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/LinearAlgebra/AffineSpace/Ordered.lean | left_lt_lineMap_iff_lt | [
{
"state_after": "no goals",
"state_before": "k : Type u_1\nE : Type u_2\nPE : Type ?u.64959\ninst✝³ : OrderedRing k\ninst✝² : OrderedAddCommGroup E\ninst✝¹ : Module k E\ninst✝ : OrderedSMul k E\na a' b b' : E\nr r' : k\nh : 0 < r\n⊢ a < ↑(lineMap a b) r ↔ ↑(lineMap a b) 0 < ↑(lineMap a b) r",
"tactic":... | [
92,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Algebra/Group/Defs.lean | left_inv_eq_right_inv | [
{
"state_after": "no goals",
"state_before": "G : Type ?u.41375\nM : Type u\ninst✝ : Monoid M\na b c : M\nhba : b * a = 1\nhac : a * c = 1\n⊢ b = c",
"tactic": "rw [← one_mul c, ← hba, mul_assoc, hac, mul_one b]"
}
] | [
648,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
647,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.blockDiag_conjTranspose | [] | [
526,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
524,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | UniformSpace.complete_of_convergent_controlled_sequences | [
{
"state_after": "case intro.intro\nα : Type u\nβ : Type v\ninst✝¹ : UniformSpace α\ninst✝ : IsCountablyGenerated (𝓤 α)\nU : ℕ → Set (α × α)\nU_mem : ∀ (n : ℕ), U n ∈ 𝓤 α\nHU : ∀ (u : ℕ → α), (∀ (N m n : ℕ), N ≤ m → N ≤ n → (u m, u n) ∈ U N) → ∃ a, Tendsto u atTop (𝓝 a)\nU' : ℕ → Set (α × α)\nhU' : ∀ {s : Se... | [
730,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
721,
1
] |
Mathlib/Analysis/NormedSpace/ContinuousAffineMap.lean | ContinuousAffineMap.norm_contLinear_le | [] | [
177,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | tsum_geometric_inv_two_ge | [
{
"state_after": "α : Type ?u.233518\nβ : Type ?u.233521\nι : Type ?u.233524\nn : ℕ\nA : Summable fun i => if n ≤ i then 2⁻¹ ^ i else 0\nB : (∑ i in Finset.range n, if n ≤ i then 2⁻¹ ^ i else 0) = 0\n⊢ (∑' (i : ℕ), if n ≤ i then 2⁻¹ ^ i else 0) = 2 * 2⁻¹ ^ n",
"state_before": "α : Type ?u.233518\nβ : Type ?... | [
241,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.top_ne_zero | [] | [
342,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.mono_right | [] | [
1032,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1030,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.darts_takeUntil_subset | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\ninst✝ : DecidableEq V\nu v w : V\np : Walk G v w\nh : u ∈ support p\nx : Dart G\nhx : x ∈ darts (takeUntil p u h)\n⊢ x ∈ darts (takeUntil p u h) ∨ x ∈ darts (dropUntil p u h)",
"state_befo... | [
1148,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1145,
1
] |
Mathlib/Data/Bundle.lean | Bundle.coe_fst | [] | [
92,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.cardDistinctFactors_zero | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.568779\n⊢ ↑ω 0 = 0",
"tactic": "simp"
}
] | [
910,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
910,
1
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.neg_zero | [] | [
1068,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1067,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.eq_of_xn_modEq | [] | [
776,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
770,
1
] |
Mathlib/Data/List/Basic.lean | List.getLast_eq_nthLe | [] | [
1353,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1351,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.conj_eq_iff_real | [
{
"state_after": "no goals",
"state_before": "z : ℂ\nx✝ : ∃ r, z = ↑r\nh : ℝ\ne : z = ↑h\n⊢ ↑(starRingEnd ℂ) z = z",
"tactic": "rw [e, conj_ofReal]"
}
] | [
548,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
] |
Mathlib/Init/Data/Nat/Bitwise.lean | Nat.shiftl_sub | [] | [
343,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/Topology/Paracompact.lean | precise_refinement_set | [
{
"state_after": "case intro.intro.intro.intro\nι : Type u\nX : Type v\nY : Type w\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : ParacompactSpace X\ns : Set X\nhs : IsClosed s\nu : ι → Set X\nuo : ∀ (i : ι), IsOpen (u i)\nus : s ⊆ ⋃ (i : ι), u i\nuc : (⋃ (i : Option ι), Option.elim' (sᶜ) u ... | [
115,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.isCauSeq | [] | [
157,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Data/Sym/Basic.lean | Sym.mem_cons_of_mem | [] | [
185,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/CategoryTheory/Arrow.lean | CategoryTheory.Arrow.iso_w | [
{
"state_after": "T : Type u\ninst✝ : Category T\nf g : Arrow T\ne : f ≅ g\neq : (e.inv ≫ e.hom).right = (𝟙 g).right\n⊢ g.hom = e.inv.left ≫ f.hom ≫ e.hom.right",
"state_before": "T : Type u\ninst✝ : Category T\nf g : Arrow T\ne : f ≅ g\n⊢ g.hom = e.inv.left ≫ f.hom ≫ e.hom.right",
"tactic": "have eq :... | [
177,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | PSet.not_mem_empty | [] | [
404,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
src/lean/Init/SimpLemmas.lean | Bool.and_eq_true | [
{
"state_after": "no goals",
"state_before": "a b : Bool\n⊢ ((a && b) = true) = (a = true ∧ b = true)",
"tactic": "cases a <;> cases b <;> decide"
}
] | [
116,
33
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
115,
9
] |
Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_comp | [
{
"state_after": "no goals",
"state_before": "J : Type u₁\ninst✝² : Category J\nK : Type u₂\ninst✝¹ : Category K\nC : Type u₃\ninst✝ : Category C\nF✝ : J ⥤ C\nt✝ : Cone F✝\nF G : J ⥤ C\ns : Cone F\nt : Cone G\nP : IsLimit s\nQ : IsLimit t\nw : F ≅ G\nj : J\n⊢ (conePointsIsoOfNatIso P Q w).inv ≫ s.π.app j = ... | [
323,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.product_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.58929\nδ : Type ?u.58932\na : α\nb : β\ns : Multiset α\nt : Multiset β\n⊢ {a} ×ˢ {b} = {(a, b)}",
"tactic": "simp only [SProd.sprod, product, bind_singleton, map_singleton]"
}
] | [
275,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.dense_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.306162\nι : Type ?u.306165\ninst✝ : PseudoMetricSpace α\nx✝ y z : α\nε ε₁ ε₂ : ℝ\ns✝ s : Set α\nx : α\n⊢ x ∈ closure s ↔ ∀ (r : ℝ), r > 0 → Set.Nonempty (ball x r ∩ s)",
"tactic": "simp only [mem_closure_iff, Set.Nonempty,... | [
1927,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1925,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.exp_strictMono | [
{
"state_after": "x✝ y✝ x y : ℝ\nh : x < y\n⊢ exp x < exp (y - x) * exp x",
"state_before": "x✝ y✝ x y : ℝ\nh : x < y\n⊢ exp x < exp y",
"tactic": "rw [← sub_add_cancel y x, Real.exp_add]"
},
{
"state_after": "no goals",
"state_before": "x✝ y✝ x y : ℝ\nh : x < y\n⊢ exp x < exp (y - x) * exp ... | [
1510,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1507,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.update_inr_comp_inl | [] | [
314,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Data/Nat/WithBot.lean | Nat.WithBot.add_eq_two_iff | [
{
"state_after": "case none.none\n\n⊢ none + none = 2 ↔ none = 0 ∧ none = 2 ∨ none = 1 ∧ none = 1 ∨ none = 2 ∧ none = 0\n\ncase none.some\nval✝ : ℕ\n⊢ none + some val✝ = 2 ↔ none = 0 ∧ some val✝ = 2 ∨ none = 1 ∧ some val✝ = 1 ∨ none = 2 ∧ some val✝ = 0\n\ncase some.none\nval✝ : ℕ\n⊢ some val✝ + none = 2 ↔ some ... | [
46,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Combinatorics/SimpleGraph/Acyclic.lean | SimpleGraph.isAcyclic_iff_forall_edge_isBridge | [
{
"state_after": "no goals",
"state_before": "V : Type u\nG : SimpleGraph V\n⊢ IsAcyclic G ↔ ∀ ⦃e : Sym2 V⦄, e ∈ edgeSet G → IsBridge G e",
"tactic": "simp [isAcyclic_iff_forall_adj_isBridge, Sym2.forall]"
}
] | [
83,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Data/Nat/Bitwise.lean | Nat.testBit_eq_inth | [
{
"state_after": "case zero\nn✝ n : ℕ\n⊢ testBit n zero = List.getI (bits n) zero\n\ncase succ\nn✝ i : ℕ\nih : ∀ (n : ℕ), testBit n i = List.getI (bits n) i\nn : ℕ\n⊢ testBit n (succ i) = List.getI (bits n) (succ i)",
"state_before": "n i : ℕ\n⊢ testBit n i = List.getI (bits n) i",
"tactic": "induction'... | [
82,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Order/Partition/Finpartition.lean | Finpartition.parts_nonempty | [] | [
188,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Order/Filter/Partial.lean | Filter.ptendsto'_def | [] | [
272,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.singleton_smul_singleton | [] | [
1353,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1352,
1
] |
Mathlib/Algebra/Divisibility/Basic.lean | dvd_trans | [] | [
70,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | DifferentiableWithinAt.csinh | [] | [
525,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/CategoryTheory/GlueData.lean | CategoryTheory.GlueData.diagramIso_hom_app_right | [] | [
324,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/Data/Finset/Preimage.lean | Finset.prod_preimage | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ninst✝ : CommMonoid β\nf : α → γ\ns : Finset γ\nhf : InjOn f (f ⁻¹' ↑s)\ng : γ → β\nhg : ∀ (x : γ), x ∈ s → ¬x ∈ Set.range f → g x = 1\n⊢ ∏ x in preimage s f hf, g (f x) = ∏ x in s, g x",
"tactic": "classical\n ... | [
162,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/NumberTheory/VonMangoldt.lean | Nat.ArithmeticFunction.vonMangoldt_apply_pow | [
{
"state_after": "no goals",
"state_before": "n k : ℕ\nhk : k ≠ 0\n⊢ ↑Λ (n ^ k) = ↑Λ n",
"tactic": "simp only [vonMangoldt_apply, isPrimePow_pow_iff hk, pow_minFac hk]"
}
] | [
90,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Antiperiodic.mul_const' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.201763\nf g : α → β\nc c₁ c₂ x : α\ninst✝¹ : DivisionSemiring α\ninst✝ : Neg β\nh : Antiperiodic f c\na : α\nha : a ≠ 0\n⊢ Antiperiodic (fun x => f (x * a)) (c / a)",
"tactic": "simpa only [div_eq_mul_inv] using h.mul_... | [
495,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/Data/Multiset/Dedup.lean | Multiset.dedup_subset' | [] | [
70,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Data/Nat/Count.lean | Nat.count_strict_mono | [] | [
133,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Data/Set/Equitable.lean | Finset.EquitableOn.le | [] | [
119,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Algebra/Group/Basic.lean | div_ne_one_of_ne | [] | [
397,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.volume_eq_stieltjes_id | [
{
"state_after": "ι : Type ?u.1963\ninst✝ : Fintype ι\nthis : IsAddLeftInvariant (StieltjesFunction.measure StieltjesFunction.id)\n⊢ volume = StieltjesFunction.measure StieltjesFunction.id",
"state_before": "ι : Type ?u.1963\ninst✝ : Fintype ι\n⊢ volume = StieltjesFunction.measure StieltjesFunction.id",
... | [
75,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Data/Fintype/Basic.lean | Finset.piecewise_univ | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.21892\nγ : Type ?u.21895\ninst✝¹ : Fintype α\ns t : Finset α\ninst✝ : (i : α) → Decidable (i ∈ univ)\nδ : α → Sort u_2\nf g : (i : α) → δ i\ni : α\n⊢ piecewise univ f g i = f i",
"state_before": "α : Type u_1\nβ : Type ?u.21892\nγ : Type ?u.21895\ninst✝¹ :... | [
286,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasStrictFDerivAt.congr_of_eventuallyEq | [] | [
833,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
831,
1
] |
Mathlib/Algebra/Order/Sub/WithTop.lean | WithTop.top_sub_coe | [] | [
44,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/FieldTheory/PerfectClosure.lean | pthRoot_eq_iff | [] | [
102,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Computability/Encoding.lean | Computability.decode_encodeNat | [
{
"state_after": "n : ℕ\n⊢ decodeNat (encodeNat n) = n",
"state_before": "⊢ ∀ (n : ℕ), decodeNat (encodeNat n) = n",
"tactic": "intro n"
},
{
"state_after": "n : ℕ\n⊢ decodeNat (encodeNat n) = ↑↑n",
"state_before": "n : ℕ\n⊢ decodeNat (encodeNat n) = n",
"tactic": "conv_rhs => rw [← Num.... | [
157,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.single_mul_coeff_add | [
{
"state_after": "case pos\nΓ : Type u_2\nR : Type u_1\ninst✝¹ : OrderedCancelAddCommMonoid Γ\ninst✝ : NonUnitalNonAssocSemiring R\nr : R\nx : HahnSeries Γ R\na b : Γ\nhr : r = 0\n⊢ coeff (↑(single b) r * x) (a + b) = r * coeff x a\n\ncase neg\nΓ : Type u_2\nR : Type u_1\ninst✝¹ : OrderedCancelAddCommMonoid Γ\n... | [
716,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
690,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.nfp_lt_ord_of_isRegular | [
{
"state_after": "α : Type ?u.164415\nr : α → α → Prop\nf : Ordinal → Ordinal\nc : Cardinal\nhc : IsRegular c\nhc' : c ≠ ℵ₀\nhf : ∀ (i : Ordinal), i < ord c → f i < ord c\na : Ordinal\n⊢ ℵ₀ < c",
"state_before": "α : Type ?u.164415\nr : α → α → Prop\nf : Ordinal → Ordinal\nc : Cardinal\nhc : IsRegular c\nhc... | [
1157,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1151,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.inr_pushoutLeftPushoutInrIso_hom | [] | [
2228,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2223,
1
] |
Mathlib/CategoryTheory/Limits/Opposites.lean | CategoryTheory.Limits.hasColimit_of_hasLimit_op | [] | [
299,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Data/Polynomial/HasseDeriv.lean | Polynomial.hasseDeriv_zero' | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nk : ℕ\nf : R[X]\n⊢ ↑(hasseDeriv 0) f = f",
"tactic": "simp only [hasseDeriv_apply, tsub_zero, Nat.choose_zero_right, Nat.cast_one, one_mul,\n sum_monomial_eq]"
}
] | [
90,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.coeff_mem_frange | [
{
"state_after": "R : Type u\nS : Type ?u.48578\ninst✝ : Semiring R\np : R[X]\nn : ℕ\nh : coeff p n ≠ 0\n⊢ ∃ a, ¬coeff p a = 0 ∧ coeff p a = coeff p n",
"state_before": "R : Type u\nS : Type ?u.48578\ninst✝ : Semiring R\np : R[X]\nn : ℕ\nh : coeff p n ≠ 0\n⊢ coeff p n ∈ frange p",
"tactic": "simp only [... | [
210,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.ofMulEquivOfLocalizations_eq_iff_eq | [] | [
1433,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1431,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Measurable.dist | [] | [
1566,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1564,
1
] |
Mathlib/Algebra/Lie/Nilpotent.lean | LieModule.nontrivial_lowerCentralSeriesLast | [
{
"state_after": "R : Type u\nL : Type v\nM : Type w\ninst✝⁸ : CommRing R\ninst✝⁷ : LieRing L\ninst✝⁶ : LieAlgebra R L\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\ninst✝³ : LieRingModule L M\ninst✝² : LieModule R L M\nk : ℕ\nN : LieSubmodule R L M\ninst✝¹ : Nontrivial M\ninst✝ : IsNilpotent R L M\n⊢ (match ni... | [
314,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/LinearAlgebra/TensorPower.lean | TensorPower.gradedMonoid_eq_of_cast | [
{
"state_after": "R : Type u_2\nM : Type u_1\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\na b : GradedMonoid fun n => ⨂[R] (x : Fin n), M\nh : a.fst = b.fst\nh2 : ↑(cast R M h) a.snd = b.snd\n⊢ ↑(reindex R M (Equiv.cast (_ : Fin a.fst = Fin b.fst))) a.snd = b.snd",
"state_before":... | [
146,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Analysis/Complex/ReImTopology.lean | Complex.frontier_setOf_le_re_and_le_im | [
{
"state_after": "no goals",
"state_before": "a b : ℝ\n⊢ frontier {z | a ≤ z.re ∧ b ≤ z.im} = {z | a ≤ z.re ∧ z.im = b ∨ z.re = a ∧ b ≤ z.im}",
"tactic": "simpa only [closure_Ici, frontier_Ici] using frontier_reProdIm (Ici a) (Ici b)"
}
] | [
193,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Analysis/LocallyConvex/Bounded.lean | Bornology.IsVonNBounded.union | [] | [
98,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Data/Finsupp/Multiset.lean | Multiset.toFinsupp_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.60610\nι : Type ?u.60613\na : α\n⊢ {a} = ↑Finsupp.toMultiset (Finsupp.single a 1)",
"tactic": "simp"
}
] | [
172,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.inv_def | [
{
"state_after": "case inl\nK : Type u_1\nE : Type ?u.5349633\ninst✝ : IsROrC K\n⊢ 0⁻¹ = ↑(starRingEnd K) 0 * ↑(‖0‖ ^ 2)⁻¹\n\ncase inr\nK : Type u_1\nE : Type ?u.5349633\ninst✝ : IsROrC K\nz : K\nh₀ : z ≠ 0\n⊢ z⁻¹ = ↑(starRingEnd K) z * ↑(‖z‖ ^ 2)⁻¹",
"state_before": "K : Type u_1\nE : Type ?u.5349633\ninst... | [
551,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
] |
Mathlib/MeasureTheory/Integral/ExpDecay.lean | integrable_of_isBigO_exp_neg | [
{
"state_after": "case intro\nf : ℝ → ℝ\na b : ℝ\nh0 : 0 < b\nh1 : ContinuousOn f (Ici a)\nh2 : f =O[atTop] fun x => exp (-b * x)\nc : ℝ\nh3 : Asymptotics.IsBigOWith c atTop f fun x => exp (-b * x)\n⊢ IntegrableOn f (Ioi a)",
"state_before": "f : ℝ → ℝ\na b : ℝ\nh0 : 0 < b\nh1 : ContinuousOn f (Ici a)\nh2 :... | [
69,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/SetTheory/Ordinal/Topology.lean | Ordinal.isClosed_iff_bsup | [
{
"state_after": "s : Set Ordinal\na : Ordinal\n⊢ (∀ {ι : Type u}, Nonempty ι → ∀ (f : ι → Ordinal), (∀ (i : ι), f i ∈ s) → sup f ∈ s) ↔\n ∀ {o : Ordinal},\n o ≠ 0 → ∀ (f : (a : Ordinal) → a < o → Ordinal), (∀ (i : Ordinal) (hi : i < o), f i hi ∈ s) → bsup o f ∈ s",
"state_before": "s : Set Ordinal\... | [
174,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.Prime.eq_one_of_pow | [] | [
611,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
610,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.ae_eq_symm | [] | [
427,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
1
] |
Mathlib/Algebra/Group/TypeTags.lean | ofAdd_sub | [] | [
332,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.lt_iff | [
{
"state_after": "no goals",
"state_before": "⊢ ∀ {x y : Bool}, x < y ↔ x = false ∧ y = true",
"tactic": "decide"
}
] | [
344,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/Algebra/Homology/ShortExact/Preadditive.lean | CategoryTheory.exact_inl_snd | [] | [
161,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Lemmas.lean | Multiset.dvd_prod | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : CommMonoid α\ns : Multiset α\na✝ : α\nl : List α\na : α\nh : a ∈ Quotient.mk (List.isSetoid α) l\n⊢ a ∣ prod (Quotient.mk (List.isSetoid α) l)",
"tactic": "simpa using List.dvd_prod h"
}
] | [
22,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
21,
1
] |
Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.principal_add_omega_opow | [] | [
217,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | ciSup_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.54850\nγ : Type ?u.54853\nι : Sort u_1\ninst✝¹ : ConditionallyCompleteLattice α\ns t : Set α\na b : α\ninst✝ : Nonempty ι\nf : ι → α\nc : α\nH : ∀ (x : ι), f x ≤ c\n⊢ ∀ (b : α), b ∈ range f → b ≤ c",
"tactic": "rwa [forall_range_iff... | [
781,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
780,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.of_decide_iff | [] | [
50,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.sInter_singleton | [] | [
1095,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1094,
1
] |
Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.exists_elementaryEmbedding_card_eq_of_ge | [
{
"state_after": "case intro\nL : Language\nT : Theory L\nα : Type w\nn : ℕ\nM : Type w'\ninst✝ : Structure L M\niM : Infinite M\nκ : Cardinal\nh1 : lift (card L) ≤ lift κ\nh2 : lift (#M) ≤ lift κ\nN0 : Theory.ModelType (elementaryDiagram L M)\nhN0 : lift κ ≤ (#↑N0)\n⊢ ∃ N, Nonempty (M ↪ₑ[L] ↑N) ∧ (#↑N) = κ",
... | [
255,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.terminates_congr | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nc₁ c₂ : Computation α\nh : c₁ ~ c₂\n⊢ Terminates c₁ ↔ Terminates c₂",
"tactic": "simp only [terminates_iff, exists_congr h]"
}
] | [
1009,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1008,
1
] |
Mathlib/Data/Multiset/Powerset.lean | Multiset.powersetLen_mono | [
{
"state_after": "α : Type u_1\nn : ℕ\ns t : Multiset α\nh✝ : s ≤ t\nl₁ l₂ : List α\nh : l₁ <+ l₂\n⊢ List.map ofList (sublistsLen n l₁) <+~ List.map ofList (sublistsLen n l₂)",
"state_before": "α : Type u_1\nn : ℕ\ns t : Multiset α\nh✝ : s ≤ t\nl₁ l₂ : List α\nh : l₁ <+ l₂\n⊢ powersetLen n ↑l₁ ≤ powersetLen... | [
281,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_le_of_ae_nnnorm_bound | [
{
"state_after": "case pos\nα : Type u_1\nE : Type ?u.1436902\nF : Type u_2\nG : Type ?u.1436908\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf : α → F\nC : ℝ≥0\nhfC : ∀ᵐ (x : α) ∂μ, ‖f x‖₊ ≤ C\nhμ : μ = ... | [
450,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
] |
Mathlib/Topology/UniformSpace/Completion.lean | UniformSpace.Completion.uniformInducing_coe | [] | [
412,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.ofSubsingleton_self | [
{
"state_after": "case h\nR : Type u_2\nR₁ : Type ?u.342124\nR₂ : Type ?u.342127\nR₃ : Type ?u.342130\nk : Type ?u.342133\nS : Type ?u.342136\nM : Type u_1\nM₁ : Type ?u.342142\nM₂ : Type ?u.342145\nM₃ : Type ?u.342148\nN₁ : Type ?u.342151\nN₂ : Type ?u.342154\nN₃ : Type ?u.342157\nN₄ : Type ?u.342160\nι : Type... | [
715,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
713,
1
] |
Mathlib/Topology/Homotopy/HomotopyGroup.lean | GenLoop.Homotopic.equiv | [] | [
189,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/GroupTheory/GroupAction/Quotient.lean | MulAction.ofQuotientStabilizer_smul | [] | [
179,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.bind₂_comp_C | [] | [
193,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Combinatorics/Quiver/Path.lean | Quiver.Path.toList_chain_nonempty | [] | [
183,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/GroupTheory/Complement.lean | Subgroup.IsComplement'.symm | [
{
"state_after": "G : Type u_1\ninst✝ : Group G\nH K : Subgroup G\nS T : Set G\nh : IsComplement' H K\nϕ : { x // x ∈ H } × { x // x ∈ K } ≃ { x // x ∈ K } × { x // x ∈ H } :=\n { toFun := fun x => (x.snd⁻¹, x.fst⁻¹), invFun := fun x => (x.snd⁻¹, x.fst⁻¹),\n left_inv :=\n (_ :\n ∀ (x : { x // x ... | [
102,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/AlgebraicTopology/SplitSimplicialObject.lean | SimplicialObject.Split.hom_ext | [] | [
426,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Data/Polynomial/Laurent.lean | LaurentPolynomial.reduce_to_polynomial_of_mul_T | [
{
"state_after": "case Qf\nR : Type u_1\ninst✝ : Semiring R\nQ : R[T;T⁻¹] → Prop\nQf : ∀ (f : R[X]), Q (↑toLaurent f)\nQT : ∀ (f : R[T;T⁻¹]), Q (f * T 1) → Q f\nf : R[X]\nn : ℕ\n⊢ Q (↑toLaurent f * T (-↑n))",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nf : R[T;T⁻¹]\nQ : R[T;T⁻¹] → Prop\nQf : ∀ (f : R... | [
428,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.two_mul | [
{
"state_after": "no goals",
"state_before": "n : Nat\n⊢ 2 * n = n + n",
"tactic": "simp [Nat.succ_mul]"
}
] | [
235,
78
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
235,
11
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.coeSubmodule_map | [] | [
715,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
1
] |
Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.Word.equivPair_symm | [] | [
402,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.splitAtPred_false | [] | [
1349,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1348,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.card_doubleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.5726\ns t : Finset α\na b : α\ninst✝ : DecidableEq α\nh : a ≠ b\n⊢ card {a, b} = 2",
"tactic": "rw [card_insert_of_not_mem (not_mem_singleton.2 h), card_singleton]"
}
] | [
132,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | MeasureTheory.Measure.ext_of_Ioc | [] | [
741,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
737,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.coeff_succ_mul_X | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\nn : ℕ\nφ : PowerSeries R\n⊢ ↑(MvPowerSeries.coeff R (single () n + single () 1)) (φ * X) = ↑(MvPowerSeries.coeff R (single () n)) φ",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nn : ℕ\nφ : PowerSeries R\n⊢ ↑(coeff R (n + 1)) (φ * X) = ↑(coeff R n) φ... | [
1524,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1521,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.update_inl_apply_inr | [] | [
308,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.log_nonneg_iff | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\nhx : 0 < x\n⊢ 0 ≤ log x ↔ 1 ≤ x",
"tactic": "rw [← not_lt, log_neg_iff hx, not_lt]"
}
] | [
188,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.mul_le_mul_right | [] | [
1034,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1033,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiffOn_fderivWithin_apply | [] | [
1088,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1084,
1
] |
Mathlib/GroupTheory/Submonoid/Centralizer.lean | Submonoid.centralizer_univ | [] | [
98,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
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