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/Algebra/Order/Group/Defs.lean | mul_inv_le_iff_le_mul | [
{
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"state_before": "α : Type u\ninst✝² : Group α\ninst✝¹ : LE α\ninst✝ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b c : α\n⊢ a * b⁻¹ * b ≤ c * b ↔ a ≤ c * b",
"tactic": "rw [inv_mul_cancel_right]"
}
] | [
246,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Basic.lean | closure_minimal | [] | [
428,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
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Mathlib/Topology/Algebra/Module/Multilinear.lean | ContinuousMultilinearMap.toMultilinearMap_smul | [] | [
175,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
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Mathlib/Algebra/Regular/Basic.lean | IsLeftRegular.subsingleton | [] | [
194,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
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Mathlib/Algebra/Group/Basic.lean | bit1_add' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.10550\nβ : Type ?u.10553\nG : Type ?u.10556\nM : Type u\ninst✝¹ : AddCommSemigroup M\ninst✝ : One M\na b : M\n⊢ bit1 (a + b) = bit1 a + bit0 b",
"tactic": "rw [add_comm, bit1_add, add_comm]"
}
] | [
142,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
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Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.nadd_zero | [
{
"state_after": "case h\na✝ b c a : Ordinal\nIH : ∀ (k : Ordinal), k < a → k ♯ 0 = k\n⊢ a ♯ 0 = a",
"state_before": "a b c : Ordinal\n⊢ a ♯ 0 = a",
"tactic": "induction' a using Ordinal.induction with a IH"
},
{
"state_after": "case h\na✝ b c a : Ordinal\nIH : ∀ (k : Ordinal), k < a → k ♯ 0 = k... | [
290,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
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Mathlib/Topology/Order/Basic.lean | eventually_lt_of_tendsto_lt | [] | [
362,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
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Mathlib/Algebra/GroupWithZero/Units/Basic.lean | Units.mul_left_eq_zero | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.430\nM₀ : Type u_1\nG₀ : Type ?u.436\nM₀' : Type ?u.439\nG₀' : Type ?u.442\nF : Type ?u.445\nF' : Type ?u.448\ninst✝ : MonoidWithZero M₀\nu : M₀ˣ\na : M₀\nh : a * ↑u = 0\n⊢ a = 0",
"tactic": "simpa using mul_eq_zero_of_left h ↑u⁻¹"
}
] | [
41,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Sheaves/Sheaf.lean | TopCat.Sheaf.comp_app | [] | [
168,
6
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166,
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Mathlib/Analysis/Convex/Topology.lean | Convex.openSegment_interior_self_subset_interior | [] | [
190,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
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Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.AECover.integral_tendsto_of_countably_generated | [
{
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494,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
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Mathlib/FieldTheory/IsAlgClosed/Basic.lean | IsAlgClosed.algebraMap_surjective_of_isAlgebraic | [] | [
170,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.denom_zero | [
{
"state_after": "no goals",
"state_before": "K : Type u\ninst✝ : Field K\n⊢ denom 0 = 1",
"tactic": "convert denom_div (0 : K[X]) one_ne_zero <;> simp"
}
] | [
1212,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1211,
1
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.card_support_eq_one | [
{
"state_after": "no goals",
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483,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
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Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | MeasureTheory.Measure.NullMeasurableSet.const_smul | [
{
"state_after": "case inl\nE : 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.1944452\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\ninst✝ : ... | [
382,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
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] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | iteratedFDerivWithin_congr | [] | [
907,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
905,
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Mathlib/Data/Set/Lattice.lean | Set.compl_iUnion | [] | [
491,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/LinearAlgebra/UnitaryGroup.lean | Matrix.UnitaryGroup.toGL_mul | [
{
"state_after": "n : Type u\ninst✝³ : DecidableEq n\ninst✝² : Fintype n\nα : Type v\ninst✝¹ : CommRing α\ninst✝ : StarRing α\nA✝ : Matrix n n α\nA B : { x // x ∈ unitaryGroup n α }\n⊢ comp (toLin' A) (toLin' B) = ↑(toGL A * toGL B)",
"state_before": "n : Type u\ninst✝³ : DecidableEq n\ninst✝² : Fintype n\n... | [
192,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.subtype_range | [
{
"state_after": "G : Type u_1\nG' : Type ?u.481704\ninst✝⁴ : Group G\ninst✝³ : Group G'\nA : Type ?u.481713\ninst✝² : AddGroup A\nN : Type ?u.481719\nP : Type ?u.481722\ninst✝¹ : Group N\ninst✝ : Group P\nK H : Subgroup G\n⊢ Subtype.val '' ↑⊤ = ↑H",
"state_before": "G : Type u_1\nG' : Type ?u.481704\ninst✝... | [
2680,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2677,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.count_apply_eq_top' | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.378090\nγ : Type ?u.378093\nδ : Type ?u.378096\nι : Type ?u.378099\nR : Type ?u.378102\nR' : Type ?u.378105\nm0 : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set α\ninst✝ : Measurable... | [
2246,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2242,
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Std/Data/Rat/Lemmas.lean | Rat.normalize_eq | [
{
"state_after": "no goals",
"state_before": "num : Int\nden : Nat\nden_nz : den ≠ 0\n⊢ normalize num den = mk' (num / ↑(Nat.gcd (Int.natAbs num) den)) (den / Nat.gcd (Int.natAbs num) den)",
"tactic": "simp only [normalize, maybeNormalize_eq,\n Int.div_eq_ediv_of_dvd (Int.ofNat_dvd_left.2 (Nat.gcd_dvd_... | [
26,
73
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/Algebra/Order/Kleene.lean | kstar_le_of_mul_le_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.37606\nι : Type ?u.37609\nπ : ι → Type ?u.37614\ninst✝ : KleeneAlgebra α\na b c : α\nhb : 1 ≤ b\n⊢ a * b ≤ b → a∗ ≤ b",
"tactic": "simpa using kstar_mul_le hb"
}
] | [
235,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_spanningSets_lt_top | [] | [
3478,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3476,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.prod_eq_two_power | [
{
"state_after": "ι : Type u\ninst✝ : Infinite ι\nc : ι → Cardinal\nh₁ : ∀ (i : ι), 2 ≤ c i\nh₂ : ∀ (i : ι), lift (c i) ≤ lift (#ι)\n⊢ (prod fun i => lift (c i)) = lift (2 ^ (#ι))",
"state_before": "ι : Type u\ninst✝ : Infinite ι\nc : ι → Cardinal\nh₁ : ∀ (i : ι), 2 ≤ c i\nh₂ : ∀ (i : ι), lift (c i) ≤ lift ... | [
944,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
935,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | continuous_inner | [] | [
2255,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2253,
1
] |
Mathlib/MeasureTheory/Measure/Stieltjes.lean | StieltjesFunction.length_empty | [
{
"state_after": "no goals",
"state_before": "f : StieltjesFunction\n⊢ (⨅ (_ : ∅ ⊆ Ioc 0 0), ofReal (↑f 0 - ↑f 0)) ≤ 0",
"tactic": "simp"
}
] | [
318,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Ring.lean | HasSum.div_const | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nκ : Type ?u.6715\nR : Type ?u.6718\nα : Type u_1\ninst✝² : DivisionSemiring α\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSemiring α\nf g : ι → α\na a₁ a₂ : α\nh : HasSum f a\nb : α\n⊢ HasSum (fun i => f i / b) (a / b)",
"tactic": "simp on... | [
85,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
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Mathlib/Data/Finset/Basic.lean | Finset.piecewise_coe | [
{
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"state_before": "α : Type u_1\nβ : Type ... | [
2461,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2458,
1
] |
Mathlib/GroupTheory/Nilpotent.lean | nilpotencyClass_eq_quotient_center_plus_one | [
{
"state_after": "G : Type u_1\ninst✝² : Group G\nH : Subgroup G\ninst✝¹ : Normal H\nhH : Group.IsNilpotent G\ninst✝ : Nontrivial G\n⊢ nilpotencyClass G = nilpotencyClass G - 1 + 1",
"state_before": "G : Type u_1\ninst✝² : Group G\nH : Subgroup G\ninst✝¹ : Normal H\nhH : Group.IsNilpotent G\ninst✝ : Nontriv... | [
651,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
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] |
Mathlib/MeasureTheory/Function/Jacobian.lean | MeasureTheory.map_withDensity_abs_det_fderiv_eq_addHaar | [
{
"state_after": "E : Type u_1\nF : Type ?u.847296\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : FiniteDimensional ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ns : Set E\nf : E → E\nf' : E → E →L[ℝ] E\ninst✝² : MeasurableSpace E\ninst✝¹ : BorelSpace E\nμ : Measure E\ninst✝ ... | [
1130,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1121,
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] |
Mathlib/Analysis/Complex/UnitDisc/Basic.lean | Complex.UnitDisc.coe_smul_circle | [] | [
142,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
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Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.type_eq_one_iff_unique | [] | [
259,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
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] |
Mathlib/Algebra/Hom/Freiman.lean | FreimanHom.comp_apply | [] | [
246,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Algebra/MonoidAlgebra/Grading.lean | AddMonoidAlgebra.grade.isInternal | [] | [
238,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.star_imI | [] | [
1096,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1096,
9
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.map_zpow | [] | [
1545,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1544,
11
] |
Mathlib/Algebra/RingQuot.lean | RingQuot.sub_quot | [
{
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264,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
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Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | BilinForm.toQuadraticForm_list_sum | [] | [
696,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
694,
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Mathlib/Data/Finset/Basic.lean | Finset.inter_right_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.182360\nγ : Type ?u.182363\ninst✝ : DecidableEq α\ns s₁✝ s₂✝ t t₁ t₂ u v : Finset α\na b : α\ns₁ s₂ s₃ : Finset α\nx✝ : α\n⊢ x✝ ∈ s₁ ∩ s₂ ∩ s₃ ↔ x✝ ∈ s₁ ∩ s₃ ∩ s₂",
"tactic": "simp only [mem_inter, and_right_comm]"
}
] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.coe_neg | [] | [
93,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
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Mathlib/Algebra/Category/GroupCat/EpiMono.lean | GroupCat.epi_iff_range_eq_top | [] | [
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71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Multiset/Basic.lean | Multiset.pmap_zero | [] | [
1484,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1482,
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.nhds_eq_comap_inf_principal | [
{
"state_after": "case intro\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.106516\nδ : Type ?u.106519\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ne : LocalHomeomorph α β\ne' : LocalHomeomorph β γ\nx : { x // x ∈ e.source }\n⊢ 𝓝 ↑x = comap (↑e) ... | [
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71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_rpow | [
{
"state_after": "a b : ℝ\nn : ℕ\nr : ℝ\nh : -1 < r ∨ r ≠ -1 ∧ ¬0 ∈ [[a, b]]\nh' : -1 < (↑r).re ∨ ↑r ≠ -1 ∧ ¬0 ∈ [[a, b]]\nthis : (∫ (x : ℝ) in a..b, ↑x ^ ↑r) = (↑b ^ (↑r + 1) - ↑a ^ (↑r + 1)) / (↑r + 1)\n⊢ (∫ (x : ℝ) in a..b, x ^ r) = (b ^ (r + 1) - a ^ (r + 1)) / (r + 1)",
"state_before": "a b : ℝ\nn : ℕ\... | [
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8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
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Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.coeFn_smul | [] | [
270,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Logic/Embedding/Basic.lean | Function.Embedding.mk_coe | [] | [
122,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ioo_subset_Iic_self | [] | [
447,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
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Mathlib/Data/Subtype.lean | Subtype.refl | [] | [
239,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
11
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Mathlib/Data/Set/Basic.lean | Set.subset_symmDiff_union_symmDiff_left | [] | [
2123,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2122,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.sin_periodic | [] | [
1141,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1140,
1
] |
Mathlib/Algebra/Group/Basic.lean | mul_eq_of_eq_div' | [
{
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"state_before": "α : Type ?u.67616\nβ : Type ?u.67619\nG : Type u_1\ninst✝ : CommGroup G\na b c d : G\nh : b = c / a\n⊢ a * b = c",
"tactic": "simp [h]"
},
{
... | [
927,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
925,
1
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Mathlib/Init/Logic.lean | not_or_of_not | [] | [
190,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.NullMeasurableSet.compl | [] | [
127,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.lift_comp_kernelIsoOfEq_hom | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁴ : Category C\ninst✝³ : HasZeroMorphisms C\nX Y : C\nf✝ : X ⟶ Y\ninst✝² : HasKernel f✝\nZ : C\nf g : X ⟶ Y\ninst✝¹ : HasKernel f\ninst✝ : HasKernel g\nh : f = g\ne : Z ⟶ X\nhe : e ≫ f = 0\n⊢ e ≫ g = 0",
"tactic": "simp [← h, he]"
},
{
... | [
372,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
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Mathlib/Algebra/Lie/Normalizer.lean | LieSubmodule.monotone_normalizer | [
{
"state_after": "R : Type u_2\nL : Type u_3\nM : Type u_1\nM' : Type ?u.16528\ninst✝¹⁰ : CommRing R\ninst✝⁹ : LieRing L\ninst✝⁸ : LieAlgebra R L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCommGroup M'\ninst✝² : Module R M'\ninst✝¹ : LieRingM... | [
81,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
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Mathlib/Algebra/BigOperators/Finprod.lean | MonoidHom.map_finprod_of_injective | [] | [
325,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
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Mathlib/Data/PEquiv.lean | PEquiv.symm_trans_self | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nf : α ≃. β\n⊢ PEquiv.symm (PEquiv.trans (PEquiv.symm f) f) = PEquiv.symm (ofSet {b | isSome (↑(PEquiv.symm f) b) = true})",
"tactic": "simp [symm_trans_rev, self_trans_symm, -symm_symm]"
}
] | [
285,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
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Mathlib/Computability/Halting.lean | Nat.Partrec.merge' | [
{
"state_after": "case intro\ng : ℕ →. ℕ\nhg : Partrec g\ncf : Code\nhf : Partrec (Code.eval cf)\n⊢ ∃ h,\n Partrec h ∧\n ∀ (a : ℕ), (∀ (x : ℕ), x ∈ h a → x ∈ Code.eval cf a ∨ x ∈ g a) ∧ ((h a).Dom ↔ (Code.eval cf a).Dom ∨ (g a).Dom)",
"state_before": "f g : ℕ →. ℕ\nhf : Partrec f\nhg : Partrec g\n⊢ ... | [
60,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
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Mathlib/Algebra/Quaternion.lean | Quaternion.smul_im | [] | [
1049,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1048,
8
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Mathlib/Data/Complex/Exponential.lean | Complex.ofReal_tan | [] | [
998,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
997,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | IsFractional.mul | [
{
"state_after": "case refine_1\nR : Type u_1\ninst✝² : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝¹ : CommRing P\ninst✝ : Algebra R P\nloc : IsLocalization S P\nI J : Submodule R P\naI : R\nhaI : aI ∈ S\nhI : ∀ (b : P), b ∈ I → IsInteger R (aI • b)\naJ : R\nhaJ : aJ ∈ S\nhJ : ∀ (b : P), b ∈ J → IsInteger ... | [
520,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
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Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.X.add_fst | [] | [
212,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
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Mathlib/Data/Fintype/Card.lean | Fintype.card_eq_one_iff_nonempty_unique | [] | [
530,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
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Mathlib/Analysis/Convex/Basic.lean | Convex.is_linear_preimage | [] | [
209,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Data/Matrix/Kronecker.lean | Matrix.kroneckerTMul_smul | [] | [
494,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
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Mathlib/NumberTheory/Fermat4.lean | Int.coprime_of_sq_sum | [
{
"state_after": "r s : ℤ\nh2 : IsCoprime s r\n⊢ IsCoprime (r * r + s * s) r",
"state_before": "r s : ℤ\nh2 : IsCoprime s r\n⊢ IsCoprime (r ^ 2 + s ^ 2) r",
"tactic": "rw [sq, sq]"
},
{
"state_after": "no goals",
"state_before": "r s : ℤ\nh2 : IsCoprime s r\n⊢ IsCoprime (r * r + s * s) r",
... | [
161,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
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Mathlib/Order/Synonym.lean | toLex_symm_eq | [] | [
178,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Data/Finset/Sort.lean | Finset.orderEmbOfFin_eq_orderEmbOfFin_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.57513\ninst✝ : LinearOrder α\ns : Finset α\ni j : Fin (card s)\n⊢ ↑(orderEmbOfFin s (_ : card s = card s)) i = ↑(orderEmbOfFin s (_ : card s = card s)) j ↔ ↑i = ↑j",
"state_before": "α : Type u_1\nβ : Type ?u.57513\ninst✝ : LinearOrder α\nk l : ℕ\ns : Finset α\ni ... | [
241,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Topology/Basic.lean | Filter.EventuallyLE.eventuallyLE_nhds | [] | [
1012,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1010,
1
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Mathlib/Order/CompleteLattice.lean | OrderIso.map_sSup | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nβ₂ : Type ?u.81152\nγ : Type ?u.81155\nι : Sort ?u.81158\nι' : Sort ?u.81161\nκ : ι → Sort ?u.81166\nκ' : ι' → Sort ?u.81171\ninst✝¹ : CompleteLattice α\nf✝ g s✝ t : ι → α\na b : α\ninst✝ : CompleteLattice β\nf : α ≃o β\ns : Set α\n⊢ ... | [
978,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
976,
1
] |
Mathlib/Combinatorics/SimpleGraph/Density.lean | SimpleGraph.edgeDensity_le_one | [] | [
407,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.map_ofDual_min | [
{
"state_after": "F : Type ?u.346509\nα : Type u_1\nβ : Type ?u.346515\nγ : Type ?u.346518\nι : Type ?u.346521\nκ : Type ?u.346524\ninst✝ : LinearOrder α\ns✝ : Finset α\nH : Finset.Nonempty s✝\nx : α\ns : Finset αᵒᵈ\n⊢ WithTop.map (↑ofDual) (Finset.min s) = sup s (WithBot.some ∘ ↑ofDual)",
"state_before": "... | [
1411,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1409,
1
] |
Mathlib/Data/Real/Irrational.lean | irrational_nrt_of_notint_nrt | [
{
"state_after": "case intro.mk'\nn : ℕ\nm : ℤ\nhnpos : 0 < n\nN : ℤ\nD : ℕ\nP : D ≠ 0\nC : Nat.coprime (Int.natAbs N) D\nhxr : ↑(mk' N D) ^ n = ↑m\nhv : ¬∃ y, ↑(mk' N D) = ↑y\n⊢ False",
"state_before": "x : ℝ\nn : ℕ\nm : ℤ\nhxr : x ^ n = ↑m\nhv : ¬∃ y, x = ↑y\nhnpos : 0 < n\n⊢ Irrational x",
"tactic": ... | [
68,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/CategoryTheory/Adjunction/Reflective.lean | CategoryTheory.mem_essImage_of_unit_isSplitMono | [
{
"state_after": "C : Type u₁\nD : Type u₂\nE : Type u₃\ninst✝⁴ : Category C\ninst✝³ : Category D\ninst✝² : Category E\ni : D ⥤ C\ninst✝¹ : Reflective i\nA : C\ninst✝ : IsSplitMono ((ofRightAdjoint i).unit.app A)\nη : 𝟭 C ⟶ leftAdjoint i ⋙ i := (ofRightAdjoint i).unit\n⊢ A ∈ Functor.essImage i",
"state_bef... | [
105,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.sigmaCongrRight_one | [] | [
255,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Order/BooleanAlgebra.lean | disjoint_sdiff_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.40724\nw x y z : α\ninst✝ : GeneralizedBooleanAlgebra α\n⊢ Disjoint (x \\ z) y ↔ Disjoint x (y \\ z)",
"tactic": "simp_rw [disjoint_iff, inf_sdiff_right_comm, inf_sdiff_assoc]"
}
] | [
462,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.exists_measurable_superset_iff_measure_eq_zero | [] | [
233,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Data/Sign.lean | sign_apply | [] | [
316,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/Topology/CompactOpen.lean | ContinuousMap.isOpen_gen | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.2117\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\ns : Set α\nhs : IsCompact s\nu : Set β\nhu : IsOpen u\n⊢ ∃ s_1 x u_1 x, CompactOpen.gen s u = CompactOpen.gen s_1 u_1",
"state_before": "α : Type u_1\nβ : Typ... | [
92,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
11
] |
Mathlib/Algebra/Order/Sub/Canonical.lean | AddLECancellable.lt_tsub_iff_right_of_le | [
{
"state_after": "α : Type u_1\ninst✝⁵ : AddCommSemigroup α\ninst✝⁴ : PartialOrder α\ninst✝³ : ExistsAddOfLE α\ninst✝² : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\na b c d : α\nhc : AddLECancellable c\nh : c ≤ b\nh' : a < b - c\n⊢ a + c ≠ b",
"state... | [
146,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
11
] |
Mathlib/Topology/List.lean | Vector.tendsto_cons | [
{
"state_after": "α : Type u_1\nβ : Type ?u.64741\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nn : ℕ\na : α\nl : Vector α n\n⊢ Tendsto (fun x => ↑(x.fst ::ᵥ x.snd)) (𝓝 a ×ˢ 𝓝 l) (𝓝 (a :: ↑l))",
"state_before": "α : Type u_1\nβ : Type ?u.64741\ninst✝¹ : TopologicalSpace α\ninst✝ : Topological... | [
195,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Data/Erased.lean | Erased.map_def | [] | [
156,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Std/Data/Array/Lemmas.lean | Array.get?_swap | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na : Array α\ni j : Fin (size a)\nk : Nat\n⊢ (swap a i j)[k]? = if j.val = k then some a[i.val] else if i.val = k then some a[j.val] else a[k]?",
"tactic": "simp [swap_def, get?_set, ← getElem_fin_eq_data_get]"
}
] | [
124,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
122,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.Iso.coe_comp | [] | [
2023,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2022,
1
] |
Mathlib/RingTheory/Valuation/ValuationRing.lean | ValuationRing.iff_isInteger_or_isInteger | [
{
"state_after": "case mp\nR : Type u_1\ninst✝⁴ : CommRing R\ninst✝³ : IsDomain R\nK : Type u_2\ninst✝² : Field K\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\n⊢ ValuationRing R → ∀ (x : K), IsLocalization.IsInteger R x ∨ IsLocalization.IsInteger R x⁻¹\n\ncase mpr\nR : Type u_1\ninst✝⁴ : CommRing R\ninst✝³... | [
338,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.completeGraph_eq_top | [] | [
391,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.length_bind | [] | [
830,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
827,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.orderIsoUnitIntervalBirational_apply_coe | [] | [
1815,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1813,
1
] |
Mathlib/Tactic/NormNum/NatFib.lean | Mathlib.Meta.NormNum.isFibAux_one | [] | [
28,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
27,
1
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.HasIntegral.add | [
{
"state_after": "no goals",
"state_before": "ι : Type u\nE : Type v\nF : Type w\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\nI J : Box ι\nπ : TaggedPrepartition I\ninst✝ : Fintype ι\nl : IntegrationParams\nf g : (ι → ℝ) → E\nvol : ι →ᵇᵃ[... | [
266,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
8
] |
Mathlib/Data/Set/Lattice.lean | Set.sInter_diff_singleton_univ | [] | [
1155,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1154,
1
] |
Mathlib/CategoryTheory/Monad/Basic.lean | CategoryTheory.Monad.assoc | [] | [
145,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Topology/ShrinkingLemma.lean | ShrinkingLemma.PartialRefinement.find_mem | [
{
"state_after": "ι : Type u_2\nX : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : NormalSpace X\nu : ι → Set X\ns : Set X\nc : Set (PartialRefinement u s)\ni : ι\nne : Set.Nonempty c\n⊢ (if hi : ∃ v, v ∈ c ∧ i ∈ v.carrier then Exists.choose hi else Set.Nonempty.some ne) ∈ c",
"state_before": "ι : Type u_2\... | [
124,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Order/RelClasses.lean | IsAntisymm.swap | [] | [
84,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Summable.vanishing | [
{
"state_after": "α : Type u_2\nβ : Type ?u.773378\nγ : Type ?u.773381\nδ : Type ?u.773384\nG : Type u_1\ninst✝² : TopologicalSpace G\ninst✝¹ : AddCommGroup G\ninst✝ : TopologicalAddGroup G\nf : α → G\nhf : Summable f\ne : Set G\nhe : e ∈ 𝓝 0\nthis : UniformSpace G := TopologicalAddGroup.toUniformSpace G\n⊢ ∃ ... | [
1255,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1250,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | MvPolynomial.isNoetherianRing_fin | [] | [
1073,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1067,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Hom.range_comp_le_range | [] | [
856,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
855,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.ofReal_set_integral_one | [] | [
204,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.isConj_of_cycleType_eq | [
{
"state_after": "case base_one\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nτ : Perm α\nh : τ = 1\n⊢ IsConj 1 τ",
"state_before": "case base_one\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nτ : Perm α\nh : cycleType 1 = cycleType τ\n⊢ IsConj 1 τ",
"tactic": "rw [cycleType_one,... | [
266,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Data/Set/Function.lean | Set.MapsTo.union_union | [] | [
467,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
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