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/Fintype/Lattice.lean | Finset.inf_univ_eq_iInf | [] | [
38,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.univ_pi_eq_iInter | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.286650\nγ : Type ?u.286653\nι : Sort ?u.286656\nι' : Sort ?u.286659\nι₂ : Sort ?u.286662\nκ : ι → Sort ?u.286667\nκ₁ : ι → Sort ?u.286672\nκ₂ : ι → Sort ?u.286677\nκ' : ι' → Sort ?u.286682\nπ : α → Type u_1\nt : (i : α) → Set (π i)\n⊢ p... | [
2025,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2024,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_comp_mul_deriv''' | [
{
"state_after": "ι : Type ?u.1930290\n𝕜 : Type ?u.1930293\nE : Type ?u.1930296\nF : Type ?u.1930299\nA : Type ?u.1930302\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\nf✝¹ : ℝ → E\ng' g✝ φ : ℝ → ℝ\nf✝ f'✝ : ℝ → E\na b : ℝ\nf f' g : ℝ → ℝ\nhf : ContinuousOn f [[a, b]]\nhff' ... | [
1469,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1462,
1
] |
Mathlib/MeasureTheory/Covering/Besicovitch.lean | Besicovitch.TauPackage.mem_iUnionUpTo_lastStep | [
{
"state_after": "α : Type u_1\ninst✝¹ : MetricSpace α\nβ : Type u\ninst✝ : Nonempty β\np : TauPackage β α\nx : β\nA :\n ∀ (z : β),\n BallPackage.c p.toBallPackage z ∈ iUnionUpTo p (lastStep p) ∨\n p.τ * BallPackage.r p.toBallPackage z < R p (lastStep p)\n⊢ BallPackage.c p.toBallPackage x ∈ iUnionUpTo ... | [
344,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/RingTheory/RootsOfUnity/Complex.lean | Complex.isPrimitiveRoot_iff | [
{
"state_after": "ζ : ℂ\nn : ℕ\nhn : n ≠ 0\nhn0 : ↑n ≠ 0\n⊢ IsPrimitiveRoot ζ n ↔ ∃ i, i < n ∧ ∃ x, exp (2 * ↑π * I * (↑i / ↑n)) = ζ",
"state_before": "ζ : ℂ\nn : ℕ\nhn : n ≠ 0\n⊢ IsPrimitiveRoot ζ n ↔ ∃ i, i < n ∧ ∃ x, exp (2 * ↑π * I * (↑i / ↑n)) = ζ",
"tactic": "have hn0 : (n : ℂ) ≠ 0 := by exact_mod... | [
71,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.toAddSubmonoid'_closure | [] | [
166,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Algebra/Field/Basic.lean | neg_div_neg_eq | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.33103\nβ : Type ?u.33106\nK : Type u_1\ninst✝¹ : DivisionMonoid K\ninst✝ : HasDistribNeg K\na✝ b✝ a b : K\n⊢ -a / -b = a / b",
"tactic": "rw [div_neg_eq_neg_div, neg_div, neg_neg]"
}
] | [
124,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Std/Logic.lean | of_iff_true | [] | [
55,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
55,
1
] |
src/lean/Init/Data/Range.lean | Membership.mem.lower | [
{
"state_after": "i : Nat\nr : Std.Range\nh : r.start ≤ i ∧ i < r.stop\n⊢ r.start ≤ i",
"state_before": "i : Nat\nr : Std.Range\nh : i ∈ r\n⊢ r.start ≤ i",
"tactic": "simp [Membership.mem] at h"
},
{
"state_after": "no goals",
"state_before": "i : Nat\nr : Std.Range\nh : r.start ≤ i ∧ i < r.... | [
85,
12
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
83,
1
] |
Mathlib/Topology/Basic.lean | closure_diff_interior | [] | [
696,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
695,
1
] |
Mathlib/Topology/Algebra/Monoid.lean | ContinuousMul.of_nhds_one | [
{
"state_after": "ι : Type ?u.47046\nα : Type ?u.47049\nX : Type ?u.47052\nM✝ : Type ?u.47055\nN : Type ?u.47058\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : TopologicalSpace M✝\ninst✝³ : Mul M✝\ninst✝² : ContinuousMul M✝\nM : Type u\ninst✝¹ : Monoid M\ninst✝ : TopologicalSpace M\nhmul : Tendsto (uncurry fun x x_1 =>... | [
292,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/Analysis/NormedSpace/Dual.lean | NormedSpace.isClosed_polar | [
{
"state_after": "𝕜 : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\ns : Set E\n⊢ IsClosed (LinearMap.polar (LinearMap.flip (dualPairing 𝕜 E)) s)",
"state_before": "𝕜 : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_1\n... | [
209,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.infs_subset_iff | [] | [
288,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Data/Set/Function.lean | Set.LeftInvOn.image_inter | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.59565\nι : Sort ?u.59568\nπ : α → Type ?u.59573\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\np : Set γ\nf f₁ f₂ f₃ : α → β\ng g₁ g₂ : β → γ\nf' f₁' f₂' : β → α\ng' : γ → β\na : α\nb : β\nhf : LeftInvOn f' f s\n⊢ f' ⁻¹' s₁ ∩ f '' s = f' ⁻¹' (s₁ ∩ s) ∩ f '' s",
... | [
1084,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1080,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_const_smul | [] | [
1289,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1288,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_sub | [] | [
754,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
754,
20
] |
Mathlib/Algebra/Free.lean | FreeMagma.map_of | [] | [
152,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.span_insert_zero | [
{
"state_after": "R : Type u_2\nR₂ : Type ?u.12510\nK : Type ?u.12513\nM : Type u_1\nM₂ : Type ?u.12519\nV : Type ?u.12522\nS : Type ?u.12525\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nx : M\np p' : Submodule R M\ninst✝² : Semiring R₂\nσ₁₂ : R →+* R₂\ninst✝¹ : AddCommMonoid M₂\ninst✝ :... | [
121,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Data/List/Nodup.lean | List.rel_nodup | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nl l₁ l₂ : List α\nr✝ : α → α → Prop\na b : α\nr : α → β → Prop\nhr : Relator.BiUnique r\n⊢ (fun x x_1 => x ↔ x_1) (Nodup []) (Nodup [])",
"tactic": "simp only [nodup_nil]"
},
{
"state_after": "no goals",
"state_before": "α... | [
56,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.all_node3R | [] | [
504,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
1
] |
Mathlib/Topology/Constructions.lean | isOpenMap_sum | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type u_1\nδ : Type ?u.143123\nε : Type ?u.143126\nζ : Type ?u.143129\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α ⊕ β → γ\n⊢ IsOpenMap f ↔ (IsOpenMap fun a =... | [
974,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
972,
1
] |
Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.rightAssocTensor_map | [] | [
445,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
Mathlib/MeasureTheory/Covering/Differentiation.lean | VitaliFamily.exists_measurable_supersets_limRatio | [
{
"state_after": "α : Type u_1\ninst✝⁵ : MetricSpace α\nm0 : MeasurableSpace α\nμ : MeasureTheory.Measure α\nv : VitaliFamily μ\nE : Type ?u.2509902\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : SecondCountableTopology α\ninst✝² : BorelSpace α\ninst✝¹ : IsLocallyFiniteMeasure μ\nρ : MeasureTheory.Measure α\ninst✝ : ... | [
420,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Algebra/Group/Prod.lean | MonoidHom.snd_comp_prod | [] | [
577,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
576,
1
] |
Mathlib/Analysis/LocallyConvex/BalancedCoreHull.lean | balancedCore_subset_balancedCoreAux | [] | [
198,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.X_add_C_ne_one | [] | [
1412,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1411,
1
] |
Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.SignedMeasure.haveLebesgueDecomposition_mk' | [
{
"state_after": "α : Type u_1\nβ : Type ?u.456531\nm : MeasurableSpace α\nμ✝ ν : Measure α\ns t : SignedMeasure α\nμ : Measure α\nf : α → ℝ\nhf : Measurable f\nhfi : Integrable f\nhtμ : t ⟂ᵥ toENNRealVectorMeasure μ\nhadd : s = t + withDensityᵥ μ f\nhtμ' : t ⟂ᵥ toENNRealVectorMeasure μ\n⊢ HaveLebesgueDecomposi... | [
1015,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1000,
9
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_biUnion_finset₀ | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.1024019\nδ : Type ?u.1024022\nm : MeasurableSpace α\nμ ν : Measure α\ns : Finset β\nt : β → Set α\nhd : Set.Pairwise (↑s) (AEDisjoint μ on t)\nhm : ∀ (b : β), b ∈ s → NullMeasurableSet (t b)\nf : α → ℝ≥0∞\n⊢ (∫⁻ (a : α) in... | [
1212,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1209,
1
] |
Mathlib/Order/UpperLower/Basic.lean | IsLowerSet.not_bot_mem | [] | [
316,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Ring.lean | tsum_mul_tsum_eq_tsum_sum_antidiagonal | [
{
"state_after": "ι : Type ?u.30248\nκ : Type ?u.30251\nR : Type ?u.30254\nα : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : NonUnitalNonAssocSemiring α\nf g : ℕ → α\ninst✝¹ : T3Space α\ninst✝ : TopologicalSemiring α\nhf : Summable f\nhg : Summable g\nhfg : Summable fun x => f x.fst * g x.snd\n⊢ ((∑' (n : ℕ),... | [
228,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Data/Num/Lemmas.lean | PosNum.of_to_nat | [] | [
527,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
1
] |
Mathlib/Data/List/Basic.lean | List.map_eq_replicate_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.139891\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l : List α\nf : α → β\nb : β\n⊢ map f l = replicate (length l) b ↔ ∀ (x : α), x ∈ l → f x = b",
"tactic": "simp [eq_replicate]"
}
] | [
1880,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1878,
1
] |
Mathlib/Data/Finset/Sym.lean | Finset.mem_sym2_iff | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\na b : α\nm : Sym2 α\n⊢ (∃ a, a ∈ s ×ˢ s ∧ Quotient.mk' a = m) → ∀ (a : α), a ∈ m → a ∈ s",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\na b : α\nm : Sym2 α\n⊢ m ∈ Finset.sym2 s ↔ ∀ (a : α), a ∈ m → a ∈ s",
"t... | [
64,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.IsFundamentalDomain.measure_zero_of_invariant | [
{
"state_after": "G : Type u_1\nH : Type ?u.244096\nα : Type u_2\nβ : Type ?u.244102\nE : Type ?u.244105\ninst✝¹⁰ : Group G\ninst✝⁹ : Group H\ninst✝⁸ : MulAction G α\ninst✝⁷ : MeasurableSpace α\ninst✝⁶ : MulAction H β\ninst✝⁵ : MeasurableSpace β\ninst✝⁴ : NormedAddCommGroup E\ns t✝ : Set α\nμ : Measure α\ninst✝... | [
308,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigOWith_of_le | [
{
"state_after": "α : Type u_3\nβ : Type ?u.95599\nE : Type u_1\nF : Type u_2\nG : Type ?u.95608\nE' : Type ?u.95611\nF' : Type ?u.95614\nG' : Type ?u.95617\nE'' : Type ?u.95620\nF'' : Type ?u.95623\nG'' : Type ?u.95626\nR : Type ?u.95629\nR' : Type ?u.95632\n𝕜 : Type ?u.95635\n𝕜' : Type ?u.95638\ninst✝¹² : N... | [
550,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.is_lub_iff_is_greatest | [] | [
1722,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1720,
1
] |
Mathlib/Data/Set/Countable.lean | Set.countable_pi | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\nπ : α → Type u_1\ninst✝ : Finite α\ns : (a : α) → Set (π a)\nhs : ∀ (a : α), Set.Countable (s a)\n⊢ Set.Countable {f | ∀ (a : α), f a ∈ s a}",
"tactic": "simpa only [← mem_univ_pi] using countable_univ_pi hs"
... | [
275,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.multiset_sum_mem | [] | [
165,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
11
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.restrictScalars_toSubfield | [] | [
647,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
645,
1
] |
Mathlib/Data/Multiset/Sections.lean | Multiset.sections_add | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns t : Multiset (Multiset α)\n⊢ Sections (0 + t) = bind (Sections 0) fun m => map ((fun x x_1 => x + x_1) m) (Sections t)",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns✝ t : Multiset (Multiset α)\... | [
59,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
src/lean/Init/Prelude.lean | of_decide_eq_self_eq_true | [] | [
868,
32
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
865,
1
] |
Mathlib/Data/List/Basic.lean | List.getD_eq_nthLe | [] | [
4399,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4398,
1
] |
Mathlib/NumberTheory/Padics/Hensel.lean | deriv_sq_norm_pos | [] | [
112,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
9
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | StrictAntiOn.const_mul' | [] | [
1397,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1395,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.inv_pure | [] | [
213,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.erase_right_comm | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.216947\nγ : Type ?u.216950\ninst✝ : DecidableEq α\ns✝ t u v : Finset α\na✝ b✝ a b : α\ns : Finset α\nx : α\n⊢ x ∈ erase (erase s a) b ↔ x ∈ erase (erase s b) a",
"state_before": "α : Type u_1\nβ : Type ?u.216947\nγ : Type ?u.216950\ninst✝ : DecidableEq α\n... | [
1986,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1983,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.coe_restrict_scalarsL' | [] | [
1289,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1288,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.centralizer_eq_top_iff_subset | [] | [
2318,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2317,
1
] |
Mathlib/Logic/Encodable/Basic.lean | Encodable.encode_injective | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.51\ninst✝ : Encodable α\nx y : α\ne : encode x = encode y\n⊢ some x = some y",
"tactic": "rw [← encodek, e, encodek]"
}
] | [
68,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.le_einfsep | [] | [
127,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Topology/Constructions.lean | isOpenMap_ofAdd | [] | [
112,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/RingTheory/Adjoin/Basic.lean | AlgHom.adjoin_le_equalizer | [] | [
425,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.IsFundamentalDomain.exists_ne_one_smul_eq | [
{
"state_after": "G : Type u_1\nH : Type ?u.435204\nα : Type u_2\nβ : Type ?u.435210\nE : Type ?u.435213\ninst✝¹² : Group G\ninst✝¹¹ : Group H\ninst✝¹⁰ : MulAction G α\ninst✝⁹ : MeasurableSpace α\ninst✝⁸ : MulAction H β\ninst✝⁷ : MeasurableSpace β\ninst✝⁶ : NormedAddCommGroup E\ns t : Set α\nμ : Measure α\ninst... | [
502,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/Order/Antichain.lean | Set.Subsingleton.isAntichain | [] | [
213,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Data/Fintype/Basic.lean | Finset.coe_filter_univ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.31041\nγ : Type ?u.31044\ninst✝¹ : Fintype α\ns t : Finset α\np : α → Prop\ninst✝ : DecidablePred p\n⊢ ↑(filter p univ) = {x | p x}",
"tactic": "simp"
}
] | [
322,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | GroupNorm.le_def | [] | [
784,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
783,
1
] |
Mathlib/Data/Nat/Size.lean | Nat.size_shiftl' | [
{
"state_after": "case succ\nb : Bool\nm n✝ : ℕ\nh✝ : shiftl' b m n✝ ≠ 0\nn : ℕ\nIH : shiftl' b m n ≠ 0 → size (shiftl' b m n) = size m + n\nh : ¬bit b (shiftl' b m n) = 0\n⊢ size (bit b (shiftl' b m n)) = size m + succ n",
"state_before": "b : Bool\nm n : ℕ\nh : shiftl' b m n ≠ 0\n⊢ size (shiftl' b m n) = ... | [
122,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.roots_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np✝ q✝ p q : R[X]\nhpq : p * q ≠ 0\nr : R\n⊢ count r (roots (p * q)) = count r (roots p + roots q)",
"tactic": "rw [count_add, count_roots, count_roots, count_roots, ... | [
628,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
626,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.π_comp_cokernelIsoOfEq_inv | [
{
"state_after": "case refl\nC : Type u\ninst✝⁴ : Category C\ninst✝³ : HasZeroMorphisms C\nX Y : C\nf✝ : X ⟶ Y\ninst✝² : HasCokernel f✝\nf : X ⟶ Y\ninst✝¹ inst✝ : HasCokernel f\n⊢ cokernel.π f ≫ (cokernelIsoOfEq (_ : f = f)).inv = cokernel.π f",
"state_before": "C : Type u\ninst✝⁴ : Category C\ninst✝³ : Has... | [
835,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
833,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.smul_union | [] | [
1389,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1388,
1
] |
Mathlib/Data/ZMod/Quotient.lean | MulAction.orbitZpowersEquiv_symm_apply | [] | [
143,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.uIcc_toDual | [] | [
877,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
876,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | IsComplete.union | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝ : UniformSpace α\ns t : Set α\nhs : ∀ (l : Ultrafilter α), Cauchy ↑l → s ∈ l → ∃ x, x ∈ s ∧ ↑l ≤ 𝓝 x\nht : ∀ (l : Ultrafilter α), Cauchy ↑l → t ∈ l → ∃ x, x ∈ t ∧ ↑l ≤ 𝓝 x\n⊢ ∀ (l : Ultrafilter α), Cauchy ↑l → (s ∈ l → ∃ x, x ∈ s ∪ t ∧ ↑l ≤ 𝓝 x) ∧ (t ∈ l → ∃ x,... | [
343,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
11
] |
Mathlib/CategoryTheory/Elements.lean | CategoryTheory.CategoryOfElements.to_fromCostructuredArrow_eq | [
{
"state_after": "case refine'_1\nC : Type u\ninst✝ : Category C\nF✝ : C ⥤ Type w\nF : Cᵒᵖ ⥤ Type v\n⊢ ∀ (X : CostructuredArrow yoneda F),\n ((fromCostructuredArrow F).rightOp ⋙ toCostructuredArrow F).obj X = (𝟭 (CostructuredArrow yoneda F)).obj X\n\ncase refine'_2\nC : Type u\ninst✝ : Category C\nF✝ : C ⥤ ... | [
254,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/LinearAlgebra/Projection.lean | LinearMap.ofIsCompl_zero | [] | [
259,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Analysis/Asymptotics/Theta.lean | Asymptotics.IsTheta.pow | [] | [
250,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Logic/Equiv/Set.lean | Equiv.Set.union_apply_left | [] | [
242,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Order/Closure.lean | ClosureOperator.mem_mk₃_closed | [] | [
221,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | LinearMap.toMatrix₂'_compl₁₂ | [
{
"state_after": "case a.h\nR : Type u_1\nR₁ : Type ?u.654456\nR₂ : Type ?u.654459\nM : Type ?u.654462\nM₁ : Type ?u.654465\nM₂ : Type ?u.654468\nM₁' : Type ?u.654471\nM₂' : Type ?u.654474\nn : Type u_2\nm : Type u_3\nn' : Type u_4\nm' : Type u_5\nι : Type ?u.654489\ninst✝¹⁰ : CommRing R\ninst✝⁹ : CommRing R₁\n... | [
305,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | Associates.mk_out | [] | [
260,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.Eventually.frequently | [] | [
1258,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1256,
1
] |
Mathlib/Data/Polynomial/HasseDeriv.lean | Polynomial.hasseDeriv_apply_one | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nk : ℕ\nf : R[X]\nhk : 0 < k\n⊢ ↑(hasseDeriv k) 1 = 0",
"tactic": "rw [← C_1, hasseDeriv_C k _ hk]"
}
] | [
139,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/RingTheory/DiscreteValuationRing/Basic.lean | DiscreteValuationRing.HasUnitMulPowIrreducibleFactorization.unique_irreducible | [
{
"state_after": "case intro.intro\nR : Type u_1\ninst✝ : CommRing R\np q : R\nhp : Irreducible p\nhq : Irreducible q\nϖ : R\nhϖ : Irreducible ϖ\nhR : ∀ {x : R}, x ≠ 0 → ∃ n, Associated (ϖ ^ n) x\n⊢ Associated p q",
"state_before": "R : Type u_1\ninst✝ : CommRing R\nhR : HasUnitMulPowIrreducibleFactorizatio... | [
194,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.coe_int_dvd_iff | [
{
"state_after": "case mp\nd z : ℤ\na : ℤ√d\n⊢ ↑z ∣ a → z ∣ a.re ∧ z ∣ a.im\n\ncase mpr\nd z : ℤ\na : ℤ√d\n⊢ z ∣ a.re ∧ z ∣ a.im → ↑z ∣ a",
"state_before": "d z : ℤ\na : ℤ√d\n⊢ ↑z ∣ a ↔ z ∣ a.re ∧ z ∣ a.im",
"tactic": "constructor"
},
{
"state_after": "case mp.intro\nd z : ℤ\nx : ℤ√d\n⊢ z ∣ (↑z ... | [
368,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/GroupTheory/Coset.lean | QuotientGroup.out_eq' | [] | [
531,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
1
] |
Mathlib/Data/List/OfFn.lean | List.ofFn_succ | [
{
"state_after": "no goals",
"state_before": "α : Type u\nn : ℕ\nf : Fin (succ n) → α\n⊢ length (ofFn f) = length (f 0 :: ofFn fun i => f (Fin.succ i))",
"tactic": "simp"
},
{
"state_after": "case zero\nα : Type u\nn : ℕ\nf : Fin (succ n) → α\nhi₁ : zero < length (ofFn f)\nhi₂ : zero < length (f... | [
121,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Tactic/NormNum/Prime.lean | Mathlib.Meta.NormNum.minFacHelper_2 | [
{
"state_after": "n k k' : ℕ\ne : k + 2 = k'\nnk : ¬Nat.Prime k\nh : MinFacHelper n k\nh2 : minFac n = k\n⊢ False",
"state_before": "n k k' : ℕ\ne : k + 2 = k'\nnk : ¬Nat.Prime k\nh : MinFacHelper n k\n⊢ MinFacHelper n k'",
"tactic": "refine minFacHelper_1 e h λ h2 ↦ ?_"
},
{
"state_after": "n k... | [
93,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Data/Analysis/Topology.lean | Ctop.Realizer.tendsto_nhds_iff | [] | [
238,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.isOrtho_top_left | [] | [
335,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Data/Finmap.lean | Finmap.lookup_isSome | [] | [
286,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.AbsTheory.abs_nonneg' | [] | [
911,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
910,
9
] |
Mathlib/Order/CompleteLattice.lean | iSup_const_mono | [] | [
881,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
880,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | eq_orthogonalProjectionFn_of_mem_of_inner_eq_zero | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.457095\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : InnerProductSpace ℝ F\nK : Submodule 𝕜 E\ninst✝ : CompleteSpace { x // x ∈ K }\nu v : E\nhvm : v ∈ K\nhvo : ∀ (w : E), w... | [
426,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Std/Data/Int/Lemmas.lean | Int.le.intro | [
{
"state_after": "a b : Int\nn : Nat\nh : a + ↑n = b\n⊢ ↑n + a - a = ↑n",
"state_before": "a b : Int\nn : Nat\nh : a + ↑n = b\n⊢ b - a = ↑n",
"tactic": "rw [← h, Int.add_comm]"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nn : Nat\nh : a + ↑n = b\n⊢ ↑n + a - a = ↑n",
"tacti... | [
561,
88
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
560,
1
] |
Mathlib/RingTheory/Ideal/AssociatedPrime.lean | exists_le_isAssociatedPrime_of_isNoetherianRing | [
{
"state_after": "R : Type u_1\ninst✝⁴ : CommRing R\nI J : Ideal R\nM : Type u_2\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\nM' : Type ?u.34132\ninst✝¹ : AddCommGroup M'\ninst✝ : Module R M'\nf : M →ₗ[R] M'\nH : IsNoetherianRing R\nx : M\nhx : x ≠ 0\nthis : Submodule.annihilator (Submodule.span R {x}) ≠ ⊤\n⊢... | [
107,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.cardDistinctFactors_apply_prime_pow | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.569893\np k : ℕ\nhp : Prime p\nhk : k ≠ 0\n⊢ ↑ω (p ^ k) = 1",
"tactic": "rw [cardDistinctFactors_apply, hp.factors_pow, List.replicate_dedup hk, List.length_singleton]"
}
] | [
934,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
932,
1
] |
Mathlib/Algebra/Squarefree.lean | squarefree_one | [] | [
50,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/CategoryTheory/EpiMono.lean | CategoryTheory.IsIso.of_epi_section | [] | [
205,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.mem_of_nth_eq | [] | [
140,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Images.lean | CategoryTheory.Limits.HasImage.uniq | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\nX Y : C\nf : X ⟶ Y\ninst✝ : HasImage f\nF' : MonoFactorisation f\nl : image f ⟶ F'.I\nw : l ≫ F'.m = image.ι f\n⊢ l ≫ F'.m = image.lift F' ≫ F'.m",
"tactic": "simp [w]"
}
] | [
384,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/Algebra/Module/Equiv.lean | AddEquiv.toNatLinearEquiv_trans | [] | [
834,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
832,
1
] |
Mathlib/Algebra/DirectSum/Basic.lean | DirectSum.sub_apply | [] | [
86,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisCoinsertion.u_inf_l | [] | [
790,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
788,
1
] |
Mathlib/Combinatorics/HalesJewett.lean | Combinatorics.Line.exists_mono_in_high_dimension' | [
{
"state_after": "no goals",
"state_before": "α α' : Type u\ne : α ≃ α'\nκ : Type (max v u)\nx✝¹ : Finite κ\nι : Type\nx✝ : Fintype ι\nh : ∀ (C : (ι → α) → κ), ∃ l, IsMono C l\nC : (ι → α') → κ\nl : Line α ι\nc : κ\nlc : ∀ (x : α), (fun v => C (↑e ∘ v)) ((fun x i => Option.getD (idxFun l i) x) x) = c\nx : α... | [
331,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
9
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.RespectsIso.op | [] | [
100,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Algebra/Ring/BooleanRing.lean | ofBoolRing_sub | [] | [
517,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm'_trim | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.3169381\nG : Type ?u.3169384\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nhm : m ≤ m0\nf : α → E\nhf : StronglyMeasurable f\n⊢ (∫⁻ (a : α), ↑‖f a‖... | [
962,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
955,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.weightedVSubOfPoint_apply_const | [
{
"state_after": "no goals",
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Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.integrableOn_finite_biUnion | [
{
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Mathlib/Analysis/Calculus/ContDiff.lean | contDiff_apply_apply | [] | [
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