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/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.orderOf_root_cyclotomic_dvd | [
{
"state_after": "case h\nn : ℕ\nhpos : 0 < n\np : ℕ\ninst✝ : Fact (Nat.Prime p)\na : ℕ\nhroot : IsRoot (cyclotomic n (ZMod p)) (↑(Nat.castRingHom (ZMod p)) a)\n⊢ ZMod.unitOfCoprime a (_ : Nat.coprime a p) ^ n = 1",
"state_before": "n : ℕ\nhpos : 0 < n\np : ℕ\ninst✝ : Fact (Nat.Prime p)\na : ℕ\nhroot : IsRo... | [
651,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.bot_eq_zero | [] | [
554,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_neg_left | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1722446\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx y : E\n⊢ ↑(starRingEnd 𝕜) (-1) * inner x y = -inner x y",
"state_bef... | [
636,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
634,
1
] |
Mathlib/RingTheory/Algebraic.lean | Subalgebra.isField_of_algebraic | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.871187\nS : Type ?u.871190\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDomain R\ninst✝³ : CommRing S\nK : Type u_1\nL : Type u_2\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Algebra K L\nA : Subalgebra K L\nhKL : Algebra.IsAlgebraic K L\n⊢ Nontrivial { x // x ∈... | [
399,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.mem_smul_pointwise_iff_exists | [] | [
382,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.comp_sup_eq_sup_comp_of_is_total | [] | [
675,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
673,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.pred | [] | [
272,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/CategoryTheory/EqToHom.lean | CategoryTheory.Functor.precomp_map_hEq | [] | [
245,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Data/Part.lean | Part.map_none | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.14360\nf : α → β\na : β\n⊢ ¬a ∈ map f none",
"tactic": "simp"
}
] | [
455,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/Algebra/Order/Sub/Canonical.lean | AddLECancellable.eq_tsub_iff_add_eq_of_le | [
{
"state_after": "α : Type u_1\ninst✝⁵ : AddCommSemigroup α\ninst✝⁴ : PartialOrder α\ninst✝³ : ExistsAddOfLE α\ninst✝² : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\nb c d : α\nhc : AddLECancellable c\nh : c ≤ b\n⊢ b - c + c = b",
"state_before": "α :... | [
83,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
11
] |
Mathlib/Data/Complex/Exponential.lean | Complex.tanh_eq_sinh_div_cosh | [] | [
693,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.continuous | [] | [
140,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
11
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.derivative_ofNat | [] | [
239,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_mul_const_Iic | [] | [
525,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/MeasureTheory/Integral/DivergenceTheorem.lean | MeasureTheory.integral_divergence_of_hasFDerivWithinAt_off_countable_of_equiv | [
{
"state_after": "case h\nE : Type u\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : CompleteSpace E\nn : ℕ\nF : Type u_1\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ninst✝² : PartialOrder F\ninst✝¹ : MeasureSpace F\ninst✝ : BorelSpace F\neL : F ≃L[ℝ] Fin (n + 1) → ℝ\nhe_ord : ∀ ... | [
361,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/CategoryTheory/Abelian/Exact.lean | CategoryTheory.Abelian.cokernel.desc.inv | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\ninst✝¹ : Abelian C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\ninst✝ : Epi g\nex : Exact f g\nthis : IsIso (cokernel.desc f g (_ : f ≫ g = 0))\n⊢ let_fun this := (_ : IsIso (cokernel.desc f g (_ : f ≫ g = 0)));\n g ≫ CategoryTheory.inv (cokernel.desc f g (_ : f ≫ g = 0... | [
192,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | Class.mem_univ_hom | [] | [
1520,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1519,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.Injective.ne_iff | [] | [
115,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | sub_toIcoDiv_zsmul_mem_Ico | [] | [
52,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/RingTheory/Nakayama.lean | Submodule.smul_sup_le_of_le_smul_of_le_jacobson_bot | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nM : Type u_2\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nI : Ideal R\nN N' : Submodule R M\nhN' : FG N'\nhIJ : I ≤ jacobson ⊥\nhNN : N ⊔ N' ≤ N ⊔ I • N'\n⊢ I • N' ≤ N",
"tactic": "rw [← sup_eq_left, smul_sup_eq_smul_sup_o... | [
102,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Data/List/Infix.lean | List.insert.def | [] | [
475,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.cast_int_comp | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝ : Ring R\np q r : R[X]\ni : ℤ\n⊢ comp (↑i) p = ↑i",
"tactic": "cases i <;> simp"
}
] | [
1285,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1285,
1
] |
Mathlib/Data/PNat/Defs.lean | PNat.one_le | [] | [
178,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.subgroupOf_eq_top | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nG' : Type ?u.293254\ninst✝⁴ : Group G\ninst✝³ : Group G'\nA : Type ?u.293263\ninst✝² : AddGroup A\nH✝ K✝ : Subgroup G\nk : Set G\nN : Type ?u.293284\ninst✝¹ : Group N\nP : Type ?u.293290\ninst✝ : Group P\nH K : Subgroup G\n⊢ subgroupOf H K = ⊤ ↔ K ... | [
1694,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1693,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_const_sub_Ioi | [] | [
232,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Data/Nat/Fib.lean | Nat.fib_gcd | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\n⊢ fib (gcd m n) = gcd (fib m) (fib n)",
"tactic": "induction m, n using Nat.gcd.induction with\n| H0 => simp\n| H1 m n _ h' =>\n rw [← gcd_rec m n] at h'\n conv_rhs => rw [← mod_add_div' n m]\n rwa [gcd_fib_add_mul_self m (n % m) (n / m), gcd_com... | [
285,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | IsDedekindDomain.HeightOneSpectrum.prime | [] | [
998,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
998,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | Measurable.ite | [] | [
336,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.image_iInter | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.190319\nι : Sort u_3\nι' : Sort ?u.190325\nι₂ : Sort ?u.190328\nκ : ι → Sort ?u.190333\nκ₁ : ι → Sort ?u.190338\nκ₂ : ι → Sort ?u.190343\nκ' : ι' → Sort ?u.190348\nf : α → β\nhf : Bijective f\ns : ι → Set α\nh✝ : IsEmpty ι\n⊢ (f '' ⋂ (i : ι), s... | [
1560,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1556,
1
] |
Mathlib/Data/Set/Function.lean | Set.mapsTo' | [] | [
386,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/CategoryTheory/DiscreteCategory.lean | CategoryTheory.Discrete.functor_obj | [] | [
186,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.toFun_embedding_empty | [] | [
989,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
988,
1
] |
Mathlib/CategoryTheory/Limits/Types.lean | CategoryTheory.Limits.Types.colimit_sound | [
{
"state_after": "no goals",
"state_before": "J : Type v\ninst✝ : SmallCategory J\nF : J ⥤ TypeMax\nj j' : J\nx : F.obj j\nx' : F.obj j'\nf : j ⟶ j'\nw : F.map f x = x'\n⊢ colimit.ι F j x = colimit.ι F j' x'",
"tactic": "rw [← w, Colimit.w_apply.{v, u}]"
}
] | [
345,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/RingTheory/ChainOfDivisors.lean | DivisorChain.eq_second_of_chain_of_prime_dvd | [
{
"state_after": "case zero\nM : Type u_1\ninst✝ : CancelCommMonoidWithZero M\np q r : Associates M\nhp : Prime p\nhr : r ∣ q\nhp' : p ∣ r\nhn : Nat.zero ≠ 0\nc : Fin (Nat.zero + 1) → Associates M\nh₁ : StrictMono c\nh₂ : ∀ {r : Associates M}, r ≤ q ↔ ∃ i, r = c i\n⊢ p = c 1\n\ncase succ\nM : Type u_1\ninst✝ : ... | [
136,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.frequently_comap | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.226477\nι : Sort x\nf : α → β\nl : Filter β\np : α → Prop\ns : Set α\n⊢ (∃ᶠ (a : α) in comap f l, p a) ↔ ∃ᶠ (b : β) in l, ∃ a, f a = b ∧ p a",
"tactic": "simp only [Filter.Frequently, eventually_comap, not_exis... | [
1921,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1920,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | edist_le_tsum_of_edist_le_of_tendsto₀ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.569045\nγ : Type ?u.569048\ninst✝ : PseudoEMetricSpace α\nf : ℕ → α\nd : ℕ → ℝ≥0∞\nhf : ∀ (n : ℕ), edist (f n) (f (Nat.succ n)) ≤ d n\na : α\nha : Tendsto f atTop (𝓝 a)\n⊢ edist (f 0) a ≤ ∑' (m : ℕ), d m",
"tactic": "simpa using ed... | [
1588,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1586,
1
] |
Mathlib/Algebra/Module/Zlattice.lean | Zspan.fract_zspan_add | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\nι : Type u_2\nK : Type u_3\ninst✝⁴ : NormedLinearOrderedField K\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace K E\nb : Basis ι K E\ninst✝¹ : FloorRing K\ninst✝ : Fintype ι\nm v : E\nh : v ∈ span ℤ (Set.range ↑b)\n⊢ fract b (v + m) = fract b ... | [
138,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.of_nonneg_disjoint_union_eq_zero | [
{
"state_after": "α : Type u_1\nβ : Type ?u.41414\nm : MeasurableSpace α\nM : Type ?u.41420\ninst✝² : AddCommMonoid M\ninst✝¹ : TopologicalSpace M\ninst✝ : T2Space M\nv : VectorMeasure α M\nf : ℕ → Set α\ns : SignedMeasure α\nA B : Set α\nh : Disjoint A B\nhA₁ : MeasurableSet A\nhB₁ : MeasurableSet B\nhA₂ : 0 ≤... | [
240,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | ModelWithCorners.toLocalEquiv_coe | [] | [
201,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.eq_of_dist_eq_of_dist_eq_of_mem_of_finrank_eq_two | [
{
"state_after": "V : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\ns : AffineSubspace ℝ P\ninst✝ : FiniteDimensional ℝ { x // x ∈ direction s }\nhd : finrank ℝ { x // x ∈ direction s } = 2\nc₁ c₂ p₁ p₂ p : P\nhc₁s : ... | [
213,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.toL1_sub | [] | [
1390,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1388,
1
] |
Mathlib/Algebra/Group/Ext.lean | LeftCancelMonoid.toMonoid_injective | [
{
"state_after": "case mk.mk.mk.mk\nM : Type u\ntoOne✝¹ : One M\nnpow✝¹ : ℕ → M → M\nnpow_zero✝¹ : ∀ (x : M), npow✝¹ 0 x = 1\ntoSemigroup✝¹ : Semigroup M\nmul_left_cancel✝¹ : ∀ (a b c : M), a * b = a * c → b = c\none_mul✝¹ : ∀ (a : M), 1 * a = a\nmul_one✝¹ : ∀ (a : M), a * 1 = a\nnpow_succ✝¹ : ∀ (n : ℕ) (x : M)... | [
65,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | intermediate_value_uIcc | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝¹⁰ : ConditionallyCompleteLinearOrder α\ninst✝⁹ : TopologicalSpace α\ninst✝⁸ : OrderTopology α\ninst✝⁷ : ConditionallyCompleteLinearOrder β\ninst✝⁶ : TopologicalSpace β\ninst✝⁵ : OrderTopology β\ninst✝⁴ : Nonempty γ\ninst... | [
546,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
544,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | VectorBundleCore.coe_coordChange | [] | [
675,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
1
] |
Mathlib/Data/Fintype/Card.lean | Fintype.exists_ne_map_eq_of_card_lt | [] | [
505,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.num_div | [
{
"state_after": "case pos\nK : Type u\ninst✝ : Field K\np q : K[X]\nhq : q = 0\n⊢ num (↑(algebraMap K[X] (RatFunc K)) p / ↑(algebraMap K[X] (RatFunc K)) q) =\n ↑C (leadingCoeff (q / gcd p q))⁻¹ * (p / gcd p q)\n\ncase neg\nK : Type u\ninst✝ : Field K\np q : K[X]\nhq : ¬q = 0\n⊢ num (↑(algebraMap K[X] (RatFu... | [
1162,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1157,
1
] |
Mathlib/Topology/Sheaves/LocalPredicate.lean | TopCat.stalkToFiber_surjective | [
{
"state_after": "case intro.intro.intro\nX : TopCat\nT : ↑X → Type v\nP : LocalPredicate T\nx : ↑X\nw : ∀ (t : T x), ∃ U f x_1, f { val := x, property := (_ : x ∈ U.obj) } = t\nU : OpenNhds x\nf : (y : { x_1 // x_1 ∈ U.obj }) → T ↑y\nh : PrelocalPredicate.pred P.toPrelocalPredicate f\n⊢ ∃ a, stalkToFiber P x a... | [
269,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.subset_countable_closure_of_almost_dense_set | [
{
"state_after": "case inl\nα : Type u\nβ : Type v\nX : Type ?u.273536\ninst✝ : PseudoEMetricSpace α\nx y z : α\nε ε₁ ε₂ : ℝ≥0∞\ns t : Set α\nhs : ∀ (ε : ℝ≥0∞), ε > 0 → ∃ t, Set.Countable t ∧ ∅ ⊆ ⋃ (x : α) (_ : x ∈ t), closedBall x ε\n⊢ ∃ t, t ⊆ ∅ ∧ Set.Countable t ∧ ∅ ⊆ closure t\n\ncase inr.intro\nα : Type u\... | [
806,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
780,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.tr_eval' | [
{
"state_after": "case intro.intro\nσ₁ σ₂ : Type u_1\nf₁ : σ₁ → Option σ₁\nf₂ : σ₂ → Option σ₂\ntr : σ₁ → σ₂\nH : Respects f₁ f₂ fun a b => tr a = b\na₁ : σ₁\nb₂ : σ₂\nh : b₂ ∈ tr <$> eval f₁ a₁\nb₁ : σ₁\nab : b₁ ∈ eval f₁ a₁\nbb : tr b₁ = b₂\n⊢ b₂ ∈ eval f₂ (tr a₁)",
"state_before": "σ₁ σ₂ : Type u_1\nf₁ :... | [
986,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
977,
1
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Mathlib/Order/RelClasses.lean | ssubset_iff_subset_not_subset | [] | [
722,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
721,
1
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Mathlib/Topology/Algebra/Order/LeftRight.lean | continuousWithinAt_Ioi_iff_Ici | [
{
"state_after": "no goals",
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"tactic": "simp only [← Ici_diff_left, continuousWithinAt_diff... | [
39,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
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Mathlib/Data/Matrix/Basic.lean | AlgEquiv.mapMatrix_trans | [] | [
1644,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1642,
1
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Std/Data/Int/Lemmas.lean | Int.sign_eq_zero_iff_zero | [
{
"state_after": "no goals",
"state_before": "a : Int\nh : a = 0\n⊢ sign a = 0",
"tactic": "rw [h, sign_zero]"
}
] | [
1294,
59
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1293,
1
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Mathlib/MeasureTheory/Group/Action.lean | MeasureTheory.NullMeasurableSet.smul | [
{
"state_after": "no goals",
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196,
68
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193,
1
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Mathlib/Data/List/Basic.lean | List.map_filter_eq_foldr | [
{
"state_after": "case nil\nι : Type ?u.136885\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf : α → β\np : α → Bool\n⊢ map f (filter p []) = foldr (fun a bs => bif p a then f a :: bs else bs) [] []\n\ncase cons\nι : Type ?u.136885\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List... | [
1866,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1861,
1
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Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_cos_sq_sub_sin_sq | [
{
"state_after": "no goals",
"state_before": "a b : ℝ\nn : ℕ\n⊢ (∫ (x : ℝ) in a..b, cos x ^ 2 - sin x ^ 2) = sin b * cos b - sin a * cos a",
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538,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
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Mathlib/Topology/Homeomorph.lean | Homeomorph.homeomorph_mk_coe_symm | [] | [
130,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Data/Real/Sign.lean | Real.sign_of_pos | [
{
"state_after": "no goals",
"state_before": "r : ℝ\nhr : 0 < r\n⊢ sign r = 1",
"tactic": "rw [sign, if_pos hr, if_neg hr.not_lt]"
}
] | [
42,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.refl_symm | [] | [
135,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
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Mathlib/Topology/UrysohnsLemma.lean | Urysohns.CU.approx_le_lim | [] | [
242,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.centralizer_eq_top_iff_subset | [] | [
547,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.map_C | [
{
"state_after": "case h\nR : Type u_2\ninst✝² : Semiring R\nS : Type u_1\nT : Type ?u.2847427\ninst✝¹ : Semiring S\ninst✝ : Semiring T\nf : R →+* S\ng : S →+* T\nr : R\nn✝ : ℕ\n⊢ ↑(coeff S n✝) (↑(map f) (↑(C R) r)) = ↑(coeff S n✝) (↑(C ((fun x => S) r)) (↑f r))",
"state_before": "R : Type u_2\ninst✝² : Sem... | [
1695,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1693,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.bsup_le_of_brange_subset | [
{
"state_after": "case intro.intro\nα : Type ?u.316558\nβ : Type ?u.316561\nγ : Type ?u.316564\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no : Ordinal\no' : Ordinal\nf : (a : Ordinal) → a < o → Ordinal\ng : (a : Ordinal) → a < o' → Ordinal\nh : brange o f ⊆ brange o' g\ni : Ordinal\nhi : i < o\nj : O... | [
1569,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1564,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.sup_eq_zero | [] | [
2488,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2487,
1
] |
Mathlib/Algebra/RingQuot.lean | RingQuot.Rel.add_right | [
{
"state_after": "R : Type u₁\ninst✝³ : Semiring R\nS : Type u₂\ninst✝² : CommSemiring S\nA : Type u₃\ninst✝¹ : Semiring A\ninst✝ : Algebra S A\nr : R → R → Prop\na b c : R\nh : Rel r b c\n⊢ Rel r (b + a) (c + a)",
"state_before": "R : Type u₁\ninst✝³ : Semiring R\nS : Type u₂\ninst✝² : CommSemiring S\nA : ... | [
69,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Data/PNat/Xgcd.lean | PNat.gcd_rel_right | [] | [
547,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_id' | [] | [
221,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.sub_right_inj | [] | [
1195,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1192,
1
] |
Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.Formula.semanticallyEquivalent_not_not | [] | [
560,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
1
] |
Mathlib/Data/Set/Function.lean | Set.EqOn.comp_right | [] | [
416,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/GroupTheory/Sylow.lean | Sylow.orbit_eq_top | [] | [
367,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.mul_cancel' | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹ : Monoid R\nS : Submonoid R\ninst✝ : OreSet S\nr₁ r₂ : R\ns t : { x // x ∈ S }\n⊢ r₁ /ₒ s * (↑s * r₂ /ₒ t) = r₁ * r₂ /ₒ t",
"tactic": "simp [oreDiv_mul_char r₁ (s * r₂) s t r₂ 1 (by simp)]"
},
{
"state_after": "no goals",
"st... | [
346,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
11
] |
Mathlib/Order/Monotone/Basic.lean | StrictAnti.cmp_map_eq | [] | [
955,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
954,
1
] |
Mathlib/FieldTheory/IsAlgClosed/Classification.lean | IsAlgClosed.cardinal_le_max_transcendence_basis | [
{
"state_after": "no goals",
"state_before": "R L K : Type u\ninst✝³ : CommRing R\ninst✝² : Field K\ninst✝¹ : Algebra R K\ninst✝ : IsAlgClosed K\nι : Type u\nv : ι → K\nhv✝ hv : IsTranscendenceBasis R v\n⊢ max (#{ x // x ∈ Algebra.adjoin R (Set.range v) }) ℵ₀ = max (#MvPolynomial ι R) ℵ₀",
"tactic": "rw... | [
153,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.fp_iff_derivFamily | [] | [
228,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.codeSupp_zero | [] | [
1819,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1818,
1
] |
Mathlib/Algebra/ContinuedFractions/Translations.lean | GeneralizedContinuedFraction.part_denom_none_iff_s_none | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ng : GeneralizedContinuedFraction α\nn : ℕ\n⊢ Stream'.Seq.get? (partialDenominators g) n = none ↔ Stream'.Seq.get? g.s n = none",
"tactic": "cases s_nth_eq : g.s.get? n <;> simp [partialDenominators, s_nth_eq]"
}
] | [
52,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.sum_measure_le_measure_univ | [
{
"state_after": "α : Type u_2\nβ : Type ?u.39043\nγ : Type ?u.39046\nδ : Type ?u.39049\nι : Type u_1\nR : Type ?u.39055\nR' : Type ?u.39058\nm : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns✝ s₁ s₂ t✝ : Set α\ns : Finset ι\nt : ι → Set α\nh : ∀ (i : ι), i ∈ s → MeasurableSet (t i)\nH : PairwiseDisjoint (↑s) t\n⊢ ↑... | [
391,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/CategoryTheory/Sites/DenseSubsite.lean | CategoryTheory.CoverDense.Types.appHom_restrict | [
{
"state_after": "C : Type u_4\ninst✝⁴ : Category C\nD : Type u_2\ninst✝³ : Category D\nE : Type ?u.63453\ninst✝² : Category E\nJ : GrothendieckTopology C\nK : GrothendieckTopology D\nL : GrothendieckTopology E\nA : Type ?u.63505\ninst✝¹ : Category A\nG : C ⥤ D\nH : CoverDense K G\ninst✝ : Full G\nℱ : Dᵒᵖ ⥤ Typ... | [
232,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.degreeLT_mono | [] | [
113,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Order/Atoms.lean | isAtom_top | [] | [
488,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.one_eq_closure | [
{
"state_after": "α : Type ?u.225159\nG : Type ?u.225162\nM : Type ?u.225165\nR : Type u_1\nA : Type ?u.225171\ninst✝² : Monoid M\ninst✝¹ : AddMonoid A\ninst✝ : AddMonoidWithOne R\n⊢ AddMonoidHom.mrange (Nat.castAddMonoidHom R) = AddMonoidHom.mrange (↑(multiplesHom R) 1)",
"state_before": "α : Type ?u.22515... | [
517,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.IsFixedPt.isPeriodicPt | [] | [
63,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Data/Nat/GCD/Basic.lean | Nat.coprime_add_self_right | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\n⊢ coprime m (n + m) ↔ coprime m n",
"tactic": "rw [coprime, coprime, gcd_add_self_right]"
}
] | [
134,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/RingTheory/ClassGroup.lean | ClassGroup.mk_eq_mk | [
{
"state_after": "R : Type u_1\nK : Type ?u.318539\nL : Type ?u.318542\ninst✝¹⁰ : CommRing R\ninst✝⁹ : Field K\ninst✝⁸ : Field L\ninst✝⁷ : DecidableEq L\ninst✝⁶ : Algebra R K\ninst✝⁵ : IsFractionRing R K\ninst✝⁴ : Algebra K L\ninst✝³ : FiniteDimensional K L\ninst✝² : Algebra R L\ninst✝¹ : IsScalarTower R K L\ni... | [
122,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Analysis/Calculus/Deriv/Mul.lean | HasDerivAt.div_const | [
{
"state_after": "no goals",
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295,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Std/Data/Nat/Gcd.lean | Nat.coprime_comm | [] | [
246,
81
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
246,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.coe_zeta_mul_apply | [] | [
475,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
1
] |
Mathlib/Data/Int/Bitwise.lean | Int.testBit_zero | [
{
"state_after": "b : Bool\nn : ℕ\n⊢ testBit (↑(Nat.bit b n)) 0 = b",
"state_before": "b : Bool\nn : ℕ\n⊢ testBit (bit b ↑n) 0 = b",
"tactic": "rw [bit_coe_nat]"
},
{
"state_after": "no goals",
"state_before": "b : Bool\nn : ℕ\n⊢ testBit (↑(Nat.bit b n)) 0 = b",
"tactic": "apply Nat.test... | [
204,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Equiv.summable_iff | [] | [
229,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Data/Set/Function.lean | Set.piecewise_eqOn_compl | [] | [
1407,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1406,
1
] |
Mathlib/Order/Bounded.lean | Set.bounded_ge_Ioo | [] | [
262,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.properDivisors_prime_pow | [
{
"state_after": "case a\nn p : ℕ\npp : Prime p\nk a : ℕ\n⊢ a ∈ properDivisors (p ^ k) ↔ a ∈ map { toFun := Nat.pow p, inj' := (_ : Function.Injective fun n => p ^ n) } (range k)",
"state_before": "n p : ℕ\npp : Prime p\nk : ℕ\n⊢ properDivisors (p ^ k) = map { toFun := Nat.pow p, inj' := (_ : Function.Injec... | [
451,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
] |
Mathlib/CategoryTheory/Idempotents/FunctorExtension.lean | CategoryTheory.Idempotents.functorExtension₁_comp | [
{
"state_after": "case refine'_1\nC : Type u_3\nD : Type u_4\nE : Type u_6\ninst✝² : Category C\ninst✝¹ : Category D\ninst✝ : Category E\nF : C ⥤ Karoubi D\nG : D ⥤ Karoubi E\n⊢ ∀ (X : Karoubi C),\n ((functorExtension₁ C E).obj (F ⋙ (functorExtension₁ D E).obj G)).obj X =\n ((functorExtension₁ C D).obj ... | [
201,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Data/Set/Function.lean | Function.LeftInverse.leftInvOn | [] | [
1604,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1603,
1
] |
Mathlib/LinearAlgebra/StdBasis.lean | Pi.basis_apply | [
{
"state_after": "no goals",
"state_before": "R : Type u_3\nη : Type u_1\nιs : η → Type u_2\nMs : η → Type u_4\ninst✝⁴ : Semiring R\ninst✝³ : (i : η) → AddCommMonoid (Ms i)\ninst✝² : (i : η) → Module R (Ms i)\ninst✝¹ : Fintype η\ninst✝ : DecidableEq η\ns : (j : η) → Basis (ιs j) R (Ms j)\nji : (j : η) × ιs ... | [
262,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.sub_lt_of_pos_le | [] | [
139,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
138,
11
] |
Mathlib/Topology/ContinuousOn.lean | ContinuousWithinAt.diff_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.325947\nδ : Type ?u.325950\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α → β\ns t : Set α\nx : α\nht : ContinuousWithinAt f t x\nh : ContinuousWit... | [
775,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
772,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.tr_clear | [] | [
1116,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1115,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.neg_star | [
{
"state_after": "no goals",
"state_before": "⊢ -star = star",
"tactic": "simp [star]"
}
] | [
1877,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1877,
1
] |
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