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/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.continuousWithinAt_arg_of_re_neg_of_im_zero | [
{
"state_after": "x z✝ z : ℂ\nhre : z.re < 0\nhim : z.im = 0\nthis : arg =ᶠ[𝓝[{z | 0 ≤ z.im}] z] fun x => arcsin ((-x).im / ↑abs x) + π\n⊢ ContinuousWithinAt arg {z | 0 ≤ z.im} z",
"state_before": "x z✝ z : ℂ\nhre : z.re < 0\nhim : z.im = 0\n⊢ ContinuousWithinAt arg {z | 0 ≤ z.im} z",
"tactic": "have :... | [
596,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
581,
1
] |
Mathlib/Order/Cover.lean | Prod.mk_wcovby_mk_iff_left | [
{
"state_after": "α : Type u_2\nβ : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : PartialOrder β\na a₁ a₂ : α\nb b₁ b₂ : β\nx y : α × β\nh : ∀ ⦃c : α⦄, a₁ < c → ¬c < a₂\nc : α × β\nh₁ : (a₁, b) < c\nh₂ : c < (a₂, b)\n⊢ False",
"state_before": "α : Type u_2\nβ : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : Partia... | [
521,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
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Mathlib/Combinatorics/Derangements/Finite.lean | card_derangements_fin_eq_numDerangements | [
{
"state_after": "case h\nα : Type ?u.13112\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nn : ℕ\nhyp : ∀ (m : ℕ), m < n → card ↑(derangements (Fin m)) = numDerangements m\n⊢ card ↑(derangements (Fin n)) = numDerangements n",
"state_before": "α : Type ?u.13112\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nn : ℕ\... | [
110,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.smul_mem | [] | [
238,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.isBigO_comp | [] | [
676,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
1
] |
Mathlib/Topology/Basic.lean | IsOpen.sdiff | [] | [
240,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Data/Set/Sups.lean | lowerClosure_infs | [
{
"state_after": "case a.h\nα : Type u_1\ninst✝ : SemilatticeInf α\ns t : Set α\na : α\n⊢ a ∈ ↑(lowerClosure (s ⊼ t)) ↔ a ∈ ↑(lowerClosure s ⊓ lowerClosure t)",
"state_before": "α : Type u_1\ninst✝ : SemilatticeInf α\ns t : Set α\n⊢ lowerClosure (s ⊼ t) = lowerClosure s ⊓ lowerClosure t",
"tactic": "ext... | [
422,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.mul_div_le_mul_div_assoc | [
{
"state_after": "no goals",
"state_before": "m n k a b c : ℕ\nhc0 : c = 0\n⊢ a * (b / c) ≤ a * b / c",
"tactic": "simp [hc0]"
},
{
"state_after": "m n k a b c : ℕ\nhc0 : ¬c = 0\n⊢ a * (b / c * c) ≤ a * b",
"state_before": "m n k a b c : ℕ\nhc0 : ¬c = 0\n⊢ a * (b / c) * c ≤ a * b",
"tact... | [
650,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
646,
1
] |
Mathlib/Topology/Bases.lean | isTopologicalBasis_iInf | [
{
"state_after": "β : Type u_1\nι : Type u_2\nX : ι → Type u_3\nt : (i : ι) → TopologicalSpace (X i)\nT : (i : ι) → Set (Set (X i))\ncond : ∀ (i : ι), IsTopologicalBasis (T i)\nf : (i : ι) → β → X i\nthis : TopologicalSpace β := ⨅ (i : ι), induced (f i) (t i)\n⊢ IsTopologicalBasis {S | ∃ U F, (∀ (i : ι), i ∈ F ... | [
487,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/Topology/Order/Basic.lean | tendsto_Ioi_atBot | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na b : α\ns : Set α\nl : Filter β\nf✝ : α → β\nf : β → ↑(Ioi a)\n⊢ Tendsto (Subtype.val ∘ f) l (𝓝[Ioi a] a) ↔ Tendsto (fun x => ↑(f x)) l (𝓝[Ioi a] a)",... | [
2572,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2570,
1
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Mathlib/Data/Setoid/Basic.lean | Setoid.comap_rel | [] | [
398,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/Analysis/Convex/Function.lean | StrictConvexOn.add_convexOn | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.276818\nα : Type ?u.276821\nβ : Type u_3\nι : Type ?u.276827\ninst✝⁵ : OrderedSemiring 𝕜\ninst✝⁴ : AddCommMonoid E\ninst✝³ : AddCommMonoid F\ninst✝² : OrderedCancelAddCommMonoid β\ninst✝¹ : SMul 𝕜 E\ninst✝ : DistribMulA... | [
508,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
1
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Mathlib/Algebra/Hom/Units.lean | IsUnit.eq_on_inv | [] | [
54,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Topology/MetricSpace/IsometricSMul.lean | Metric.preimage_mul_right_closedBall | [
{
"state_after": "M : Type u\nG : Type v\nX : Type w\ninst✝⁵ : PseudoMetricSpace X\ninst✝⁴ : Group G\ninst✝³ : MulAction G X\ninst✝² : IsometricSMul G X\ninst✝¹ : PseudoMetricSpace G\ninst✝ : IsometricSMul Gᵐᵒᵖ G\na b : G\nr : ℝ\n⊢ (fun x => x * a) ⁻¹' closedBall b r = closedBall (b * a⁻¹) r",
"state_before... | [
494,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.biUnion_iUnion | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.169471\nι : Sort u_3\nι' : Sort ?u.169477\nι₂ : Sort ?u.169480\nκ : ι → Sort ?u.169485\nκ₁ : ι → Sort ?u.169490\nκ₂ : ι → Sort ?u.169495\nκ' : ι' → Sort ?u.169500\ns : ι → Set α\nt : α → Set β\n⊢ (⋃ (x : α) (_ : x ∈ ⋃ (i :... | [
1360,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1359,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | CategoryTheory.Limits.IsInitial.to_comp | [] | [
164,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Dynamics/Ergodic/Ergodic.lean | MeasureTheory.MeasurePreserving.preErgodic_conjugate_iff | [
{
"state_after": "case refine'_1\nα : Type u_1\nm : MeasurableSpace α\nf : α → α\ns : Set α\nμ : Measure α\nβ : Type u_2\nm' : MeasurableSpace β\nμ' : Measure β\ns' : Set β\ng : α → β\ne : α ≃ᵐ β\nh : MeasurePreserving ↑e\nhf : PreErgodic (↑e ∘ f ∘ ↑(MeasurableEquiv.symm e))\n⊢ ↑(MeasurableEquiv.symm e) ∘ ↑e ∘ ... | [
105,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | HomologicalComplex.Hom.sqFrom_comp | [] | [
579,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
577,
1
] |
Mathlib/Logic/IsEmpty.lean | isEmpty_Prop | [
{
"state_after": "no goals",
"state_before": "α : Sort ?u.2122\nβ : Sort ?u.2125\nγ : Sort ?u.2128\np : Prop\n⊢ IsEmpty p ↔ ¬p",
"tactic": "simp only [← not_nonempty_iff, nonempty_Prop]"
}
] | [
146,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/FieldTheory/Minpoly/Basic.lean | minpoly.mem_range_of_degree_eq_one | [
{
"state_after": "A : Type u_1\nB : Type u_2\nB' : Type ?u.31272\ninst✝⁴ : CommRing A\ninst✝³ : Ring B\ninst✝² : Ring B'\ninst✝¹ : Algebra A B\ninst✝ : Algebra A B'\nx : B\nhx : degree (minpoly A x) = 1\nh : IsIntegral A x\n⊢ x ∈ RingHom.range (algebraMap A B)",
"state_before": "A : Type u_1\nB : Type u_2\n... | [
127,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.pred_add_one | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\ni : Fin (n + 2)\nh : ↑i < n + 1\n⊢ 0 < i + 1",
"tactic": "exact\n(add_one_pos _ (lt_iff_val_lt_val.2 h))"
},
{
"state_after": "n m : ℕ\ni : Fin (n + 2)\nh : ↑i < n + 1\n⊢ ↑i + 1 < n + 1 + 1",
"state_before": "n m : ℕ\ni : Fin (n + 2)\nh ... | [
1568,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1564,
1
] |
Std/Logic.lean | exists_eq_right | [
{
"state_after": "no goals",
"state_before": "α : Sort u_1\np q : α → Prop\nb : Prop\na' : α\n⊢ ∀ (a : α), p a ∧ a = a' ↔ a = a' ∧ p a",
"tactic": "exact fun a => And.comm"
}
] | [
460,
68
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
459,
9
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.le_nfp | [] | [
444,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
1
] |
Mathlib/Order/Disjoint.lean | Disjoint.left_le_of_le_sup_right | [] | [
205,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | subset_comp_self | [] | [
198,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Std/Data/BinomialHeap.lean | Std.BinomialHeapImp.HeapNode.WellFormed.toHeap | [
{
"state_after": "α : Type u_1\nle : α → α → Bool\na : α\nn : Nat\ns : HeapNode α\nh : WellFormed le a s n\n⊢ Heap.WellFormed le 0 (HeapNode.toHeap.go s (rank s) Heap.nil)",
"state_before": "α : Type u_1\nle : α → α → Bool\na : α\nn : Nat\ns : HeapNode α\nh : WellFormed le a s n\n⊢ Heap.WellFormed le 0 (Hea... | [
456,
75
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
447,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.support_subset_singleton | [] | [
494,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiffWithinAt.congr_of_eventually_eq' | [] | [
465,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasAntitoneBasis.mem | [] | [
1057,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1055,
11
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.ofRealAm_coe | [] | [
989,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
988,
1
] |
Mathlib/Algebra/MonoidAlgebra/Degree.lean | AddMonoidAlgebra.sup_support_mul_le | [
{
"state_after": "R : Type u_3\nA : Type u_2\nT : Type ?u.14182\nB : Type u_1\nι : Type ?u.14188\ninst✝¹¹ : SemilatticeSup B\ninst✝¹⁰ : OrderBot B\ninst✝⁹ : SemilatticeInf T\ninst✝⁸ : OrderTop T\ninst✝⁷ : Semiring R\ninst✝⁶ : Add A\ninst✝⁵ : Add B\ninst✝⁴ : Add T\ninst✝³ : CovariantClass B B (fun x x_1 => x + x... | [
74,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.IsFundamentalDomain.preimage_of_equiv | [
{
"state_after": "no goals",
"state_before": "G : Type u_2\nH : Type u_4\nα : Type u_3\nβ : Type u_1\nE : Type ?u.43941\ninst✝⁶ : Group G\ninst✝⁵ : Group H\ninst✝⁴ : MulAction G α\ninst✝³ : MeasurableSpace α\ninst✝² : MulAction H β\ninst✝¹ : MeasurableSpace β\ninst✝ : NormedAddCommGroup E\ns t : Set α\nμ : ... | [
161,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Topology/Basic.lean | DenseRange.mem_nhds | [] | [
1874,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1871,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.cos_eq_zero_iff_angle_eq_pi_div_two | [
{
"state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\n⊢ cos (angle x y) = cos (π / 2) ↔ angle x y = π / 2",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\n⊢ cos (angle x y) = 0 ↔ angle x y = π / 2",
"... | [
355,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.monic_of_b_eq_one' | [] | [
259,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Std/Data/List/Lemmas.lean | List.range_succ_eq_map | [
{
"state_after": "n : Nat\n⊢ 0 :: map (fun x => 1 + x) (range' 0 n) = 0 :: map succ (range' 0 n)",
"state_before": "n : Nat\n⊢ range (n + 1) = 0 :: map succ (range n)",
"tactic": "rw [range_eq_range', range_eq_range', range', Nat.add_comm, ← map_add_range']"
},
{
"state_after": "case e_tail.e_f\... | [
1895,
30
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1893,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.add_im | [] | [
200,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/SetTheory/Ordinal/NaturalOps.lean | NatOrdinal.toOrdinal_eq_zero | [] | [
115,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.isClopen_setOf_rel | [
{
"state_after": "α : Type ?u.6073\nX : Type u_1\nY : Type ?u.6079\nZ : Type ?u.6082\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\nS : DiscreteQuotient X\nx : X\n⊢ IsClopen (proj S ⁻¹' {proj S x})",
"state_before": "α : Type ?u.6073\nX : Type u_1\nY : Type ?u.6079\nZ... | [
155,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Matrix.lean | AffineBasis.toMatrix_mul_toMatrix | [
{
"state_after": "case a.h\nι : Type u₁\nk : Type u₂\nV : Type u₃\nP : Type u₄\ninst✝⁶ : AddCommGroup V\ninst✝⁵ : AffineSpace V P\ninst✝⁴ : Ring k\ninst✝³ : Module k V\nb : AffineBasis ι k P\nι' : Type ?u.67411\ninst✝² : Fintype ι'\ninst✝¹ : Fintype ι\nb₂ : AffineBasis ι k P\ninst✝ : DecidableEq ι\nl m : ι\n⊢ (... | [
126,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Algebra/Order/WithZero.lean | le_zero_iff | [] | [
104,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.lift_def | [] | [
907,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
906,
1
] |
Mathlib/MeasureTheory/Function/Jacobian.lean | MeasureTheory.restrict_map_withDensity_abs_det_fderiv_eq_addHaar | [
{
"state_after": "case intro.intro\nE : Type u_1\nF : Type ?u.850332\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 :... | [
1163,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1140,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.coe_iSup_of_directed | [
{
"state_after": "no goals",
"state_before": "G : Type u_2\nG' : Type ?u.226690\ninst✝³ : Group G\ninst✝² : Group G'\nA : Type ?u.226699\ninst✝¹ : AddGroup A\nH K : Subgroup G\nk : Set G\nι : Sort u_1\ninst✝ : Nonempty ι\nS : ι → Subgroup G\nhS : Directed (fun x x_1 => x ≤ x_1) S\nx : G\n⊢ x ∈ ↑(⨆ (i : ι), ... | [
1335,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1333,
1
] |
Mathlib/Data/Set/Function.lean | Set.restrict_apply | [] | [
59,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | IsBoundedBilinearMap.isBigO_comp | [] | [
377,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
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Mathlib/LinearAlgebra/FiniteDimensional.lean | FiniteDimensional.finiteDimensional_of_finrank_eq_succ | [
{
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210,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_mul_le | [
{
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1034,
55
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1029,
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Mathlib/Geometry/Euclidean/Sphere/Basic.lean | EuclideanGeometry.dist_of_mem_subset_sphere | [] | [
112,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
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Mathlib/Order/SuccPred/IntervalSucc.lean | Monotone.pairwise_disjoint_on_Ico_pred | [] | [
89,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | Set.Countable.measure_zero | [
{
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3305,
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Mathlib/Data/Finset/Lattice.lean | Finset.sup_product_right | [
{
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183,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
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Mathlib/Algebra/Homology/Additive.lean | HomologicalComplex.add_f_apply | [] | [
74,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasFDerivAt.csin | [] | [
379,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
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Mathlib/Algebra/Lie/Quotient.lean | LieSubmodule.Quotient.map_mk'_eq_bot_le | [
{
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207,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.indicator | [] | [
1506,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1504,
11
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Mathlib/Analysis/Calculus/BumpFunctionInner.lean | ContDiffBump.normed_sub | [
{
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505,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
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Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.mem_centralizer_iff | [] | [
772,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
770,
1
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src/lean/Init/Classical.lean | Classical.propComplete | [] | [
116,
86
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
113,
1
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Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.Completion.ofRat_sub | [] | [
185,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
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Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPullback.cone_fst | [] | [
211,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
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Mathlib/Computability/RegularExpressions.lean | RegularExpression.matches'_star | [] | [
156,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
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Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.coe_symm_mk | [] | [
195,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
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Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | Seminorm.isBounded_const | [
{
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234,
38
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231,
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Mathlib/Order/Concept.lean | intentClosure_anti | [] | [
160,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
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Std/Data/Fin/Lemmas.lean | USize.zero_toNat | [] | [
28,
69
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
28,
9
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Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.nadd_lt_nadd_left | [] | [
227,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
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Mathlib/SetTheory/Cardinal/Continuum.lean | Cardinal.aleph0_add_continuum | [] | [
127,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
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Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.Multiequalizer.hom_ext | [
{
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809,
93
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803,
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Mathlib/RingTheory/Subring/Basic.lean | Subring.sub_mem | [] | [
368,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
11
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Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableEquiv.toEquiv_injective | [
{
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1171,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1169,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.tan_pi_div_two_sub | [
{
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}
] | [
1023,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1022,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_eq_of_ae_subset_of_measure_ge | [
{
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316,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
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Mathlib/Algebra/GroupPower/Ring.lean | sq_eq_zero_iff | [] | [
96,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
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Mathlib/Algebra/PUnitInstances.lean | PUnit.norm_unit_eq | [] | [
112,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
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Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.map_toSubalgebra | [] | [
229,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/GroupTheory/Subsemigroup/Basic.lean | Subsemigroup.coe_copy | [] | [
156,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.inter_val | [] | [
1566,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1565,
1
] |
Mathlib/Data/Real/Pi/Wallis.lean | Real.Wallis.W_pos | [
{
"state_after": "case zero\n\n⊢ 0 < W Nat.zero\n\ncase succ\nk : ℕ\nhk : 0 < W k\n⊢ 0 < W (Nat.succ k)",
"state_before": "k : ℕ\n⊢ 0 < W k",
"tactic": "induction' k with k hk"
},
{
"state_after": "case zero\n\n⊢ 0 < ∏ i in range Nat.zero, (2 * ↑i + 2) / (2 * ↑i + 1) * ((2 * ↑i + 2) / (2 * ↑i + ... | [
64,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
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Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.le_basis_iff | [
{
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467,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
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Mathlib/Data/Fintype/Card.lean | Finite.exists_univ_list | [
{
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451,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
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Mathlib/Analysis/Calculus/Deriv/Basic.lean | hasDerivAt_deriv_iff | [] | [
438,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Mathlib/Topology/Filter.lean | Filter.specializes_iff_le | [
{
"state_after": "no goals",
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"tactic": "simp only [specializes_iff_closure_subset, Filter.closure_singleton, Ici_subset_Ici]"
}
] | [
181,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.isRefl_zero | [] | [
887,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
887,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | IsGδ.measurableSet | [
{
"state_after": "case intro.intro.intro\nα : Type u_1\nβ : Type ?u.147561\nγ : Type ?u.147564\nγ₂ : Type ?u.147567\nδ : Type ?u.147570\nι : Sort y\nt u : Set α\ninst✝¹² : TopologicalSpace α\ninst✝¹¹ : MeasurableSpace α\ninst✝¹⁰ : OpensMeasurableSpace α\ninst✝⁹ : TopologicalSpace β\ninst✝⁸ : MeasurableSpace β\n... | [
316,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
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src/lean/Init/Data/Nat/Basic.lean | Nat.zero_eq | [] | [
83,
46
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
83,
9
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Mathlib/Topology/Order.lean | coinduced_iSup | [] | [
460,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.coe_eq_pi | [] | [
124,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Algebra/Order/Interval.lean | NonemptyInterval.coe_pow_interval | [] | [
311,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Analysis/Convex/Extreme.lean | IsExtreme.extremePoints_eq | [] | [
180,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_of_empty | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.263261\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf g : α → β\ninst✝¹ : CommMonoid β\ninst✝ : IsEmpty α\ns : Finset α\n⊢ ∏ i in s, f i = 1",
"tactic": "rw [eq_empty_of_isEmpty s, prod_empty]"
}
] | [
308,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Analysis/InnerProductSpace/Calculus.lean | ContDiffWithinAt.norm_sq | [] | [
168,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/LinearAlgebra/FreeModule/Finite/Rank.lean | Submodule.finrank_le_finrank_of_le | [] | [
228,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgHom.id_comp | [] | [
465,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Path.cons_isCycle | [
{
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"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V\np : Path G v u\nh : Adj G u v\nhe : ¬Quotient.mk (Sym2.Rel.setoid V) (u, v) ∈ Walk.edges ↑p\n⊢ Walk.IsCycle (Walk.cons h ↑p)",
"tactic": "simp [Wal... | [
1336,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1334,
1
] |
Mathlib/Data/Real/Sqrt.lean | Real.sqrt_lt_sqrt_iff_of_pos | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\nhy : 0 < y\n⊢ sqrt x < sqrt y ↔ x < y",
"tactic": "rw [sqrt, sqrt, NNReal.coe_lt_coe, NNReal.sqrt_lt_sqrt_iff, toNNReal_lt_toNNReal_iff hy]"
}
] | [
272,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iio_diff_Iio | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.63600\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\n⊢ Iio b \\ Iio a = Ico a b",
"tactic": "rw [diff_eq, compl_Iio, inter_comm, Ici_inter_Iio]"
}
] | [
1112,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1111,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.insert_eq_cons | [] | [
133,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Std/Data/AssocList.lean | List.toAssocList_toList | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nl : List (α × β)\n⊢ toList (List.toAssocList l) = l",
"tactic": "induction l <;> simp [*]"
}
] | [
235,
27
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
234,
9
] |
Mathlib/Data/List/Range.lean | List.pairwise_lt_range | [
{
"state_after": "no goals",
"state_before": "α : Type u\nn : ℕ\n⊢ Pairwise (fun x x_1 => x < x_1) (range n)",
"tactic": "simp only [range_eq_range', pairwise_lt_range']"
}
] | [
78,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
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