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/Data/Matrix/Notation.lean | Matrix.smul_mat_empty | [] | [
362,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.zero_apply | [] | [
299,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.infEdist_lt_iff | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.4012\nα : Type u\nβ : Type v\ninst✝¹ : PseudoEMetricSpace α\ninst✝ : PseudoEMetricSpace β\nx y : α\ns t : Set α\nΦ : α → β\nr : ℝ≥0∞\n⊢ infEdist x s < r ↔ ∃ y, y ∈ s ∧ edist x y < r",
"tactic": "simp_rw [infEdist, iInf_lt_iff, exists_prop]"
}
] | [
102,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Topology/PathConnected.lean | JoinedIn.refl | [] | [
877,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
876,
1
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Mathlib/Data/Fintype/Perm.lean | mem_of_mem_permsOfList | [
{
"state_after": "α : Type u_1\nβ : Type ?u.25960\nγ : Type ?u.25963\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\nf : Equiv.Perm α\nh : f ∈ permsOfList []\nheq_iff_eq : α\nthis : f = 1\n⊢ ↑f heq_iff_eq ≠ heq_iff_eq → heq_iff_eq ∈ []",
"state_before": "α : Type u_1\nβ : Type ?u.25960\nγ : Type ?u.25963\ni... | [
97,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
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Mathlib/Data/Real/Irrational.lean | irrational_rat_mul_iff | [] | [
604,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.iSup_adj | [
{
"state_after": "no goals",
"state_before": "ι : Sort u_1\n𝕜 : Type ?u.18891\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v w : V\ne : Sym2 V\nf : ι → SimpleGraph V\n⊢ Adj (⨆ (i : ι), f i) a b ↔ ∃ i, Adj (f i) a b",
"tactic": "simp [iSup]"
}
] | [
319,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.smul_finset_subset_smul | [] | [
1675,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1674,
1
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Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.moebius_mul_coe_zeta | [
{
"state_after": "case h\nR : Type ?u.598712\nn : ℕ\n⊢ ↑(μ * ↑ζ) n = ↑1 n",
"state_before": "R : Type ?u.598712\n⊢ μ * ↑ζ = 1",
"tactic": "ext n"
},
{
"state_after": "case h.refine'_1\nR : Type ?u.598712\nn : ℕ\n⊢ ∀ (p n : ℕ), Prime p → 0 < n → ↑(μ * ↑ζ) (p ^ n) = ↑1 (p ^ n)\n\ncase h.refine'_2\... | [
1041,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1024,
1
] |
Mathlib/Order/Bounds/Basic.lean | lowerBounds_mono_set | [] | [
196,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.center_toSubsemiring | [] | [
795,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
1
] |
Mathlib/Topology/Algebra/Order/LeftRightLim.lean | Antitone.countable_not_continuousAt | [] | [
377,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Std/Data/List/Init/Lemmas.lean | List.tail?_cons | [] | [
30,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
30,
9
] |
Mathlib/Order/SuccPred/Relation.lean | reflTransGen_of_succ_of_le | [
{
"state_after": "α : Type u_1\ninst✝² : PartialOrder α\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nr : α → α → Prop\nn m : α\nhnm : n ≤ m\n⊢ (∀ (i : α), i ∈ Ico n m → r i (succ i)) → ReflTransGen r n m",
"state_before": "α : Type u_1\ninst✝² : PartialOrder α\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArc... | [
38,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
29,
1
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Mathlib/Topology/LocalExtr.lean | IsLocalMin.inf | [] | [
477,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
8
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.mul_invOf_mul_self_cancel | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.13040\nm : Type u\nn : Type u'\nα : Type v\ninst✝³ : Fintype n\ninst✝² : DecidableEq n\ninst✝¹ : CommRing α\nA : Matrix m n α\nB : Matrix n n α\ninst✝ : Invertible B\n⊢ A ⬝ ⅟B ⬝ B = A",
"tactic": "rw [Matrix.mul_assoc, Matrix.invOf_mul_self, Matr... | [
92,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
11
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.aestronglyMeasurable | [] | [
141,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
11
] |
Mathlib/RingTheory/DiscreteValuationRing/Basic.lean | DiscreteValuationRing.not_a_field | [] | [
67,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Analysis/Normed/Group/AddCircle.lean | AddCircle.norm_neg_period | [
{
"state_after": "p x : ℝ\n⊢ ‖↑(-1 * x)‖ = ‖↑x‖",
"state_before": "p x : ℝ\n⊢ ‖↑x‖ = ‖↑x‖",
"tactic": "suffices ‖(↑(-1 * x) : AddCircle (-1 * p))‖ = ‖(x : AddCircle p)‖ by\n rw [← this, neg_one_mul]\n simp"
},
{
"state_after": "no goals",
"state_before": "p x : ℝ\n⊢ ‖↑(-1 * x)‖ = ‖↑x‖",
... | [
78,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | Submodule.isClosed_or_dense_of_isCoatom | [
{
"state_after": "R R' : Type u\nM M' : Type v\ninst✝¹⁰ : Semiring R\ninst✝⁹ : Ring R'\ninst✝⁸ : TopologicalSpace M\ninst✝⁷ : AddCommMonoid M\ninst✝⁶ : TopologicalSpace M'\ninst✝⁵ : AddCommGroup M'\ninst✝⁴ : Module R M\ninst✝³ : ContinuousConstSMul R M\ninst✝² : Module R' M'\ninst✝¹ : ContinuousConstSMul R' M'\... | [
205,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.mk'_eq_iff_eq' | [] | [
329,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Combinatorics/Composition.lean | CompositionAsSet.boundary_zero | [
{
"state_after": "n : ℕ\nc : CompositionAsSet n\n⊢ Finset.min' c.boundaries (_ : Finset.Nonempty c.boundaries) = 0",
"state_before": "n : ℕ\nc : CompositionAsSet n\n⊢ ↑(boundary c) { val := 0, isLt := (_ : 0 < Finset.card c.boundaries) } = 0",
"tactic": "rw [boundary, Finset.orderEmbOfFin_zero rfl c.car... | [
915,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
913,
1
] |
Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingHom.coe_orderAddMonoidHom_apply | [] | [
241,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.exp_sub_sinh | [] | [
742,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
741,
1
] |
Mathlib/RingTheory/FiniteType.lean | MonoidAlgebra.mem_adjoin_support | [
{
"state_after": "R : Type u_1\nM : Type u_2\ninst✝¹ : CommSemiring R\ninst✝ : Monoid M\nf : MonoidAlgebra R M\n⊢ span R (↑(of R M) '' ↑f.support) ≤ ↑Subalgebra.toSubmodule (adjoin R (↑(of R M) '' ↑f.support))",
"state_before": "R : Type u_1\nM : Type u_2\ninst✝¹ : CommSemiring R\ninst✝ : Monoid M\nf : Mono... | [
503,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/Topology/Order/Basic.lean | lt_subset_interior_le | [] | [
626,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
624,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.restrict_apply_measure | [] | [
287,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.inductionOn | [] | [
1195,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1194,
1
] |
Mathlib/Order/Hom/Lattice.lean | SupHom.coe_bot | [] | [
490,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
src/lean/Init/Control/Lawful.lean | ReaderT.run_bind | [] | [
187,
68
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
186,
9
] |
Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.MulticospanIndex.sndPiMap_π | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\nI : MulticospanIndex C\ninst✝¹ : HasProduct I.left\ninst✝ : HasProduct I.right\nb : I.R\n⊢ sndPiMap I ≫ Pi.π I.right b = Pi.π I.left (sndTo I b) ≫ snd I b",
"tactic": "simp [sndPiMap]"
}
] | [
235,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
src/lean/Init/Data/List/Basic.lean | List.iota_eq_iotaTR | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nn : Nat\nr : List Nat\n⊢ iotaTR.go n r = reverse r ++ iota n",
"tactic": "induction n generalizing r with\n| zero => simp [iota, iotaTR.go]\n| succ n ih => simp [iota, iotaTR.go, ih, append_assoc]"
},
{
"state_afte... | [
600,
40
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
595,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Fintype.prod_equiv | [] | [
1998,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1996,
1
] |
Mathlib/LinearAlgebra/Pi.lean | LinearMap.ker_pi | [
{
"state_after": "case h\nR : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nι' : Type x'\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M₂\ninst✝⁴ : Module R M₂\ninst✝³ : AddCommMonoid M₃\ninst✝² : Module R M₃\nφ : ι → Type i\ninst✝¹ :... | [
64,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Order/Bounds/Basic.lean | AntitoneOn.mem_upperBounds_image | [] | [
1213,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1212,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.fract_eq_fract | [
{
"state_after": "F : Type ?u.164824\nα : Type u_1\nβ : Type ?u.164830\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na✝ a b : α\nh : a - ↑⌊a⌋ = b - ↑⌊b⌋\n⊢ a - b = ↑(⌊a⌋ - ⌊b⌋)",
"state_before": "F : Type ?u.164824\nα : Type u_1\nβ : Type ?u.164830\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRi... | [
942,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
936,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.symm_apply_of_not_mem | [] | [
607,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
605,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.Red.Step.append_left_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nL L₁ L₂ L₃ L₄ : List (α × Bool)\n⊢ Step ([] ++ L₁) ([] ++ L₂) ↔ Step L₁ L₂",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nL L₁ L₂ L₃ L₄ : List (α × Bool)\np : α × Bool\nl : List (α × Bool)\n⊢ Step (p :... | [
195,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Data/Finset/Pi.lean | Finset.pi_const_singleton | [] | [
127,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Algebra/Module/Injective.lean | Module.Baer.chain_linearPMap_of_chain_extensionOf | [
{
"state_after": "case intro.intro.intro.intro\nR : Type u\ninst✝⁶ : Ring R\nQ : TypeMax\ninst✝⁵ : AddCommGroup Q\ninst✝⁴ : Module R Q\nM N : Type (max u v)\ninst✝³ : AddCommGroup M\ninst✝² : AddCommGroup N\ninst✝¹ : Module R M\ninst✝ : Module R N\ni : M →ₗ[R] N\nf : M →ₗ[R] Q\nc : Set (ExtensionOf i f)\nhchain... | [
174,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_add_le | [
{
"state_after": "case pos\nα : Type u_1\nE : Type u_2\nF : Type ?u.2940197\nG : Type ?u.2940200\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf g : α → E\nhf : AEStronglyMeasurable f μ\nhg : AEStronglyMea... | [
785,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
776,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.cthickening_eq_iInter_thickening'' | [
{
"state_after": "case δ_nn\nι : Sort ?u.143302\nα : Type u\nβ : Type v\ninst✝ : PseudoEMetricSpace α\nδ✝ ε : ℝ\ns t : Set α\nx : α\nδ : ℝ\nE : Set α\n⊢ 0 ≤ max 0 δ",
"state_before": "ι : Sort ?u.143302\nα : Type u\nβ : Type v\ninst✝ : PseudoEMetricSpace α\nδ✝ ε : ℝ\ns t : Set α\nx : α\nδ : ℝ\nE : Set α\n⊢ ... | [
1341,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1338,
1
] |
Mathlib/Data/Finset/Powerset.lean | Finset.mem_powerset_self | [] | [
57,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.FiniteAtFilter.measure_mono | [] | [
4129,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4128,
11
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | HasFDerivAt.snd | [] | [
264,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
18
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | NNReal.tendsto_const_div_atTop_nhds_0_nat | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.1738\nβ : Type ?u.1741\nι : Type ?u.1744\nC : ℝ≥0\n⊢ Tendsto (fun n => C / ↑n) atTop (𝓝 0)",
"tactic": "simpa using tendsto_const_nhds.mul NNReal.tendsto_inverse_atTop_nhds_0_nat"
}
] | [
50,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.card_infs_iff | [] | [
253,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | Collinear.affineSpan_eq_of_ne | [] | [
533,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
1
] |
Mathlib/AlgebraicGeometry/RingedSpace.lean | AlgebraicGeometry.RingedSpace.basicOpen_res_eq | [
{
"state_after": "case a\nX : RingedSpace\nU V : (Opens ↑↑X.toPresheafedSpace)ᵒᵖ\ni : U ⟶ V\ninst✝ : IsIso i\nf : ↑(X.presheaf.obj U)\n⊢ basicOpen X (↑(X.presheaf.map i) f) ≤ basicOpen X f\n\ncase a\nX : RingedSpace\nU V : (Opens ↑↑X.toPresheafedSpace)ᵒᵖ\ni : U ⟶ V\ninst✝ : IsIso i\nf : ↑(X.presheaf.obj U)\n⊢ b... | [
232,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Data/List/Basic.lean | List.cons_nthLe_drop_succ | [] | [
2129,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2128,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.SimpleFunc.setToSimpleFunc_add_left' | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type ?u.231450\nG : Type ?u.231453\n𝕜 : Type ?u.231456\np : ℝ≥0∞\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ninst✝² : NormedAddCommGroup F'\ninst✝¹ : NormedSpace ℝ F'\ninst✝ :... | [
428,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
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Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.pullback_eq_top_iff_mem | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF : C ⥤ D\nX Y Z : C\nf✝ : Y ⟶ X\nS R : Sieve X\nf : Y ⟶ X\n⊢ S.arrows f ↔ pullback f S = ⊤",
"tactic": "rw [← id_mem_iff_eq_top, pullback_apply, id_comp]"
}
] | [
482,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/Topology/Sets/Closeds.lean | TopologicalSpace.Closeds.mem_sInf | [] | [
161,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.zero_rpow | [] | [
67,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Data/List/Pairwise.lean | List.Pairwise.iff | [] | [
103,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.diagonal_mul | [] | [
1025,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1023,
1
] |
Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.Ico_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\na b c : α\n⊢ Ico a a = 0",
"tactic": "rw [Ico, Finset.Ico_self, Finset.empty_val]"
}
] | [
104,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Algebra/Group/Conj.lean | IsConj.symm | [] | [
42,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.natAdd_last | [] | [
1469,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1468,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.self_mem_mk' | [] | [
463,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/Analysis/InnerProductSpace/PiL2.lean | OrthonormalBasis.toMatrix_orthonormalBasis_mem_orthogonal | [] | [
723,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
721,
1
] |
Mathlib/Order/Filter/CountableInter.lean | EventuallyEq.countable_bInter | [] | [
127,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Data/List/Forall2.lean | List.forall₂_drop | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.129991\nδ : Type ?u.129994\nR S : α → β → Prop\nP : γ → δ → Prop\nRₐ : α → α → Prop\nx✝¹ : List α\nx✝ : List β\nh : Forall₂ R x✝¹ x✝\n⊢ Forall₂ R (drop 0 x✝¹) (drop 0 x✝)",
"tactic": "simp only [drop, h]"
},
{
... | [
222,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Deprecated/Subgroup.lean | IsSubgroup.mem_trivial | [] | [
242,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Complex.lean | Complex.cpow_def | [] | [
40,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Dynamics/OmegaLimit.lean | Flow.omegaLimit_omegaLimit | [
{
"state_after": "τ : Type u_1\ninst✝³ : TopologicalSpace τ\ninst✝² : AddCommGroup τ\ninst✝¹ : TopologicalAddGroup τ\nα : Type u_2\ninst✝ : TopologicalSpace α\nf : Filter τ\nϕ : Flow τ α\ns : Set α\nhf : ∀ (t : τ), Tendsto ((fun x x_1 => x + x_1) t) f f\n⊢ ∀ (x : α),\n (∀ (n : Set α), n ∈ 𝓝 x → ∀ {U : Set τ... | [
398,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/Data/Nat/ModEq.lean | Nat.ModEq.refl | [] | [
50,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
11
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.prod_mono | [] | [
1712,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1712,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arcsin_mem_Icc | [] | [
42,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Std/Data/Int/Lemmas.lean | Int.lt.intro | [] | [
594,
22
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
593,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.volume_subtype_coe_eq_zero_of_volume_eq_zero | [] | [
1467,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1465,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.prob_compl_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.708423\nγ : Type ?u.708426\nδ : Type ?u.708429\nι : Type ?u.708432\nR : Type ?u.708435\nR' : Type ?u.708438\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... | [
3256,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3254,
1
] |
Mathlib/RingTheory/Ideal/Over.lean | Ideal.isMaximal_comap_of_isIntegral_of_is_maximal' | [] | [
304,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.mk.eta | [] | [
103,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.opow_le_opow_right | [
{
"state_after": "case inl\na b c : Ordinal\nh₁✝ : 0 < a\nh₂ : b ≤ c\nh₁ : 1 < a\n⊢ a ^ b ≤ a ^ c\n\ncase inr\na b c : Ordinal\nh₁✝ : 0 < a\nh₂ : b ≤ c\nh₁ : 1 = a\n⊢ a ^ b ≤ a ^ c",
"state_before": "a b c : Ordinal\nh₁ : 0 < a\nh₂ : b ≤ c\n⊢ a ^ b ≤ a ^ c",
"tactic": "cases' lt_or_eq_of_le (one_le_iff_... | [
144,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.Measure.ae_ae_of_ae_prod | [] | [
453,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | MeasureTheory.Measure.add_haar_closed_unit_ball_eq_add_haar_unit_ball | [
{
"state_after": "E : Type u_1\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : MeasurableSpace E\ninst✝⁵ : BorelSpace E\ninst✝⁴ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝³ : IsAddHaarMeasure μ\nF : Type ?u.2005530\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\ninst✝ : CompleteSp... | [
476,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.sup_const | [] | [
1316,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1315,
1
] |
Mathlib/Data/Rat/NNRat.lean | Rat.toNNRat_zero | [] | [
340,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.continuous_cosh | [
{
"state_after": "⊢ Continuous fun z => (exp z + exp (-z)) / 2",
"state_before": "⊢ Continuous cosh",
"tactic": "change Continuous fun z => (exp z + exp (-z)) / 2"
},
{
"state_after": "no goals",
"state_before": "⊢ Continuous fun z => (exp z + exp (-z)) / 2",
"tactic": "continuity"
}
] | [
82,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | SubringClass.coe_natCast | [] | [
169,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/ModelTheory/Definability.lean | Set.Definable.inter | [
{
"state_after": "case intro\nM : Type w\nA : Set M\nL : Language\ninst✝ : Structure L M\nα : Type u₁\nβ : Type ?u.10841\nB : Set M\ns g : Set (α → M)\nhg : Definable A L g\nφ : Formula (L[[↑A]]) α\n⊢ Definable A L (setOf (Formula.Realize φ) ∩ g)",
"state_before": "M : Type w\nA : Set M\nL : Language\ninst✝... | [
99,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/SetTheory/Cardinal/Divisibility.lean | Cardinal.le_of_dvd | [
{
"state_after": "no goals",
"state_before": "a✝ b✝ : Cardinal\nn m : ℕ\na x : Cardinal\nb0 : x ≠ 0\nb : Cardinal\nhab : x = a * b\n⊢ a ≤ x",
"tactic": "simpa only [hab, mul_one] using\n mul_le_mul_left' (one_le_iff_ne_zero.2 fun h : b = 0 => b0 (by rwa [h, mul_zero] at hab)) a"
},
{
"state_aft... | [
71,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Algebra/Order/Floor.lean | subsingleton_floorSemiring | [
{
"state_after": "F : Type ?u.99218\nα✝ : Type ?u.99221\nβ : Type ?u.99224\nα : Type u_1\ninst✝ : LinearOrderedSemiring α\nH₁ H₂ : FloorSemiring α\n⊢ H₁ = H₂",
"state_before": "F : Type ?u.99218\nα✝ : Type ?u.99221\nβ : Type ?u.99224\nα : Type u_1\ninst✝ : LinearOrderedSemiring α\n⊢ Subsingleton (FloorSemir... | [
546,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/Order/BooleanAlgebra.lean | sdiff_inf_sdiff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.4198\nw x y z : α\ninst✝ : GeneralizedBooleanAlgebra α\n⊢ ⊥ = x ⊓ y ⊓ x \\ y",
"tactic": "rw [inf_inf_sdiff]"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.4198\nw x y z : α\ninst✝ : GeneralizedB... | [
163,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Algebra/Group/Basic.lean | mul_right_comm | [] | [
104,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Data/Set/Basic.lean | Set.subset_compl_comm | [] | [
1730,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1729,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.mem_orthogonal_iff | [] | [
1196,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1194,
1
] |
Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | LiouvilleWith.int_add_iff | [
{
"state_after": "no goals",
"state_before": "p q x y : ℝ\nr : ℚ\nm : ℤ\nn : ℕ\n⊢ LiouvilleWith p (↑m + x) ↔ LiouvilleWith p x",
"tactic": "rw [add_comm, add_int_iff]"
}
] | [
220,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Algebra/Hom/Iterate.lean | AddMonoidHom.iterate_map_zsmul | [] | [
110,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.depthUB_le | [] | [
61,
30
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
59,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.comp_mul_right | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.7203111\n𝕜 : Type ?u.7203114\nE : Type u_1\nF : Type ?u.7203120\nA : Type ?u.7203123\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedRing A\nf g : ℝ → E\na b : ℝ\nμ : MeasureTheory.Measure ℝ\nhf : IntervalIntegrable f volume a b\nc : ℝ\n⊢ IntervalInte... | [
316,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | ENNReal.exists_pos_sum_of_countable' | [] | [
515,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
1
] |
Mathlib/Analysis/NormedSpace/AddTorsor.lean | nndist_center_homothety | [] | [
58,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion₂_eq_univ_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.128133\nγ : Type ?u.128136\nι : Sort u_2\nι' : Sort ?u.128142\nι₂ : Sort ?u.128145\nκ : ι → Sort u_3\nκ₁ : ι → Sort ?u.128155\nκ₂ : ι → Sort ?u.128160\nκ' : ι' → Sort ?u.128165\ns : (i : ι) → κ i → Set α\n⊢ (⋃ (i : ι) (j : κ i), s i j) ... | [
1193,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1191,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.lintegral_map | [] | [
1159,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1157,
1
] |
Mathlib/Order/Disjointed.lean | disjointed_zero | [] | [
59,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Analysis/SpecialFunctions/Exponential.lean | hasStrictDerivAt_exp_smul_const_of_mem_ball | [
{
"state_after": "no goals",
"state_before": "𝕂 : Type u_2\n𝕊 : Type ?u.195497\n𝔸 : Type u_1\ninst✝⁹ : NontriviallyNormedField 𝕂\ninst✝⁸ : CharZero 𝕂\ninst✝⁷ : NormedCommRing 𝕊\ninst✝⁶ : NormedRing 𝔸\ninst✝⁵ : NormedSpace 𝕂 𝕊\ninst✝⁴ : NormedAlgebra 𝕂 𝔸\ninst✝³ : Algebra 𝕊 𝔸\ninst✝² : Continuou... | [
346,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/Analysis/Calculus/Conformal/NormedSpace.lean | ConformalAt.const_smul | [] | [
113,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.set_lintegral_strict_mono | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.988367\nγ : Type ?u.988370\nδ : Type ?u.988373\nm : MeasurableSpace α\nμ ν : Measure α\nf g : α → ℝ≥0∞\ns : Set α\nhsm : MeasurableSet s\nhs : ↑↑μ s ≠ 0\nhg : Measurable g\nhfi : (∫⁻ (x : α) in s, f x ∂μ) ≠ ⊤\nh : ∀ᵐ (x : α) ∂μ, x ∈ s →... | [
962,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
959,
1
] |
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