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/GroupTheory/SemidirectProduct.lean | SemidirectProduct.map_inr | [
{
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304,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
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Mathlib/Data/Finset/Card.lean | Finset.one_lt_card_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.55605\ns t : Finset α\nf : α → β\nn : ℕ\n⊢ (∃ a, a ∈ s ∧ ∃ b, b ∈ s ∧ a ≠ b) ↔ ∃ a b, a ∈ s ∧ b ∈ s ∧ a ≠ b",
"state_before": "α : Type u_1\nβ : Type ?u.55605\ns t : Finset α\nf : α → β\nn : ℕ\n⊢ 1 < card s ↔ ∃ a b, a ∈ s ∧ b ∈ s ∧ a ≠ b",
"tactic": "rw [one_l... | [
567,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
565,
1
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.set_smul_subset_set_smul_iff | [] | [
910,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
909,
1
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.direction_lt_of_nonempty | [
{
"state_after": "case intro\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nS : AffineSpace V P\np₁ p₂ : P\ns1 s2 : AffineSubspace k P\nh : s1 < s2\np : P\nhp : p ∈ ↑s1\n⊢ direction s1 < direction s2",
"state_before": "k : Type u_1\nV : Type u_2\nP :... | [
940,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
931,
1
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.denseRange_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.306971\nι : Type ?u.306974\ninst✝ : PseudoMetricSpace α\nx✝ y z : α\nε ε₁ ε₂ : ℝ\ns : Set α\nf : β → α\nx : α\n⊢ x ∈ closure (range f) ↔ ∀ (r : ℝ), r > 0 → ∃ y, dist x (f y) < r",
"tactic": "simp only [mem_closure_iff, exi... | [
1931,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1930,
1
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Mathlib/Data/List/Basic.lean | List.map_const | [] | [
1884,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1883,
9
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Mathlib/Algebra/Order/Ring/Abs.lean | abs_dvd_self | [] | [
129,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
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Mathlib/Topology/UniformSpace/Pi.lean | Pi.uniformContinuous_proj | [] | [
53,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.div_zero | [] | [
881,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
880,
1
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Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | Collinear.subset | [] | [
344,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
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Mathlib/Algebra/Order/Sub/Canonical.lean | AddLECancellable.tsub_lt_tsub_left_of_le | [] | [
169,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
11
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Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_I | [
{
"state_after": "no goals",
"state_before": "⊢ arg I = π / 2",
"tactic": "simp [arg, le_refl]"
}
] | [
205,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | Matrix.nondegenerate_toBilin_iff | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.2835547\nM✝ : Type ?u.2835550\ninst✝¹⁹ : Semiring R\ninst✝¹⁸ : AddCommMonoid M✝\ninst✝¹⁷ : Module R M✝\nR₁ : Type ?u.2835586\nM₁ : Type ?u.2835589\ninst✝¹⁶ : Ring R₁\ninst✝¹⁵ : AddCommGroup M₁\ninst✝¹⁴ : Module R₁ M₁\nR₂ : Type ?u.2836198\nM₂ : Type ... | [
571,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
1
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Mathlib/Data/Set/Finite.lean | Set.finite_subset_iUnion | [
{
"state_after": "case intro\nα : Type u\nβ : Type v\nι✝ : Sort w\nγ : Type x\ns : Set α\nι : Type u_1\nt : ι → Set α\nh : s ⊆ ⋃ (i : ι), t i\na✝ : Fintype ↑s\n⊢ ∃ I, Set.Finite I ∧ s ⊆ ⋃ (i : ι) (_ : i ∈ I), t i",
"state_before": "α : Type u\nβ : Type v\nι✝ : Sort w\nγ : Type x\ns : Set α\nhs : Set.Finite ... | [
1114,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1108,
1
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Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.Measure.toOuterMeasure_injective | [
{
"state_after": "no goals",
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134,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Std/Data/List/Lemmas.lean | List.diff_cons_right | [
{
"state_after": "case h\nα : Type u_1\ninst✝ : DecidableEq α\nl₁ l₂ : List α\na : α\n⊢ List.erase (List.diff l₁ l₂) a = List.diff l₁ (a :: l₂)",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\nl₁ l₂ : List α\na : α\n⊢ List.diff l₁ (a :: l₂) = List.erase (List.diff l₁ l₂) a",
"tactic": "apply Eq.s... | [
1498,
71
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1497,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinite_mul_of_not_infinitesimal_infinite | [
{
"state_after": "x y : ℝ*\nhx : ¬Infinitesimal x\nhy : Infinite y\n⊢ Infinite (y * x)",
"state_before": "x y : ℝ*\nhx : ¬Infinitesimal x\nhy : Infinite y\n⊢ Infinite (x * y)",
"tactic": "rw [mul_comm]"
},
{
"state_after": "no goals",
"state_before": "x y : ℝ*\nhx : ¬Infinitesimal x\nhy : In... | [
896,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
894,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.lift'_id | [] | [
386,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.normSq_ofReal | [
{
"state_after": "no goals",
"state_before": "r : ℝ\n⊢ ↑normSq ↑r = r * r",
"tactic": "simp [normSq, ofReal']"
}
] | [
589,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
Mathlib/Order/Minimal.lean | IsAntichain.max_minimals | [
{
"state_after": "α : Type u_1\nr r₁ r₂ : α → α → Prop\ns t : Set α\na✝ b : α\nht : IsAntichain r t\nh : minimals r s ⊆ t\nhs : ∀ ⦃a : α⦄, a ∈ t → ∃ b, b ∈ minimals r s ∧ r a b\na : α\nha : a ∈ t\n⊢ a ∈ minimals r s",
"state_before": "α : Type u_1\nr r₁ r₂ : α → α → Prop\ns t : Set α\na b : α\nht : IsAntich... | [
212,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
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Mathlib/Order/LiminfLimsup.lean | Filter.liminf_le_limsup | [] | [
494,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/Data/Set/Basic.lean | Set.compl_union | [] | [
1665,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1664,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.rat_cast_imI | [] | [
1356,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1355,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.map_neg | [] | [
205,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
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Mathlib/Data/Sum/Basic.lean | Sum.LiftRel.mono_right | [] | [
441,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_add | [] | [
1616,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1614,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.natAdd_cast | [
{
"state_after": "case h\nn✝ m✝ n n' m : ℕ\ni : Fin n'\nh : n' = n\n⊢ ↑(↑(natAdd m) (↑(cast h) i)) = ↑(↑(cast (_ : m + n' = m + n)) (↑(natAdd m) i))",
"state_before": "n✝ m✝ n n' m : ℕ\ni : Fin n'\nh : n' = n\n⊢ ↑(natAdd m) (↑(cast h) i) = ↑(cast (_ : m + n' = m + n)) (↑(natAdd m) i)",
"tactic": "ext"
... | [
1419,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1416,
1
] |
Std/Data/String/Lemmas.lean | String.data_takeWhile | [
{
"state_after": "no goals",
"state_before": "p : Char → Bool\ns : String\n⊢ (takeWhile s p).data = List.takeWhile p s.data",
"tactic": "rw [takeWhile_eq]"
}
] | [
1105,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1104,
9
] |
Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | NNReal.continuous_rpow_const | [] | [
482,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.coeff_fun_eq_zero_iff | [] | [
127,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_dvd | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.347101\nι : Type ?u.347104\nG : Type ?u.347107\nM : Type ?u.347110\nN : Type u_2\ninst✝¹ : CommMonoid M\ninst✝ : CommMonoid N\nf✝ g : α → M\na✝ b : α\ns t : Set α\nf : α → N\na : α\nhf : Set.Finite (mulSupport f)\nha : a ∈ mulSupport f\n⊢ f a ∣ finprod f\n\n... | [
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30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
894,
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] |
Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isRat_lt_true | [
{
"state_after": "α : Type u_1\ninst✝¹ : LinearOrderedRing α\ninst✝ : Nontrivial α\nnum✝¹ num✝ : ℤ\nda db : ℕ\ninv✝¹ : Invertible ↑da\ninv✝ : Invertible ↑db\nh✝ : decide (num✝¹ * ↑db < num✝ * ↑da) = true\nh : (fun x => ↑x) (num✝¹ * ↑db) < (fun x => ↑x) (num✝ * ↑da)\n⊢ ↑num✝¹ * ⅟↑da < ↑num✝ * ⅟↑db",
"state_b... | [
743,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
734,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_range_eq_of_injective | [] | [
2022,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2020,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.map_singleton | [] | [
1187,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1186,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.blimsup_sup_le_or | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.139592\nι : Type ?u.139595\ninst✝ : CompleteLattice α\nf g : Filter β\np q : β → Prop\nu v : β → α\n⊢ ∀ (x : β), p x → p x ∨ q x",
"tactic": "tauto"
},
{
"state_after": "no goals",
"state_before": "α : Type... | [
921,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
920,
1
] |
Mathlib/Order/Antichain.lean | IsWeakAntichain.subset | [] | [
369,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
11
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csSup_Icc | [] | [
750,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
749,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Localization.liftOn_mk' | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type ?u.3266990\ninst✝¹ : CommMonoid N\nP : Type ?u.3266996\ninst✝ : CommMonoid P\np : Sort u\nf : M → { x // x ∈ S } → p\nH : ∀ {a c : M} {b d : { x // x ∈ S }}, ↑(r S) (a, b) (c, d) → f a b = f c d\na :... | [
1663,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1662,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.sin_neg | [
{
"state_after": "case h\nx✝ : ℝ\n⊢ sin (-↑x✝) = -sin ↑x✝",
"state_before": "θ : Angle\n⊢ sin (-θ) = -sin θ",
"tactic": "induction θ using Real.Angle.induction_on"
},
{
"state_after": "no goals",
"state_before": "case h\nx✝ : ℝ\n⊢ sin (-↑x✝) = -sin ↑x✝",
"tactic": "exact Real.sin_neg _"
... | [
378,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/LinearAlgebra/ProjectiveSpace/Basic.lean | Projectivization.mk_eq_mk_iff' | [
{
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"state_before": "K : Type u_2\nV : Type u_1\ninst✝² : DivisionRing K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nv w : ... | [
116,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.map_piecewise_add | [
{
"state_after": "R : Type u\nι : Type u'\nn : ℕ\nM : Fin (Nat.succ n) → Type v\nM₁ : ι → Type v₁\nM₂ : Type v₂\nM₃ : Type v₃\nM' : Type v'\ninst✝¹¹ : Semiring R\ninst✝¹⁰ : (i : Fin (Nat.succ n)) → AddCommMonoid (M i)\ninst✝⁹ : (i : ι) → AddCommMonoid (M₁ i)\ninst✝⁸ : AddCommMonoid M₂\ninst✝⁷ : AddCommMonoid M₃... | [
485,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
456,
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Mathlib/Logic/Relation.lean | Relation.ReflTransGen.head | [
{
"state_after": "case refl\nα : Type u_1\nβ : Type ?u.16575\nγ : Type ?u.16578\nδ : Type ?u.16581\nr : α → α → Prop\na b c d : α\nhab : r a b\n⊢ ReflTransGen r a b\n\ncase tail\nα : Type u_1\nβ : Type ?u.16575\nγ : Type ?u.16578\nδ : Type ?u.16581\nr : α → α → Prop\na b c d : α\nhab : r a b\nb✝ c✝ : α\na✝¹ : R... | [
283,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Data/Set/Intervals/Instances.lean | Set.Icc.coe_ne_one | [] | [
96,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
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Mathlib/LinearAlgebra/Matrix/Transvection.lean | Matrix.TransvectionStruct.mul_inv | [
{
"state_after": "case mk\nn : Type u_1\np : Type ?u.34495\nR : Type u₂\n𝕜 : Type ?u.34500\ninst✝⁴ : Field 𝕜\ninst✝³ : DecidableEq n\ninst✝² : DecidableEq p\ninst✝¹ : CommRing R\ni j : n\ninst✝ : Fintype n\ni✝ j✝ : n\nt_hij : i✝ ≠ j✝\nc✝ : R\n⊢ toMatrix { i := i✝, j := j✝, hij := t_hij, c := c✝ } ⬝\n toM... | [
216,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.L1.measurable_coeFn | [] | [
1287,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1286,
1
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Mathlib/Data/Set/Basic.lean | Set.nontrivial_coe_sort | [
{
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"tactic"... | [
2587,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2579,
1
] |
Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.cast_toZModPow | [
{
"state_after": "p : ℕ\nhp_prime : Fact (Nat.Prime p)\nr : ℚ\nx✝ : ℤ_[p]\nm n : ℕ\nh : m ≤ n\nx : ℤ_[p]\n⊢ ↑(↑(toZModPow n) x) = ↑(RingHom.comp (ZMod.castHom (_ : p ^ m ∣ p ^ n) (ZMod (p ^ m))) (toZModPow n)) x",
"state_before": "p : ℕ\nhp_prime : Fact (Nat.Prime p)\nr : ℚ\nx✝ : ℤ_[p]\nm n : ℕ\nh : m ≤ n\n... | [
450,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.smul_apply | [] | [
586,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
1
] |
src/lean/Init/Data/AC.lean | Lean.Data.AC.Context.evalList_append | [
{
"state_after": "no goals",
"state_before": "α : Sort u_1\nctx : Context α\nl r : List Nat\nh₁ : l ≠ []\nh₂ : r ≠ []\n⊢ evalList α ctx (List.append l r) = op ctx (evalList α ctx l) (evalList α ctx r)",
"tactic": "induction l using List.two_step_induction with\n| empty => simp_all\n| single x =>\n case... | [
303,
109
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
291,
1
] |
Mathlib/Algebra/IsPrimePow.lean | Nat.disjoint_divisors_filter_isPrimePow | [
{
"state_after": "R : Type ?u.84416\ninst✝ : CommMonoidWithZero R\nn p : R\nk a b : ℕ\nhab : coprime a b\n⊢ ∀ ⦃a_1 : ℕ⦄, a_1 ∣ a → a ≠ 0 → IsPrimePow a_1 → a_1 ∣ b → b ≠ 0 → ¬IsPrimePow a_1",
"state_before": "R : Type ?u.84416\ninst✝ : CommMonoidWithZero R\nn p : R\nk a b : ℕ\nhab : coprime a b\n⊢ Disjoint ... | [
114,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Order/CompleteBooleanAlgebra.lean | compl_sInf' | [] | [
314,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mk'_eq_iff_eq | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type u_2\ninst✝¹ : CommMonoid N\nP : Type ?u.817224\ninst✝ : CommMonoid P\nf : LocalizationMap S N\nx₁ x₂ : M\ny₁ y₂ : { x // x ∈ S }\nH : mk' f x₁ y₁ = mk' f x₂ y₂\n⊢ ↑(toMap f) (↑y₂ * x₁) = ↑(toMap f) (... | [
773,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
765,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.rpow_two | [
{
"state_after": "x : ℝ≥0\n⊢ x ^ 2 = x ^ ↑2",
"state_before": "x : ℝ≥0\n⊢ x ^ 2 = x ^ 2",
"tactic": "rw [← rpow_nat_cast]"
},
{
"state_after": "no goals",
"state_before": "x : ℝ≥0\n⊢ x ^ 2 = x ^ ↑2",
"tactic": "simp only [Nat.cast_ofNat]"
}
] | [
137,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_log | [
{
"state_after": "a b : ℝ\nn : ℕ\nh : ¬0 ∈ [[a, b]]\nh' : ∀ (x : ℝ), x ∈ [[a, b]] → x ≠ 0\n⊢ (∫ (x : ℝ) in a..b, Real.log x) = b * Real.log b - a * Real.log a - b + a",
"state_before": "a b : ℝ\nn : ℕ\nh : ¬0 ∈ [[a, b]]\n⊢ (∫ (x : ℝ) in a..b, Real.log x) = b * Real.log b - a * Real.log a - b + a",
"tact... | [
485,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/Order/WithBot.lean | WithBot.le_toDual_iff | [] | [
983,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
981,
1
] |
Mathlib/Order/Monotone/Basic.lean | Monotone.monotoneOn | [] | [
380,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
11
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.preimage_inv | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.40275\nα : Type u_1\nβ : Type ?u.40281\nγ : Type ?u.40284\ninst✝¹ : DecidableEq α\ninst✝ : InvolutiveInv α\ns : Finset α\n⊢ ↑(preimage s Inv.inv (_ : Set.InjOn Inv.inv (Inv.inv ⁻¹' ↑s))) = ↑s⁻¹",
"tactic": "rw [coe_preimage, Set.inv_preimage, coe... | [
285,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/CategoryTheory/Sites/Sheafification.lean | CategoryTheory.Meq.ext | [] | [
67,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | norm_sub_mul_self_real | [
{
"state_after": "𝕜 : Type ?u.2475426\nE : Type ?u.2475429\nF : Type u_1\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx y : F\nh : ‖x - y‖ * ‖x - y‖ = ‖x‖ * ‖x‖ - 2 * ↑re (inner x y) + ‖... | [
1091,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1088,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.toSubsemiring_inj | [] | [
85,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | intermediate_value_Icc | [] | [
533,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_le_of_le | [] | [
795,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
1
] |
Mathlib/Dynamics/Ergodic/Ergodic.lean | Ergodic.quasiErgodic | [] | [
135,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.log_neg | [] | [
185,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Topology/Inseparable.lean | SeparationQuotient.comap_mk_nhdsSet_image | [] | [
483,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
] |
Std/Data/Int/DivMod.lean | Int.eq_zero_of_div_eq_zero | [
{
"state_after": "no goals",
"state_before": "d n : Int\nh : d ∣ n\nH : div n d = 0\n⊢ n = 0",
"tactic": "rw [← Int.mul_div_cancel' h, H, Int.mul_zero]"
}
] | [
788,
48
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
787,
11
] |
Mathlib/Order/Max.lean | IsMax.eq_of_ge | [] | [
398,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
11
] |
Mathlib/Topology/ContinuousOn.lean | IsOpen.ite | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.397946\nγ : Type ?u.397949\nδ : Type ?u.397952\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ns s' t : Set α\nhs : IsOpen s\nhs' : IsOpen s'\nht : s ∩ frontier t = s' ... | [
1225,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1223,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDense.lean | MeasureTheory.SimpleFunc.edist_approxOn_le | [] | [
179,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.two_nsmul_coe_div_two | [
{
"state_after": "no goals",
"state_before": "θ : ℝ\n⊢ 2 • ↑(θ / 2) = ↑θ",
"tactic": "rw [← coe_nsmul, two_nsmul, add_halves]"
}
] | [
142,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Topology/Instances/NNReal.lean | NNReal.tendsto_coe | [] | [
106,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Data/List/Intervals.lean | List.Ico.filter_le | [
{
"state_after": "case inl\nn m l : ℕ\nhnl : n ≤ l\n⊢ filter (fun x => decide (l ≤ x)) (Ico n m) = Ico (max n l) m\n\ncase inr\nn m l : ℕ\nhln : l ≤ n\n⊢ filter (fun x => decide (l ≤ x)) (Ico n m) = Ico (max n l) m",
"state_before": "n m l : ℕ\n⊢ filter (fun x => decide (l ≤ x)) (Ico n m) = Ico (max n l) m"... | [
212,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.sum | [
{
"state_after": "case empty\nα : Type u_2\nβ : Type ?u.595990\nE : Type ?u.595993\nF : Type ?u.595996\nG : Type ?u.595999\nE' : Type u_3\nF' : Type u_4\nG' : Type ?u.596008\nE'' : Type ?u.596011\nF'' : Type ?u.596014\nG'' : Type ?u.596017\nR : Type ?u.596020\nR' : Type ?u.596023\n𝕜 : Type ?u.596026\n𝕜' : Typ... | [
1807,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1803,
1
] |
Mathlib/Data/Set/Basic.lean | Set.union_self | [] | [
761,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
760,
1
] |
Mathlib/Data/Set/Intervals/Group.lean | Set.add_mem_Ioo_iff_left | [] | [
78,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.one_toGerm | [] | [
581,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.fst_inl | [] | [
120,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Data/Nat/Cast/Prod.lean | Prod.fst_natCast | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : AddMonoidWithOne α\ninst✝ : AddMonoidWithOne β\nn : ℕ\n⊢ (↑n).fst = ↑n",
"tactic": "induction n <;> simp [*]"
}
] | [
32,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Ring.lean | tsum_div_const | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nκ : Type ?u.21514\nR : Type ?u.21517\nα : Type u_1\ninst✝³ : DivisionSemiring α\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSemiring α\nf g : ι → α\na a₁ a₂ : α\ninst✝ : T2Space α\n⊢ (∑' (x : ι), f x / a) = (∑' (x : ι), f x) / a",
"tactic... | [
131,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Topology/Hom/Open.lean | ContinuousOpenMap.toFun_eq_coe | [] | [
78,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/MeasureTheory/CardMeasurableSpace.lean | MeasurableSpace.iUnion_mem_generateMeasurableRec | [
{
"state_after": "α : Type u\ns : Set (Set α)\ni : (Quotient.out (ord (aleph 1))).α\nf : ℕ → Set α\nhf : ∀ (n : ℕ), ∃ j, j < i ∧ f n ∈ generateMeasurableRec s j\n⊢ (⋃ (n : ℕ), f n) ∈\n let i := i;\n let S := ⋃ (j : ↑(Iio i)), generateMeasurableRec s ↑j;\n s ∪ {∅} ∪ compl '' S ∪ range fun f => ⋃ (n : ℕ)... | [
81,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iInter_union | [] | [
561,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
560,
1
] |
Mathlib/Algebra/Order/AbsoluteValue.lean | AbsoluteValue.eq_zero | [] | [
109,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
11
] |
Mathlib/Algebra/Lie/Nilpotent.lean | Equiv.lieModule_isNilpotent_iff | [
{
"state_after": "case mp\nR : Type u\nL : Type v\nM : Type w\ninst✝¹² : CommRing R\ninst✝¹¹ : LieRing L\ninst✝¹⁰ : LieAlgebra R L\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : Module R M\ninst✝⁷ : LieRingModule L M\ninst✝⁶ : LieModule R L M\nk : ℕ\nN : LieSubmodule R L M\nL₂ : Type u_1\nM₂ : Type u_2\ninst✝⁵ : LieRing L₂... | [
498,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.filterMap_eq_filter | [
{
"state_after": "α : Type u_1\nβ : Type ?u.277023\nγ : Type ?u.277026\np : α → Prop\ninst✝ : DecidablePred p\ns : Multiset α\nl : List α\n⊢ List.filterMap (Option.guard p) l = List.filterMap (Option.guard fun x => decide (p x) = true) l",
"state_before": "α : Type u_1\nβ : Type ?u.277023\nγ : Type ?u.27702... | [
2139,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2135,
1
] |
Mathlib/Topology/FiberBundle/Basic.lean | FiberBundle.continuousWithinAt_totalSpace | [
{
"state_after": "case refine'_1\nι : Type ?u.8243\nB : Type u_1\nF : Type u_4\nX : Type u_3\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : TopologicalSpace B\ninst✝³ : TopologicalSpace F\nE : B → Type u_2\ninst✝² : TopologicalSpace (TotalSpace E)\ninst✝¹ : (b : B) → TopologicalSpace (E b)\ninst✝ : FiberBundle F E\nf :... | [
319,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.prod_nil | [] | [
33,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.smul_re | [] | [
1035,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1034,
1
] |
Mathlib/Algebra/Hom/Units.lean | Units.val_zpow_eq_zpow_val | [] | [
139,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.single_apply_eq_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.49894\nγ : Type ?u.49897\nι : Type ?u.49900\nM : Type u_1\nM' : Type ?u.49906\nN : Type ?u.49909\nP : Type ?u.49912\nG : Type ?u.49915\nH : Type ?u.49918\nR : Type ?u.49921\nS : Type ?u.49924\ninst✝ : Zero M\na✝ a' : α\nb✝ : M\na x : α\... | [
385,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
1
] |
Mathlib/Topology/Connected.lean | connectedComponent_eq | [] | [
673,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
668,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.count_nsmul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.355480\nγ : Type ?u.355483\ninst✝ : DecidableEq α\na : α\nn : ℕ\ns : Multiset α\n⊢ count a (n • s) = n * count a s",
"tactic": "induction n <;> simp [*, succ_nsmul', succ_mul, zero_nsmul]"
}
] | [
2404,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2403,
1
] |
Mathlib/Data/Set/Intervals/OrdConnectedComponent.lean | Set.disjoint_ordT5Nhd | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrder α\ns t : Set α\nx y z : α\n⊢ ordT5Nhd s t ⊓ ordT5Nhd t s ≤ ⊥",
"state_before": "α : Type u_1\ninst✝ : LinearOrder α\ns t : Set α\nx y z : α\n⊢ Disjoint (ordT5Nhd s t) (ordT5Nhd t s)",
"tactic": "rw [disjoint_iff_inf_le]"
},
{
"state_after": "ca... | [
237,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Topology/Algebra/ConstMulAction.lean | continuousAt_const_smul_iff | [] | [
224,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/MeasureTheory/CardMeasurableSpace.lean | MeasurableSpace.cardinalMeasurableSet_le | [] | [
174,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Std/Data/RBMap/WF.lean | Std.RBNode.Balanced.insert | [
{
"state_after": "α : Type u_1\nc : RBColor\nn : Nat\ncmp : α → α → Ordering\nv : α\nt : RBNode α\nh : Balanced t c n\n⊢ ∃ c' n',\n Balanced\n (match isRed t with\n | red => setBlack (ins cmp v t)\n | black => ins cmp v t)\n c' n'",
"state_before": "α : Type u_1\nc : RBColor\nn : Nat\... | [
226,
77
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
222,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.toList_nil | [] | [
1340,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1339,
1
] |
Mathlib/Topology/Constructions.lean | prod_induced_induced | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type u_1\nδ : Type u_2\nε : Type ?u.49234\nζ : Type ?u.49237\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : TopologicalSpace β\ninst✝³ : TopologicalSpace γ\ninst✝² : TopologicalSpace δ\ninst✝¹ : TopologicalSpace ε\ninst✝ : TopologicalSpace ζ\nf : α → β\ng : γ → δ\n⊢ induced... | [
674,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
669,
1
] |
Mathlib/Order/Hom/Lattice.lean | InfHom.bot_apply | [] | [
691,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
690,
1
] |
Mathlib/Topology/SubsetProperties.lean | countable_cover_nhds_of_sigma_compact | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.165278\nπ : ι → Type ?u.165283\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ns t : Set α\ninst✝ : SigmaCompactSpace α\nf : α → Set α\nhf : ∀ (x : α), f x ∈ 𝓝[univ] x\n⊢ ∃ s, Set.Countable s ∧ (⋃ (x : α) (_ : x ∈ s), f x) = univ",
"state_bef... | [
1414,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1409,
1
] |
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