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/Geometry/Manifold/ChartedSpace.lean | closedUnderRestriction' | [] | [
397,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_sub | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\n⊢ toIcoMod hp a (b - p) = toIcoMod hp a b",
"tactic": "simpa only [one_zsmul] using toIcoMod_sub_zsmul hp a b 1"
}
] | [
514,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
1
] |
Mathlib/Order/Antichain.lean | isWeakAntichain_insert | [] | [
386,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
1
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Mathlib/Algebra/GroupPower/Order.lean | Left.pow_lt_one_iff' | [] | [
345,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.and_not_self | [
{
"state_after": "no goals",
"state_before": "⊢ ∀ (x : Bool), (x && !x) = false",
"tactic": "decide"
}
] | [
248,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.IntegrableOn.of_ae_diff_eq_zero | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1647552\nE : Type u_2\nF : Type ?u.1647558\ninst✝¹ : MeasurableSpace α\ninst✝ : NormedAddCommGroup E\nf g : α → E\ns t : Set α\nμ ν : Measure α\nhf : IntegrableOn f s\nht : NullMeasurableSet t\nh't : ∀ᵐ (x : α) ∂μ, x ∈ t \\ s → f x = 0\nu : Set α := {x | x ∈ s ∧ f x ≠... | [
332,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
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Mathlib/RingTheory/PrincipalIdealDomain.lean | nonPrincipals_zorn | [
{
"state_after": "R : Type u\nM : Type v\ninst✝ : CommRing R\nc : Set (Ideal R)\nhs : c ⊆ nonPrincipals R\nhchain : IsChain (fun x x_1 => x ≤ x_1) c\nK : Ideal R\nhKmem : K ∈ c\n⊢ sSup c ∈ nonPrincipals R",
"state_before": "R : Type u\nM : Type v\ninst✝ : CommRing R\nc : Set (Ideal R)\nhs : c ⊆ nonPrincipal... | [
501,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.map_left_cancel | [] | [
218,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Algebra/Star/Unitary.lean | unitary.star_mul_self_of_mem | [] | [
61,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Topology/Algebra/Order/MonotoneConvergence.lean | tendsto_atTop_iSup | [] | [
160,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | circleIntegrable_sub_zpow_iff | [
{
"state_after": "case mp\nE : Type ?u.111922\ninst✝ : NormedAddCommGroup E\nc w : ℂ\nR : ℝ\nn : ℤ\n⊢ CircleIntegrable (fun z => (z - w) ^ n) c R → R = 0 ∨ 0 ≤ n ∨ ¬w ∈ sphere c (Abs.abs R)\n\ncase mpr\nE : Type ?u.111922\ninst✝ : NormedAddCommGroup E\nc w : ℂ\nR : ℝ\nn : ℤ\n⊢ R = 0 ∨ 0 ≤ n ∨ ¬w ∈ sphere c (Abs... | [
334,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
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Mathlib/Data/Nat/Interval.lean | Nat.card_Ioo | [] | [
113,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_one_div_of_pos | [
{
"state_after": "no goals",
"state_before": "a b : ℝ\nn : ℕ\nha : 0 < a\nhb : 0 < b\n⊢ (∫ (x : ℝ) in a..b, 1 / x) = Real.log (b / a)",
"tactic": "simp only [one_div, integral_inv_of_pos ha hb]"
}
] | [
448,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.singleton_ne_zero | [] | [
595,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
594,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.IsStrongLimit.two_power_lt | [] | [
868,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
867,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | FractionalIdeal.inv_nonzero | [] | [
81,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.zeroLocus_singleton_pow | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nA : Type u_1\ninst✝³ : CommSemiring R\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\n𝒜 : ℕ → Submodule R A\ninst✝ : GradedAlgebra 𝒜\nf : A\nn : ℕ\nhn : 0 < n\nx : ProjectiveSpectrum 𝒜\n⊢ x ∈ zeroLocus 𝒜 {f ^ n} ↔ x ∈ zeroLocus 𝒜 {f}",
"tactic... | [
308,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Data/Finset/Prod.lean | Finset.product_sdiff_offDiag | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.120722\nγ : Type ?u.120725\ninst✝ : DecidableEq α\ns t : Finset α\nx : α × α\n⊢ s ×ˢ s \\ offDiag s = diag s",
"tactic": "rw [← diag_union_offDiag, union_sdiff_self, sdiff_eq_self_of_disjoint (disjoint_diag_offDiag _)]"
}
] | [
379,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/Data/List/Rotate.lean | List.zipWith_rotate_distrib | [
{
"state_after": "case h\nα✝ : Type u\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → β → γ\nl : List α\nl' : List β\nn : ℕ\nh : length l = length l'\n⊢ length (drop (n % length l') l) = length (drop (n % length l') l')",
"state_before": "α✝ : Type u\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → β →... | [
226,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Topology/Order/Basic.lean | le_of_tendsto' | [] | [
193,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
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Mathlib/Data/List/Basic.lean | List.enumFrom_map | [
{
"state_after": "case nil\nι : Type ?u.450424\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nn : ℕ\nf : α → β\n⊢ enumFrom n (map f []) = map (Prod.map id f) (enumFrom n [])\n\ncase cons\nι : Type ?u.450424\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nn : ℕ\nf : α → β\nhd :... | [
3936,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3931,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.reindexRange_apply | [
{
"state_after": "case mk.intro\nι : Type u_2\nι' : Type ?u.390057\nR : Type u_3\nR₂ : Type ?u.390063\nK : Type ?u.390066\nM : Type u_1\nM' : Type ?u.390072\nM'' : Type ?u.390075\nV : Type u\nV' : Type ?u.390080\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\ninst✝¹ : AddCommMonoid M'\ninst... | [
489,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
1
] |
Mathlib/Computability/RegularExpressions.lean | RegularExpression.mul_rmatch_iff | [
{
"state_after": "case nil\nα : Type u_1\nβ : Type ?u.43048\nγ : Type ?u.43051\ndec : DecidableEq α\na b : α\nP✝ Q✝ P Q : RegularExpression α\n⊢ rmatch (P * Q) [] = true ↔ ∃ t u, [] = t ++ u ∧ rmatch P t = true ∧ rmatch Q u = true\n\ncase cons\nα : Type u_1\nβ : Type ?u.43048\nγ : Type ?u.43051\ndec : Decidable... | [
293,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.filter_nonempty_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.324507\nγ : Type ?u.324510\np q : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred q\ns : Finset α\n⊢ Finset.Nonempty (filter p s) ↔ ∃ a, a ∈ s ∧ p a",
"tactic": "simp [nonempty_iff_ne_empty, Ne.def, filter_eq_empty_iff, no... | [
2715,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2714,
1
] |
src/lean/Init/Core.lean | Prod.lexLt_def | [] | [
1035,
6
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1034,
1
] |
Mathlib/Analysis/Convex/StrictConvexSpace.lean | StrictConvexSpace.ofStrictConvexClosedUnitBall | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\nE : Type u_1\ninst✝⁴ : NormedLinearOrderedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : LinearMap.CompatibleSMul E E 𝕜 ℝ\nh : StrictConvex 𝕜 (closedBall 0 1)\nr : ℝ\nhr : 0 < r\n⊢ StrictCon... | [
95,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.smul_finset_subset_smul_finset | [] | [
1651,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1650,
1
] |
Mathlib/Order/Filter/NAry.lean | Filter.map₂_left_comm | [
{
"state_after": "α : Type u_2\nα' : Type ?u.38698\nβ : Type u_4\nβ' : Type ?u.38704\nγ : Type u_5\nγ' : Type ?u.38710\nδ : Type u_3\nδ' : Type u_6\nε : Type u_1\nε' : Type ?u.38722\nm✝ : α → β → γ\nf f₁ f₂ : Filter α\ng g₁ g₂ : Filter β\nh h₁ h₂ : Filter γ\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\nu : Set γ\nv : Set ... | [
316,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.sum_univ_single' | [
{
"state_after": "α : Type u_2\nι : Type ?u.487120\nγ : Type ?u.487123\nA : Type ?u.487126\nB : Type ?u.487129\nC : Type ?u.487132\ninst✝⁴ : AddCommMonoid A\ninst✝³ : AddCommMonoid B\ninst✝² : AddCommMonoid C\nt : ι → A → C\nh0 : ∀ (i : ι), t i 0 = 0\nh1 : ∀ (i : ι) (x y : A), t i (x + y) = t i x + t i y\ns : F... | [
482,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/Data/Int/GCD.lean | Int.gcd_neg_left | [
{
"state_after": "no goals",
"state_before": "x y : ℤ\n⊢ gcd (-x) y = gcd x y",
"tactic": "rw [Int.gcd, Int.gcd, natAbs_neg]"
}
] | [
298,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.lt_or_equiv_of_le | [] | [
866,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
865,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Quot.congr_mk | [] | [
942,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
940,
9
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.uniformContinuous_iff | [] | [
287,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.subtypePermOfFintype_one | [] | [
113,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Order/CompleteLattice.lean | Monotone.le_map_sSup | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nβ₂ : Type ?u.78898\nγ : Type ?u.78901\nι : Sort ?u.78904\nι' : Sort ?u.78907\nκ : ι → Sort ?u.78912\nκ' : ι' → Sort ?u.78917\ninst✝¹ : CompleteLattice α\nf✝ g s✝ t : ι → α\na b : α\ninst✝ : CompleteLattice β\ns : Set α\nf : α → β\nhf : Monotone f\n⊢ (⨆ (a : α) (_ : ... | [
957,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
956,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | PSet.Resp.Equiv.euc | [] | [
571,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
11
] |
Mathlib/Data/Finset/Basic.lean | Finset.disjoint_self_iff_empty | [] | [
973,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
972,
1
] |
Mathlib/Deprecated/Group.lean | IsMonoidHom.comp | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝² : MulOneClass α\ninst✝¹ : MulOneClass β\nf : α → β\nhf : IsMonoidHom f\nγ : Type u_1\ninst✝ : MulOneClass γ\ng : β → γ\nhg : IsMonoidHom g\nsrc✝ : IsMulHom (g ∘ f) := IsMulHom.comp hf.toIsMulHom hg.toIsMulHom\n⊢ g (f 1) = 1",
"... | [
220,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.interpolate_eq_of_values_eq_on | [
{
"state_after": "no goals",
"state_before": "F : Type u_2\ninst✝¹ : Field F\nι : Type u_1\ninst✝ : DecidableEq ι\ns t : Finset ι\ni✝ j : ι\nv r r' : ι → F\nhrr' : ∀ (i : ι), i ∈ s → r i = r' i\ni : ι\nhi : i ∈ s\n⊢ ↑C (r i) * Lagrange.basis s v i = ↑C (r' i) * Lagrange.basis s v i",
"tactic": "rw [hrr'... | [
366,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | DoubleQuot.quotQuotEquivComm_comp_quotQuotMk | [] | [
598,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
596,
1
] |
Mathlib/Topology/Instances/AddCircle.lean | AddCircle.continuous_equivIoc_symm | [] | [
276,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | HomologicalComplex.xPrevIsoSelf_comp_dTo | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nV : Type u\ninst✝¹ : Category V\ninst✝ : HasZeroMorphisms V\nc : ComplexShape ι\nC : HomologicalComplex V c\nj : ι\nh : ¬ComplexShape.Rel c (ComplexShape.prev c j) j\n⊢ (xPrevIsoSelf C h).inv ≫ dTo C j = 0",
"tactic": "simp [h]"
}
] | [
438,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Mathlib/MeasureTheory/Measure/Stieltjes.lean | StieltjesFunction.measure_Ici | [
{
"state_after": "f : StieltjesFunction\nl : ℝ\nhf : Tendsto (↑f) atTop (𝓝 l)\nx : ℝ\n⊢ Tendsto (fun x_1 => ↑↑(StieltjesFunction.measure f) (Ico x x_1)) atTop (𝓝 (ofReal (l - leftLim (↑f) x)))",
"state_before": "f : StieltjesFunction\nl : ℝ\nhf : Tendsto (↑f) atTop (𝓝 l)\nx : ℝ\n⊢ ↑↑(StieltjesFunction.me... | [
602,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/Data/List/Basic.lean | List.takeD_length | [] | [
2358,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2356,
1
] |
Mathlib/LinearAlgebra/FreeModule/PID.lean | Submodule.nonempty_basis_of_pid | [
{
"state_after": "ι✝ : Type ?u.130175\nR : Type u_2\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDomain R\ninst✝³ : IsPrincipalIdealRing R\nM : Type u_3\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\nb✝ : ι✝ → M\nι : Type u_1\ninst✝ : Finite ι\nb : Basis ι R M\nN : Submodule R M\nthis : DecidableEq M\n⊢ ∃ n, Nonempty (Basi... | [
315,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | continuousAt_inv | [] | [
217,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Algebra/Order/Group/Abs.lean | sub_lt_of_abs_sub_lt_right | [] | [
305,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_sum_of_nonneg | [
{
"state_after": "case empty\nx y z : ℝ\nι : Type u_1\na : ℝ\nha : 0 ≤ a\ns : Finset ι\nf : ι → ℝ\nh✝ : ∀ (x : ι), x ∈ s → 0 ≤ f x\nh : ∀ (x : ι), x ∈ ∅ → 0 ≤ f x\n⊢ a ^ ∑ x in ∅, f x = ∏ x in ∅, a ^ f x\n\ncase cons\nx y z : ℝ\nι : Type u_1\na : ℝ\nha : 0 ≤ a\ns✝ : Finset ι\nf : ι → ℝ\nh✝ : ∀ (x : ι), x ∈ s✝ →... | [
221,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.compRight_apply | [] | [
506,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/CategoryTheory/Opposites.lean | CategoryTheory.Functor.rightOp_leftOp_eq | [
{
"state_after": "case mk\nC : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\ntoPrefunctor✝ : Cᵒᵖ ⥤q D\nmap_id✝ : ∀ (X : Cᵒᵖ), toPrefunctor✝.map (𝟙 X) = 𝟙 (toPrefunctor✝.obj X)\nmap_comp✝ :\n ∀ {X Y Z : Cᵒᵖ} (f : X ⟶ Y) (g : Y ⟶ Z), toPrefunctor✝.map (f ≫ g) = toPrefunctor✝.map f ≫ toPrefunct... | [
302,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.volume_pi_le_diam_pow | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\ninst✝ : Fintype ι\ns : Set (ι → ℝ)\n⊢ ∏ _i : ι, ↑1 * EMetric.diam s = EMetric.diam s ^ Fintype.card ι",
"tactic": "simp only [ENNReal.coe_one, one_mul, Finset.prod_const, Fintype.card]"
}
] | [
290,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.le_succ_iff_eq_or_le | [
{
"state_after": "case pos\nα : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : SuccOrder α\na b : α\nhb : IsMax b\n⊢ a ≤ succ b ↔ a = succ b ∨ a ≤ b\n\ncase neg\nα : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : SuccOrder α\na b : α\nhb : ¬IsMax b\n⊢ a ≤ succ b ↔ a = succ b ∨ a ≤ b",
"state_before": "α : Type u_1\... | [
441,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.X_pow_mul_assoc | [
{
"state_after": "no goals",
"state_before": "R : Type u\na b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q : R[X]\nn : ℕ\n⊢ p * X ^ n * q = p * q * X ^ n",
"tactic": "rw [mul_assoc, X_pow_mul, ← mul_assoc]"
}
] | [
603,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
] |
Mathlib/Data/Fin/VecNotation.lean | Matrix.tail_zero | [] | [
551,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
550,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.add_dotProduct | [
{
"state_after": "no goals",
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768,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
767,
1
] |
Mathlib/Data/ZMod/Basic.lean | Prod.fst_zmod_cast | [
{
"state_after": "case zero\nR : Type u_1\ninst✝¹ : AddGroupWithOne R\nS : Type u_2\ninst✝ : AddGroupWithOne S\na : ZMod Nat.zero\n⊢ (↑a).fst = ↑a\n\ncase succ\nR : Type u_1\ninst✝¹ : AddGroupWithOne R\nS : Type u_2\ninst✝ : AddGroupWithOne S\nn✝ : ℕ\na : ZMod (Nat.succ n✝)\n⊢ (↑a).fst = ↑a",
"state_before"... | [
180,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Algebra/BigOperators/Fin.lean | Fin.partialProd_left_inv | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.96916\nβ : Type ?u.96919\ninst✝¹ : Monoid α\nn : ℕ\nG : Type u_1\ninst✝ : Group G\nf : Fin (n + 1) → G\nx : Fin (n + 1)\n⊢ (f 0 • partialProd fun i => (f ↑↑i)⁻¹ * f (succ i)) 0 = f 0",
"tactic": "simp"
},
{
"state_after": "α : Type ?u.969... | [
252,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.partiallyWellOrderedOn_iff_exists_monotone_subseq | [
{
"state_after": "case mp\nι : Type ?u.86706\nα : Type u_1\nβ : Type ?u.86712\nr : α → α → Prop\nr' : β → β → Prop\nf✝ : α → β\ns t : Set α\na : α\ninst✝¹ : IsRefl α r\ninst✝ : IsTrans α r\nh : PartiallyWellOrderedOn s r\nf : ℕ → α\nhf : ∀ (n : ℕ), f n ∈ s\n⊢ ∃ g, ∀ (m n : ℕ), m ≤ n → r (f (↑g m)) (f (↑g n))\n\... | [
365,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Order/Monotone/Basic.lean | strictAnti_nat_of_succ_lt | [] | [
1003,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1002,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.IsWf.union | [] | [
208,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
18
] |
Mathlib/Data/List/Perm.lean | List.Subperm.erase | [] | [
793,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
791,
1
] |
Mathlib/Data/Set/Image.lean | Subtype.preimage_coe_eq_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns t : Set α\n⊢ val ⁻¹' t = ∅ ↔ s ∩ t = ∅",
"tactic": "simp [← not_nonempty_iff_eq_empty, preimage_coe_nonempty]"
}
] | [
1471,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1470,
1
] |
Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.Ico_filter_lt | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : LocallyFiniteOrder α\na✝ b✝ c✝ d a b c : α\n⊢ filter (fun x => x < c) (Ico a b) = Ico a (min b c)",
"tactic": "rw [Ico, Ico, ← Finset.filter_val, Finset.Ico_filter_lt]"
}
] | [
265,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Topology/Spectral/Hom.lean | SpectralMap.coe_comp | [] | [
181,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Analysis/Convex/Join.lean | convexJoin_right_comm | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.70849\n𝕜 : Type u_2\nE : Type u_1\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\ns✝ t✝ u✝ : Set E\nx y : E\ns t u : Set E\n⊢ convexJoin 𝕜 (convexJoin 𝕜 s t) u = convexJoin 𝕜 (convexJoin 𝕜 s u) t",
"tactic": "s... | [
171,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Analysis/NormedSpace/Basic.lean | interior_closedBall | [
{
"state_after": "case inl\nα : Type ?u.47288\nβ : Type ?u.47291\nγ : Type ?u.47294\nι : Type ?u.47297\ninst✝⁶ : NormedField α\ninst✝⁵ : SeminormedAddCommGroup β\nE : Type u_1\ninst✝⁴ : SeminormedAddCommGroup E\ninst✝³ : NormedSpace α E\nF : Type ?u.47328\ninst✝² : SeminormedAddCommGroup F\ninst✝¹ : NormedSpace... | [
150,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Topology/NoetherianSpace.lean | TopologicalSpace.NoetherianSpace.finite_irreducibleComponents | [
{
"state_after": "case intro.intro.intro.intro\nα : Type u_1\nβ : Type ?u.25119\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : NoetherianSpace α\nS : Set (Set α)\nhSf : Set.Finite S\nhSc : ∀ (t : Set α), t ∈ S → IsClosed t\nhSi : ∀ (t : Set α), t ∈ S → IsIrreducible t\nhSU : Set.univ = ⋃₀ S\... | [
220,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.add_antiperiod | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.211684\nf g : α → β\nc c₁ c₂ x : α\ninst✝¹ : AddGroup α\ninst✝ : Neg β\nh1 : Periodic f c₁\nh2 : Antiperiodic f c₂\n⊢ Antiperiodic f (c₁ + c₂)",
"tactic": "simp_all [← add_assoc]"
}
] | [
518,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/GroupTheory/GroupAction/Group.lean | MulAction.surjective₀ | [] | [
233,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
11
] |
Mathlib/CategoryTheory/Functor/Basic.lean | CategoryTheory.Functor.toPrefunctor_comp | [] | [
151,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Order/Bounds/Basic.lean | isGLB_iff_le_iff | [] | [
325,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Data/PFunctor/Univariate/Basic.lean | PFunctor.liftr_iff | [
{
"state_after": "case mp\nP : PFunctor\nα : Type u\nr : α → α → Prop\nx y : Obj P α\n⊢ Liftr r x y → ∃ a f₀ f₁, x = { fst := a, snd := f₀ } ∧ y = { fst := a, snd := f₁ } ∧ ∀ (i : B P a), r (f₀ i) (f₁ i)\n\ncase mpr\nP : PFunctor\nα : Type u\nr : α → α → Prop\nx y : Obj P α\n⊢ (∃ a f₀ f₁, x = { fst := a, snd :=... | [
228,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Topology/Semicontinuous.lean | IsClosed.lowerSemicontinuousOn_indicator | [] | [
239,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/SetTheory/Lists.lean | Lists'.Subset.refl | [
{
"state_after": "α : Type u_1\nl : Lists' α true\n⊢ ofList (toList l) ⊆ ofList (toList l)",
"state_before": "α : Type u_1\nl : Lists' α true\n⊢ l ⊆ l",
"tactic": "rw [← Lists'.of_toList l]"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : Lists' α true\n⊢ ofList (toList l)... | [
186,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Tactic/NormNum/Prime.lean | Mathlib.Meta.NormNum.isNat_prime_0 | [] | [
173,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Topology/Maps.lean | Inducing.nhds_eq_comap | [] | [
96,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.norm_integral_le_of_norm_le_const | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type u_2\nF : Type ?u.1268526\n𝕜 : Type ?u.1268529\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace ℝ E\ninst✝⁹ : CompleteSpace E\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : NormedSpace 𝕜 E\ninst✝⁶ : SMulCommClass ℝ 𝕜 E\ninst✝⁵ : No... | [
1378,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1374,
1
] |
Mathlib/Init/Algebra/Order.lean | not_lt_of_ge | [] | [
156,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Algebra/Group/Defs.lean | mul_left_inv | [] | [
1079,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1078,
1
] |
Mathlib/Order/Hom/Lattice.lean | InfHom.comp_apply | [] | [
598,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.div_zero | [] | [
1102,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1101,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.diagonal_add | [
{
"state_after": "case a.h\nl : Type ?u.51115\nm : Type ?u.51118\nn : Type u_1\no : Type ?u.51124\nm' : o → Type ?u.51129\nn' : o → Type ?u.51134\nR : Type ?u.51137\nS : Type ?u.51140\nα : Type v\nβ : Type w\nγ : Type ?u.51147\ninst✝¹ : DecidableEq n\ninst✝ : AddZeroClass α\nd₁ d₂ : n → α\ni j : n\n⊢ (diagonal ... | [
477,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.sSameSide_self_iff | [] | [
249,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Geometry/Euclidean/Sphere/Basic.lean | EuclideanGeometry.dist_center_eq_dist_center_of_mem_sphere | [
{
"state_after": "no goals",
"state_before": "V : Type ?u.5000\nP : Type u_1\ninst✝ : MetricSpace P\np₁ p₂ : P\ns : Sphere P\nhp₁ : p₁ ∈ s\nhp₂ : p₂ ∈ s\n⊢ dist p₁ s.center = dist p₂ s.center",
"tactic": "rw [mem_sphere.1 hp₁, mem_sphere.1 hp₂]"
}
] | [
139,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Analysis/Calculus/Deriv/Add.lean | HasStrictDerivAt.neg | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type w\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL : Filter �... | [
217,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
8
] |
Mathlib/Order/Atoms.lean | GaloisCoinsertion.isCoatom_iff | [] | [
777,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
774,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.coe_map | [] | [
232,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Data/List/Card.lean | List.insert_equiv_cons | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\na : α\nas : List α\nx : α\n⊢ x ∈ List.insert a as ↔ x ∈ a :: as",
"tactic": "simp"
}
] | [
27,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
26,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Basic.lean | Pmf.ext_iff | [] | [
63,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Algebra/Algebra/Basic.lean | algebraMap.coe_neg | [] | [
180,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Topology/FiberBundle/IsHomeomorphicTrivialBundle.lean | isHomeomorphicTrivialFiberBundle_fst | [] | [
73,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidWithZeroHom.copy_eq | [] | [
656,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
1
] |
Mathlib/Order/Filter/Archimedean.lean | Filter.Tendsto.atTop_mul_neg_const' | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nR : Type u_1\nl : Filter α\nf : α → R\nr : R\ninst✝¹ : LinearOrderedRing R\ninst✝ : Archimedean R\nhr : r < 0\nhf : Tendsto f l atTop\n⊢ Tendsto (fun x => f x * r) l atBot",
"tactic": "simpa only [tendsto_neg_atTop_iff, mul_neg] using hf.atTop_... | [
190,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.kernelSubobject_arrow_comp | [
{
"state_after": "C : Type u\ninst✝² : Category C\nX Y Z : C\ninst✝¹ : HasZeroMorphisms C\nf : X ⟶ Y\ninst✝ : HasKernel f\n⊢ ((kernelSubobjectIso f).hom ≫ kernel.ι f) ≫ f = 0",
"state_before": "C : Type u\ninst✝² : Category C\nX Y Z : C\ninst✝¹ : HasZeroMorphisms C\nf : X ⟶ Y\ninst✝ : HasKernel f\n⊢ arrow (... | [
115,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.ofDigits_zmod | [] | [
538,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
1
] |
Mathlib/Data/List/Rotate.lean | List.isRotated_iff_mod | [
{
"state_after": "α : Type u\nl l' : List α\nh : l ~r l'\n⊢ ∃ n, n ≤ length l ∧ rotate l n = l'",
"state_before": "α : Type u\nl l' : List α\n⊢ l ~r l' ↔ ∃ n, n ≤ length l ∧ rotate l n = l'",
"tactic": "refine' ⟨fun h => _, fun ⟨n, _, h⟩ => ⟨n, h⟩⟩"
},
{
"state_after": "case intro\nα : Type u\nl... | [
541,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Complex.differentiable_cos | [] | [
88,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.mono_measure | [] | [
198,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Algebra/Bounds.lean | ciSup_mul | [] | [
152,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integral_indicator | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.36984\nE : Type u_2\nF : Type ?u.36990\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\nhs : MeasurableSet s\nhfi : IntegrableOn f s\n⊢ ... | [
183,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
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