F ⋙ G).obj X\n⊢ (functorPushforward (F ⋙ G) R).arrows f✝ ↔ (functorPushforward G (functorPush... | [
652,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
1
] |
Std/Data/String/Lemmas.lean | String.Iterator.Valid.prevn | [] | [
659,
26
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
657,
1
] |
Mathlib/Data/Finmap.lean | Finmap.erase_union_singleton | [
{
"state_after": "case pos\nα : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb : β a\ns : Finmap β\nh : lookup a s = some b\nx : α\nh' : x = a\n⊢ lookup x (erase a s ∪ singleton a b) = lookup x s\n\ncase neg\nα : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb : β a\ns : Finmap β\nh : lookup a ... | [
643,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
1
] |
Mathlib/Algebra/Homology/ShortExact/Preadditive.lean | CategoryTheory.Splitting.inr_iso_inv | [] | [
238,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Combinatorics/Quiver/SingleObj.lean | Quiver.SingleObj.listToPath_pathToList | [
{
"state_after": "case nil\nα : Type u_1\nβ : Type ?u.4805\nγ : Type ?u.4808\nx : SingleObj α\n⊢ listToPath (pathToList Path.nil) = Path.cast (_ : star α = star α) (_ : star α = star α) Path.nil\n\ncase cons\nα : Type u_1\nβ : Type ?u.4805\nγ : Type ?u.4808\nx y z : SingleObj α\np : Path (star α) y\na : y ⟶ z\n... | [
142,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Std/Data/Int/DivMod.lean | Int.fmod_self | [
{
"state_after": "a : Int\nthis : fmod (1 * a) a = 0\n⊢ fmod a a = 0",
"state_before": "a : Int\n⊢ fmod a a = 0",
"tactic": "have := mul_fmod_left 1 a"
},
{
"state_after": "no goals",
"state_before": "a : Int\nthis : fmod (1 * a) a = 0\n⊢ fmod a a = 0",
"tactic": "rwa [Int.one_mul] at th... | [
483,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
482,
9
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.get_natCast | [] | [
181,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/RingTheory/FreeCommRing.lean | FreeCommRing.isSupported_one | [] | [
210,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.snd_list_prod | [
{
"state_after": "case nil\nR : Type u\nM : Type v\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\ninst✝¹ : Module Rᵐᵒᵖ M\ninst✝ : SMulCommClass R Rᵐᵒᵖ M\n⊢ snd (List.prod []) =\n List.sum\n (List.map\n (fun x =>\n List.prod (List.take x.fst (List.map fst [])) •\n ... | [
691,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Homeomorph.isBigOWith_congr | [] | [
2221,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2219,
1
] |
Mathlib/GroupTheory/Perm/Fin.lean | Fin.isCycle_cycleRange | [
{
"state_after": "case mk\nn i : ℕ\nhi : i < n + 1\nh0 : { val := i, isLt := hi } ≠ 0\n⊢ IsCycle (cycleRange { val := i, isLt := hi })",
"state_before": "n : ℕ\ni : Fin (n + 1)\nh0 : i ≠ 0\n⊢ IsCycle (cycleRange i)",
"tactic": "cases' i with i hi"
},
{
"state_after": "case mk.zero\nn : ℕ\nhi : N... | [
299,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/Algebra/CharP/Basic.lean | frobenius_def | [] | [
349,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | add_nsmul | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.9319\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝¹ : Monoid M\ninst✝ : AddMonoid A\na : A\nm n : ℕ\n⊢ (m + n) • a = m • a + n • a",
"tactic": "induction m with\n| zero => rw [Nat.zero_ad... | [
88,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.support_add | [] | [
984,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
982,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.comp_mulIndicator | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nι : Type ?u.16343\nM : Type u_3\nN : Type ?u.16349\ninst✝² : One M\ninst✝¹ : One N\ns✝ t : Set α\nf✝ g : α → M\na : α\nh : M → β\nf : α → M\ns : Set α\nx : α\ninst✝ : DecidablePred fun x => x ∈ s\nthis : DecidablePred fun x => x ∈ s :... | [
255,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.castLE_rfl | [
{
"state_after": "case falsum\nL : Language\nL' : Language\nM : Type w\nN : Type ?u.48561\nP : Type ?u.48564\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nγ : Type ?u.48592\nn✝¹ n : ℕ\nh✝ : n ≤ n\nn✝ : ℕ\nh : n✝ ≤ n✝\n⊢ castLE h falsum = falsum\n\ncase equal\n... | [
456,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.le_sup_lintegral | [
{
"state_after": "α : Type u_1\nβ : Type ?u.897639\nγ : Type ?u.897642\nδ : Type ?u.897645\nm : MeasurableSpace α\nμ ν : Measure α\nf g : α →ₛ ℝ≥0∞\n⊢ (∑ x in SimpleFunc.range (pair f g), x.fst * ↑↑μ (↑(pair f g) ⁻¹' {x})) ⊔\n ∑ x in SimpleFunc.range (pair f g), x.snd * ↑↑μ (↑(pair f g) ⁻¹' {x}) ≤\n ∑ x... | [
1117,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1107,
1
] |
Mathlib/MeasureTheory/Function/AEMeasurableSequence.lean | aeSeq.measure_compl_aeSeqSet_eq_zero | [
{
"state_after": "ι : Sort u_1\nα : Type u_2\nβ : Type u_3\nγ : Type ?u.519115\ninst✝² : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\nf : ι → α → β\nμ : MeasureTheory.Measure α\np : α → (ι → β) → Prop\ninst✝ : Countable ι\nhf : ∀ (i : ι), AEMeasurable (f i)\nhp : ∀ᵐ (x : α) ∂μ, p x fun n => f n x\n⊢ ↑↑μ ({x |... | [
108,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.comp_measurable | [] | [
1556,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1553,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.mul_inv_rev | [
{
"state_after": "case pos\nσ : Type u_1\nR : Type ?u.1945318\nk : Type u_2\ninst✝ : Field k\nφ ψ : MvPowerSeries σ k\nh : ↑(constantCoeff σ k) (φ * ψ) = 0\n⊢ (φ * ψ)⁻¹ = ψ⁻¹ * φ⁻¹\n\ncase neg\nσ : Type u_1\nR : Type ?u.1945318\nk : Type u_2\ninst✝ : Field k\nφ ψ : MvPowerSeries σ k\nh : ¬↑(constantCoeff σ k) (... | [
1019,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1009,
11
] |
Mathlib/Algebra/Homology/Augment.lean | CochainComplex.augment_X_zero | [] | [
263,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.adjugate_adjugate | [
{
"state_after": "case zero\nm : Type u\nn : Type v\nα : Type w\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\ninst✝ : CommRing α\nA : Matrix n n α\nh : Fintype.card n ≠ 1\nh_card : Fintype.card n = Nat.zero\n⊢ adjugate (adjugate A) = det A ^ (Nat.zero - 2) • A\n\ncase ... | [
548,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
1
] |
Mathlib/Data/PNat/Xgcd.lean | PNat.XgcdType.reduce_isSpecial' | [] | [
390,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.inv_prodComparison_map_fst | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁶ : Category C\nX Y : C\nD : Type u₂\ninst✝⁵ : Category D\nF : C ⥤ D\nA A' B B' : C\ninst✝⁴ : HasBinaryProduct A B\ninst✝³ : HasBinaryProduct A' B'\ninst✝² : HasBinaryProduct (F.obj A) (F.obj B)\ninst✝¹ : HasBinaryProduct (F.obj A') (F.obj B')\n... | [
1290,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1289,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ioc_subset_Ici_self | [] | [
413,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | AnalyticAt.neg | [] | [
572,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
570,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.degree_basisDivisor_of_ne | [
{
"state_after": "F : Type u_1\ninst✝ : Field F\nx y : F\nhxy : x ≠ y\n⊢ (x - y)⁻¹ ≠ 0",
"state_before": "F : Type u_1\ninst✝ : Field F\nx y : F\nhxy : x ≠ y\n⊢ degree (basisDivisor x y) = 1",
"tactic": "rw [basisDivisor, degree_mul, degree_X_sub_C, degree_C, zero_add]"
},
{
"state_after": "no g... | [
153,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean | SimpleGraph.ComponentCompl.hom_trans | [
{
"state_after": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nC : ComponentCompl G L\nh : K ⊆ L\nh' : M ⊆ K\n⊢ ConnectedComponent.map (InduceHom Hom.id (_ : Lᶜ ⊆ Mᶜ)) C =\n ConnectedComponent.map (InduceHom Hom.id (_ : Kᶜ ⊆ Mᶜ)) (ConnectedComponent.map (InduceHom Hom.id (_ : Lᶜ ⊆ Kᶜ)) C)",
"state_be... | [
219,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.basisDivisor_inj | [
{
"state_after": "F : Type u_1\ninst✝ : Field F\nx y : F\nhxy : x = y\n⊢ x = y",
"state_before": "F : Type u_1\ninst✝ : Field F\nx y : F\nhxy : basisDivisor x y = 0\n⊢ x = y",
"tactic": "simp_rw [basisDivisor, mul_eq_zero, X_sub_C_ne_zero, or_false_iff, C_eq_zero, inv_eq_zero,\n sub_eq_zero] at hxy"
... | [
139,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.transpose_submatrix | [] | [
2403,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2401,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/LogDeriv.lean | HasFDerivAt.clog | [] | [
99,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_quadratic_le | [] | [
1196,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1195,
1
] |
Std/Data/String/Lemmas.lean | Substring.Valid.all | [
{
"state_after": "no goals",
"state_before": "f : Char → Bool\nx✝ : Substring\nh✝ : Valid x✝\nw✝² w✝¹ w✝ : List Char\nh : ValidFor w✝² w✝¹ w✝ x✝\n⊢ Substring.all x✝ f = List.all (toString x✝).data f",
"tactic": "simp [h.all, h.toString]"
}
] | [
1063,
72
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1062,
1
] |
Mathlib/Data/Pi/Lex.lean | Pi.lex_lt_of_lt_of_preorder | [] | [
70,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Order/WithBot.lean | WithTop.ofDual_le_ofDual_iff | [] | [
823,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
822,
1
] |
Mathlib/Topology/Algebra/Nonarchimedean/Basic.lean | NonarchimedeanGroup.prod_self_subset | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝⁸ : Group G\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : NonarchimedeanGroup G\nH : Type ?u.61803\ninst✝⁵ : Group H\ninst✝⁴ : TopologicalSpace H\ninst✝³ : TopologicalGroup H\nK : Type ?u.61824\ninst✝² : Group K\ninst✝¹ : TopologicalSpace K\ninst✝ : ... | [
110,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiff_top_iff_deriv | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝⁹ : NormedAddCommGroup D\ninst✝⁸ : NormedSpace 𝕜 D\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : Normed... | [
2164,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2161,
1
] |
Mathlib/Algebra/Star/SelfAdjoint.lean | skewAdjoint.conjugate | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nA : Type ?u.109551\ninst✝¹ : Ring R\ninst✝ : StarRing R\nx : R\nhx : x ∈ skewAdjoint R\nz : R\n⊢ z * x * star z ∈ skewAdjoint R",
"tactic": "simp only [mem_iff, star_mul, star_star, mem_iff.mp hx, neg_mul, mul_neg, mul_assoc]"
}
] | [
491,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | Besicovitch.SatelliteConfig.exists_normalized | [
{
"state_after": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nN : ℕ\nτ : ℝ\na : SatelliteConfig E N τ\nlastc : c a (last N) = 0\nlastr : r a (last N) = 1\nhτ : 1 ≤ τ\nδ : ℝ\nhδ1 : τ ≤ 1 + δ / 4\nhδ2 : δ ≤ 1\nc' : Fin (Nat.succ N) → E := fun i => if ‖c a i‖ ≤ 2 then c a i else (2 / ‖c a... | [
529,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.seq_mono | [] | [
1967,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1966,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.support_single_subset | [] | [
179,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | local_isCompact_isClosed_nhds_of_group | [
{
"state_after": "case intro.intro.intro\nα : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝³ : TopologicalSpace G\ninst✝² : Group G\ninst✝¹ : TopologicalGroup G\ninst✝ : LocallyCompactSpace G\nU : Set G\nhU : U ∈ 𝓝 1\nL : Set G\nLint : L ∈ 𝓝 1\nLU : L ⊆ U\nLcomp : IsCompact L\n⊢ ∃ K, IsCompact K ∧ IsClose... | [
1668,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1643,
1
] |
Mathlib/MeasureTheory/Group/Action.lean | MeasureTheory.isLocallyFiniteMeasure_of_smulInvariant | [
{
"state_after": "no goals",
"state_before": "G : Type ?u.57418\nM : Type ?u.57421\nα : Type u_1\ns : Set α\nm : MeasurableSpace α\ninst✝⁷ : Group G\ninst✝⁶ : MulAction G α\ninst✝⁵ : MeasurableSpace G\ninst✝⁴ : MeasurableSMul G α\nc : G\nμ : Measure α\ninst✝³ : SMulInvariantMeasure G α μ\ninst✝² : Topologic... | [
233,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Data/Nat/Multiplicity.lean | Nat.Prime.multiplicity_factorial_mul_succ | [
{
"state_after": "n p : ℕ\nhp : Prime p\nhp' : _root_.Prime p\n⊢ multiplicity p (p * (n + 1))! = multiplicity p (p * n)! + multiplicity p (n + 1) + 1",
"state_before": "n p : ℕ\nhp : Prime p\n⊢ multiplicity p (p * (n + 1))! = multiplicity p (p * n)! + multiplicity p (n + 1) + 1",
"tactic": "have hp' := ... | [
148,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
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