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/EqHaar.lean | MeasureTheory.Measure.add_haar_ball_mul_of_pos | [
{
"state_after": "E : Type u_1\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : MeasurableSpace E\ninst✝⁵ : BorelSpace E\ninst✝⁴ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝³ : IsAddHaarMeasure μ\nF : Type ?u.1974470\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\ninst✝ : CompleteSp... | [
420,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/Data/Int/Cast/Lemmas.lean | Int.cast_pos | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.18775\nι : Type ?u.18778\nα : Type u_1\nβ : Type ?u.18784\ninst✝¹ : OrderedRing α\ninst✝ : Nontrivial α\nn : ℤ\n⊢ 0 < ↑n ↔ 0 < n",
"tactic": "rw [← cast_zero, cast_lt]"
}
] | [
151,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Measurable.infNndist | [] | [
1551,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1549,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.one_re | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nE : Type ?u.1627867\ninst✝ : IsROrC K\n⊢ ↑re 1 = 1",
"tactic": "rw [← ofReal_one, ofReal_re]"
}
] | [
160,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/MeasureTheory/Function/UniformIntegrable.lean | MeasureTheory.unifIntegrable_zero_meas | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nι : Type u_3\nm : MeasurableSpace α\nμ : Measure α\ninst✝¹ : NormedAddCommGroup β\ninst✝ : MeasurableSpace α\np : ℝ≥0∞\nf : ι → α → β\nε : ℝ\nx✝² : 0 < ε\ni : ι\ns : Set α\nx✝¹ : MeasurableSet s\nx✝ : ↑↑0 s ≤ ENNReal.ofReal 1\n⊢ snorm... | [
153,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/RingTheory/PrincipalIdealDomain.lean | PrincipalIdealRing.associates_irreducible_iff_prime | [] | [
271,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Topology/Sets/Closeds.lean | TopologicalSpace.Closeds.coe_nonempty | [] | [
139,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.coe_replicate | [] | [
888,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
888,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_nnnorm_le_of_lipschitz | [] | [
435,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/Topology/Order/Basic.lean | induced_orderTopology' | [] | [
1046,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1041,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/ContinuousLinearMap.lean | ContinuousLinearMap.measurable_comp | [] | [
39,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/Data/Real/ConjugateExponents.lean | Real.IsConjugateExponent.one_div_pos | [] | [
65,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Memℒp.toLp_congr | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nE : Type u_1\nF : Type ?u.347109\nG : Type ?u.347112\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf g : α → E\nhf : Memℒp f p\nhg : Memℒp g ... | [
126,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Topology/ContinuousOn.lean | nhdsWithin_restrict | [] | [
198,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.mul_div_le | [
{
"state_after": "no goals",
"state_before": "m n : Nat\n⊢ n * (m / n) ≤ m",
"tactic": "match n, Nat.eq_zero_or_pos n with\n| _, Or.inl rfl => rw [Nat.zero_mul]; exact m.zero_le\n| n, Or.inr h => rw [Nat.mul_comm, ← Nat.le_div_iff_mul_le h]; exact Nat.le_refl _"
},
{
"state_after": "m n : Nat\n⊢... | [
647,
85
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
644,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image_image₂_antidistrib_right | [
{
"state_after": "α : Type u_3\nα' : Type u_5\nβ : Type u_4\nβ' : Type ?u.95037\nγ : Type u_2\nγ' : Type ?u.95043\nδ : Type u_1\nδ' : Type ?u.95049\nε : Type ?u.95052\nε' : Type ?u.95055\nζ : Type ?u.95058\nζ' : Type ?u.95061\nν : Type ?u.95064\ninst✝⁷ : DecidableEq α'\ninst✝⁶ : DecidableEq β'\ninst✝⁵ : Decidab... | [
491,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | Valuation.map_sum_le | [
{
"state_after": "K : Type ?u.625793\nF : Type ?u.625796\nR : Type u_3\ninst✝⁴ : DivisionRing K\nΓ₀ : Type u_2\nΓ'₀ : Type ?u.625808\nΓ''₀ : Type ?u.625811\ninst✝³ : LinearOrderedCommMonoidWithZero Γ''₀\ninst✝² : Ring R\ninst✝¹ : LinearOrderedCommMonoidWithZero Γ₀\ninst✝ : LinearOrderedCommMonoidWithZero Γ'₀\nv... | [
196,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Analysis/Complex/ReImTopology.lean | Metric.Bounded.reProdIm | [] | [
217,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/FieldTheory/Subfield.lean | RingHom.eqOn_field_closure | [] | [
882,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
880,
1
] |
Mathlib/Tactic/Sat/FromLRAT.lean | Sat.Valuation.mk_implies | [
{
"state_after": "no goals",
"state_before": "as ps : List Prop\np : Prop\nas₁ : List Prop\n⊢ as = List.reverseAux as₁ ps → implies (mk as) p ps (List.length as₁) → p",
"tactic": "induction ps generalizing as₁ with\n| nil => exact fun _ ↦ id\n| cons a as ih =>\n refine fun e H ↦ @ih (a::as₁) e (H ?_)\n... | [
164,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/LinearAlgebra/Matrix/Hermitian.lean | Matrix.isHermitian_transpose_mul_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type ?u.28730\nm : Type u_1\nn : Type u_2\nA✝ : Matrix n n α\ninst✝⁴ : NonUnitalSemiring α\ninst✝³ : StarRing α\ninst✝² : NonUnitalSemiring β\ninst✝¹ : StarRing β\ninst✝ : Fintype m\nA : Matrix m n α\n⊢ IsHermitian (Aᴴ ⬝ A)",
"tactic": "rw ... | [
206,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.singleton_subset_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.35449\nγ : Type ?u.35452\ns : Finset α\na b : α\n⊢ {a} ⊆ {b} ↔ a = b",
"tactic": "simp"
}
] | [
784,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.aleph0_le | [
{
"state_after": "case intro\nα β : Type u\nn : ℕ\nh : ∀ (n_1 : ℕ), ↑n_1 ≤ ↑n\nhn : ↑n < ℵ₀\n⊢ False",
"state_before": "α β : Type u\nc : Cardinal\nh : ∀ (n : ℕ), ↑n ≤ c\nhn : c < ℵ₀\n⊢ False",
"tactic": "rcases lt_aleph0.1 hn with ⟨n, rfl⟩"
},
{
"state_after": "no goals",
"state_before": "c... | [
1437,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1433,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/InverseDeriv.lean | Real.contDiffOn_arccos | [] | [
188,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_div_two_eq_sqrt | [
{
"state_after": "z x✝ y x r : ℝ\nhx : 0 ≤ x\n⊢ x ^ (r / 2) = x ^ (1 / 2 * r)",
"state_before": "z x✝ y x r : ℝ\nhx : 0 ≤ x\n⊢ x ^ (r / 2) = sqrt x ^ r",
"tactic": "rw [sqrt_eq_rpow, ← rpow_mul hx]"
},
{
"state_after": "case e_a\nz x✝ y x r : ℝ\nhx : 0 ≤ x\n⊢ r / 2 = 1 / 2 * r",
"state_befor... | [
663,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
] |
Mathlib/Data/Set/Sigma.lean | Set.fst_image_sigma | [] | [
248,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Computability/PartrecCode.lean | Nat.Partrec.Code.const_prim | [
{
"state_after": "n : ℕ\n⊢ ((fun b => comp succ b)^[n]) zero = Code.const n",
"state_before": "n : ℕ\n⊢ ((fun b => comp succ (n, b).snd)^[id n]) zero = Code.const n",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ ((fun b => comp succ b)^[n]) zero = Code.const n",... | [
677,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
673,
1
] |
Mathlib/CategoryTheory/Limits/Constructions/Equalizers.lean | CategoryTheory.Limits.hasCoequalizers_of_hasPushouts_and_binary_coproducts | [] | [
201,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Algebra/Associated.lean | Associates.Prime.le_or_le | [] | [
1010,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1008,
1
] |
Std/Data/List/Lemmas.lean | List.ext | [
{
"state_after": "α : Type u_1\na : α\nl₁ : List α\na' : α\nl₂ : List α\nh : ∀ (n : Nat), get? (a :: l₁) n = get? (a' :: l₂) n\nh0 : some a = some a'\n⊢ a :: l₁ = a' :: l₂",
"state_before": "α : Type u_1\na : α\nl₁ : List α\na' : α\nl₂ : List α\nh : ∀ (n : Nat), get? (a :: l₁) n = get? (a' :: l₂) n\n⊢ a :: ... | [
655,
63
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
649,
8
] |
Mathlib/Data/Finset/Slice.lean | Finset.sized_slice | [] | [
152,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.Finite.isPwo | [] | [
444,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
11
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_C_mul_X_pow | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn✝ m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nn : ℕ\nha : a ≠ 0\n⊢ degree (↑C a * X ^ n) = ↑n",
"tactic": "rw [C_mul_X_pow_eq_monomial, degree_monomial n ha]"
}
] | [
295,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Algebra/Order/Group/Abs.lean | abs_le' | [] | [
53,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | differentiableWithinAt_sub_const_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.497137\ninst✝³ : NormedAddCommGroup G\ninst✝² : Normed... | [
555,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.SubgroupNormal.mem_comm | [
{
"state_after": "G : Type u_1\nG' : Type ?u.714616\ninst✝³ : Group G\ninst✝² : Group G'\nA : Type ?u.714625\ninst✝¹ : AddGroup A\nN : Type ?u.714631\ninst✝ : Group N\nH K : Subgroup G\nhK : H ≤ K\nhN : Normal (subgroupOf H K)\na b : G\nhb : b ∈ K\nh : a * b ∈ H\nthis : b * (a * b) * b⁻¹ ∈ H\n⊢ b * a ∈ H",
... | [
3609,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3606,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.le_lift_iff | [] | [
1128,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1123,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.infty_coeFn_mul | [] | [
800,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
799,
1
] |
Mathlib/CategoryTheory/Monoidal/Preadditive.lean | CategoryTheory.leftDistributor_inv | [
{
"state_after": "case w\nC : Type u_2\ninst✝⁵ : Category C\ninst✝⁴ : Preadditive C\ninst✝³ : MonoidalCategory C\ninst✝² : MonoidalPreadditive C\ninst✝¹ : HasFiniteBiproducts C\nJ : Type\ninst✝ : Fintype J\nX : C\nf : J → C\nj✝ : J\n⊢ biproduct.ι (fun j => X ⊗ f j) j✝ ≫ (leftDistributor X f).inv =\n biproduc... | [
162,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.sum_inr | [] | [
1001,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1000,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.ringEquivOfRingEquiv_mk' | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁷ : CommSemiring R\nM : Submonoid R\nS : Type u_4\ninst✝⁶ : CommSemiring S\ninst✝⁵ : Algebra R S\nP : Type u_2\ninst✝⁴ : CommSemiring P\ninst✝³ : IsLocalization M S\ng : R →+* P\nhg : ∀ (y : { x // x ∈ M }), IsUnit (↑g ↑y)\nT : Submonoid P\nQ ... | [
710,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
707,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | inv_pow_le_inv_pow_of_le | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.126922\nα : Type u_1\nβ : Type ?u.126928\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm✝ n✝ : ℤ\na1 : 1 ≤ a\nm n : ℕ\nmn : m ≤ n\n⊢ (a ^ n)⁻¹ ≤ (a ^ m)⁻¹",
"tactic": "convert one_div_pow_le_one_div_pow_of_le a1 mn using 1 <;> simp"
}
] | [
640,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
639,
1
] |
Mathlib/GroupTheory/PGroup.lean | IsPGroup.card_center_eq_prime_pow | [
{
"state_after": "p : ℕ\nG : Type u_1\ninst✝³ : Group G\ninst✝² : Fintype G\ninst✝¹ : Fact (Nat.Prime p)\nn : ℕ\nhGpn : card G = p ^ n\nhn : 0 < n\ninst✝ : Fintype { x // x ∈ center G }\nhcG : IsPGroup p { x // x ∈ center G }\n⊢ ∃ k, k > 0 ∧ card { x // x ∈ center G } = p ^ k",
"state_before": "p : ℕ\nG : T... | [
379,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.eq_of_smul_eq_smul_left | [
{
"state_after": "d a : ℤ\nb c : ℤ√d\nha : a ≠ 0\nh : (↑a * b).re = (↑a * c).re ∧ (↑a * b).im = (↑a * c).im\n⊢ b.re = c.re ∧ b.im = c.im",
"state_before": "d a : ℤ\nb c : ℤ√d\nha : a ≠ 0\nh : ↑a * b = ↑a * c\n⊢ b = c",
"tactic": "rw [ext] at h⊢"
},
{
"state_after": "no goals",
"state_before"... | [
384,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
11
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.ker_snd | [] | [
161,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Data/List/Basic.lean | List.takeD_left' | [
{
"state_after": "ι : Type ?u.228301\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁✝ l₂✝ l₁ l₂ : List α\nn : ℕ\na : α\nh : length l₁ = n\n⊢ takeD (length l₁) (l₁ ++ l₂) a = l₁",
"state_before": "ι : Type ?u.228301\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁✝ l₂✝ l₁ l₂ : List α\nn : ℕ\na : α\nh ... | [
2371,
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.map_eq_map_iff | [
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Mathlib/RingTheory/HahnSeries.lean | HahnSeries.sub_coeff' | [
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Mathlib/LinearAlgebra/Quotient.lean | Submodule.comap_map_mkQ | [
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Mathlib/Algebra/Star/Pointwise.lean | Set.star_singleton | [
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Mathlib/Topology/Algebra/Order/Floor.lean | tendsto_ceil_atBot | [
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Mathlib/Data/Sign.lean | sign_eq_neg_one_iff | [
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Mathlib/Order/WithBot.lean | WithBot.coe_max | [] | [
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Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_mul_rpow_one_add_sq | [
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Mathlib/Order/Filter/AtTopBot.lean | Filter.exists_le_of_tendsto_atTop | [
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Mathlib/Data/Analysis/Filter.lean | Filter.Realizer.bot_σ | [] | [
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Mathlib/Order/Ideal.lean | Order.cofinal_meets_idealOfCofinals | [] | [
601,
54
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Mathlib/Data/Real/Hyperreal.lean | Hyperreal.isSt_iff_abs_sub_lt_delta | [
{
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74
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Mathlib/Algebra/Homology/Homotopy.lean | Homotopy.dNext_zero_chainComplex | [
{
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Mathlib/MeasureTheory/Function/ContinuousMapDense.lean | MeasureTheory.Memℒp.exists_boundedContinuous_snorm_sub_le | [
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Mathlib/Algebra/Hom/NonUnitalAlg.lean | NonUnitalAlgHom.zero_apply | [] | [
267,
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Mathlib/Data/ULift.lean | PLift.forall | [] | [
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Mathlib/Topology/Semicontinuous.lean | lowerSemicontinuousWithinAt_univ_iff | [
{
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141,
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Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.inf' | [
{
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.map_direction | [
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Mathlib/Data/Set/Image.lean | Set.preimage_const_of_mem | [] | [
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Mathlib/Data/List/Basic.lean | List.reverse_foldl | [
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Mathlib/Computability/Ackermann.lean | one_lt_ack_succ_left | [
{
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126,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Convex/Side.lean | AffineSubspace.WSameSide.trans | [
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Mathlib/Data/Set/Image.lean | Set.image_univ | [
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.map_inf_le | [] | [
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82
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Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.prod_mono | [] | [
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22
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Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.eq_of_eqOn_top | [] | [
2912,
26
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2911,
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Mathlib/Data/Real/NNReal.lean | Real.coe_toNNReal_le | [] | [
1075,
40
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.complete_of_cauchySeq_tendsto | [] | [
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40
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Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.isUnit_comp | [] | [
882,
96
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880,
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Mathlib/Algebra/Module/LinearMap.lean | LinearMap.one_eq_id | [] | [
1022,
6
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1021,
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.diam_empty | [] | [
910,
39
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909,
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Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | regionBetween_subset | [
{
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] | [
474,
98
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473,
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Mathlib/GroupTheory/Abelianization.lean | abelianizationCongr_trans | [] | [
244,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
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Mathlib/Algebra/CharP/Basic.lean | sub_pow_char_of_commute | [
{
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Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.iSup_def | [] | [
236,
20
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Mathlib/LinearAlgebra/UnitaryGroup.lean | Matrix.mem_unitaryGroup_iff' | [
{
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Mathlib/FieldTheory/Normal.lean | AlgHom.restrictNormal_comp | [
{
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Mathlib/Topology/UniformSpace/AbstractCompletion.lean | AbstractCompletion.uniformContinuous_compareEquiv_symm | [] | [
286,
37
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285,
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Mathlib/Data/Fin/Basic.lean | Fin.zero_eq_one_iff | [
{
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},
{
"state_after": "case mp\nn m : ℕ\ninst✝ : NeZero n\nh : 0 = 1\n⊢ n = 1",
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854,
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847,
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Mathlib/Data/Finsupp/ToDfinsupp.lean | Finsupp.toDfinsupp_zero | [] | [
155,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Control/Basic.lean | guard_false | [
{
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}
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206,
36
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Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.Integrable.sum_integral_congr | [
{
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1
] |
Mathlib/LinearAlgebra/Matrix/DotProduct.lean | Matrix.dotProduct_stdBasis_eq_mul | [
{
"state_after": "case h₀\nR : Type v\nn : Type w\ninst✝² : Semiring R\ninst✝¹ : Fintype n\ninst✝ : DecidableEq n\nv : n → R\nc : R\ni : n\n⊢ ∀ (b : n), b ∈ Finset.univ → b ≠ i → v b * ↑(LinearMap.stdBasis R (fun x => R) i) c b = 0\n\ncase h₁\nR : Type v\nn : Type w\ninst✝² : Semiring R\ninst✝¹ : Fintype n\nins... | [
50,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | PadicSeq.stationary | [
{
"state_after": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nf : CauSeq ℚ (padicNorm p)\nhf : ¬f ≈ 0\nthis✝ : ∃ ε, ε > 0 ∧ ∃ N1, ∀ (j : ℕ), j ≥ N1 → ε ≤ padicNorm p (↑f j)\nε : ℚ\nhε : ε > 0\nN1 : ℕ\nhN1 : ∀ (j : ℕ), j ≥ N1 → ε ≤ padicNorm p (↑f j)\nN2 : ℕ\nhN2 : ∀ (j : ℕ), j ≥ N2 → ∀ (k : ℕ), k ≥ N2 → padicNorm p (↑f ... | [
104,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Std/Data/String/Lemmas.lean | String.Iterator.ValidFor.prevn | [
{
"state_after": "no goals",
"state_before": "l r : List Char\nit : Iterator\nh : ValidFor l r it\nx✝ : 0 ≤ List.length l\n⊢ ValidFor (List.drop 0 l) (List.reverse (List.take 0 l) ++ r) (Iterator.prevn it 0)",
"tactic": "simp [h, Iterator.prevn]"
},
{
"state_after": "l r : List Char\nit : Iterat... | [
619,
59
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
613,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.lt_succAbove_iff | [
{
"state_after": "case refine'_1\nn m : ℕ\np : Fin (n + 1)\ni : Fin n\n⊢ p < ↑(succAbove p) i → p ≤ ↑castSucc i\n\ncase refine'_2\nn m : ℕ\np : Fin (n + 1)\ni : Fin n\n⊢ p ≤ ↑castSucc i → p < ↑(succAbove p) i",
"state_before": "n m : ℕ\np : Fin (n + 1)\ni : Fin n\n⊢ p < ↑(succAbove p) i ↔ p ≤ ↑castSucc i",
... | [
2112,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2103,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arcsin_lt_pi_div_two | [
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ x < sin (π / 2) ↔ x < 1",
"tactic": "rw [sin_pi_div_two]"
}
] | [
234,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | Finset.measure_zero | [] | [
3320,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3318,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | LinearMap.coe_comp | [] | [
549,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | div_le_div_left' | [] | [
787,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
786,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.one_lt_rpow_iff_of_pos | [
{
"state_after": "no goals",
"state_before": "x y z : ℝ\nhx : 0 < x\n⊢ 1 < x ^ y ↔ 1 < x ∧ 0 < y ∨ x < 1 ∧ y < 0",
"tactic": "rw [rpow_def_of_pos hx, one_lt_exp_iff, mul_pos_iff, log_pos_iff hx, log_neg_iff hx]"
}
] | [
568,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | inv_lt_inv | [] | [
278,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.sub_int_mul_eq | [] | [
249,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
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