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/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.add_apply | [] | [
317,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
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Mathlib/Analysis/Convex/Body.lean | ConvexBody.isClosed | [] | [
77,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
11
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | MulLECancellable.mul_le_mul_iff_left | [] | [
1635,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1633,
11
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Mathlib/Order/SuccPred/Limit.lean | Order.IsSuccLimit.isMin | [
{
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221,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
11
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Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | HasFDerivWithinAt.uniqueDiffWithinAt_of_continuousLinearEquiv | [] | [
518,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
1
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.zero_toNat | [
{
"state_after": "no goals",
"state_before": "α β : Type u\n⊢ ↑toNat 0 = 0",
"tactic": "rw [← toNat_cast 0, Nat.cast_zero]"
}
] | [
1752,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1752,
1
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Std/Data/List/Lemmas.lean | List.cons_eq_append | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\nx : α✝\nc a b : List α✝\n⊢ x :: c = a ++ b ↔ a = [] ∧ b = x :: c ∨ ∃ a', a = x :: a' ∧ c = a' ++ b",
"tactic": "rw [eq_comm, append_eq_cons]"
}
] | [
129,
31
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
127,
1
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Mathlib/Order/Iterate.lean | Function.antitone_iterate_of_le_id | [] | [
151,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
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Mathlib/Topology/Algebra/Order/LeftRightLim.lean | Monotone.countable_not_continuousWithinAt_Iio | [] | [
277,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
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Mathlib/Data/MvPolynomial/Division.lean | MvPolynomial.mul_X_modMonomial | [] | [
193,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
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Mathlib/MeasureTheory/Function/EssSup.lean | essSup_map_measure_of_measurable | [
{
"state_after": "α : Type u_3\nβ : Type u_2\nm : MeasurableSpace α\nμ ν : MeasureTheory.Measure α\ninst✝⁵ : CompleteLattice β\nγ : Type u_1\nmγ : MeasurableSpace γ\nf : α → γ\ng : γ → β\ninst✝⁴ : MeasurableSpace β\ninst✝³ : TopologicalSpace β\ninst✝² : SecondCountableTopology β\ninst✝¹ : OrderClosedTopology β\... | [
254,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
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Mathlib/CategoryTheory/Core.lean | CategoryTheory.Core.comp_hom | [] | [
61,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
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Mathlib/Order/Filter/AtTopBot.lean | Filter.atTop_basis' | [] | [
140,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
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Mathlib/Data/Complex/Basic.lean | Complex.ofReal_nat_cast | [] | [
835,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
834,
1
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Mathlib/Control/Functor.lean | Functor.Comp.functor_id_comp | [] | [
234,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
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Mathlib/Data/FunLike/Embedding.lean | EmbeddingLike.injective | [] | [
147,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
11
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Mathlib/MeasureTheory/Function/Egorov.lean | MeasureTheory.Egorov.exists_notConvergentSeq_lt | [
{
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111,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
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Mathlib/Deprecated/Group.lean | MulEquiv.isGroupHom | [] | [
263,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
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Mathlib/Data/Set/Intervals/ProjIcc.lean | Set.monotone_projIcc | [] | [
96,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
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Mathlib/Data/Finsupp/Fin.lean | Finsupp.cons_ne_zero_iff | [
{
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"state_before": "n : ℕ\ni : Fin n\nM : Type u_1\ninst✝ : Zero M\ny : M\nt : Fin (n + 1) →₀ M\ns : Fin n →₀ M\n⊢ cons y s ≠ 0 ↔ y ≠ 0 ∨ s ≠ 0",
"tactic": "ref... | [
95,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
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Mathlib/CategoryTheory/NatTrans.lean | CategoryTheory.NatTrans.id_app' | [] | [
80,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
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Mathlib/Init/Logic.lean | let_body_eq | [
{
"state_after": "no goals",
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"tactic": "exact h _ ▸ rfl"
}
] | [
450,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_eq_measure_smaller_of_between_null_diff | [] | [
283,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
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Mathlib/Algebra/BigOperators/Order.lean | GCongr.prod_le_prod | [] | [
615,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
1
] |
Mathlib/Algebra/Ring/Prod.lean | RingHom.prod_comp_prodMap | [] | [
268,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
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] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.apply_inv_self | [] | [
561,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
561,
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Mathlib/RingTheory/DedekindDomain/Ideal.lean | FractionalIdeal.coe_ideal_span_singleton_mul_inv | [
{
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184,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
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Mathlib/Topology/Instances/AddCircle.lean | continuousAt_toIocMod | [] | [
119,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
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Mathlib/Data/Fin/Basic.lean | Fin.induction_zero | [
{
"state_after": "no goals",
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"tactic": "simp only [mk_zero]"
},
{
"state_after": "n m : ℕ\nC : Fin (n + 1) → Sort u_1\nthis : { val := 0, isLt := (_ : 0 < Nat.succ n) } = 0\ni : Fin (n + 1)\n... | [
1705,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.lintegral_nnnorm_add_right | [] | [
97,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
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Mathlib/Data/Complex/Exponential.lean | Real.exp_1_approx_succ_eq | [
{
"state_after": "n : ℕ\na₁ b₁ : ℝ\nm : ℕ\nen : n + 1 = m\nh : abs' (exp 1 - expNear m 1 ((a₁ - 1) * ↑m)) ≤ abs' 1 ^ m / ↑(Nat.factorial m) * (b₁ * ↑m)\n⊢ abs' (exp 1 - expNear n 1 a₁) ≤ abs' 1 ^ n / ↑(Nat.factorial n) * b₁",
"state_before": "n : ℕ\na₁ b₁ : ℝ\nm : ℕ\nen : n + 1 = m\nrm : ℝ\ner : ↑m = rm\nh ... | [
1800,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1795,
1
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Mathlib/Analysis/Normed/Group/HomCompletion.lean | NormedAddGroupHom.norm_completion | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝² : SeminormedAddCommGroup G\nH : Type u_2\ninst✝¹ : SeminormedAddCommGroup H\nK : Type ?u.13769\ninst✝ : SeminormedAddCommGroup K\nf : NormedAddGroupHom G H\nx : G\n⊢ ‖↑f x‖ ≤ ‖completion f‖ * ‖x‖",
"tactic": "simpa using f.completion.le_... | [
165,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
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Mathlib/Topology/UniformSpace/UniformEmbedding.lean | completeSpace_extension | [
{
"state_after": "no goals",
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383,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/CategoryTheory/Limits/Types.lean | CategoryTheory.Limits.Types.jointly_surjective | [
{
"state_after": "J : Type v\ninst✝ : SmallCategory J\nF : J ⥤ TypeMax\nt : Cocone F\nh : IsColimit t\nx : t.pt\n⊢ (fun x => { down := ∃ j y, t.ι.app j y = x }) = fun x => { down := True }",
"state_before": "J : Type v\ninst✝ : SmallCategory J\nF : J ⥤ TypeMax\nt : Cocone F\nh : IsColimit t\nx : t.pt\n⊢ ∃ j... | [
371,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Data/List/Infix.lean | List.suffix_insert | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.53447\nl✝ l₁ l₂ l₃ : List α\na✝ b : α\nm n : ℕ\ninst✝ : DecidableEq α\na : α\nl : List α\nh : a ∈ l\n⊢ l <:+ List.insert a l\n\ncase neg\nα : Type u_1\nβ : Type ?u.53447\nl✝ l₁ l₂ l₃ : List α\na✝ b : α\nm n : ℕ\ninst✝ : DecidableEq α\na : α\nl : List α\nh : ... | [
486,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
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Mathlib/Algebra/Periodic.lean | Function.Antiperiodic.eq | [
{
"state_after": "no goals",
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"tactic": "simpa only [zero_add] using h 0"
}
] | [
384,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
11
] |
Mathlib/Computability/TuringMachine.lean | Turing.TM1to1.trTape'_move_left | [
{
"state_after": "case intro.intro\nΓ : Type u_1\ninst✝² : Inhabited Γ\nΛ : Type ?u.366855\ninst✝¹ : Inhabited Λ\nσ : Type ?u.366861\ninst✝ : Inhabited σ\nn : ℕ\nenc : Γ → Vector Bool n\ndec : Vector Bool n → Γ\nenc0 : enc default = Vector.replicate n false\nM : Λ → Stmt₁\nR : ListBlank Γ\na : Γ\nL : ListBlank ... | [
1786,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1771,
1
] |
Mathlib/MeasureTheory/Group/Measure.lean | MulEquiv.isHaarMeasure_map | [] | [
774,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
769,
8
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | LocalHomeomorph.extend_image_source_inter | [
{
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"state_before": "𝕜 : Type u_3\nE : Type u_1\nM : Type u_2\nH : Type u_4\nE' : Type ?u.167966\nM' : Type ?u.167969\nH' : Type ?u.167972\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : TopologicalSpace H\ninst✝⁴ : Topologic... | [
972,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
969,
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] |
Mathlib/Algebra/ContinuedFractions/Computation/Translations.lean | GeneralizedContinuedFraction.IntFractPair.stream_succ_of_some | [] | [
103,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/FieldTheory/Normal.lean | Normal.isAlgebraic | [] | [
49,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.IsRefl.ortho_comm | [] | [
866,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
865,
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Mathlib/RingTheory/IntegralClosure.lean | leadingCoeff_smul_normalizeScaleRoots | [
{
"state_after": "case a\nR : Type u_1\nA : Type ?u.873552\nB : Type ?u.873555\nS : Type ?u.873558\ninst✝⁵ : CommRing R\ninst✝⁴ : CommRing A\ninst✝³ : CommRing B\ninst✝² : CommRing S\ninst✝¹ : Algebra R A\ninst✝ : Algebra R B\nf : R →+* S\np✝ : R[X]\nx : S\np : R[X]\nn✝ : ℕ\n⊢ coeff (leadingCoeff p • normalizeS... | [
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Mathlib/Algebra/GroupWithZero/Units/Basic.lean | not_isUnit_zero | [] | [
78,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.inter_nonempty_of_nonempty_of_sup_direction_eq_top | [
{
"state_after": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nS : AffineSpace V P\np₁ p₂ : P\ns1 s2 : AffineSubspace k P\nh1 : Set.Nonempty ↑s1\nh2 : Set.Nonempty ↑s2\nhd : direction s1 ⊔ direction s2 = ⊤\nh : ¬Set.Nonempty (↑s1 ∩ ↑s2)\n⊢ False",
"... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Chain.lean | Flag.mem_coe_iff | [] | [
319,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
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Mathlib/Order/Iterate.lean | Function.Commute.iterate_pos_lt_iff_map_lt | [
{
"state_after": "case inl\nα : Type u_1\ninst✝ : LinearOrder α\nf g : α → α\nh : Commute f g\nhf : Monotone f\nhg : StrictMono g\nx : α\nn : ℕ\nhn : 0 < n\nH : f x < g x\n⊢ (f^[n]) x < (g^[n]) x ↔ f x < g x\n\ncase inr.inl\nα : Type u_1\ninst✝ : LinearOrder α\nf g : α → α\nh : Commute f g\nhf : Monotone f\nhg ... | [
201,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
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Std/Data/String/Lemmas.lean | String.extract.go₂_append_left | [
{
"state_after": "no goals",
"state_before": "t : List Char\ni : Nat\n⊢ go₂ ([] ++ t) { byteIdx := i } { byteIdx := utf8Len [] + i } = []",
"tactic": "cases t <;> simp [go₂]"
},
{
"state_after": "c : Char\ncs t : List Char\ni : Nat\n⊢ go₂ (cs ++ t) { byteIdx := i + csize c } { byteIdx := utf8Len... | [
402,
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] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
397,
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Mathlib/LinearAlgebra/Dimension.lean | rank_le | [
{
"state_after": "K : Type u\nV V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.12896\nR : Type u\ninst✝⁶ : Ring R\nM : Type v\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\nM' : Type v'\ninst✝³ : AddCommGroup M'\ninst✝² : Module R M'\nM₁ : Type v\nin... | [
148,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Tactic/LinearCombination.lean | Mathlib.Tactic.LinearCombination.pf_div_c | [] | [
48,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.zero_dotProduct' | [] | [
763,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
762,
1
] |
Mathlib/Data/Nat/Totient.lean | Nat.totient_super_multiplicative | [
{
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"state_before": "a b : ℕ\n⊢ φ a * φ b ≤ φ (a * b)",
"tactic": "let d := a.gcd b"
},
{
"state_after": "case inl\nb : ℕ\nd : ℕ := gcd 0 b\n⊢ φ 0 * φ b ≤ φ (0 * b)\n\ncase inr\na b : ℕ\nd : ℕ := gcd a b\nha0 : 0 < a\n⊢ φ a * φ b... | [
359,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
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Mathlib/CategoryTheory/Sites/Grothendieck.lean | CategoryTheory.GrothendieckTopology.top_covers | [
{
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}
] | [
344,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
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Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinitePos_iff_infinite_of_pos | [] | [
512,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
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Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.affineCombinationLineMapWeights_self | [
{
"state_after": "no goals",
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716,
41
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714,
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Mathlib/Algebra/Hom/Group.lean | map_eq_one_iff | [] | [
232,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
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Mathlib/Topology/ContinuousOn.lean | continuousWithinAt_id | [] | [
991,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
990,
1
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Mathlib/LinearAlgebra/Matrix/Diagonal.lean | Matrix.diagonal_toLin' | [] | [
50,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
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Mathlib/Data/Finset/Basic.lean | Finset.filter_ssubset | [] | [
2671,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2667,
1
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Mathlib/Order/SuccPred/Limit.lean | Order.isPredLimit_of_dense | [] | [
255,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
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Mathlib/Data/Fin/Tuple/Monotone.lean | StrictAnti.vecCons | [] | [
77,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/LinearAlgebra/Matrix/AbsoluteValue.lean | Matrix.det_sum_le | [
{
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67,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
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Mathlib/Data/Nat/Parity.lean | Nat.odd_iff | [
{
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},
{
"state_after": "no goals",
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49,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
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Mathlib/Topology/FiberBundle/Trivialization.lean | Pretrivialization.symm_apply_of_not_mem | [] | [
266,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
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Mathlib/Data/Finset/Sigma.lean | Finset.mem_sigmaLift | [
{
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144,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_pos_iff_support_of_nonneg_ae' | [
{
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1289,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1279,
1
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Mathlib/RingTheory/Valuation/Basic.lean | Valuation.unit_map_eq | [] | [
242,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
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] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_sub_eq_left_of_natDegree_lt | [] | [
1339,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1337,
1
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Mathlib/LinearAlgebra/Span.lean | Submodule.span_zero | [
{
"state_after": "no goals",
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538,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
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Mathlib/Topology/Algebra/Monoid.lean | continuous_finprod_cond | [
{
"state_after": "ι : Type u_3\nα : Type ?u.453927\nX : Type u_1\nM : Type u_2\nN : Type ?u.453936\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace M\ninst✝¹ : CommMonoid M\ninst✝ : ContinuousMul M\nf : ι → X → M\np : ι → Prop\nhc : ∀ (i : ι), p i → Continuous (f i)\nhf : LocallyFinite fun i => mulSuppor... | [
823,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
819,
1
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | uniformity_basis_edist | [] | [
177,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.map_comap_map | [] | [
318,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
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Mathlib/Topology/Homotopy/HSpaces.lean | unitInterval.qRight_one_right | [
{
"state_after": "t : ↑I\n⊢ Set.projIcc 0 1 qRight.proof_1 (2 * ↑(t, 1).fst / (1 + ↑(t, 1).snd)) = Set.projIcc 0 1 (_ : 0 ≤ 1) ↑t",
"state_before": "t : ↑I\n⊢ qRight (t, 1) = Set.projIcc 0 1 (_ : 0 ≤ 1) ↑t",
"tactic": "rw [qRight]"
},
{
"state_after": "case e_x\nt : ↑I\n⊢ 2 * ↑(t, 1).fst / (1 + ... | [
225,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
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Mathlib/Topology/Algebra/Algebra.lean | Subalgebra.topologicalClosure_comap_homeomorph | [
{
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147,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
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Mathlib/RingTheory/DedekindDomain/Ideal.lean | irreducible_pow_sup_of_le | [
{
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951,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
946,
1
] |
Mathlib/LinearAlgebra/BilinearMap.lean | LinearMap.ext₂ | [] | [
119,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Finset.infsep_zero_iff_subsingleton | [] | [
565,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
563,
1
] |
Mathlib/Algebra/GroupPower/Ring.lean | min_pow_dvd_add | [
{
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"state_before": "R : Type u_1\nS : Type ?u.85157\nM : Type ?u.85160\ninst✝¹ : Semiring R\ninst✝ : Semiring S\nn m :... | [
164,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Algebra/Star/SelfAdjoint.lean | IsSelfAdjoint.conjugate' | [
{
"state_after": "no goals",
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"tactic": "simp only [isSelfAdjoint_iff, star_mul, star_star, mul_assoc, hx.star_eq]"
}
] | [
164,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_union | [
{
"state_after": "ι : Type ?u.286983\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nf g : α → β\ninst✝¹ : CommMonoid β\ninst✝ : DecidableEq α\nh : Disjoint s₁ s₂\n⊢ ∏ x in s₁ ∪ s₂, f x = (∏ x in s₁ ∪ s₂, f x) * ∏ x in ∅, f x",
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413,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.map_neg | [] | [
1236,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1235,
11
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.natTrailingDegree_one | [] | [
244,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.eq_symm_comp | [] | [
423,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.int_cyclotomic_unique | [
{
"state_after": "case a\nn : ℕ\nP : ℤ[X]\nh : map (Int.castRingHom ℂ) P = cyclotomic' n ℂ\n⊢ map (Int.castRingHom ℂ) P = map (Int.castRingHom ℂ) (cyclotomic n ℤ)",
"state_before": "n : ℕ\nP : ℤ[X]\nh : map (Int.castRingHom ℂ) P = cyclotomic' n ℂ\n⊢ P = cyclotomic n ℤ",
"tactic": "apply map_injective (I... | [
289,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Analysis/Calculus/LocalExtr.lean | IsLocalMinOn.fderivWithin_nonneg | [
{
"state_after": "E : Type u\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : E → ℝ\na : E\nf' : E →L[ℝ] ℝ\ns : Set E\nh : IsLocalMinOn f s a\ny : E\nhy : y ∈ posTangentConeAt s a\nhf : ¬DifferentiableWithinAt ℝ f s a\n⊢ 0 ≤ ↑0 y",
"state_before": "E : Type u\ninst✝¹ : NormedAddCommGroup E\ninst... | [
167,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.deleteVerts_mono | [] | [
1239,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1237,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.symm_trans_self | [
{
"state_after": "case h\nR : Type ?u.219981\nR₁ : Type u_1\nR₂ : Type u_2\nR₃ : Type ?u.219990\nk : Type ?u.219993\nS : Type ?u.219996\nM : Type ?u.219999\nM₁ : Type u_3\nM₂ : Type u_4\nM₃ : Type ?u.220008\nN₁ : Type ?u.220011\nN₂ : Type ?u.220014\nN₃ : Type ?u.220017\nN₄ : Type ?u.220020\nι : Type ?u.220023\n... | [
474,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
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Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.Measure.mutuallySingular_singularPart | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.33482\nm : MeasurableSpace α\nμ✝ ν✝ μ ν : Measure α\nh : HaveLebesgueDecomposition μ ν\n⊢ singularPart μ ν ⟂ₘ ν\n\ncase neg\nα : Type u_1\nβ : Type ?u.33482\nm : MeasurableSpace α\nμ✝ ν✝ μ ν : Measure α\nh : ¬HaveLebesgueDecomposition μ ν\n⊢ singularPart μ ν... | [
138,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Algebra/Associated.lean | Irreducible.dvd_comm | [] | [
243,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | continuous_iff_continuous_dist | [] | [
1832,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1828,
1
] |
Mathlib/Data/Set/Prod.lean | Set.offDiag_insert | [
{
"state_after": "α : Type u_1\ns t : Set α\nx : α × α\na : α\nha : ¬a ∈ s\n⊢ Disjoint s {a}",
"state_before": "α : Type u_1\ns t : Set α\nx : α × α\na : α\nha : ¬a ∈ s\n⊢ offDiag (insert a s) = offDiag s ∪ {a} ×ˢ s ∪ s ×ˢ {a}",
"tactic": "rw [insert_eq, union_comm, offDiag_union, offDiag_singleton, uni... | [
623,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
619,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.repeat_apply | [] | [
379,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/RingTheory/Localization/Integral.lean | IsLocalization.coeffIntegerNormalization_mem_support | [
{
"state_after": "R : Type u_2\ninst✝⁴ : CommRing R\nM : Submonoid R\nS : Type u_1\ninst✝³ : CommRing S\ninst✝² : Algebra R S\nP : Type ?u.5885\ninst✝¹ : CommRing P\ninst✝ : IsLocalization M S\np : S[X]\ni : ℕ\nh : ¬i ∈ support p\n⊢ ¬coeffIntegerNormalization M p i ≠ 0",
"state_before": "R : Type u_2\ninst✝... | [
68,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Std/Data/List/Init/Lemmas.lean | List.eq_nil_of_length_eq_zero | [] | [
45,
89
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
45,
1
] |
Mathlib/MeasureTheory/Group/Prod.lean | MeasureTheory.absolutelyContinuous_inv | [
{
"state_after": "G : Type u_1\ninst✝⁶ : MeasurableSpace G\ninst✝⁵ : Group G\ninst✝⁴ : MeasurableMul₂ G\nμ ν : Measure G\ninst✝³ : SigmaFinite ν\ninst✝² : SigmaFinite μ\ns✝ : Set G\ninst✝¹ : MeasurableInv G\ninst✝ : IsMulLeftInvariant μ\ns : Set G\nx✝ : MeasurableSet s\n⊢ ↑↑(Measure.inv μ) s = 0 → ↑↑μ s = 0",
... | [
193,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.closedBall_subset_ball | [] | [
611,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
610,
1
] |
Mathlib/Order/InitialSeg.lean | InitialSeg.refl_apply | [] | [
126,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingHom.coe_comp | [] | [
309,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
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Mathlib/Data/Rat/Cast.lean | Rat.cast_sub | [] | [
225,
100
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224,
1
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Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | measurableSet_integrable | [
{
"state_after": "α : Type u_2\nα' : Type ?u.1147235\nβ : Type u_1\nβ' : Type ?u.1147241\nγ : Type ?u.1147244\nE : Type u_3\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : MeasurableSpace α'\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace β'\ninst✝² : MeasurableSpace γ\nμ μ' : MeasureTheory.Measure α\nν ν' : Measur... | [
70,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
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