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/Module/Basic.lean | inv_nat_cast_smul_eq | [] | [
515,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.cast_ceil_eq_int_ceil | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.311143\nα : Type u_1\nβ : Type ?u.311149\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\na : α\nha : 0 ≤ a\n⊢ ↑⌈a⌉₊ = ⌈a⌉",
"tactic": "rw [← Int.ceil_toNat, Int.toNat_of_nonneg (Int.ceil_nonneg ha)]"
}
] | [
1611,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1610,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_diff_add_mk | [
{
"state_after": "α β : Type u\nS T : Set α\nh : T ⊆ S\n⊢ Disjoint (S \\ T) T",
"state_before": "α β : Type u\nS T : Set α\nh : T ⊆ S\n⊢ (#↑(S \\ T)) + (#↑T) = (#↑S)",
"tactic": "refine (mk_union_of_disjoint <| ?_).symm.trans <| by rw [diff_union_of_subset h]"
},
{
"state_after": "no goals",
... | [
2131,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2129,
1
] |
Std/Data/HashMap/WF.lean | Std.HashMap.Imp.reinsertAux_size | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝ : Hashable α\ndata : Bucket α β\na : α\nb : β\n⊢ Nat.sum\n (List.map (fun x => List.length (AssocList.toList x))\n (Bucket.update data (mkIdx (_ : 0 < Array.size data.val) (UInt64.toUSize (hash a))).val\n (AssocList.cons a b\n ... | [
68,
31
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
64,
1
] |
Mathlib/CategoryTheory/Arrow.lean | CategoryTheory.Arrow.hom.congr_right | [
{
"state_after": "no goals",
"state_before": "T : Type u\ninst✝ : Category T\nf g : Arrow T\nφ₁ φ₂ : f ⟶ g\nh : φ₁ = φ₂\n⊢ φ₁.right = φ₂.right",
"tactic": "rw [h]"
}
] | [
171,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Data/Real/Sqrt.lean | Real.sqrt_le_iff | [
{
"state_after": "x y : ℝ\n⊢ 0 ≤ y → (sqrt x ≤ y ↔ x ≤ y ^ 2)",
"state_before": "x y : ℝ\n⊢ sqrt x ≤ y ↔ 0 ≤ y ∧ x ≤ y ^ 2",
"tactic": "rw [← and_iff_right_of_imp fun h => (sqrt_nonneg x).trans h, and_congr_right_iff]"
},
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ 0 ≤ y → (sqrt... | [
291,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/GroupTheory/Congruence.lean | Con.ker_rel | [] | [
826,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
825,
1
] |
Mathlib/Topology/Semicontinuous.lean | ContinuousAt.comp_lowerSemicontinuousWithinAt_antitone | [] | [
347,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
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Mathlib/CategoryTheory/Monoidal/Opposite.lean | CategoryTheory.mop_unmop | [] | [
120,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.toList_ofList | [
{
"state_after": "case cons\nα : Type u\nβ : Type v\nγ : Type w\na : α\nl : List α\nIH : l ∈ toList ↑l\n⊢ a :: l ∈ Computation.think (List.cons a <$> toList ↑l)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nl : List α\n⊢ l ∈ toList ↑l",
"tactic": "induction' l with a l IH <;> simp [ret_mem]"
... | [
1344,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1343,
1
] |
Mathlib/Init/Logic.lean | right_comm | [] | [
543,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.Equiv.isEmpty | [] | [
1138,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1137,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.lintegral_eq_zero_iff | [] | [
864,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
863,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.erase_cons_head | [] | [
1014,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1013,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | HasFDerivAt.smul | [] | [
194,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.MulticospanIndex.multicospan_obj_right | [] | [
203,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Topology/FiberBundle/Basic.lean | FiberBundle.quotientMap_proj | [] | [
270,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSet.sUnion | [
{
"state_after": "α : Type u_1\nβ : Type ?u.6742\nγ : Type ?u.6745\nδ : Type ?u.6748\nδ' : Type ?u.6751\nι : Sort ?u.6754\ns✝ t u : Set α\nm : MeasurableSpace α\ns : Set (Set α)\nhs : Set.Countable s\nh : ∀ (t : Set α), t ∈ s → MeasurableSet t\n⊢ MeasurableSet (⋃ (i : Set α) (_ : i ∈ s), i)",
"state_before"... | [
153,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
11
] |
Mathlib/Order/Basic.lean | Function.const_lt_const | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.73668\nα : Type u\nβ : Type v\nγ : Type w\nπ : ι → Type ?u.73679\nr : α → α → Prop\ninst✝¹ : Preorder α\ninst✝ : Nonempty β\na b : α\n⊢ const β a < const β b ↔ a < b",
"tactic": "simpa [Pi.lt_def] using le_of_lt"
}
] | [
927,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
927,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.isCycle_cycleOf_iff | [
{
"state_after": "ι : Type ?u.2582968\nα : Type u_1\nβ : Type ?u.2582974\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf✝ g : Perm α\nx y : α\nf : Perm α\nhx : IsCycle (cycleOf f x)\n⊢ ↑f x ≠ x",
"state_before": "ι : Type ?u.2582968\nα : Type u_1\nβ : Type ?u.2582974\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α... | [
1180,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1177,
1
] |
Mathlib/Analysis/Fourier/FourierTransform.lean | VectorFourier.fourierIntegral_add | [
{
"state_after": "case h\n𝕜 : Type u_1\ninst✝¹³ : CommRing 𝕜\nV : Type u_2\ninst✝¹² : AddCommGroup V\ninst✝¹¹ : Module 𝕜 V\ninst✝¹⁰ : MeasurableSpace V\nW : Type u_3\ninst✝⁹ : AddCommGroup W\ninst✝⁸ : Module 𝕜 W\nE : Type u_4\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℂ E\ninst✝⁵ : TopologicalSpac... | [
165,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/WidePullbacks.lean | CategoryTheory.Limits.WidePushout.hom_ext | [
{
"state_after": "J : Type w\nC : Type u\ninst✝² : Category C\nD : Type u_1\ninst✝¹ : Category D\nB : D\nobjs : J → D\narrows : (j : J) → B ⟶ objs j\ninst✝ : HasWidePushout B objs arrows\nX : D\nf : B ⟶ X\nfs : (j : J) → objs j ⟶ X\nw : ∀ (j : J), arrows j ≫ fs j = f\ng1 g2 : widePushout B (fun j => objs j) arr... | [
459,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | measurable_mul_unop | [] | [
795,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
1
] |
Mathlib/Algebra/Star/Basic.lean | star_ne_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹ : AddMonoid R\ninst✝ : StarAddMonoid R\nx : R\n⊢ star x ≠ 0 ↔ x ≠ 0",
"tactic": "simp only [ne_eq, star_eq_zero]"
}
] | [
291,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_finset_range | [] | [
1359,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1358,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.coe_normComp | [] | [
913,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
913,
1
] |
Mathlib/Data/Part.lean | Part.left_dom_of_inter_dom | [] | [
827,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
827,
1
] |
Mathlib/CategoryTheory/Limits/Opposites.lean | CategoryTheory.Limits.PushoutCocone.op_snd | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nJ : Type u₂\ninst✝ : Category J\nX✝ : Type v₂\nX Y Z : C\nf : X ⟶ Y\ng : X ⟶ Z\nc : PushoutCocone f g\n⊢ PullbackCone.snd (op c) = (inr c).op",
"tactic": "aesop_cat"
}
] | [
505,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
1
] |
Mathlib/Algebra/CovariantAndContravariant.lean | contravariant_flip_mul_iff | [
{
"state_after": "no goals",
"state_before": "M : Type ?u.7068\nN : Type u_1\nμ : M → N → N\nr : N → N → Prop\ninst✝ : CommSemigroup N\n⊢ Contravariant N N (flip fun x x_1 => x * x_1) r ↔ Contravariant N N (fun x x_1 => x * x_1) r",
"tactic": "rw [flip_mul]"
}
] | [
326,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/Topology/SubsetProperties.lean | isCompact_iff_finite_subfamily_closed | [] | [
365,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
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] |
Mathlib/Data/Complex/Basic.lean | Complex.sub_re | [] | [
700,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
699,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ioi_insert | [
{
"state_after": "case a\nι : Type ?u.114646\nα : Type u_1\ninst✝² : PartialOrder α\ninst✝¹ : LocallyFiniteOrderTop α\ninst✝ : DecidableEq α\na a✝ : α\n⊢ a✝ ∈ insert a (Ioi a) ↔ a✝ ∈ Ici a",
"state_before": "ι : Type ?u.114646\nα : Type u_1\ninst✝² : PartialOrder α\ninst✝¹ : LocallyFiniteOrderTop α\ninst✝ :... | [
688,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
686,
1
] |
Mathlib/CategoryTheory/NatIso.lean | CategoryTheory.Iso.inv_hom_id_app | [] | [
78,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/LinearAlgebra/Eigenspace/Basic.lean | Module.End.hasGeneralizedEigenvalue_iff_hasEigenvalue | [] | [
368,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.unique | [] | [
66,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Algebra/Module/LocalizedModule.lean | LocalizedModule.algebraMap_mk | [
{
"state_after": "R : Type u\ninst✝⁴ : CommSemiring R\nS : Submonoid R\nM : Type v\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\nA : Type u_1\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\na : R\ns : { x // x ∈ S }\n⊢ Localization.mk a s • 1 = mk (↑(algebraMap R A) a) s",
"state_before": "R : Type u\ninst✝⁴ :... | [
445,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
] |
Mathlib/Topology/Connected.lean | isTotallyDisconnected_singleton | [] | [
1229,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1228,
1
] |
Mathlib/ModelTheory/ElementaryMaps.lean | FirstOrder.Language.ElementarySubstructure.realize_sentence | [] | [
450,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_inter_lt_top_of_left_ne_top | [] | [
336,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/Order/CompleteLattice.lean | Monotone.le_map_iSup₂ | [] | [
948,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
946,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | mem_closedBall_iff_norm'' | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.94329\n𝕜 : Type ?u.94332\nα : Type ?u.94335\nι : Type ?u.94338\nκ : Type ?u.94341\nE : Type u_1\nF : Type ?u.94347\nG : Type ?u.94350\ninst✝² : SeminormedGroup E\ninst✝¹ : SeminormedGroup F\ninst✝ : SeminormedGroup G\ns : Set E\na a₁ a₂ b b₁ b₂ : E... | [
634,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
633,
1
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Mathlib/Data/Set/Lattice.lean | Set.iInter_option | [] | [
619,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
1
] |
Mathlib/Tactic/CancelDenoms.lean | CancelDenoms.cancel_factors_eq_div | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Field α\nn e e' : α\nh : n * e = e'\nh2 : n ≠ 0\n⊢ e * n = e'",
"tactic": "rwa [mul_comm] at h"
}
] | [
50,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.ofFintype_apply | [] | [
211,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.curryFinFinset_symm_apply | [] | [
1554,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1547,
1
] |
Mathlib/Order/RelClasses.lean | isStrictWeakOrder_of_isOrderConnected | [] | [
257,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/MeasureTheory/Function/ContinuousMapDense.lean | MeasureTheory.Integrable.exists_boundedContinuous_integral_sub_le | [
{
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324,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
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Mathlib/Topology/Instances/Matrix.lean | Continuous.matrix_vecMul | [] | [
164,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.continuous_im | [] | [
932,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
931,
1
] |
Mathlib/LinearAlgebra/StdBasis.lean | LinearMap.proj_comp_stdBasis | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nι : Type u_3\ninst✝³ : Semiring R\nφ : ι → Type u_1\ninst✝² : (i : ι) → AddCommMonoid (φ i)\ninst✝¹ : (i : ι) → Module R (φ i)\ninst✝ : DecidableEq ι\ni j : ι\n⊢ comp (proj i) (stdBasis R φ j) = diag j i",
"tactic": "rw [stdBasis_eq_pi_diag, pr... | [
90,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Data/Int/CharZero.lean | Int.cast_div_charZero | [
{
"state_after": "case inl\nα : Type ?u.3615\nk : Type u_1\ninst✝¹ : DivisionRing k\ninst✝ : CharZero k\nm : ℤ\nn_dvd : 0 ∣ m\n⊢ ↑(m / 0) = ↑m / ↑0\n\ncase inr\nα : Type ?u.3615\nk : Type u_1\ninst✝¹ : DivisionRing k\ninst✝ : CharZero k\nm n : ℤ\nn_dvd : n ∣ m\nhn : n ≠ 0\n⊢ ↑(m / n) = ↑m / ↑n",
"state_befo... | [
63,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.cons_left_injective | [] | [
113,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/GroupTheory/FreeAbelianGroupFinsupp.lean | FreeAbelianGroup.toFinsupp_of | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\nx : X\n⊢ ↑toFinsupp (of x) = single x 1",
"tactic": "simp only [toFinsupp, lift.of]"
}
] | [
90,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/CategoryTheory/Limits/Types.lean | CategoryTheory.Limits.Types.FilteredColimit.colimit_eq_iff | [] | [
493,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/CategoryTheory/Subobject/FactorThru.lean | CategoryTheory.Subobject.factors_self | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nX✝ Y Z : C\nD : Type u₂\ninst✝ : Category D\nX : C\nP : Subobject X\n⊢ 𝟙 (underlying.obj P) ≫ MonoOver.arrow (representative.obj P) = arrow P",
"tactic": "simp"
}
] | [
93,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Data/Polynomial/Div.lean | Polynomial.rootMultiplicity_C | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na✝ b : R\nn : ℕ\ninst✝ : CommRing R\np q : R[X]\nr a : R\n⊢ rootMultiplicity a (↑C r) = 0",
"tactic": "simp only [rootMultiplicity_eq_zero_iff, IsRoot, eval_C, C_eq_zero, imp_self]"
}
] | [
584,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
] |
Mathlib/Algebra/Lie/Basic.lean | zsmul_lie | [] | [
203,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Data/Real/GoldenRatio.lean | neg_one_lt_goldConj | [
{
"state_after": "⊢ φ⁻¹ < 1",
"state_before": "⊢ -1 < ψ",
"tactic": "rw [neg_lt, ← inv_gold]"
},
{
"state_after": "no goals",
"state_before": "⊢ φ⁻¹ < 1",
"tactic": "exact inv_lt_one one_lt_gold"
}
] | [
132,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Data/Int/Parity.lean | Int.two_mul_ediv_two_add_one_of_odd | [
{
"state_after": "case intro\nm c : ℤ\n⊢ 2 * ((2 * c + 1) / 2) + 1 = 2 * c + 1",
"state_before": "m n : ℤ\n⊢ Odd n → 2 * (n / 2) + 1 = n",
"tactic": "rintro ⟨c, rfl⟩"
},
{
"state_after": "case intro\nm c : ℤ\n⊢ (2 * c + 1) / 2 * 2 + 1 = 2 * c + 1",
"state_before": "case intro\nm c : ℤ\n⊢ 2 *... | [
264,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.log_nonpos | [] | [
205,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Topology/Algebra/Constructions.lean | Units.continuous_embedProduct | [] | [
149,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/FiniteLimits.lean | CategoryTheory.Limits.hasFiniteColimits_of_hasFiniteColimits_of_size | [
{
"state_after": "C : Type u\ninst✝ : Category C\nh : ∀ (J : Type w) {𝒥 : SmallCategory J}, FinCategory J → HasColimitsOfShape J C\nJ : Type\nhJ : SmallCategory J\nhhJ : FinCategory J\nthis : HasColimitsOfShape (ULiftHom (ULift J)) C\n⊢ HasColimitsOfShape J C",
"state_before": "C : Type u\ninst✝ : Category... | [
126,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.multiplicity_zero_eq_zero_of_ne_zero | [] | [
366,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.exp_re | [
{
"state_after": "x y : ℂ\n⊢ (exp ↑x.re * (cos ↑x.im + sin ↑x.im * I)).re = Real.exp x.re * Real.cos x.im",
"state_before": "x y : ℂ\n⊢ (exp x).re = Real.exp x.re * Real.cos x.im",
"tactic": "rw [exp_eq_exp_re_mul_sin_add_cos]"
},
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ (exp... | [
1095,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1093,
1
] |
Mathlib/Init/Data/Nat/Lemmas.lean | Nat.bit0_lt | [] | [
178,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
11
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycle.of_pow | [
{
"state_after": "ι : Type ?u.1024464\nα : Type u_1\nβ : Type ?u.1024470\nf g : Perm α\nx y : α\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nn : ℕ\nh1 : IsCycle (f ^ n)\nh2 : support f ⊆ support (f ^ n)\nkey : ∀ (x : α), ↑(f ^ n) x ≠ x ↔ ↑f x ≠ x\n⊢ IsCycle f",
"state_before": "ι : Type ?u.1024464\nα : Type ... | [
568,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
560,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | HasFDerivAt.lim_real | [
{
"state_after": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : E → F\nf' : E →L[ℝ] F\nx : E\nhf : HasFDerivAt f f' x\nv : E\n⊢ Tendsto (fun n => ‖n‖) atTop atTop",
"state_before": "E : Type u_1\ninst✝³ : Norm... | [
475,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
1
] |
Mathlib/Analysis/Calculus/Deriv/Comp.lean | HasDerivAtFilter.iterate | [
{
"state_after": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace 𝕜 F\nE : Type w\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nf✝ f₀ f₁ g : 𝕜 → F\nf'✝ f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL L₁ L₂ : Filter 𝕜\n𝕜' : Type ?u.181000... | [
208,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
18
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.germ_to_top | [] | [
462,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.23076\nβ : Type ?u.23079\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx : ℝ≥0∞\n⊢ ENNReal.toReal x = 0 ↔ x = 0 ∨ x = ⊤",
"tactic": "simp [ENNReal.toReal, toNNReal_eq_zero_iff]"
}
] | [
272,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.isCountablySpanning_spanningSets | [] | [
3487,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3485,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.support_binomial' | [] | [
869,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
863,
1
] |
Mathlib/RingTheory/Ideal/LocalRing.lean | LocalRing.of_surjective' | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nK : Type u'\ninst✝³ : CommRing R\ninst✝² : LocalRing R\ninst✝¹ : CommRing S\ninst✝ : Nontrivial S\nf : R →+* S\nhf : Function.Surjective ↑f\nb : S\n⊢ IsUnit b ∨ IsUnit (1 - b)",
"state_before": "R : Type u\nS : Type v\nT : Type w\nK : Type u'\ninst✝³ : C... | [
191,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Data/List/MinMax.lean | List.minimum_nil | [] | [
292,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
src/lean/Init/Prelude.lean | Nat.lt_or_ge | [] | [
1653,
31
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1644,
11
] |
Mathlib/Topology/MetricSpace/IsometricSMul.lean | IsometryEquiv.inv_symm | [] | [
267,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
31
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.mono_fun' | [] | [
225,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Topology/ContinuousOn.lean | nhdsWithin_compl_singleton_sup_pure | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.22542\nγ : Type ?u.22545\nδ : Type ?u.22548\ninst✝ : TopologicalSpace α\na : α\n⊢ 𝓝[{a}ᶜ] a ⊔ pure a = 𝓝 a",
"tactic": "rw [← nhdsWithin_singleton, ← nhdsWithin_union, compl_union_self, nhdsWithin_univ]"
}
] | [
305,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Topology/Category/TopCat/Opens.lean | TopologicalSpace.Opens.map_coe | [] | [
156,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/GroupTheory/GroupAction/Sum.lean | Sum.smul_swap | [
{
"state_after": "no goals",
"state_before": "M : Type u_3\nN : Type ?u.1873\nP : Type ?u.1876\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.1885\ninst✝³ : SMul M α\ninst✝² : SMul M β\ninst✝¹ : SMul N α\ninst✝ : SMul N β\na : M\nb : α\nc : β\nx : α ⊕ β\n⊢ swap (a • x) = a • swap x",
"tactic": "cases x <;> rf... | [
59,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | Homeomorph.coe_mulRight | [] | [
114,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Data/Nat/Factors.lean | Nat.factors_prime | [
{
"state_after": "p : ℕ\nhp : Prime p\nthis : p = p - 2 + 2\n⊢ factors p = [p]",
"state_before": "p : ℕ\nhp : Prime p\n⊢ factors p = [p]",
"tactic": "have : p = p - 2 + 2 := (tsub_eq_iff_eq_add_of_le hp.two_le).mp rfl"
},
{
"state_after": "p : ℕ\nhp : Prime p\nthis : p = p - 2 + 2\n⊢ (let m := m... | [
90,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Analysis/Complex/Basic.lean | IsROrC.im_tsum | [] | [
539,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
] |
Mathlib/Analysis/NormedSpace/AddTorsor.lean | dist_right_midpoint | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.69523\nV : Type u_3\nP : Type u_1\nW : Type ?u.69532\nQ : Type ?u.69535\ninst✝⁹ : SeminormedAddCommGroup V\ninst✝⁸ : PseudoMetricSpace P\ninst✝⁷ : NormedAddTorsor V P\ninst✝⁶ : NormedAddCommGroup W\ninst✝⁵ : MetricSpace Q\ninst✝⁴ : NormedAddTorsor W ... | [
206,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Analysis/Calculus/Deriv/AffineMap.lean | AffineMap.derivWithin | [] | [
45,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
11
] |
Mathlib/Geometry/Euclidean/Sphere/Basic.lean | EuclideanGeometry.cospherical_empty | [] | [
185,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.le_filter | [] | [
2009,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2007,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.hasFiniteIntegral_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.721960\nδ : Type ?u.721963\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\n⊢ HasFiniteIntegral fun x => 0",
"tactic": "simp [HasFiniteIn... | [
233,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Analysis/MeanInequalities.lean | NNReal.summable_mul_of_Lp_Lq | [] | [
407,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_div_of_pos | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.816967\nβ : Type ?u.816970\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx y : ℝ\nhy : 0 < y\n⊢ ENNReal.ofReal (x / y) = ENNReal.ofReal x / ENNReal.ofReal y",
"tactic": "rw [div_eq_mul_inv, div_eq_mul_inv, ofReal_mul' (inv_nonneg.2 hy.le), ofReal_inv_of_pos hy]"... | [
2192,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2190,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsGreatest.unique | [] | [
1081,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1080,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.rat_mul | [] | [
352,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.prod_left | [] | [
1009,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1006,
1
] |
Mathlib/Order/Interval.lean | NonemptyInterval.coe_coeHom | [] | [
267,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integral_finset_biUnion | [
{
"state_after": "case empty\nα : Type u_2\nβ : Type ?u.12684\nE : Type u_3\nF : Type ?u.12690\ninst✝³ : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\nf g : α → E\ns✝ t✝ : Set α\nμ ν : Measure α\nl l' : Filter α\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\nι : Type u_1\nt : Finset ι\ns : ι → Set α\nh... | [
140,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Algebra/Homology/Additive.lean | HomologicalComplex.sub_f_apply | [] | [
84,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurable_edist_right | [] | [
1636,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1635,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_Prop_eq | [] | [
1733,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1731,
1
] |
Mathlib/Algebra/Group/Semiconj.lean | SemiconjBy.one_left | [] | [
100,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.cosh_sq | [
{
"state_after": "x y : ℝ\n⊢ ↑(cosh x ^ 2) = ↑(sinh x ^ 2 + 1)",
"state_before": "x y : ℝ\n⊢ cosh x ^ 2 = sinh x ^ 2 + 1",
"tactic": "rw [← ofReal_inj]"
},
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ ↑(cosh x ^ 2) = ↑(sinh x ^ 2 + 1)",
"tactic": "simp [cosh_sq]"
}
] | [
1434,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1434,
8
] |
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