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/Integral/DivergenceTheorem.lean | MeasureTheory.integral_divergence_of_hasFDerivWithinAt_off_countable' | [] | [
315,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Topology/MetricSpace/Antilipschitz.lean | AntilipschitzWith.id | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.6535\nγ : Type ?u.6538\ninst✝² : PseudoEMetricSpace α\ninst✝¹ : PseudoEMetricSpace β\ninst✝ : PseudoEMetricSpace γ\nK : ℝ≥0\nf : α → β\nx y : α\n⊢ edist x y ≤ ↑1 * edist (id x) (id y)",
"tactic": "simp only [ENNReal.coe_one, one_mul... | [
128,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
11
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.coe_iInf₂ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.57093\nγ : Type ?u.57096\nι : Sort u_2\nκ : ι → Sort u_3\ninst✝ : LE α\nS : Set (UpperSet α)\ns t : UpperSet α\na : α\nf : (i : ι) → κ i → UpperSet α\n⊢ ↑(⨅ (i : ι) (j : κ i), f i j) = ⋃ (i : ι) (j : κ i), ↑(f i j)",
"tactic": "simp... | [
567,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
566,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.frequently_atBot | [] | [
330,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/CategoryTheory/Limits/Preserves/Limits.lean | CategoryTheory.preservesColimitsIso_inv_comp_desc | [
{
"state_after": "case w\nC : Type u₁\ninst✝⁵ : Category C\nD : Type u₂\ninst✝⁴ : Category D\nG : C ⥤ D\nJ : Type w\ninst✝³ : Category J\nF : J ⥤ C\ninst✝² : PreservesColimit F G\ninst✝¹ : HasColimit F\ninst✝ : HasColimit (F ⋙ G)\nt : Cocone F\nj✝ : J\n⊢ colimit.ι (F ⋙ G) j✝ ≫ (preservesColimitIso G F).inv ≫ G.... | [
137,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Analysis/Calculus/FDerivMeasurable.lean | measurable_fderiv_apply_const | [] | [
426,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.divInt_zero_one | [
{
"state_after": "a b c : ℚ\n⊢ (match 0, 1 with\n | n, Int.ofNat d => inline (mkRat n d)\n | n, Int.negSucc d => normalize (-n) (Nat.succ d)) =\n 0",
"state_before": "a b c : ℚ\n⊢ 0 /. 1 = 0",
"tactic": "rw [divInt]"
},
{
"state_after": "no goals",
"state_before": "a b c : ℚ\n⊢ (mat... | [
233,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/Topology/CompactOpen.lean | ContinuousMap.preimage_gen | [
{
"state_after": "case h.mk\nα : Type u_1\nβ : Type u_3\nγ : Type u_2\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\ng : C(β, γ)\ns : Set α\nx✝¹ : IsCompact s\nu : Set γ\nx✝ : IsOpen u\nf : α → β\ncontinuous_toFun✝ : Continuous f\n⊢ mk f ∈ comp g ⁻¹' CompactOpen.gen s u ↔... | [
103,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
9
] |
Mathlib/RingTheory/Finiteness.lean | Ideal.exists_radical_pow_le_of_fg | [
{
"state_after": "R✝ : Type ?u.375076\nM : Type ?u.375079\ninst✝³ : Semiring R✝\ninst✝² : AddCommMonoid M\ninst✝¹ : Module R✝ M\nR : Type u_1\ninst✝ : CommSemiring R\nI : Ideal R\nh : FG (radical I)\nthis : radical I ≤ radical I\n⊢ ∃ n, radical I ^ n ≤ I",
"state_before": "R✝ : Type ?u.375076\nM : Type ?u.3... | [
515,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/Algebra/Order/Group/Abs.lean | abs_of_nonpos | [] | [
119,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Data/Sym/Sym2.lean | Sym2.mem_iff_exists | [] | [
321,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | circleMap_ne_center | [] | [
172,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/CategoryTheory/PathCategory.lean | CategoryTheory.composePath_comp | [
{
"state_after": "case nil\nC : Type u₁\ninst✝ : Category C\nX Y Z : C\nf : Path X Y\n⊢ composePath (Path.comp f Path.nil) = composePath f ≫ composePath Path.nil\n\ncase cons\nC : Type u₁\ninst✝ : Category C\nX Y Z : C\nf : Path X Y\nY' Z' : C\ng : Path Y Y'\ne : Y' ⟶ Z'\nih : composePath (Path.comp f g) = comp... | [
183,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Order/Heyting/Basic.lean | snd_hnot | [] | [
128,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_down | [
{
"state_after": "α✝ β✝ : Type u\na : Cardinal\nb : Cardinal\nα : Type u\nβ : Type (max u v)\n⊢ Nonempty (β ↪ α) → ∃ a', lift a' = lift (#β)",
"state_before": "α✝ β✝ : Type u\na : Cardinal\nb : Cardinal\nα : Type u\nβ : Type (max u v)\n⊢ (#β) ≤ lift (#α) → ∃ a', lift a' = (#β)",
"tactic": "rw [← lift_id... | [
1119,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1111,
1
] |
Mathlib/Data/List/Infix.lean | List.infix_rfl | [] | [
68,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Data/Set/Opposite.lean | Set.singleton_unop_op | [
{
"state_after": "case h\nα : Type u_1\nx x✝ : αᵒᵖ\n⊢ x✝ ∈ Set.op {x.unop} ↔ x✝ ∈ {x}",
"state_before": "α : Type u_1\nx : αᵒᵖ\n⊢ Set.op {x.unop} = {x}",
"tactic": "ext"
},
{
"state_after": "case h.mp\nα : Type u_1\nx x✝ : αᵒᵖ\n⊢ x✝ ∈ Set.op {x.unop} → x✝ ∈ {x}\n\ncase h.mpr\nα : Type u_1\nx x✝ ... | [
108,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Icc_subset_uIcc' | [] | [
909,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
908,
1
] |
Mathlib/Data/PNat/Xgcd.lean | PNat.XgcdType.flip_v | [
{
"state_after": "u : XgcdType\n⊢ (↑(z u) * ↑(b u) + u.y * ↑(a u), u.x * ↑(b u) + ↑(w u) * ↑(a u)) =\n (u.y * ↑(a u) + ↑(z u) * ↑(b u), ↑(w u) * ↑(a u) + u.x * ↑(b u))",
"state_before": "u : XgcdType\n⊢ v (flip u) = Prod.swap (v u)",
"tactic": "dsimp [v]"
},
{
"state_after": "case h₁\nu : Xgc... | [
236,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.coe_sub | [] | [
261,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/CategoryTheory/Limits/Types.lean | CategoryTheory.Limits.Types.isLimitEquivSections_symm_apply | [
{
"state_after": "case intro\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ TypeMax\nc : Cone F\nt : IsLimit c\nj : J\nx : c.pt\n⊢ c.π.app j (↑(isLimitEquivSections t).symm (↑(isLimitEquivSections t) x)) = ↑(↑(isLimitEquivSections t) x) j",
"state_before": "J : Type v\ninst✝ : SmallCategory J\nF : J ⥤ TypeMa... | [
102,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.parallel_iff_direction_eq_and_eq_bot_iff_eq_bot | [
{
"state_after": "case refine'_1\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\ns₁ s₂ : AffineSubspace k P\nh : s₁ ∥ s₂\n⊢ s₁ = ⊥ → s₂ = ⊥\n\ncase refine'_2\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : Ad... | [
1783,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1765,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.of_mem_append | [] | [
1075,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1074,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.C_dvd_iff_dvd_coeff | [
{
"state_after": "case mp\nR : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type u_1\na a' a₁ a₂ : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S₁\np q : MvPolynomial σ R\nr : R\nφ : MvPolynomial σ R\n⊢ ↑C r ∣ φ → ∀ (i : σ →₀ ℕ), r ∣ coeff i φ\n\ncase mpr\nR : Type u\nS₁ : ... | [
844,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
827,
1
] |
Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.dist_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nE : Type ?u.72363\ninst✝³ : TopologicalSpace α\ninst✝² : CompactSpace α\ninst✝¹ : MetricSpace β\ninst✝ : NormedAddCommGroup E\nf g : C(α, β)\nC : ℝ\nC0 : 0 ≤ C\n⊢ dist f g ≤ C ↔ ∀ (x : α), dist (↑f x) (↑g x) ≤ C",
"tactic": "simp ... | [
139,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.HomotopyWith.symm_symm | [] | [
506,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.bot_mul_of_pos | [
{
"state_after": "x : EReal\nh : 0 < x\n⊢ x * ⊥ = ⊥",
"state_before": "x : EReal\nh : 0 < x\n⊢ ⊥ * x = ⊥",
"tactic": "rw [EReal.mul_comm]"
},
{
"state_after": "no goals",
"state_before": "x : EReal\nh : 0 < x\n⊢ x * ⊥ = ⊥",
"tactic": "exact mul_bot_of_pos h"
}
] | [
974,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
972,
1
] |
Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | LiouvilleWith.rat_add | [] | [
211,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | Valuation.map_sum_lt' | [] | [
210,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.ae_withDensity_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1776303\nγ : Type ?u.1776306\nδ : Type ?u.1776309\nm : MeasurableSpace α\nμ ν : Measure α\np : α → Prop\nf : α → ℝ≥0∞\nhf : Measurable f\n⊢ (↑↑μ ({x | f x ≠ 0} ∩ {a | ¬p a}) = 0) = (↑↑μ {a | ¬(f a ≠ 0 → p a)} = 0)",
"state_before": "α : Type u_1\nβ : Type ?u.17763... | [
1714,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1709,
1
] |
Mathlib/Analysis/Calculus/Deriv/Pow.lean | hasStrictDerivAt_pow | [
{
"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... | [
61,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Order/GameAdd.lean | Acc.prod_gameAdd | [
{
"state_after": "case intro\nα : Type u_1\nβ : Type u_2\nrα : α → α → Prop\nrβ : β → β → Prop\na✝ : α\nb✝ : β\nhb✝ : Acc rβ b✝\na : α\nh✝ : ∀ (y : α), rα y a → Acc rα y\niha : ∀ (y : α), rα y a → ∀ {b : β}, Acc rβ b → Acc (Prod.GameAdd rα rβ) (y, b)\nb : β\nhb : Acc rβ b\n⊢ Acc (Prod.GameAdd rα rβ) (a, b)",
... | [
109,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.map_sub | [] | [
200,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Geometry/Euclidean/Sphere/Basic.lean | EuclideanGeometry.Cospherical.affineIndependent_of_ne | [] | [
294,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Init/Logic.lean | iff_self_iff | [] | [
204,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Topology/PartitionOfUnity.lean | PartitionOfUnity.exists_isSubordinate | [] | [
518,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
1
] |
Mathlib/Data/List/Basic.lean | List.exists_mem_cons_of | [] | [
287,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Data/Finset/Powerset.lean | Finset.card_powerset | [] | [
92,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/MeasureTheory/Group/Integration.lean | MeasureTheory.Integrable.comp_mul_left | [] | [
152,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Std/Data/String/Lemmas.lean | String.utf8Len_eq_zero | [
{
"state_after": "no goals",
"state_before": "l : List Char\n⊢ utf8Len l = 0 ↔ l = []",
"tactic": "cases l <;> simp [Nat.ne_of_gt add_csize_pos]"
}
] | [
61,
48
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
60,
9
] |
Mathlib/Data/Complex/Module.lean | Complex.real_smul | [] | [
72,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.continuousAt_of_dominated | [
{
"state_after": "α : Type u_2\nE : Type u_3\nF✝ : Type ?u.1019635\n𝕜 : Type ?u.1019638\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace ℝ E\ninst✝⁸ : CompleteSpace E\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : SMulCommClass ℝ 𝕜 E\ninst✝⁴ : NormedAddCommGroup F✝\ninst✝³ : No... | [
1061,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1054,
1
] |
Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.toNatOrdinal_zero | [] | [
165,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Data/Finite/Basic.lean | Finite.sum_left | [] | [
90,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Inner.lean | MeasureTheory.AEStronglyMeasurable.re | [] | [
46,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
11
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.zneg_pos | [] | [
1072,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1071,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Cardinal.small_iff_lift_mk_lt_univ | [
{
"state_after": "α✝ : Type ?u.236087\nβ : Type ?u.236090\nγ : Type ?u.236093\nr : α✝ → α✝ → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nα : Type u\n⊢ Small α ↔ ∃ c', lift (#α) = lift c'",
"state_before": "α✝ : Type ?u.236087\nβ : Type ?u.236090\nγ : Type ?u.236093\nr : α✝ → α✝ → Prop\ns : β → β → Prop\nt : γ... | [
1547,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1540,
1
] |
Mathlib/Analysis/Convex/Between.lean | mem_const_vadd_affineSegment | [
{
"state_after": "no goals",
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121,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.disjoint_closedBall_of_lt_infEdist | [
{
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192,
26
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184,
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Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae | [
{
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436,
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409,
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Mathlib/Data/Fin/Tuple/Sort.lean | Tuple.monotone_proj | [
{
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105,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
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Mathlib/Data/Real/NNReal.lean | NNReal.coe_sub_def | [] | [
762,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
761,
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Mathlib/Analysis/Convex/Body.lean | ConvexBody.coe_smul' | [] | [
153,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | UniformSpace.SeparationQuotient.edist_mk | [] | [
1157,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1155,
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Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.exists_quadraticForm_ne_zero | [
{
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844,
57
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837,
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Mathlib/Data/Complex/Exponential.lean | Complex.cos_sq | [
{
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}
] | [
1042,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1041,
1
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Mathlib/Logic/Function/Basic.lean | Function.Involutive.surjective | [] | [
899,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
899,
11
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Mathlib/Data/Nat/Log.lean | Nat.log_eq_iff | [
{
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"state_before": "b m n : ℕ\nh : m ≠ 0 ∨ 1 < b ∧... | [
149,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
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Mathlib/Algebra/BigOperators/Fin.lean | Fin.prod_univ_two | [
{
"state_after": "no goals",
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}
] | [
113,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.mono_left | [] | [
1027,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1025,
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Mathlib/Topology/Algebra/OpenSubgroup.lean | OpenSubgroup.mem_toOpens | [] | [
109,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
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Mathlib/Data/Complex/Basic.lean | Complex.bit1_re | [] | [
212,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
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Mathlib/Deprecated/Subgroup.lean | IsSubgroup.div_mem | [
{
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"tactic": "simpa only [div_eq_mul_inv] using hs.mul_mem hx (hs.inv_mem hy)"
... | [
61,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
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Mathlib/RingTheory/WittVector/Defs.lean | WittVector.zsmul_coeff | [] | [
382,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
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Mathlib/Data/Set/Pointwise/BigOperators.lean | Set.mem_fintype_prod | [
{
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"state_before": "ι : Type u_1\nα : Type u_2\nβ : T... | [
93,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
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Mathlib/Data/ZMod/Basic.lean | ZMod.cast_one | [
{
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"state_before": "n : ℕ\nR : Type u_1\ninst✝¹ : Ring R\nm : ℕ\ninst✝ : CharP R m\nh : m... | [
298,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.sameCycle_inv_apply_right | [
{
"state_after": "no goals",
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}
] | [
160,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasDerivAt.sinh | [] | [
891,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
889,
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] |
Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.one_le_abs | [
{
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"state_before": "α : Type u\ninst✝² : Lattice α\ninst✝¹ : CommGroup α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\... | [
372,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.Bicone.toCocone_ι_app | [] | [
136,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
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Mathlib/Data/Finset/Lattice.lean | Finset.iInf_insert_update | [] | [
1984,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1982,
1
] |
Mathlib/Order/InitialSeg.lean | PrincipalSeg.down | [] | [
264,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Images.lean | CategoryTheory.Limits.epi_image_of_epi | [
{
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473,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
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Mathlib/Data/Prod/Basic.lean | Prod.map_snd | [] | [
70,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.QuasiMeasurePreserving.mono_right | [] | [
2465,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2463,
1
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Std/Data/List/Lemmas.lean | List.replaceF_of_forall_none | [
{
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"state_before": "α : Type u_1\np : α → Option α\nl : List α\nh : ∀ (a : α), a ∈ l → p a = none\n⊢ replaceF p l = l",
"tactic": "induction l with\n| nil => rfl\n| cons _ _ ih => simp [h _ (.head ..), ih (forall_mem_cons.1 h).2]"
},
{
"state_after": "no goals",
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1319,
69
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1316,
1
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Mathlib/Data/Matrix/Basis.lean | Matrix.StdBasisMatrix.diag_same | [
{
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159,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Algebra/GeomSum.lean | RingHom.map_geom_sum₂ | [
{
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"tactic": "simp [f.map_sum]"
}
] | [
402,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.prod_add_index | [
{
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385,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
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Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.roots_smul_nonzero | [
{
"state_after": "no goals",
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"tactic": "rw [smul_eq_C_mul, roots_C_mul _ ha]"
}
] | [
683,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.bit0_re | [] | [
179,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.HomClass.map_constants | [] | [
489,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
1
] |
Mathlib/RingTheory/Polynomial/Chebyshev.lean | Polynomial.Chebyshev.T_derivative_eq_U | [
{
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"tactic": "simp only [T_one, U_zero, derivative_X, Nat.cast_zero, zero_add, mul_one]"
},
{
"state_after": "no goals",
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200,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.of_add_mul_right_left | [
{
"state_after": "R : Type u\ninst✝ : CommSemiring R\nx y z : R\nh : IsCoprime (x + y * z) y\n⊢ IsCoprime x y",
"state_before": "R : Type u\ninst✝ : CommSemiring R\nx y z : R\nh : IsCoprime (x + z * y) y\n⊢ IsCoprime x y",
"tactic": "rw [mul_comm] at h"
},
{
"state_after": "no goals",
"state... | [
191,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Aesop/BuiltinRules.lean | Aesop.BuiltinRules.pEmpty_false | [] | [
49,
55
] | ca73109cc40837bc61df8024c9016da4b4f99d4c | https://github.com/JLimperg/aesop | [
49,
1
] |
Mathlib/Data/Finsupp/Interval.lean | Finsupp.card_Icc | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : Type u_2\ninst✝² : PartialOrder α\ninst✝¹ : Zero α\ninst✝ : LocallyFiniteOrder α\nf g : ι →₀ α\n⊢ card (Icc f g) = ∏ i in f.support ∪ g.support, card (Icc (↑f i) (↑g i))",
"tactic": "simp_rw [icc_eq, card_finsupp, coe_rangeIcc]"
}
] | [
111,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Data/Set/Image.lean | Set.Nontrivial.preimage | [
{
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"state_before": "α : Type u_2\nβ... | [
1250,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1246,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.Eventually.exists_mem | [] | [
1122,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1120,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.sum_mk | [] | [
948,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
947,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Sized.rotateL_size | [
{
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"state_before": "α : Type ... | [
426,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/Data/List/Pairwise.lean | List.Pairwise.iff_of_mem | [] | [
98,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Deprecated/Subgroup.lean | Group.closure_subgroup | [] | [
568,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisInsertion.l_iInf_u | [] | [
567,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
563,
1
] |
Mathlib/Algebra/ContinuedFractions/ConvergentsEquiv.lean | GeneralizedContinuedFraction.squashSeq_nth_of_lt | [
{
"state_after": "case none\nK : Type u_1\nn : ℕ\ng : GeneralizedContinuedFraction K\ns : Stream'.Seq (Pair K)\ninst✝ : DivisionRing K\nm : ℕ\nm_lt_n : m < n\ns_succ_nth_eq : Stream'.Seq.get? s (n + 1) = none\n⊢ Stream'.Seq.get? (squashSeq s n) m = Stream'.Seq.get? s m\n\ncase some\nK : Type u_1\nn : ℕ\ng : Gen... | [
132,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.mem_center_iff | [] | [
490,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/Topology/Algebra/Order/Filter.lean | Filter.tendsto_nhds_atBot | [] | [
33,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
11
] |
Mathlib/Topology/Algebra/InfiniteSum/Order.lean | tsum_le_of_sum_le | [] | [
118,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Topology/Algebra/Order/LeftRight.lean | continuousAt_iff_continuous_left'_right' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝² : TopologicalSpace α\ninst✝¹ : LinearOrder α\ninst✝ : TopologicalSpace β\na : α\nf : α → β\n⊢ ContinuousAt f a ↔ ContinuousWithinAt f (Iio a) a ∧ ContinuousWithinAt f (Ioi a) a",
"tactic": "rw [continuousWithinAt_Ioi_iff_Ic... | [
85,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.filter_inter | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.378112\nγ : Type ?u.378115\np q : α → Prop\ninst✝² : DecidablePred p\ninst✝¹ : DecidablePred q\ninst✝ : DecidableEq α\ns t : Finset α\na✝ : α\n⊢ a✝ ∈ filter p s ∩ t ↔ a✝ ∈ filter p (s ∩ t)",
"state_before": "α : Type u_1\nβ : Type ?u.378112\nγ : Type ?u.37... | [
2832,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2830,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.MeasurePreserving.lintegral_comp | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.1686621\nδ : Type ?u.1686624\nm : MeasurableSpace α\nμ ν✝ : Measure α\nmb : MeasurableSpace β\nν : Measure β\ng : α → β\nhg : MeasurePreserving g\nf : β → ℝ≥0∞\nhf : Measurable f\n⊢ (∫⁻ (a : α), f (g a) ∂μ) = ∫⁻ (b : β), f... | [
1334,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1332,
1
] |
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