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/FieldTheory/RatFunc.lean | RatFunc.X_ne_zero | [] | [
1459,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1458,
1
] |
Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean | TopCat.pullback_snd_range | [
{
"state_after": "case h\nJ : Type v\ninst✝ : SmallCategory J\nX✝ Y✝ Z : TopCat\nX Y S : TopCat\nf : X ⟶ S\ng : Y ⟶ S\ny : (forget TopCat).obj Y\n⊢ y ∈ Set.range ((forget TopCat).map pullback.snd) ↔ y ∈ {y | ∃ x, (forget TopCat).map f x = (forget TopCat).map g y}",
"state_before": "J : Type v\ninst✝ : Small... | [
239,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | IsFiniteMeasureOnCompacts.map | [
{
"state_after": "α✝ : Type ?u.1653244\nβ✝ : Type ?u.1653247\nγ : Type ?u.1653250\nγ₂ : Type ?u.1653253\nδ : Type ?u.1653256\nι : Sort y\ns t u : Set α✝\ninst✝¹⁶ : TopologicalSpace α✝\ninst✝¹⁵ : MeasurableSpace α✝\ninst✝¹⁴ : BorelSpace α✝\ninst✝¹³ : TopologicalSpace β✝\ninst✝¹² : MeasurableSpace β✝\ninst✝¹¹ : B... | [
1396,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1388,
11
] |
Mathlib/Topology/Instances/Nat.lean | Nat.dist_eq | [] | [
28,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
28,
1
] |
Mathlib/FieldTheory/Finite/Basic.lean | FiniteField.prod_univ_units_id_eq_neg_one | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nR : Type ?u.99451\ninst✝² : CommRing K\ninst✝¹ : IsDomain K\ninst✝ : Fintype Kˣ\n⊢ ∏ x : Kˣ, x = -1",
"tactic": "classical\n have : (∏ x in (@univ Kˣ _).erase (-1), x) = 1 :=\n prod_involution (fun x _ => x⁻¹) (by simp)\n (fun a => by ... | [
114,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/NumberTheory/Primorial.lean | primorial_add_le | [] | [
74,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Algebra/ModEq.lean | AddCommGroup.zsmul_modEq_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddCommGroup α\np a a₁ a₂ b b₁ b₂ c : α\nn : ℕ\nz✝ z : ℤ\n⊢ 0 - z • p = -z • p",
"tactic": "simp"
}
] | [
114,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Data/Nat/Sqrt.lean | Nat.not_exists_sq | [
{
"state_after": "case intro\nm t : ℕ\nhl : m * m < t * t\nhr : t * t < (m + 1) * (m + 1)\n⊢ False",
"state_before": "n m : ℕ\nhl : m * m < n\nhr : n < (m + 1) * (m + 1)\n⊢ ¬∃ t, t * t = n",
"tactic": "rintro ⟨t, rfl⟩"
},
{
"state_after": "case intro\nm t : ℕ\nhl : m * m < t * t\nhr : t * t < (m... | [
204,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.Nonempty.mul_zero | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.595307\nα : Type u_1\nβ : Type ?u.595313\nγ : Type ?u.595316\ninst✝² : DecidableEq α\ninst✝¹ : DecidableEq β\ninst✝ : MulZeroClass α\ns t : Finset α\nhs : Finset.Nonempty s\n⊢ 0 ⊆ s * 0",
"tactic": "simpa [mem_mul] using hs"
}
] | [
1098,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1097,
1
] |
Mathlib/Data/List/Basic.lean | List.span_eq_take_drop | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.385314\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\np : α → Bool\nl : List α\n⊢ span p l = (takeWhile p l, dropWhile p l)",
"tactic": "simpa using span.loop_eq_take_drop p l []"
}
] | [
3608,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3607,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.lhom_ext | [] | [
68,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Analysis/Convex/SpecificFunctions/Deriv.lean | deriv_sqrt_mul_log | [
{
"state_after": "case inl\nx : ℝ\nhx : 0 < x\n⊢ deriv (fun x => sqrt x * log x) x = (2 + log x) / (2 * sqrt x)\n\ncase inr\nx : ℝ\nhx : x ≤ 0\n⊢ deriv (fun x => sqrt x * log x) x = (2 + log x) / (2 * sqrt x)",
"state_before": "x : ℝ\n⊢ deriv (fun x => sqrt x * log x) x = (2 + log x) / (2 * sqrt x)",
"t... | [
133,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Chebyshev.lean | Polynomial.Chebyshev.algebraMap_eval_U | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nA : Type u_1\ninst✝² : CommRing R\ninst✝¹ : CommRing A\ninst✝ : Algebra R A\nx : R\nn : ℕ\n⊢ ↑(algebraMap R A) (eval x (U R n)) = eval (↑(algebraMap R A) x) (U A n)",
"tactic": "rw [← aeval_algebraMap_apply_eq_algebraMap_eval, aeval_U]"
}
] | [
50,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/MeasureTheory/Measure/Haar/OfBasis.lean | EuclideanSpace.coe_measurableEquiv | [] | [
292,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.cos_arg | [
{
"state_after": "x : ℂ\nhx : x ≠ 0\n⊢ Real.cos\n (if 0 ≤ x.re then arcsin (x.im / ↑abs x)\n else if 0 ≤ x.im then arcsin ((-x).im / ↑abs x) + π else arcsin ((-x).im / ↑abs x) - π) =\n x.re / ↑abs x",
"state_before": "x : ℂ\nhx : x ≠ 0\n⊢ Real.cos (arg x) = x.re / ↑abs x",
"tactic": "rw [ar... | [
56,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.lowerBound?_le' | [
{
"state_after": "no goals",
"state_before": "case nil\nα : Type u_1\ncut : α → Ordering\nx : α\nlb : Option α\nH : ∀ {x : α}, x ∈ lb → cut x ≠ Ordering.lt\n⊢ x ∈ lowerBound? cut nil lb → cut x ≠ Ordering.lt",
"tactic": "exact H"
},
{
"state_after": "case node\nα : Type u_1\ncut : α → Ordering\n... | [
227,
57
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
219,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | Monotone.inv | [] | [
1287,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1286,
1
] |
Mathlib/Data/Rat/NNRat.lean | NNRat.nsmul_coe | [] | [
298,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.curryFinFinset_symm_apply_piecewise_const | [] | [
1879,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1875,
1
] |
Mathlib/Data/Int/ModEq.lean | Int.ModEq.pow | [
{
"state_after": "case zero\nm n a b c d : ℤ\nh : a ≡ b [ZMOD n]\n⊢ a ^ Nat.zero ≡ b ^ Nat.zero [ZMOD n]\n\ncase succ\nm n a b c d✝ : ℤ\nh : a ≡ b [ZMOD n]\nd : ℕ\nhd : a ^ d ≡ b ^ d [ZMOD n]\n⊢ a ^ Nat.succ d ≡ b ^ Nat.succ d [ZMOD n]",
"state_before": "m✝ n a b c d : ℤ\nm : ℕ\nh : a ≡ b [ZMOD n]\n⊢ a ^ m ... | [
214,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
21
] |
Mathlib/Topology/Algebra/UniformGroup.lean | uniformContinuous_mul | [] | [
113,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.indicatorConstLp_eq_toSpanSingleton_compLp | [
{
"state_after": "case h\nα : Type u_1\nE : Type ?u.8082404\nF : Type u_2\nG : Type ?u.8082410\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedAddCommGroup G\ng : E → F\nc : ℝ≥0\ns : Set α\ninst✝ : NormedSpace ℝ F\nhs : Me... | [
1082,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1068,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.map.id' | [] | [
814,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
813,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.mem_domain_iff_of_eq_graph | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁹ : Ring R\nE : Type u_2\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : Module R E\nF : Type u_3\ninst✝⁶ : AddCommGroup F\ninst✝⁵ : Module R F\nG : Type ?u.590759\ninst✝⁴ : AddCommGroup G\ninst✝³ : Module R G\nM : Type ?u.591275\ninst✝² : Monoid M\ninst✝¹... | [
877,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
876,
1
] |
Mathlib/Analysis/InnerProductSpace/PiL2.lean | Complex.orthonormalBasisOneI_repr_apply | [] | [
632,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/GroupTheory/PGroup.lean | IsPGroup.of_card | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nG : Type u_1\ninst✝¹ : Group G\ninst✝ : Fintype G\nn : ℕ\nhG : card G = p ^ n\ng : G\n⊢ g ^ p ^ n = 1",
"tactic": "rw [← hG, pow_card_eq_one]"
}
] | [
52,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Data/Quot.lean | Quotient.mk_out | [] | [
380,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.algebraMap_apply_div | [
{
"state_after": "no goals",
"state_before": "K F : Type u\ninst✝ : Field F\np q : F[X]\nf g : RatFunc F\n⊢ ↑(algebraMap (RatFunc F) (LaurentSeries F)) (↑(algebraMap F[X] (RatFunc F)) p / ↑(algebraMap F[X] (RatFunc F)) q) =\n ↑(algebraMap F[X] (LaurentSeries F)) p / ↑(algebraMap F[X] (LaurentSeries F)) q... | [
1775,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1769,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffWithinAt.add | [] | [
1198,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1196,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | Trivialization.apply_symm_apply_eq_coordChangeL | [
{
"state_after": "no goals",
"state_before": "R : Type u_4\nB : Type u_1\nF : Type u_2\nE : B → Type u_3\ninst✝⁹ : Semiring R\ninst✝⁸ : TopologicalSpace F\ninst✝⁷ : TopologicalSpace B\ninst✝⁶ : TopologicalSpace (TotalSpace E)\ne✝ : Trivialization F TotalSpace.proj\nx : TotalSpace E\nb✝ : B\ny : E b✝\ninst✝⁵... | [
349,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/Topology/Order/Basic.lean | not_tendsto_atTop_of_tendsto_nhds | [] | [
1559,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1557,
1
] |
Mathlib/RingTheory/Ideal/Quotient.lean | Ideal.Quotient.zero_eq_one_iff | [] | [
145,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.cast_bit1 | [
{
"state_after": "α : Type u_1\ninst✝ : Semiring α\nn : Num\n⊢ _root_.bit0 ↑n + ↑1 = _root_.bit1 ↑n",
"state_before": "α : Type u_1\ninst✝ : Semiring α\nn : Num\n⊢ ↑(Num.bit1 n) = _root_.bit1 ↑n",
"tactic": "rw [← bit1_of_bit1, _root_.bit1, bit0_of_bit0, cast_add, cast_bit0]"
},
{
"state_after":... | [
741,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.BoundedFormula.realize_all | [] | [
345,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinitesimal_real_iff | [] | [
693,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
9
] |
Mathlib/Algebra/DualQuaternion.lean | Quaternion.imI_snd_dualNumberEquiv | [] | [
97,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Data/List/Basic.lean | List.take_one_drop_eq_of_lt_length | [
{
"state_after": "case nil\nι : Type ?u.89571\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l : List α\nn✝ : ℕ\nh✝ : n✝ < length l\nn : ℕ\nh : n < length []\n⊢ take 1 (drop n []) = [get [] { val := n, isLt := h }]\n\ncase cons\nι : Type ?u.89571\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l✝... | [
1388,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1373,
1
] |
Mathlib/Computability/EpsilonNFA.lean | εNFA.evalFrom_singleton | [] | [
104,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Algebra/CovariantAndContravariant.lean | rel_act_of_act_rel_act_of_rel_act | [] | [
240,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.Nontrivial.einfsep_lt_top | [
{
"state_after": "α : Type u_1\nβ : Type ?u.50351\ninst✝ : PseudoMetricSpace α\ns : Set α\nhs : Set.Nontrivial s\n⊢ einfsep s ≠ ⊤",
"state_before": "α : Type u_1\nβ : Type ?u.50351\ninst✝ : PseudoMetricSpace α\ns : Set α\nhs : Set.Nontrivial s\n⊢ einfsep s < ⊤",
"tactic": "rw [lt_top_iff_ne_top]"
},
... | [
273,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Algebra/Group/Basic.lean | inv_eq_one | [] | [
437,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.comp_apply | [] | [
1125,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1124,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.iSup_biInf_of_monotone | [
{
"state_after": "case H0\nα✝ : Type u\nβ : Type v\nι✝ : Sort w\nγ : Type x\nι : Type u_1\nι' : Type u_2\nα : Type u_3\ninst✝³ : Preorder ι'\ninst✝² : Nonempty ι'\ninst✝¹ : IsDirected ι' fun x x_1 => x ≤ x_1\ninst✝ : Order.Frame α\ns : Set ι\nf : ι → ι' → α\nhf✝ : ∀ (i : ι), i ∈ s → Monotone (f i)\nhf : ∀ (i : ... | [
1477,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1470,
1
] |
Mathlib/Logic/Equiv/TransferInstance.lean | Equiv.mul_def | [] | [
72,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Data/Set/Intervals/Monoid.lean | Set.image_const_add_Ioi | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝¹ : OrderedCancelAddCommMonoid M\ninst✝ : ExistsAddOfLE M\na b c d : M\n⊢ (fun x => a + x) '' Ioi b = Ioi (a + b)",
"tactic": "simp only [add_comm a, image_add_const_Ioi]"
}
] | [
122,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Analysis/NormedSpace/Int.lean | Int.toNat_add_toNat_neg_eq_norm | [
{
"state_after": "no goals",
"state_before": "n : ℤ\n⊢ ↑(toNat n) + ↑(toNat (-n)) = ‖n‖",
"tactic": "simpa only [NNReal.coe_nat_cast, NNReal.coe_add] using\n congrArg NNReal.toReal (toNat_add_toNat_neg_eq_nnnorm n)"
}
] | [
51,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Combinatorics/SimpleGraph/Partition.lean | SimpleGraph.partitionable_iff_colorable | [
{
"state_after": "case mp\nV : Type u\nG : SimpleGraph V\nn : ℕ\n⊢ Partitionable G n → Colorable G n\n\ncase mpr\nV : Type u\nG : SimpleGraph V\nn : ℕ\n⊢ Colorable G n → Partitionable G n",
"state_before": "V : Type u\nG : SimpleGraph V\nn : ℕ\n⊢ Partitionable G n ↔ Colorable G n",
"tactic": "constructo... | [
155,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Tactic/IntervalCases.lean | Mathlib.Tactic.IntervalCases.of_lt_left | [] | [
136,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Data/Set/NAry.lean | Set.image2_left_comm | [
{
"state_after": "α : Type u_2\nα' : Type ?u.41219\nβ : Type u_4\nβ' : Type ?u.41225\nγ : Type u_5\nγ' : Type ?u.41231\nδ : Type u_3\nδ' : Type u_6\nε : Type u_1\nε' : Type ?u.41243\nζ : Type ?u.41246\nζ' : Type ?u.41249\nν : Type ?u.41252\nf✝ f'✝ : α → β → γ\ng✝ g'✝ : α → β → γ → δ\ns s' : Set α\nt t' : Set β\... | [
324,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/RingTheory/Int/Basic.lean | Nat.factors_eq | [
{
"state_after": "case zero\n\n⊢ normalizedFactors zero = ↑(factors zero)\n\ncase succ\nn✝ : ℕ\n⊢ normalizedFactors (succ n✝) = ↑(factors (succ n✝))",
"state_before": "n : ℕ\n⊢ normalizedFactors n = ↑(factors n)",
"tactic": "cases n"
},
{
"state_after": "case succ\nn✝ : ℕ\n⊢ normalizedFactors (s... | [
320,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Data/List/Basic.lean | List.forall_mem_of_forall_mem_cons | [] | [
274,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Std/Data/HashMap/WF.lean | Std.HashMap.Imp.reinsertAux_WF | [] | [
77,
31
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
70,
1
] |
Mathlib/FieldTheory/Separable.lean | Polynomial.Separable.mul | [
{
"state_after": "R : Type u\ninst✝ : CommRing R\nf g : R[X]\nhf : Separable f\nhg : Separable g\nh : IsCoprime f g\n⊢ IsCoprime (f * g) (↑derivative f * g + f * ↑derivative g)",
"state_before": "R : Type u\ninst✝ : CommRing R\nf g : R[X]\nhf : Separable f\nhg : Separable g\nh : IsCoprime f g\n⊢ Separable (... | [
183,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | LinearEquiv.coe_isometryOfOrthonormal | [] | [
1377,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1375,
1
] |
Mathlib/Data/List/Basic.lean | List.getD_cons_zero | [] | [
4381,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4380,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.closure_empty | [] | [
767,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
766,
1
] |
Mathlib/Computability/PartrecCode.lean | Nat.Partrec.Code.hG | [
{
"state_after": "a : Primrec fun a => ofNat (ℕ × Code) (List.length a)\n⊢ Primrec Nat.Partrec.Code.G",
"state_before": "⊢ Primrec Nat.Partrec.Code.G",
"tactic": "have a := (Primrec.ofNat (ℕ × Code)).comp (Primrec.list_length (α := List (Option ℕ)))"
},
{
"state_after": "a : Primrec fun a => ofN... | [
1074,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
974,
9
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.comap_sup_eq_of_le_range | [
{
"state_after": "no goals",
"state_before": "G : Type u_2\nG' : Type ?u.606769\ninst✝³ : Group G\ninst✝² : Group G'\nA : Type ?u.606778\ninst✝¹ : AddGroup A\nN : Type u_1\ninst✝ : Group N\nf : G →* N\nH K : Subgroup N\nhH : H ≤ range f\nhK : K ≤ range f\n⊢ map f (comap f H ⊔ comap f K) = map f (comap f (H ... | [
3151,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3146,
1
] |
Mathlib/Topology/UniformSpace/CompactConvergence.lean | ContinuousMap.mem_compactConvergenceUniformity | [
{
"state_after": "no goals",
"state_before": "α : Type u₁\nβ : Type u₂\ninst✝¹ : TopologicalSpace α\ninst✝ : UniformSpace β\nK : Set α\nV : Set (β × β)\nf : C(α, β)\nX : Set (C(α, β) × C(α, β))\n⊢ X ∈ compactConvergenceUniformity ↔ ∃ K V _hK _hV, {fg | ∀ (x : α), x ∈ K → (↑fg.fst x, ↑fg.snd x) ∈ V} ⊆ X",
... | [
317,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Algebra/Algebra/Basic.lean | Algebra.id.map_eq_id | [] | [
450,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Complex.hasStrictDerivAt_cosh | [
{
"state_after": "x : ℂ\n⊢ HasStrictDerivAt cosh ((exp x - exp (-x)) * 2⁻¹) x",
"state_before": "x : ℂ\n⊢ HasStrictDerivAt cosh (sinh x) x",
"tactic": "simp only [sinh, div_eq_mul_inv]"
},
{
"state_after": "case h.e'_7\nx : ℂ\n⊢ (exp x - exp (-x)) * 2⁻¹ = (exp x + exp (-id x) * -1) * 2⁻¹",
"... | [
141,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Algebra/ModEq.lean | AddCommGroup.modEq_sub_iff_add_modEq' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddCommGroup α\np a a₁ a₂ b b₁ b₂ c : α\nn : ℕ\nz : ℤ\n⊢ a ≡ b - c [PMOD p] ↔ c + a ≡ b [PMOD p]",
"tactic": "simp [ModEq, sub_sub]"
}
] | [
265,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.subset_iUnion₂_of_subset | [] | [
361,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.weightedSMul_union | [] | [
228,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_eq_sub_of_hasDerivAt | [] | [
1210,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1207,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_subset_Icc_left | [] | [
464,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.trailingDegree_eq_natTrailingDegree | [
{
"state_after": "R : Type u\nS : Type v\na b : R\nn✝ m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nhp : p ≠ 0\nn : ℕ\nhn : ¬¬n ∈ trailingDegree p\n⊢ trailingDegree p = ↑(natTrailingDegree p)",
"state_before": "R : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nhp : p ≠ 0\n⊢ trailingDegr... | [
111,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Order/Filter/SmallSets.lean | Filter.smallSets_comap | [] | [
115,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/LinearAlgebra/ProjectiveSpace/Subspace.lean | Projectivization.Subspace.span_eq_sInf | [
{
"state_after": "case carrier.h\nK : Type u_2\nV : Type u_1\ninst✝² : Field K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nS : Set (ℙ K V)\nx : ℙ K V\n⊢ x ∈ (span S).carrier ↔ x ∈ (sInf {W | S ⊆ ↑W}).carrier",
"state_before": "K : Type u_2\nV : Type u_1\ninst✝² : Field K\ninst✝¹ : AddCommGroup V\ninst✝ : ... | [
218,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Iso.cancel_iso_inv_right_assoc | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX✝ Y✝ Z✝ W X X' Y Z : C\nf : W ⟶ X\ng : X ⟶ Y\nf' : W ⟶ X'\ng' : X' ⟶ Y\nh : Z ≅ Y\n⊢ f ≫ g ≫ h.inv = f' ≫ g' ≫ h.inv ↔ f ≫ g = f' ≫ g'",
"tactic": "simp only [← Category.assoc, cancel_mono]"
}
] | [
575,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_le_zero_iff | [] | [
631,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/MeasureTheory/Function/SpecialFunctions/Basic.lean | Measurable.exp | [] | [
143,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/RingTheory/Localization/Integer.lean | IsLocalization.isInteger_one | [] | [
58,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Topology/Order.lean | generateFrom_iUnion_isOpen | [] | [
975,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
973,
1
] |
Mathlib/Analysis/Complex/PhragmenLindelof.lean | PhragmenLindelof.eq_zero_on_quadrant_III | [] | [
579,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_int_mod | [
{
"state_after": "ι : Type ?u.877667\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ns : Finset α\nn : ℤ\nf : α → ℤ\n⊢ Multiset.prod (Multiset.map ((fun x => x % n) ∘ fun i => f i) s.val) % n =\n Multiset.prod (Multiset.map (fun i => f i % n) s.val) % n",
"state_before": "ι... | [
1962,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1960,
1
] |
Mathlib/Topology/Separation.lean | SeparatedNhds.union_left | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : TopologicalSpace α\ns s₁ s₂ t t₁ t₂ u : Set α\n⊢ SeparatedNhds s u → SeparatedNhds t u → SeparatedNhds (s ∪ t) u",
"tactic": "simpa only [separatedNhds_iff_disjoint, nhdsSet_union, disjoint_sup_left] using And.intro"
}
] | [
164,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Algebra/MonoidAlgebra/Support.lean | MonoidAlgebra.support_single_mul | [
{
"state_after": "no goals",
"state_before": "k : Type u₁\nG : Type u₂\ninst✝¹ : Semiring k\ninst✝ : LeftCancelSemigroup G\nf : MonoidAlgebra k G\nr : k\nhr : ∀ (y : k), r * y = 0 ↔ y = 0\nx : G\n⊢ (single x r * f).support = map (mulLeftEmbedding x) f.support",
"tactic": "classical\n ext\n simp only [... | [
100,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Topology/LocallyConstant/Basic.lean | IsLocallyConstant.apply_eq_of_preconnectedSpace | [] | [
167,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/CategoryTheory/Products/Basic.lean | CategoryTheory.Functor.diag_obj | [] | [
272,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Combinatorics/SetFamily/Shadow.lean | Finset.Set.Sized.shadow | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\n𝒜 : Finset (Finset α)\ns t : Finset α\na : α\nk r : ℕ\nh𝒜 : Set.Sized r ↑𝒜\nA : Finset α\nh : A ∈ ↑((∂ ) 𝒜)\n⊢ card A = r - 1",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\n𝒜 : Finset (Finset α)\ns t : Finset α\na : α\nk r : ℕ\nh𝒜 : Set.S... | [
116,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
11
] |
Std/Logic.lean | Or.imp_right | [] | [
253,
62
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
253,
1
] |
Mathlib/Data/Set/Sups.lean | Set.forall_sups_iff | [] | [
106,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tendsto_nhds_zero | [] | [
284,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
11
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.mapDomain_sum | [] | [
536,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/Topology/Inseparable.lean | specializes_rfl | [] | [
162,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Topology/Category/TopCat/Limits/Products.lean | TopCat.induced_of_isLimit | [
{
"state_after": "J : Type v\ninst✝ : SmallCategory J\nF : J ⥤ TopCatMax\nC : Cone F\nhC : IsLimit C\nhomeo : ↑C.pt ≃ₜ ↑(limitConeInfi F).pt := homeoOfIso (IsLimit.conePointUniqueUpToIso hC (limitConeInfiIsLimit F))\n⊢ C.pt.str = ⨅ (j : J), induced ((forget TopCat).map (C.π.app j)) (F.obj j).str",
"state_be... | [
150,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycle.eq_on_support_inter_nonempty_congr | [
{
"state_after": "ι : Type ?u.1125909\nα : Type u_1\nβ : Type ?u.1125915\nf g : Perm α\nx y : α\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nhf : IsCycle f\nhg : IsCycle g\nh : ∀ (x : α), x ∈ support f ∩ support g → ↑f x = ↑g x\nhx : ↑f x = ↑g x\nhx' : x ∈ support f\nhx'' : x ∈ support g\n⊢ f = g",
"state_be... | [
618,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
1
] |
Mathlib/Computability/Primrec.lean | Primrec₂.curry | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nσ : Type u_3\ninst✝² : Primcodable α\ninst✝¹ : Primcodable β\ninst✝ : Primcodable σ\nf : α × β → σ\n⊢ Primrec₂ (Function.curry f) ↔ Primrec f",
"tactic": "rw [← uncurry, Function.uncurry_curry]"
}
] | [
466,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | Right.mul_lt_one_of_le_of_lt_of_nonneg | [] | [
843,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Deriv.lean | Real.hasStrictDerivAt_log_of_pos | [
{
"state_after": "x : ℝ\nhx : 0 < x\nthis : HasStrictDerivAt log (exp (log x))⁻¹ x\n⊢ HasStrictDerivAt log x⁻¹ x",
"state_before": "x : ℝ\nhx : 0 < x\n⊢ HasStrictDerivAt log x⁻¹ x",
"tactic": "have : HasStrictDerivAt log (exp <| log x)⁻¹ x :=\n (hasStrictDerivAt_exp <| log x).of_local_left_inverse (con... | [
42,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_zero | [] | [
379,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.WSameSide.trans_sSameSide | [] | [
538,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
536,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Ideal.eq_zero_of_constant_mem_of_maximal | [
{
"state_after": "R : Type u\nS : Type ?u.193946\ninst✝ : Ring R\nhR : IsField R\nI : Ideal R[X]\nhI : IsMaximal I\nx : R\nhx : ↑C x ∈ I\nhx0 : ¬x = 0\n⊢ 1 ∈ I",
"state_before": "R : Type u\nS : Type ?u.193946\ninst✝ : Ring R\nhR : IsField R\nI : Ideal R[X]\nhI : IsMaximal I\nx : R\nhx : ↑C x ∈ I\n⊢ x = 0",... | [
659,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
654,
1
] |
Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.smul_of | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nK : Type w\ninst✝² : CommRing R\nf : R[X]\ninst✝¹ : DistribSMul S R\ninst✝ : IsScalarTower S R R\na : S\nx : R\n⊢ a • ↑(of f) x = ↑(of f) (a • x)",
"tactic": "rw [of, RingHom.comp_apply, RingHom.comp_apply, smul_mk, smul_C]"
}
] | [
124,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.ext_iff | [] | [
278,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
11
] |
Mathlib/Order/Bounds/Basic.lean | IsGLB.of_subset_of_superset | [] | [
238,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Cardinal.card_ord | [
{
"state_after": "α✝ : Type ?u.224717\nβ : Type ?u.224720\nγ : Type ?u.224723\nr✝ : α✝ → α✝ → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nc : Cardinal\nα : Type u_1\nr : α → α → Prop\nw✝ : IsWellOrder α r\ne : ord (#α) = type r\n⊢ card (ord (Quotient.mk isEquivalent α)) = Quotient.mk isEquivalent α",
"state_b... | [
1385,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1381,
1
] |
Mathlib/Data/Fintype/Sort.lean | finSumEquivOfFinset_inr | [] | [
58,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Algebra/Hom/Freiman.lean | FreimanHom.inv_apply | [] | [
368,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
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