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/Normed/Group/Basic.lean | pi_norm_const' | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.1275542\n𝕜 : Type ?u.1275545\nα : Type ?u.1275548\nι : Type u_1\nκ : Type ?u.1275554\nE : Type u_2\nF : Type ?u.1275560\nG : Type ?u.1275563\nπ : ι → Type ?u.1275568\ninst✝³ : Fintype ι\ninst✝² : (i : ι) → SeminormedGroup (π i)\ninst✝¹ : Seminormed... | [
2535,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2534,
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Mathlib/Data/Nat/Count.lean | Nat.count_add' | [
{
"state_after": "p : ℕ → Prop\ninst✝ : DecidablePred p\na b : ℕ\n⊢ count (fun k => p (b + k)) a + count p b = count (fun k => p (k + b)) a + count p b",
"state_before": "p : ℕ → Prop\ninst✝ : DecidablePred p\na b : ℕ\n⊢ count p (a + b) = count (fun k => p (k + b)) a + count p b",
"tactic": "rw [add_com... | [
91,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
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Mathlib/Data/Set/Countable.lean | Set.countable_univ_pi | [] | [
270,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
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Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.powers_one | [] | [
455,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
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Mathlib/Analysis/Calculus/Deriv/Basic.lean | hasFDerivAtFilter_iff_hasDerivAtFilter | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type w\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf'✝ f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL L₁ L₂ : F... | [
163,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
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Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.IsInvertedBy.leftOp | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\nD : Type u_2\ninst✝ : Category D\nW : MorphismProperty C\nL : C ⥤ Dᵒᵖ\nh : IsInvertedBy W L\nX Y : Cᵒᵖ\nf : X ⟶ Y\nhf : MorphismProperty.op W f\nthis : IsIso (L.map f.unop)\n⊢ IsIso (L.leftOp.map f)",
"state_before": "C : Type u\ninst✝¹ : Category C\nD : Ty... | [
328,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.add_ne_top | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.82044\nβ : Type ?u.82047\na b c d : ℝ≥0∞\nr p q : ℝ≥0\n⊢ a + b ≠ ⊤ ↔ a ≠ ⊤ ∧ b ≠ ⊤",
"tactic": "simpa only [lt_top_iff_ne_top] using add_lt_top"
}
] | [
546,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.repr_range | [
{
"state_after": "no goals",
"state_before": "ι : Type u'\nι' : Type ?u.444864\nR : Type u_1\nK : Type ?u.444870\nM : Type u_2\nM' : Type ?u.444876\nM'' : Type ?u.444879\nV : Type u\nV' : Type ?u.444884\nv : ι → M\ninst✝⁶ : Ring R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : AddCommGroup M'\ninst✝³ : AddCommGroup M''... | [
795,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
1
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Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.zero_of_eval_zero | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\np✝ q : R[X]\ninst✝ : Infinite R\np : R[X]\nh : ∀ (x : R), eval x p = 0\nhp : ¬p = 0\n⊢ False",
"state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝² : CommRing R\ninst✝¹ : Is... | [
872,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
869,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasurableSet.map_coe_volume | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1818394\nγ : Type ?u.1818397\nδ : Type ?u.1818400\nι : Type ?u.1818403\nR : Type ?u.1818406\nR' : Type ?u.1818409\ninst✝ : MeasureSpace α\ns✝ t s : Set α\nhs : MeasurableSet s\n⊢ Measure.map Subtype.val volume = Measure.restrict volume ... | [
4261,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4259,
1
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Mathlib/Data/Rat/NNRat.lean | NNRat.coe_pos | [] | [
177,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
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Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.biInf_mem | [] | [
819,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
814,
11
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pullbackRightPullbackFstIso_inv_snd_fst | [
{
"state_after": "C : Type u\ninst✝⁴ : Category C\nD : Type u₂\ninst✝³ : Category D\nW X Y Z : C\nf : X ⟶ Z\ng : Y ⟶ Z\nf' : W ⟶ X\ninst✝² : HasPullback f g\ninst✝¹ : HasPullback f' pullback.fst\ninst✝ : HasPullback (f' ≫ f) g\n⊢ (pullbackRightPullbackFstIso f g f').inv ≫ pullback.fst ≫ f' = pullback.fst ≫ f'",... | [
2191,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2188,
1
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Mathlib/Topology/Bases.lean | TopologicalSpace.IsTopologicalBasis.nhds_hasBasis | [
{
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"tactic": "simp only [exists_prop, and_assoc]"
}
] | [
165,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
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Mathlib/Data/Rat/Cast.lean | Rat.preimage_cast_Icc | [
{
"state_after": "case h\nF : Type ?u.68729\nι : Type ?u.68732\nα : Type ?u.68735\nβ : Type ?u.68738\nK : Type u_1\ninst✝ : LinearOrderedField K\na b x : ℚ\n⊢ x ∈ Rat.cast ⁻¹' Icc ↑a ↑b ↔ x ∈ Icc a b",
"state_before": "F : Type ?u.68729\nι : Type ?u.68732\nα : Type ?u.68735\nβ : Type ?u.68738\nK : Type u_1\... | [
371,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
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Mathlib/Order/CompleteLattice.lean | unary_relation_sInf_iff | [
{
"state_after": "α✝ : Type ?u.198791\nβ : Type ?u.198794\nβ₂ : Type ?u.198797\nγ : Type ?u.198800\nι : Sort ?u.198803\nι' : Sort ?u.198806\nκ : ι → Sort ?u.198811\nκ' : ι' → Sort ?u.198816\nα : Type u_1\ns : Set (α → Prop)\na : α\n⊢ (⨅ (f : ↑s), ↑f a) ↔ ∀ (r : α → Prop), r ∈ s → r a",
"state_before": "α✝ :... | [
1790,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1787,
1
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Mathlib/Order/Bounds/Basic.lean | bddBelow_def | [] | [
99,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Data/Multiset/Powerset.lean | Multiset.mem_powersetAux | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : List α\ns : Multiset α\n⊢ ∀ (a : List α), Quotient.mk (isSetoid α) a ∈ powersetAux l ↔ Quotient.mk (isSetoid α) a ≤ ↑l",
"tactic": "simp [powersetAux_eq_map_coe, Subperm, and_comm]"
}
] | [
40,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
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Mathlib/Algebra/Symmetrized.lean | SymAlg.unsym_bijective | [] | [
99,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
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Mathlib/Data/Set/Intervals/UnorderedInterval.lean | Set.uIcc_prod_uIcc | [] | [
149,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | fderiv_id' | [] | [
1038,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1037,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.iff_le_add_mul | [] | [
348,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
11
] |
Mathlib/Data/Dfinsupp/NeLocus.lean | Dfinsupp.coe_neLocus | [] | [
55,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Circle.lean | Real.Angle.expMapCircle_add | [
{
"state_after": "case h\nθ₂ : Angle\nx✝ : ℝ\n⊢ expMapCircle (↑x✝ + θ₂) = expMapCircle ↑x✝ * expMapCircle θ₂",
"state_before": "θ₁ θ₂ : Angle\n⊢ expMapCircle (θ₁ + θ₂) = expMapCircle θ₁ * expMapCircle θ₂",
"tactic": "induction θ₁ using Real.Angle.induction_on"
},
{
"state_after": "case h.h\nx✝¹ ... | [
146,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
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Mathlib/Topology/Order/Basic.lean | isClosed_Iic | [] | [
139,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.toIsometryEquiv_inj | [] | [
644,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
642,
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Mathlib/Algebra/Order/Archimedean.lean | exists_int_lt | [
{
"state_after": "α : Type u_1\ninst✝¹ : StrictOrderedRing α\ninst✝ : Archimedean α\nx : α\nn : ℤ\nh : -x < ↑n\n⊢ -↑n < x",
"state_before": "α : Type u_1\ninst✝¹ : StrictOrderedRing α\ninst✝ : Archimedean α\nx : α\nn : ℤ\nh : -x < ↑n\n⊢ ↑(-n) < x",
"tactic": "rw [Int.cast_neg]"
},
{
"state_after... | [
156,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
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Mathlib/Algebra/Hom/Aut.lean | AddAut.one_apply | [] | [
226,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
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Mathlib/RingTheory/IntegralClosure.lean | isIntegral_sub | [] | [
518,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
1
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Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.not_sqLe_succ | [] | [
872,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
871,
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Mathlib/LinearAlgebra/Quotient.lean | Submodule.mapQ_zero | [
{
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426,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
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Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.HasColimit.isoOfEquivalence_inv_π | [
{
"state_after": "no goals",
"state_before": "J : Type u₁\ninst✝⁴ : Category J\nK : Type u₂\ninst✝³ : Category K\nC : Type u\ninst✝² : Category C\nF✝ F : J ⥤ C\ninst✝¹ : HasColimit F\nG : K ⥤ C\ninst✝ : HasColimit G\ne : J ≌ K\nw : e.functor ⋙ G ≅ F\nk : K\n⊢ colimit.ι G k ≫ (isoOfEquivalence e w).inv =\n ... | [
960,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
956,
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Mathlib/Data/Finset/Image.lean | Finset.mem_image | [
{
"state_after": "no goals",
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"tactic": "simp only [mem_def, image_val, mem_dedup, Multiset.mem_map, exists_prop]"
}
] | [
328,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.IsNormal.blsub_eq | [
{
"state_after": "α : Type ?u.366269\nβ : Type ?u.366272\nγ : Type ?u.366275\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nf : Ordinal → Ordinal\nH : IsNormal f\no : Ordinal\nh : IsLimit o\n⊢ ∀ (a : Ordinal), a < o → f a < f (succ a)",
"state_before": "α : Type ?u.366269\nβ : Type ?u.366272\nγ : Ty... | [
1970,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1967,
1
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Mathlib/MeasureTheory/MeasurableSpace.lean | Measurable.subtype_coe | [] | [
564,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
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Mathlib/GroupTheory/Perm/Basic.lean | Equiv.swap_mul_self | [] | [
519,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
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Mathlib/Combinatorics/SimpleGraph/Coloring.lean | SimpleGraph.chromaticNumber_bddBelow | [] | [
250,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
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Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.principal_add_isLimit | [
{
"state_after": "case refine'_1\no : Ordinal\nho₁ : 1 < o\nho : Principal (fun x x_1 => x + x_1) o\nho₀ : o = 0\n⊢ False\n\ncase refine'_2\no : Ordinal\nho₁ : 1 < o\nho : Principal (fun x x_1 => x + x_1) o\na : Ordinal\nhao : a < o\n⊢ succ a < o",
"state_before": "o : Ordinal\nho₁ : 1 < o\nho : Principal (... | [
152,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
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Mathlib/Data/Finset/Pointwise.lean | Finset.op_smul_finset_smul_eq_smul_smul_finset | [
{
"state_after": "case a\nF : Type ?u.755717\nα : Type u_3\nβ : Type u_1\nγ : Type u_2\ninst✝⁴ : DecidableEq β\ninst✝³ : DecidableEq γ\ninst✝² : SMul αᵐᵒᵖ β\ninst✝¹ : SMul β γ\ninst✝ : SMul α γ\na : α\ns : Finset β\nt : Finset γ\nh : ∀ (a : α) (b : β) (c : γ), (op a • b) • c = b • a • c\na✝ : γ\n⊢ a✝ ∈ (op a • ... | [
1826,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1823,
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Mathlib/Data/Finset/Basic.lean | Finset.Insert.comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.108268\nγ : Type ?u.108271\ninst✝ : DecidableEq α\ns✝ t u v : Finset α\na✝ b✝ a b : α\ns : Finset α\nx : α\n⊢ x ∈ insert a (insert b s) ↔ x ∈ insert b (insert a s)",
"tactic": "simp only [mem_insert, or_left_comm]"
}
] | [
1117,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1116,
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Mathlib/Data/Sym/Basic.lean | Sym.attach_nil | [] | [
452,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
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Mathlib/Data/Complex/Basic.lean | Complex.AbsTheory.abs_re_le_abs | [
{
"state_after": "z : ℂ\n⊢ z.re * z.re ≤ ↑normSq z",
"state_before": "z : ℂ\n⊢ abs z.re ≤ Real.sqrt (↑normSq z)",
"tactic": "rw [mul_self_le_mul_self_iff (abs_nonneg z.re) (abs_nonneg' _), abs_mul_abs_self, mul_self_abs]"
},
{
"state_after": "no goals",
"state_before": "z : ℂ\n⊢ z.re * z.re ... | [
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24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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9
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Mathlib/Algebra/Lie/Nilpotent.lean | LieModule.isNilpotent_of_top_iff | [] | [
504,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
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Mathlib/Algebra/MonoidAlgebra/Support.lean | AddMonoidAlgebra.mem_span_support | [
{
"state_after": "no goals",
"state_before": "k : Type u₁\nG : Type u₂\ninst✝¹ : Semiring k\ninst✝ : AddZeroClass G\nf : AddMonoidAlgebra k G\n⊢ f ∈ Submodule.span k (↑(of k G) '' ↑f.support)",
"tactic": "erw [of, MonoidHom.coe_mk, ← Finsupp.supported_eq_span_single, Finsupp.mem_supported]"
}
] | [
145,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Analysis/NormedSpace/MStructure.lean | IsLprojection.Lcomplement_iff | [] | [
105,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Diagonal.lean | CategoryTheory.Limits.pullback_diagonal_map_snd_fst_fst | [
{
"state_after": "no goals",
"state_before": "C : Type ?u.9333\ninst✝¹ : Category C\nX Y Z : C\ninst✝ : HasPullbacks C\nU V₁ V₂ : C\nf : X ⟶ Y\ni : U ⟶ Y\ni₁ : V₁ ⟶ pullback f i\ni₂ : V₂ ⟶ pullback f i\n⊢ (i₁ ≫ snd) ≫ i = (i₁ ≫ fst) ≫ f",
"tactic": "simp [condition]"
},
{
"state_after": "no goal... | [
100,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_restrictScalars | [] | [
1680,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1678,
1
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Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.mulVec_stdBasis_apply | [] | [
273,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
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Mathlib/Algebra/Homology/ImageToKernel.lean | imageToKernel_comp_mono | [
{
"state_after": "no goals",
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"tactic": "simpa using... | [
122,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
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Mathlib/FieldTheory/Separable.lean | Polynomial.multiplicity_le_one_of_separable | [
{
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"state_before": "R : Type u\ninst✝¹ : CommSemiring R\nS : Type v\ninst✝ : CommSemiring S\np✝ q✝ : ℕ\np q : R[X]\nhq : ¬IsUnit q\nhsep ... | [
160,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
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Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.orthogonalProjection_vsub_mem_direction_orthogonal | [] | [
432,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
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Mathlib/Data/Finset/Basic.lean | Finset.sdiff_sdiff_eq_sdiff_union | [] | [
2303,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2302,
1
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Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.get_rowLens | [
{
"state_after": "no goals",
"state_before": "μ : YoungDiagram\ni : Fin (List.length (rowLens μ))\n⊢ List.get (rowLens μ) i = rowLen μ ↑i",
"tactic": "simp only [rowLens, List.get_range, List.get_map]"
}
] | [
421,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
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Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffWithinAt.prod_map' | [] | [
1597,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1593,
1
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.mk'_mem_incidenceSet_iff | [] | [
835,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
834,
1
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Mathlib/Algebra/Group/Prod.lean | Prod.fst_mul_snd | [] | [
128,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.map_add_left_Ioc | [
{
"state_after": "ι : Type ?u.221440\nα : Type u_1\ninst✝² : OrderedCancelAddCommMonoid α\ninst✝¹ : ExistsAddOfLE α\ninst✝ : LocallyFiniteOrder α\na b c : α\n⊢ ↑(addLeftEmbedding c) '' Set.Ioc a b = Set.Ioc (c + a) (c + b)",
"state_before": "ι : Type ?u.221440\nα : Type u_1\ninst✝² : OrderedCancelAddCommMon... | [
1072,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1069,
1
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Mathlib/RingTheory/Polynomial/Pochhammer.lean | pochhammer_eval_cast | [
{
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"state_before": "S : Type u\ninst✝ : Semiring S\nn k : ℕ\n⊢ ↑(eval k (pochhammer ℕ n)) = eval (↑k) (pochhammer S n)",
"tactic": "rw [← pochhammer_map (algebraMap ℕ S), eval_map, ← eq_natCast (algebraMap ℕ S), eval₂_at_nat_cast,\n Nat.cast_id, eq_natCast]"
}
] | [
82,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/CategoryTheory/Preadditive/Mat.lean | CategoryTheory.Mat.comp_def | [] | [
609,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
1
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.ofReal_intCast | [] | [
665,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
664,
1
] |
Mathlib/RingTheory/NonZeroDivisors.lean | mul_left_coe_nonZeroDivisors_eq_zero_iff | [] | [
65,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
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Std/Data/Int/DivMod.lean | Int.div_eq_ediv_of_dvd | [
{
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},
{
"state_after": "no goals",
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795,
80
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
793,
1
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Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.cylinder_eq_pi | [
{
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"state_before": "E : ℕ → Type u_1\nx : (n : ℕ) → E n\nn : ℕ\n⊢ cylinder x n = Set.pi ↑(Finset.range n) fun i => {x i}",
"tactic": "ext y"
},
{
... | [
117,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
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Mathlib/Analysis/Convex/Combination.lean | convexHull_prod | [] | [
426,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.smul_const | [] | [
1344,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1342,
11
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Mathlib/Probability/ProbabilityMassFunction/Basic.lean | Pmf.toOuterMeasure_apply_eq_zero_iff | [
{
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197,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
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Mathlib/Data/Int/Cast/Lemmas.lean | Int.cast_le | [
{
"state_after": "no goals",
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"tactic": "rw [← sub_nonneg, ← cast_sub, cast_nonneg, sub_nonneg]"
}
] | [
132,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
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Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.NullMeasurableSet.const | [] | [
217,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
11
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.toLinearMap_symm_comp_eq | [
{
"state_after": "case mp.h\nR : Type ?u.209595\nR₁ : Type u_2\nR₂ : Type u_5\nR₃ : Type u_1\nk : Type ?u.209607\nS : Type ?u.209610\nM : Type ?u.209613\nM₁ : Type u_4\nM₂ : Type u_6\nM₃ : Type u_3\nN₁ : Type ?u.209625\nN₂ : Type ?u.209628\nN₃ : Type ?u.209631\nN₄ : Type ?u.209634\nι : Type ?u.209637\nM₄ : Type... | [
457,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
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Mathlib/CategoryTheory/Whiskering.lean | CategoryTheory.isoWhiskerRight_inv | [] | [
189,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.update_eq_single_add_erase | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.295412\nγ : Type ?u.295415\nι : Type ?u.295418\nM : Type u_2\nM' : Type ?u.295424\nN : Type ?u.295427\nP : Type ?u.295430\nG : Type ?u.295433\nH : Type ?u.295436\nR : Type ?u.295439\nS : Type ?u.295442\ninst✝ : AddZeroClass M\nf : α →₀ M\na : α\nb : M\nj : α\n... | [
1047,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1041,
1
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Mathlib/Order/CompleteBooleanAlgebra.lean | iSup₂_inf_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nκ : ι → Sort u_1\ninst✝ : Frame α\ns t : Set α\na✝ b : α\nf : (i : ι) → κ i → α\na : α\n⊢ (⨆ (i : ι) (j : κ i), f i j) ⊓ a = ⨆ (i : ι) (j : κ i), f i j ⊓ a",
"tactic": "simp only [iSup_inf_eq]"
}
] | [
110,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Order/SymmDiff.lean | sdiff_symmDiff' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.61584\nα : Type u_1\nβ : Type ?u.61590\nπ : ι → Type ?u.61595\ninst✝ : GeneralizedBooleanAlgebra α\na b c d : α\n⊢ c \\ a ∆ b = c ⊓ a ⊓ b ⊔ c \\ (a ⊔ b)",
"tactic": "rw [sdiff_symmDiff, sdiff_sup, sup_comm]"
}
] | [
420,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffAt.inv | [] | [
1711,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1709,
8
] |
Mathlib/RingTheory/FractionalIdeal.lean | IsFractional.div_of_nonzero | [
{
"state_after": "case intro.intro\nR : Type ?u.1138684\ninst✝⁶ : CommRing R\nS : Submonoid R\nP : Type ?u.1138891\ninst✝⁵ : CommRing P\ninst✝⁴ : Algebra R P\nloc : IsLocalization S P\nR₁ : Type u_1\ninst✝³ : CommRing R₁\nK : Type u_2\ninst✝² : Field K\ninst✝¹ : Algebra R₁ K\nfrac : IsFractionRing R₁ K\ninst✝ :... | [
1086,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1066,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | tendstoUniformlyOn_iff_tendsto | [
{
"state_after": "no goals",
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129,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Data/Set/Intervals/OrderIso.lean | OrderIso.preimage_Iio | [
{
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"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ne : α ≃o β\nb : β\n⊢ ↑e ⁻¹' Iio b = Iio (↑(symm e) b)",
... | [
40,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/Init/Data/Nat/Basic.lean | Nat.bit0_ne_zero | [] | [
35,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
11
] |
Std/Data/RBMap/Alter.lean | Std.RBNode.Ordered.zoom' | [] | [
287,
38
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
282,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.mul_inv_eq_iff_eq_mul_of_invertible | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.235209\nm : Type u\nn : Type u'\nα : Type v\ninst✝³ : Fintype n\ninst✝² : DecidableEq n\ninst✝¹ : CommRing α\nA✝ B✝ A B C : Matrix n n α\ninst✝ : Invertible A\nh : B ⬝ A⁻¹ = C\n⊢ B = C ⬝ A",
"tactic": "rw [← h, inv_mul_cancel_right_of_invertible]... | [
383,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/Order/OrdContinuous.lean | RightOrdContinuous.map_sInf' | [] | [
238,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_false | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.105197\nβ₂ : Type ?u.105200\nγ : Type ?u.105203\nι : Sort ?u.105206\nι' : Sort ?u.105209\nκ : ι → Sort ?u.105214\nκ' : ι' → Sort ?u.105219\ninst✝ : CompleteLattice α\nf g s✝ t : ι → α\na b : α\ns : False → α\n⊢ iInf s = ⊤",
"tactic"... | [
1296,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1295,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.codisjoint_inf_left | [] | [
563,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
561,
11
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.div_subset_iff | [] | [
656,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
1
] |
Mathlib/Topology/Algebra/Order/LeftRightLim.lean | Antitone.leftLim_le | [] | [
306,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Set.Infinite.exists_gt | [] | [
840,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
839,
1
] |
Mathlib/Combinatorics/Pigeonhole.lean | Fintype.exists_le_card_fiber_of_nsmul_le_card | [] | [
426,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/Analysis/SpecialFunctions/Bernstein.lean | bernsteinApproximation.apply | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nf : C(↑I, ℝ)\nx : ↑I\n⊢ ↑(bernsteinApproximation n f) x = ∑ k : Fin (n + 1), ↑f k/ₙ * ↑(bernstein n ↑k) x",
"tactic": "simp [bernsteinApproximation]"
}
] | [
175,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Data/Semiquot.lean | Semiquot.map_def | [] | [
154,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.continuousAt_angle | [
{
"state_after": "V : Type u_2\nP : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nx : P × P × P\nhx12 : x.fst ≠ x.snd.fst\nhx32 : x.snd.snd ≠ x.snd.fst\nf : P × P × P → V × V := fun y => (y.fst -ᵥ y.snd.fst, y.snd.snd -ᵥ y.snd.fst)\... | [
55,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Algebra/Order/Group/MinMax.lean | max_one_div_max_inv_one_eq_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝² : Group 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\n⊢ max a 1 / max a⁻¹ 1 = a",
"tactic": "rcases le_total a 1 with (h | h) <;> simp [h]"
}
] | [
25,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
24,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.frequently_imp_distrib | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.165345\nι : Sort x\nf : Filter α\np q : α → Prop\n⊢ (∃ᶠ (x : α) in f, p x → q x) ↔ (∀ᶠ (x : α) in f, p x) → ∃ᶠ (x : α) in f, q x",
"tactic": "simp [imp_iff_not_or, not_eventually, frequently_or_distrib]"
}
] | [
1356,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1354,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | Set.Countable.ae_not_mem | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.712897\nβ : Type ?u.712900\nγ : Type ?u.712903\nδ : Type ?u.712906\nι : Type ?u.712909\nR : Type ?u.712912\nR' : Type ?u.712915\nm0 : MeasurableSpace α✝\ninst✝³ : MeasurableSpace β\ninst✝² : MeasurableSpace γ\nμ✝ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α✝\ns✝... | [
3310,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3308,
1
] |
Mathlib/MeasureTheory/Measure/Stieltjes.lean | StieltjesFunction.measure_Ioc | [
{
"state_after": "f : StieltjesFunction\na b : ℝ\n⊢ ↑↑{ toOuterMeasure := StieltjesFunction.outer f,\n m_iUnion :=\n (_ :\n ∀ (_s : ℕ → Set ℝ),\n (∀ (i : ℕ), MeasurableSet (_s i)) →\n Pairwise (Disjoint on _s) →\n ↑(... | [
517,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | padicNormE.eq_ratNorm | [] | [
894,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
893,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.mul_apply | [] | [
555,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.liftPropOn_chart | [] | [
519,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.le_natTrailingDegree_mul | [
{
"state_after": "R : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nh : p * q ≠ 0\nhp : p ≠ 0\n⊢ natTrailingDegree p + natTrailingDegree q ≤ natTrailingDegree (p * q)",
"state_before": "R : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nh : p * q ≠ 0\n⊢ nat... | [
380,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/Algebra/GeomSum.lean | Odd.add_dvd_pow_add_pow | [
{
"state_after": "α : Type u\ninst✝ : CommRing α\nx y : α\nn : ℕ\nh : Odd n\nh₁ : (∑ i in range n, x ^ i * (-y) ^ (n - 1 - i)) * (x - -y) = x ^ n - (-y) ^ n\n⊢ x + y ∣ x ^ n + y ^ n",
"state_before": "α : Type u\ninst✝ : CommRing α\nx y : α\nn : ℕ\nh : Odd n\n⊢ x + y ∣ x ^ n + y ^ n",
"tactic": "have h₁... | [
212,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Computability/Partrec.lean | Computable.to₂ | [] | [
297,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
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