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/MeasureTheory/Measure/Lebesgue/Basic.lean | Filter.Eventually.volume_pos_of_nhds_real | [
{
"state_after": "case intro.intro.intro\nι : Type ?u.374914\ninst✝ : Fintype ι\np : ℝ → Prop\na : ℝ\nh : ∀ᶠ (x : ℝ) in 𝓝 a, p x\nl u : ℝ\nhx : a ∈ Ioo l u\nhs : Ioo l u ⊆ {x | p x}\n⊢ 0 < ↑↑volume {x | p x}",
"state_before": "ι : Type ?u.374914\ninst✝ : Fintype ι\np : ℝ → Prop\na : ℝ\nh : ∀ᶠ (x : ℝ) in 𝓝... | [
207,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.erase_add_single | [
{
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1064,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1063,
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Mathlib/Analysis/InnerProductSpace/Orientation.lean | Orientation.abs_volumeForm_apply_le | [
{
"state_after": "case zero\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : InnerProductSpace ℝ E\n_i : Fact (finrank ℝ E = Nat.zero)\no : Orientation ℝ E (Fin Nat.zero)\nv : Fin Nat.zero → E\n⊢ abs (↑(volumeForm o) v) ≤ ∏ i : Fin Nat.zero, ‖v i‖\n\ncase succ\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\n... | [
281,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
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Mathlib/Topology/Algebra/ContinuousAffineMap.lean | ContinuousAffineMap.ext_iff | [] | [
88,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
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Mathlib/Algebra/Order/Nonneg/Ring.lean | Nonneg.coe_toNonneg | [] | [
361,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
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Mathlib/Data/Finset/Sups.lean | Finset.sups_subset_left | [] | [
93,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
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Mathlib/Data/Finmap.lean | Finmap.mem_keys | [] | [
206,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
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Mathlib/Topology/Connected.lean | IsConnected.preimage_of_openMap | [] | [
408,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
1
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Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.coe_toLinearMap | [] | [
225,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Logic/Embedding/Basic.lean | Function.Embedding.swap_apply | [] | [
377,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
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Mathlib/Algebra/Order/AbsoluteValue.lean | AbsoluteValue.add_le | [] | [
113,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
11
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Mathlib/Data/Vector/Zip.lean | Vector.zipWith_tail | [
{
"state_after": "case x\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nn : ℕ\nf : α → β → γ\nx : Vector α n\ny : Vector β n\nm✝ : Fin (n - 1)\n⊢ get (tail (zipWith f x y)) m✝ = get (zipWith f (tail x) (tail y)) m✝",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nn : ℕ\nf : α → β → γ\nx : Vector α n... | [
47,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
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Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Presieve.isSeparatedFor_top | [
{
"state_after": "C : Type u₁\ninst✝ : Category C\nP✝ Q U : Cᵒᵖ ⥤ Type w\nX Y : C\nS : Sieve X\nR : Presieve X\nJ J₂ : GrothendieckTopology C\nP : Cᵒᵖ ⥤ Type w\nx : FamilyOfElements P ⊤\nt₁ t₂ : P.obj X.op\nh₁ : FamilyOfElements.IsAmalgamation x t₁\nh₂ : FamilyOfElements.IsAmalgamation x t₂\nq₁ : P.map (𝟙 X).o... | [
439,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
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Mathlib/CategoryTheory/Functor/Category.lean | CategoryTheory.NatTrans.vcomp_app' | [] | [
68,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.setToFun_zero_left | [
{
"state_after": "case pos\nα : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type ?u.1394453\nG : Type ?u.1394456\n𝕜 : Type ?u.1394459\np : ℝ≥0∞\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace ℝ F\ninst✝³ : NormedAddCommGroup F'\ninst✝² : NormedSpace ... | [
1361,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1357,
1
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Mathlib/Analysis/SpecificLimits/Basic.lean | tendsto_pow_atTop_nhds_0_of_lt_1 | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.27357\nβ : Type ?u.27360\nι : Type ?u.27363\n𝕜 : Type u_1\ninst✝³ : LinearOrderedField 𝕜\ninst✝² : Archimedean 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nr : 𝕜\nh₁ : 0 ≤ r\nh₂ : r < 1\nhr : 0 = r\n⊢ Tendsto (fun n => r ^ (n + 1)) ... | [
110,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Data/Polynomial/Taylor.lean | Polynomial.taylor_X | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nr : R\nf : R[X]\n⊢ ↑(taylor r) X = X + ↑C r",
"tactic": "simp only [taylor_apply, X_comp]"
}
] | [
49,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.zero_opow | [
{
"state_after": "no goals",
"state_before": "a : Ordinal\na0 : a ≠ 0\n⊢ 0 ^ a = 0",
"tactic": "rwa [zero_opow', Ordinal.sub_eq_zero_iff_le, one_le_iff_ne_zero]"
}
] | [
49,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
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Mathlib/CategoryTheory/SingleObj.lean | CategoryTheory.SingleObj.toEnd_def | [] | [
112,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Algebra/Tropical/BigOperators.lean | trop_sInf_image | [
{
"state_after": "case inl\nR : Type u_1\nS : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder R\nf : S → WithTop R\n⊢ trop (sInf (f '' ↑∅)) = ∑ i in ∅, trop (f i)\n\ncase inr\nR : Type u_1\nS : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder R\ns : Finset S\nf : S → WithTop R\nh : Finset.Nonempty s\n⊢ tro... | [
108,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_withDensity_eq_lintegral_mul_non_measurable₀ | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1811893\nγ : Type ?u.1811896\nδ : Type ?u.1811899\nm m0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ≥0∞\nhf : AEMeasurable f\nh'f : ∀ᵐ (x : α) ∂μ, f x < ⊤\ng : α → ℝ≥0∞\nf' : α → ℝ≥0∞ := AEMeasurable.mk f hf\n⊢ (∫⁻ (a : α), g a ∂Measure.withDensity μ f) = ∫⁻ (a : α),... | [
1884,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1868,
1
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Mathlib/RingTheory/Multiplicity.lean | multiplicity.finite_mul_aux | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : CancelCommMonoidWithZero α\np : α\nhp : Prime p\na b : α\nn m : ℕ\nha : ¬p ^ (n + 1) ∣ a\nhb : ¬p ^ (m + 1) ∣ b\nx✝ : p ^ (n + m + 1) ∣ a * b\ns : α\nhs : a * b = p ^ (n + m + 1) * s\n⊢ a * b = p * (p ^ (n + m) * s)",
"tactic": "simp [h... | [
509,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
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Mathlib/Analysis/Calculus/FormalMultilinearSeries.lean | neg_apply | [] | [
67,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
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Mathlib/RingTheory/Artinian.lean | Ring.isArtinian_of_zero_eq_one | [] | [
321,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
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Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.log_div_log | [] | [
48,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
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Mathlib/Topology/Basic.lean | eventually_eventuallyLE_nhds | [] | [
998,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
996,
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Mathlib/FieldTheory/Normal.lean | Normal.tower_top_of_normal | [
{
"state_after": "case intro\nF : Type u_1\nK : Type u_3\ninst✝⁶ : Field F\ninst✝⁵ : Field K\ninst✝⁴ : Algebra F K\nE : Type u_2\ninst✝³ : Field E\ninst✝² : Algebra F E\ninst✝¹ : Algebra K E\ninst✝ : IsScalarTower F K E\nh : Normal F E\nx : E\nhx : IsIntegral F x\nhhx : Splits (algebraMap F E) (minpoly F x)\n⊢ ... | [
112,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSet.iUnion | [
{
"state_after": "case inl\nα : Type u_2\nβ : Type ?u.3894\nγ : Type ?u.3897\nδ : Type ?u.3900\nδ' : Type ?u.3903\nι : Sort u_1\ns t u : Set α\nm : MeasurableSpace α\ninst✝ : Countable ι\nf : ι → Set α\nh : ∀ (b : ι), MeasurableSet (f b)\nh✝ : IsEmpty ι\n⊢ MeasurableSet (⋃ (b : ι), f b)\n\ncase inr\nα : Type u_... | [
124,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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11
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Mathlib/FieldTheory/Subfield.lean | Subfield.mem_closure_iff | [
{
"state_after": "K : Type u\nL : Type v\nM : Type w\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Field M\ns : Set K\nx : K\n⊢ x ∈ (closure s).toSubring.toSubsemiring.toSubmonoid.toSubsemigroup.carrier ↔\n ∃ y, y ∈ Subring.closure s ∧ ∃ z, z ∈ Subring.closure s ∧ y / z = x",
"state_before": "K : Type u\n... | [
692,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
689,
1
] |
Std/Data/String/Lemmas.lean | Substring.Valid.any | [
{
"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.any x✝ f = List.any (toString x✝).data f",
"tactic": "simp [h.any, h.toString]"
}
] | [
1060,
72
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1059,
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Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.ext | [] | [
245,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.pointReflection_fixed_iff_of_injective_bit0 | [] | [
590,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
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Mathlib/Order/Filter/Basic.lean | Filter.Frequently.mp | [] | [
1268,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1266,
1
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Std/WF.lean | WellFounded.fixF_eq_fixFC | [
{
"state_after": "case h.h.h.h.h.h\nα : Sort u_1\nr : α → α → Prop\nC : α → Sort u_2\nF : (x : α) → ((y : α) → r y x → C y) → C x\nx : α\na : Acc r x\n⊢ fixF F x a = WellFounded.fixFC F x a",
"state_before": "⊢ @fixF = @WellFounded.fixFC",
"tactic": "funext α r C F x a"
},
{
"state_after": "no g... | [
102,
36
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
100,
18
] |
Mathlib/Analysis/SpecificLimits/Normed.lean | summable_of_ratio_norm_eventually_le | [
{
"state_after": "case pos\nα✝ : Type ?u.1269724\nβ : Type ?u.1269727\nι : Type ?u.1269730\nα : Type u_1\ninst✝¹ : SeminormedAddCommGroup α\ninst✝ : CompleteSpace α\nf : ℕ → α\nr : ℝ\nhr₁ : r < 1\nh : ∀ᶠ (n : ℕ) in atTop, ‖f (n + 1)‖ ≤ r * ‖f n‖\nhr₀ : 0 ≤ r\n⊢ Summable f\n\ncase neg\nα✝ : Type ?u.1269724\nβ : ... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | AlgHom.mem_range_self | [] | [
615,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
614,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.SimpleFunc.setToSimpleFunc_zero' | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.131782\nF' : Type u_3\nG : Type ?u.131788\n𝕜 : Type ?u.131791\np : ℝ≥0∞\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ninst✝² : NormedAddCommGroup F'\ninst✝¹ : NormedSpace ℝ F'\ninst✝ :... | [
302,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
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Mathlib/Data/Nat/Parity.lean | Nat.two_not_dvd_two_mul_sub_one | [] | [
137,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.trans_right | [] | [
1042,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1040,
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] |
Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.MultispanIndex.ι_fstSigmaMap | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\nI : MultispanIndex C\ninst✝¹ : HasCoproduct I.left\ninst✝ : HasCoproduct I.right\nb : I.L\n⊢ Sigma.ι I.left b ≫ fstSigmaMap I = fst I b ≫ Sigma.ι I.right (fstFrom I b)",
"tactic": "simp [fstSigmaMap]"
}
] | [
303,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/RingTheory/ClassGroup.lean | mem_principal_ideals_iff | [
{
"state_after": "R : Type u_2\nK : Type u_1\nL : Type ?u.220909\ninst✝⁹ : CommRing R\ninst✝⁸ : Field K\ninst✝⁷ : Field L\ninst✝⁶ : DecidableEq L\ninst✝⁵ : Algebra R K\ninst✝⁴ : IsFractionRing R K\ninst✝³ : Algebra K L\ninst✝² : FiniteDimensional K L\ninst✝¹ : Algebra R L\ninst✝ : IsScalarTower R K L\nI : (Frac... | [
86,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Homeomorph.lean | Homeomorph.range_coe | [] | [
206,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.map_iInf | [
{
"state_after": "α : Type u_3\nι : Sort u_1\nβ : Type u_2\nf : α → β\nhf : Injective f\nm : ι → OuterMeasure α\n⊢ ↑(map f) (⨅ (i : ι), m i) = ↑(map f) (↑(comap f) (⨅ (i : ι), ↑(map f) (m i)))",
"state_before": "α : Type u_3\nι : Sort u_1\nβ : Type u_2\nf : α → β\nhf : Injective f\nm : ι → OuterMeasure α\n⊢... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1237,
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Mathlib/Topology/Order/Basic.lean | closure_lt_subset_le | [] | [
214,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Data/Sum/Order.lean | OrderIso.sumComm_symm | [] | [
561,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
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] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.lieSpan_eq | [] | [
710,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
1
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Mathlib/GroupTheory/Perm/List.lean | List.formPerm_eq_one_iff | [
{
"state_after": "case nil\nα : Type u_1\nβ : Type ?u.817926\ninst✝ : DecidableEq α\nx : α\nhl : Nodup []\n⊢ formPerm [] = 1 ↔ length [] ≤ 1\n\ncase cons\nα : Type u_1\nβ : Type ?u.817926\ninst✝ : DecidableEq α\nx hd : α\ntl : List α\nhl : Nodup (hd :: tl)\n⊢ formPerm (hd :: tl) = 1 ↔ length (hd :: tl) ≤ 1",
... | [
423,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | not_summable_iff_tendsto_nat_atTop_of_nonneg | [
{
"state_after": "case intro\nα : Type ?u.343727\nβ : Type ?u.343730\nγ : Type ?u.343733\nf : ℕ → ℝ≥0\n⊢ (¬Summable fun i => ↑(f i)) ↔ Tendsto (fun n => ∑ i in Finset.range n, (fun i => ↑(f i)) i) atTop atTop",
"state_before": "α : Type ?u.343727\nβ : Type ?u.343730\nγ : Type ?u.343733\nf : ℕ → ℝ\nhf : ∀ (n... | [
1325,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1322,
1
] |
Mathlib/Topology/Semicontinuous.lean | lowerSemicontinuousWithinAt_ciSup | [
{
"state_after": "case inl\nα : Type u_1\ninst✝³ : TopologicalSpace α\nβ : Type ?u.113012\ninst✝² : Preorder β\nf✝ g : α → β\nx : α\ns t : Set α\ny z : β\nι : Sort u_3\nδ : Type ?u.113041\nδ' : Type u_2\ninst✝¹ : CompleteLinearOrder δ\ninst✝ : ConditionallyCompleteLinearOrder δ'\nf : ι → α → δ'\nbdd : ∀ᶠ (y : α... | [
561,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | DifferentiableOn.sum | [] | [
372,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/LinearAlgebra/Dual.lean | TensorProduct.dualDistrib_dualDistribInvOfBasis_left_inverse | [
{
"state_after": "R : Type u_2\nM : Type u_3\nN : Type u_5\nι : Type u_1\nκ : Type u_4\ninst✝⁸ : DecidableEq ι\ninst✝⁷ : DecidableEq κ\ninst✝⁶ : Fintype ι\ninst✝⁵ : Fintype κ\ninst✝⁴ : CommRing R\ninst✝³ : AddCommGroup M\ninst✝² : AddCommGroup N\ninst✝¹ : Module R M\ninst✝ : Module R N\nb : Basis ι R M\nc : Bas... | [
1603,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1591,
1
] |
Mathlib/Order/SuccPred/LinearLocallyFinite.lean | toZ_iterate_pred_of_not_isMin | [
{
"state_after": "case zero\nι : Type u_1\ninst✝³ : LinearOrder ι\ninst✝² : SuccOrder ι\ninst✝¹ : IsSuccArchimedean ι\ninst✝ : PredOrder ι\ni0 i : ι\nhn : ¬IsMin ((pred^[Nat.zero]) i0)\n⊢ toZ i0 ((pred^[Nat.zero]) i0) = -↑Nat.zero\n\ncase succ\nι : Type u_1\ninst✝³ : LinearOrder ι\ninst✝² : SuccOrder ι\ninst✝¹ ... | [
287,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Data/Fin/Interval.lean | Fin.card_fintypeIcc | [
{
"state_after": "no goals",
"state_before": "n : ℕ\na b : Fin n\n⊢ Fintype.card ↑(Set.Icc a b) = ↑b + 1 - ↑a",
"tactic": "rw [← card_Icc, Fintype.card_ofFinset]"
}
] | [
101,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Path.nodup_support | [] | [
1321,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1320,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_lt_top | [] | [
3051,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3050,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.trans_refl | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.47438\nδ : Type ?u.47441\ne : LocalEquiv α β\ne' : LocalEquiv β γ\n⊢ (LocalEquiv.trans e (LocalEquiv.refl β)).source = e.source",
"tactic": "simp [trans_source]"
}
] | [
749,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
748,
1
] |
Mathlib/NumberTheory/ClassNumber/AdmissibleCardPowDegree.lean | Polynomial.exists_partition_polynomial | [
{
"state_after": "case intro\nFq : Type u_1\ninst✝¹ : Fintype Fq\ninst✝ : Field Fq\nn : ℕ\nε : ℝ\nhε : 0 < ε\nb : Fq[X]\nhb : b ≠ 0\nA : Fin n → Fq[X]\nt : Fin n → Fin (Fintype.card Fq ^ ⌈-log ε / log ↑(Fintype.card Fq)⌉₊)\nht : ∀ (i₀ i₁ : Fin n), t i₀ = t i₁ ↔ ↑(↑cardPowDegree (A i₁ % b - A i₀ % b)) < ↑cardPow... | [
259,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.Stream.toList_cons | [
{
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"state_before": "α : Type u_1\nx : α\nr : RBNode α\ns : RBNode.Stream α\n⊢ toList (cons x r s) = x :: R... | [
377,
53
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
375,
9
] |
Mathlib/Topology/Order/Basic.lean | exists_Ioc_subset_of_mem_nhds | [] | [
1225,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1223,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.scanl_head | [
{
"state_after": "case zero\nα : Type u_2\nβ : Type u_1\nf : β → α → β\nb : β\nv : Vector α Nat.zero\n⊢ head (scanl f b v) = b\n\ncase succ\nα : Type u_2\nβ : Type u_1\nf : β → α → β\nb : β\nn✝ : ℕ\nv : Vector α (Nat.succ n✝)\n⊢ head (scanl f b v) = b",
"state_before": "n : ℕ\nα : Type u_2\nβ : Type u_1\nf ... | [
371,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Algebra/GradedMonoid.lean | SetLike.one_mem_graded | [] | [
498,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
] |
Mathlib/Data/Polynomial/Monic.lean | Polynomial.monic_of_degree_le | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b : R\nm n✝ : ℕ\nι : Type y\ninst✝ : Semiring R\np q r : R[X]\nn : ℕ\nH1 : degree p ≤ ↑n\nH2 : coeff p n = 1\nH : ¬degree p < ↑n\n⊢ Monic p",
"tactic": "rwa [Monic, Polynomial.leadingCoeff, natDegree, (lt_or_eq_of_le H1).resolve_lef... | [
99,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/CategoryTheory/Limits/Fubini.lean | CategoryTheory.Limits.limitCurrySwapCompLimIsoLimitCurryCompLim_hom_π_π | [
{
"state_after": "J K : Type v\ninst✝³ : SmallCategory J\ninst✝² : SmallCategory K\nC : Type u\ninst✝¹ : Category C\nF : J ⥤ K ⥤ C\nG : J × K ⥤ C\ninst✝ : HasLimits C\nj : J\nk : K\n⊢ (((limitIsoLimitCurryCompLim (Prod.swap K J ⋙ G)).inv ≫\n (HasLimit.isoOfEquivalence (Prod.braiding K J) (Iso.refl ((Pr... | [
329,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Std/Data/List/Lemmas.lean | List.cons_inj | [] | [
29,
35
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
28,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | antitone_iff_map_nonpos | [] | [
247,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Order/Lattice.lean | inf_le_inf_left | [] | [
484,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidWithZeroHom.coe_id | [] | [
668,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
667,
1
] |
Mathlib/RingTheory/Derivation/Basic.lean | Derivation.leibniz_inv | [
{
"state_after": "case inl\nR : Type u_3\ninst✝⁸ : CommRing R\nA : Type ?u.578634\ninst✝⁷ : CommRing A\ninst✝⁶ : Algebra R A\nM : Type u_2\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module A M\ninst✝³ : Module R M\nD✝ D1 D2 : Derivation R A M\nr : R\na b : A\nK : Type u_1\ninst✝² : Field K\ninst✝¹ : Module K M\ninst✝ :... | [
417,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.set_integral_prod | [
{
"state_after": "α : Type u_1\nα' : Type ?u.2462095\nβ : Type u_2\nβ' : Type ?u.2462101\nγ : Type ?u.2462104\nE : Type u_3\ninst✝¹² : MeasurableSpace α\ninst✝¹¹ : MeasurableSpace α'\ninst✝¹⁰ : MeasurableSpace β\ninst✝⁹ : MeasurableSpace β'\ninst✝⁸ : MeasurableSpace γ\nμ μ' : Measure α\nν ν' : Measure β\nτ : Me... | [
511,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.piecewise_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.302885\nγ : Type ?u.302888\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\n⊢ piecewise {i} f g = update g i (f i)",
"tactic": "rw [← insert_emptyc_eq, piecewi... | [
2505,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2504,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Split.lean | BoxIntegral.Box.coe_splitUpper | [
{
"state_after": "ι : Type u_1\nM : Type ?u.11166\nn : ℕ\nI : Box ι\ni : ι\nx : ℝ\ny : ι → ℝ\n⊢ (Set.pi univ fun i_1 => Ioc (update I.lower i (max x (lower I i)) i_1) (upper I i_1)) = ↑I ∩ {y | x < y i}",
"state_before": "ι : Type u_1\nM : Type ?u.11166\nn : ℕ\nI : Box ι\ni : ι\nx : ℝ\ny : ι → ℝ\n⊢ ↑(splitU... | [
113,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.univ_fin2 | [
{
"state_after": "case a\nx : Fin 2\n⊢ x ∈ univ ↔ x ∈ {0, 1}",
"state_before": "⊢ univ = {0, 1}",
"tactic": "ext x"
},
{
"state_after": "no goals",
"state_before": "case a\nx : Fin 2\n⊢ x ∈ univ ↔ x ∈ {0, 1}",
"tactic": "fin_cases x <;> simp"
}
] | [
59,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.ofReal_pow | [
{
"state_after": "no goals",
"state_before": "r : ℝ\nn : ℕ\n⊢ ↑(r ^ n) = ↑r ^ n",
"tactic": "induction n <;> simp [*, ofReal_mul, pow_succ]"
}
] | [
715,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.div_re_ofReal | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nE : Type ?u.5998790\ninst✝ : IsROrC K\nz : K\nr : ℝ\n⊢ ↑re (z / ↑r) = ↑re z / r",
"tactic": "rw [div_eq_inv_mul, div_eq_inv_mul, ← ofReal_inv, ofReal_mul_re]"
}
] | [
585,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
584,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.edist_eq_iSup | [
{
"state_after": "p : ℝ≥0∞\n𝕜 : Type ?u.7794\n𝕜' : Type ?u.7797\nι : Type u_1\nα : ι → Type ?u.7805\nβ : ι → Type u_2\ninst✝¹ : Fintype ι\ninst✝ : (i : ι) → EDist (β i)\nf g : PiLp ⊤ β\n⊢ (if ⊤ = 0 then ↑(Finset.card (Finite.toFinset (_ : Set.Finite {i | f i ≠ g i})))\n else if ⊤ = ⊤ then ⨆ (i : ι), edist ... | [
160,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.domain_sup | [] | [
343,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Order/Atoms.lean | OrderEmbedding.isAtom_of_map_bot_of_image | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝³ : PartialOrder α\ninst✝² : PartialOrder β\ninst✝¹ : OrderBot α\ninst✝ : OrderBot β\nf : β ↪o α\nhbot : ↑f ⊥ = ⊥\nb : β\nhb : ⊥ ⋖ ↑f b\n⊢ ⊥ ⋖ b",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝³ : PartialOrder α\ninst✝² : PartialOrder β\ninst✝¹ : OrderB... | [
703,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biprod.map_snd | [] | [
1516,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1514,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.mk_zero | [
{
"state_after": "no goals",
"state_before": "K : Type u\ninst✝¹ : CommRing K\ninst✝ : IsDomain K\np : K[X]\n⊢ RatFunc.mk p 0 = { toFractionRing := 0 }",
"tactic": "rw [mk_eq_div', RingHom.map_zero, div_zero]"
}
] | [
204,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Order/Antichain.lean | IsAntichain.preimage_relIso | [] | [
141,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Algebra/Order/Group/Abs.lean | abs_of_nonneg | [] | [
111,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Topology/MetricSpace/GromovHausdorffRealized.lean | GromovHausdorff.candidates_lipschitz | [
{
"state_after": "case a\nX : Type u\nY : Type v\ninst✝⁵ : MetricSpace X\ninst✝⁴ : CompactSpace X\ninst✝³ : Nonempty X\ninst✝² : MetricSpace Y\ninst✝¹ : CompactSpace Y\ninst✝ : Nonempty Y\nf : GromovHausdorff.ProdSpaceFun X Y\nx y z t : X ⊕ Y\nfA : f ∈ candidates X Y\n⊢ ∀ (x y : (X ⊕ Y) × (X ⊕ Y)), dist (f x) (... | [
208,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
9
] |
Mathlib/Topology/Semicontinuous.lean | IsClosed.upperSemicontinuousAt_indicator | [] | [
770,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
768,
1
] |
Mathlib/Order/WithBot.lean | WithBot.ofDual_le_ofDual_iff | [] | [
1003,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1002,
1
] |
Mathlib/Topology/SubsetProperties.lean | IsCompact.nonempty_iInter_of_directed_nonempty_compact_closed | [
{
"state_after": "α : Type u\nβ : Type v\nι✝ : Type ?u.21500\nπ : ι✝ → Type ?u.21505\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t : Set α\nι : Type v\nhι : Nonempty ι\nZ : ι → Set α\nhZd : Directed (fun x x_1 => x ⊇ x_1) Z\nhZn : ∀ (i : ι), Set.Nonempty (Z i)\nhZc : ∀ (i : ι), IsCompact (Z i)\n... | [
295,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.fst | [
{
"state_after": "α✝ : Type ?u.35741\nσ : Type ?u.35744\ninst✝³ : Primcodable α✝\ninst✝² : Primcodable σ\nα : Type u_1\nβ : Type u_2\ninst✝¹ : Primcodable α\ninst✝ : Primcodable β\nn : ℕ\n⊢ Nat.rec 0 (fun n_1 n_ih => Nat.rec 0 (fun n n_ih => Nat.succ n_1) (encode (decode (Nat.unpair n).snd)))\n (encode (de... | [
351,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.support_update_ne_zero | [
{
"state_after": "case a\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝¹ : (i : ι) → Zero (β i)\ninst✝ : (i : ι) → (x : β i) → Decidable (x ≠ 0)\nf : Π₀ (i : ι), β i\ni : ι\nb : β i\nh : b ≠ 0\nj : ι\n⊢ j ∈ support (update i f b) ↔ j ∈ insert i (support f... | [
1234,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1229,
1
] |
Mathlib/Algebra/AddTorsor.lean | vadd_eq_vadd_iff_sub_eq_vsub | [
{
"state_after": "no goals",
"state_before": "G : Type u_2\nP : Type u_1\ninst✝¹ : AddCommGroup G\ninst✝ : AddTorsor G P\nv₁ v₂ : G\np₁ p₂ : P\n⊢ v₁ +ᵥ p₁ = v₂ +ᵥ p₂ ↔ v₂ - v₁ = p₁ -ᵥ p₂",
"tactic": "rw [vadd_eq_vadd_iff_neg_add_eq_vsub, neg_add_eq_sub]"
}
] | [
273,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Algebra/EuclideanDomain/Defs.lean | EuclideanDomain.xgcd_val | [] | [
279,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.prod_assoc_symm | [
{
"state_after": "no goals",
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312,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
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Mathlib/CategoryTheory/Limits/Opposites.lean | CategoryTheory.Limits.pullbackIsoUnopPushout_inv_fst | [
{
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Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.pointwise_smul_le_iff₀ | [] | [
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Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.polar_zero_right | [
{
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"tactic": "simp only [add_zero, polar, QuadraticForm... | [
288,
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287,
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Mathlib/Data/Set/Basic.lean | Set.nonempty_of_ssubset | [] | [
487,
30
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486,
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Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | extChartAt_coe_symm | [] | [
1038,
6
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Mathlib/Logic/Basic.lean | forall_true_left | [] | [
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24
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_zpow | [] | [
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25
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Mathlib/Order/RelIso/Basic.lean | acc_liftOn₂'_iff | [] | [
465,
25
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Mathlib/Analysis/NormedSpace/WeakDual.lean | WeakDual.isClosed_polar | [
{
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Mathlib/Data/Complex/Exponential.lean | Complex.exp_zero | [
{
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},
{
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"tacti... | [
495,
11
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