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/FractionalIdeal.lean | FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mul | [
{
"state_after": "case pos\nR : Type ?u.1759313\ninst✝⁶ : CommRing R\nS : Submonoid R\nP : Type ?u.1759520\ninst✝⁵ : CommRing P\ninst✝⁴ : Algebra R P\nloc : IsLocalization S P\nR₁ : Type u_1\ninst✝³ : CommRing R₁\nK : Type u_2\ninst✝² : Field K\ninst✝¹ : Algebra R₁ K\nfrac : IsFractionRing R₁ K\ninst✝ : IsDomai... | [
1592,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1576,
1
] |
Mathlib/Data/Fin/SuccPred.lean | Fin.pred_eq | [] | [
72,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Analysis/Calculus/DiffContOnCl.lean | DiffContOnCl.const_sub | [] | [
118,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Data/Nat/Totient.lean | Nat.totient_one | [
{
"state_after": "no goals",
"state_before": "⊢ φ 1 = 1",
"tactic": "simp [totient]"
}
] | [
48,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Logic/Nonempty.lean | nonempty_Prop | [] | [
41,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometry.lipschitz | [] | [
177,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
11
] |
Mathlib/RingTheory/IntegralClosure.lean | isField_of_isIntegral_of_isField | [
{
"state_after": "R✝ : Type ?u.1593781\nA : Type ?u.1593784\nB : Type ?u.1593787\nS✝ : Type ?u.1593790\nT : Type ?u.1593793\ninst✝¹³ : CommRing R✝\ninst✝¹² : CommRing A\ninst✝¹¹ : CommRing B\ninst✝¹⁰ : CommRing S✝\ninst✝⁹ : CommRing T\ninst✝⁸ : Algebra A B\ninst✝⁷ : Algebra R✝ B\nf : R✝ →+* S✝\ng : S✝ →+* T\nin... | [
1142,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1107,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.Multiequalizer.lift_ι | [] | [
799,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
] |
Mathlib/Data/PNat/Prime.lean | PNat.Prime.ne_one | [
{
"state_after": "p : ℕ+\npp : Prime p\n⊢ p ≠ 1",
"state_before": "p : ℕ+\n⊢ Prime p → p ≠ 1",
"tactic": "intro pp"
},
{
"state_after": "p : ℕ+\npp : Prime p\ncontra : p = 1\n⊢ False",
"state_before": "p : ℕ+\npp : Prime p\n⊢ p ≠ 1",
"tactic": "intro contra"
},
{
"state_after": "... | [
140,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Std/Data/List/Lemmas.lean | List.map_eq_nil | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nf : α → β\nl : List α\n⊢ map f l = [] ↔ l = []",
"tactic": "constructor <;> exact fun _ => match l with | [] => rfl"
}
] | [
169,
58
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
168,
9
] |
Mathlib/Data/Int/Order/Basic.lean | Int.abs_lt_one_iff | [
{
"state_after": "a : ℤ\na0 : abs a < 1\nhn : -1 < a\nhp : a < 1\n⊢ a = 0",
"state_before": "a : ℤ\na0 : abs a < 1\n⊢ a = 0",
"tactic": "let ⟨hn, hp⟩ := abs_lt.mp a0"
},
{
"state_after": "a : ℤ\na0 : abs a < 1\nhn : -1 < a\nhp✝ : a < 1\nhp : a ≤ 0\n⊢ a = 0",
"state_before": "a : ℤ\na0 : abs ... | [
129,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | hasSum_nat_add_iff' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.453865\nγ : Type ?u.453868\nδ : Type ?u.453871\ninst✝² : AddCommGroup α\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalAddGroup α\nf✝ g : β → α\na✝ a₁ a₂ : α\nf : ℕ → α\nk : ℕ\na : α\n⊢ HasSum (fun n => f (n + k)) (a - ∑ i in range k,... | [
955,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
953,
1
] |
Mathlib/Data/Finmap.lean | Finmap.liftOn₂_toFinmap | [
{
"state_after": "case mk\nα : Type u\nβ : α → Type v\nγ : Type u_1\ns₂ : AList β\nf : AList β → AList β → γ\nH : ∀ (a₁ b₁ a₂ b₂ : AList β), a₁.entries ~ a₂.entries → b₁.entries ~ b₂.entries → f a₁ b₁ = f a₂ b₂\nentries✝ : List (Sigma β)\nnodupKeys✝ : NodupKeys entries✝\n⊢ liftOn₂ ⟦{ entries := entries✝, nodupK... | [
139,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.toList_set | [] | [
588,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
586,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.sUnion_eq_univ_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.128718\nγ : Type ?u.128721\nι : Sort ?u.128724\nι' : Sort ?u.128727\nι₂ : Sort ?u.128730\nκ : ι → Sort ?u.128735\nκ₁ : ι → Sort ?u.128740\nκ₂ : ι → Sort ?u.128745\nκ' : ι' → Sort ?u.128750\nc : Set (Set α)\n⊢ ⋃₀ c = univ ↔ ∀ (a : α), ∃ ... | [
1197,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1196,
1
] |
Mathlib/Order/SuccPred/LinearLocallyFinite.lean | toZ_iterate_succ | [] | [
355,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/CategoryTheory/Pi/Basic.lean | CategoryTheory.Pi.comp_apply | [] | [
57,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | expSeries_div_hasSum_exp | [] | [
598,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
1
] |
Mathlib/Algebra/Bounds.lean | subset_lowerBounds_mul | [] | [
125,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.toEnd_injective | [] | [
143,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Topology/List.lean | List.tendsto_cons | [
{
"state_after": "α : Type u_1\nβ : Type ?u.4553\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\na : α\nl : List α\n⊢ Filter.seq (Filter.map (fun a b => (a, b).fst :: (a, b).snd) (𝓝 a)) (𝓝 l) ≤ Seq.seq (cons <$> 𝓝 a) fun x => 𝓝 l",
"state_before": "α : Type u_1\nβ : Type ?u.4553\ninst✝¹ : Topo... | [
79,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Order/BoundedOrder.lean | Ne.bot_lt' | [] | [
402,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Ring.lean | summable_mul_right_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nκ : Type ?u.14348\nR : Type ?u.14351\nα : Type u_1\ninst✝² : DivisionSemiring α\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSemiring α\nf g : ι → α\na a₁ a₂ : α\nh : a ≠ 0\nH : Summable fun i => f i * a\n⊢ Summable f",
"tactic": "simpa onl... | [
109,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.image_smul | [] | [
1591,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1590,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_two_power | [
{
"state_after": "no goals",
"state_before": "α β : Type u\na : Cardinal\n⊢ lift (2 ^ a) = 2 ^ lift a",
"tactic": "simp [←one_add_one_eq_two]"
}
] | [
648,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
1
] |
Std/Data/Int/Lemmas.lean | Int.eq_neg_of_eq_neg | [
{
"state_after": "no goals",
"state_before": "a b : Int\nh : a = -b\n⊢ b = -a",
"tactic": "rw [h, Int.neg_neg]"
}
] | [
309,
22
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
308,
11
] |
Mathlib/Data/Finsupp/AList.lean | AList.insert_lookupFinsupp | [
{
"state_after": "case h\nα : Type u_1\nM : Type u_2\ninst✝¹ : Zero M\ninst✝ : DecidableEq α\nl : AList fun _x => M\na : α\nm : M\nb : α\n⊢ ↑(lookupFinsupp (insert a m l)) b = ↑(Finsupp.update (lookupFinsupp l) a m) b",
"state_before": "α : Type u_1\nM : Type u_2\ninst✝¹ : Zero M\ninst✝ : DecidableEq α\nl :... | [
118,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Algebra/Order/Floor.lean | round_add_int | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.254324\nα : Type u_1\nβ : Type ?u.254330\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nx : α\ny : ℤ\n⊢ round (x + ↑y) = round x + y",
"tactic": "rw [round, round, Int.fract_add_int, Int.floor_add_int, Int.ceil_add_int, ← apply_ite₂, ite_sel... | [
1356,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1355,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.einfsep_eq_iInf | [
{
"state_after": "α : Type u_1\nβ : Type ?u.28409\ninst✝ : EDist α\nx y : α\ns t : Set α\nx✝ : ℝ≥0∞\n⊢ x✝ ≤ einfsep s ↔ x✝ ≤ ⨅ (d : ↑(offDiag s)), uncurry edist ↑d",
"state_before": "α : Type u_1\nβ : Type ?u.28409\ninst✝ : EDist α\nx y : α\ns t : Set α\n⊢ einfsep s = ⨅ (d : ↑(offDiag s)), uncurry edist ↑d"... | [
173,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Order/Lattice.lean | inf_congr_right | [] | [
548,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.centralizer_le | [] | [
780,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
779,
1
] |
Mathlib/Data/Int/Order/Lemmas.lean | Int.eq_zero_of_abs_lt_dvd | [
{
"state_after": "case pos\na b : ℤ\nn : ℕ\nm x : ℤ\nh1 : m ∣ x\nh2 : abs x < m\nhm : m = 0\n⊢ x = 0\n\ncase neg\na b : ℤ\nn : ℕ\nm x : ℤ\nh1 : m ∣ x\nh2 : abs x < m\nhm : ¬m = 0\n⊢ x = 0",
"state_before": "a b : ℤ\nn : ℕ\nm x : ℤ\nh1 : m ∣ x\nh2 : abs x < m\n⊢ x = 0",
"tactic": "by_cases hm : m = 0"
... | [
68,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Algebra/Support.lean | Function.mulSupport_inv | [] | [
280,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Algebra/Hom/Ring.lean | NonUnitalRingHom.coe_comp_addMonoidHom | [] | [
270,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/Topology/UrysohnsLemma.lean | Urysohns.CU.lim_of_nmem_U | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : NormalSpace X\nc : CU X\nx : X\nh : ¬x ∈ c.U\n⊢ CU.lim c x = 1",
"tactic": "simp only [CU.lim, approx_of_nmem_U c _ h, ciSup_const]"
}
] | [
231,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/Order/Monotone/Basic.lean | monotone_iff_forall_lt | [] | [
435,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/Data/List/Sublists.lean | List.sublistsLen_succ_nil | [] | [
269,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.bot_le_of_mem | [] | [
364,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Data/List/Lex.lean | List.Lex.not_nil_right | [] | [
64,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Data/Part.lean | Part.inter_mem_inter | [
{
"state_after": "α : Type u_1\nβ : Type ?u.81876\nγ : Type ?u.81879\ninst✝ : Inter α\na b : Part α\nma mb : α\nha : ma ∈ a\nhb : mb ∈ b\n⊢ ∃ a_1, a_1 ∈ a ∧ ∃ a, a ∈ b ∧ a_1 ∩ a = ma ∩ mb",
"state_before": "α : Type u_1\nβ : Type ?u.81876\nγ : Type ?u.81879\ninst✝ : Inter α\na b : Part α\nma mb : α\nha : ma... | [
824,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
823,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | AlgHom.mem_range | [] | [
611,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
610,
1
] |
Mathlib/Algebra/Group/Basic.lean | inv_ne_one | [] | [
449,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.isRoot_gcd_iff_isRoot_left_right | [] | [
356,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_image_eq_of_injOn_lift | [] | [
2147,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2145,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.finiteAtBot | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.722328\nγ : Type ?u.722331\nδ : Type ?u.722334\nι : Type ?u.722337\nR : Type ?u.722340\nR' : Type ?u.722343\nm0✝ : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ✝ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Se... | [
3410,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3409,
1
] |
Mathlib/CategoryTheory/Types.lean | CategoryTheory.FunctorToTypes.comp | [] | [
159,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Data/Set/Intervals/Monotone.lean | AntitoneOn.Ico | [] | [
141,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
11
] |
Mathlib/Order/Filter/Bases.lean | Filter.hasBasis_biInf_of_directed' | [
{
"state_after": "α : Type u_3\nβ : Type ?u.36496\nγ : Type ?u.36499\nι✝ : Sort ?u.36502\nι'✝ : Sort ?u.36505\nl✝ l' : Filter α\np✝ : ι✝ → Prop\ns✝ : ι✝ → Set α\nt✝ : Set α\ni : ι✝\np' : ι'✝ → Prop\ns' : ι'✝ → Set α\ni' : ι'✝\nι : Type u_1\nι' : ι → Type u_2\ndom : Set ι\nhdom : Set.Nonempty dom\nl : ι → Filter... | [
559,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
1
] |
Mathlib/LinearAlgebra/Determinant.lean | Basis.det_isUnitSMul | [] | [
684,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
1
] |
Mathlib/RepresentationTheory/Action.lean | Action.functorCategoryMonoidalEquivalence.ε_app | [
{
"state_after": "V : Type (u + 1)\ninst✝¹ : LargeCategory V\nG : MonCat\ninst✝ : MonoidalCategory V\n⊢ (Monoidal.fromTransported\n (CategoryTheory.Equivalence.symm (functorCategoryEquivalence V G))).toLaxMonoidalFunctor.ε.app\n PUnit.unit =\n 𝟙 ((𝟙_ (SingleObj ↑G ⥤ V)).obj PUnit.unit)",
... | [
662,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
658,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.floor_zero | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.25771\nα : Type u_1\nβ : Type ?u.25777\ninst✝¹ : LinearOrderedSemiring α\ninst✝ : FloorSemiring α\na : α\nn : ℕ\n⊢ ⌊0⌋₊ = 0",
"tactic": "rw [← Nat.cast_zero, floor_coe]"
}
] | [
175,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Data/List/Forall2.lean | List.Forall₂.length_eq | [] | [
164,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Order/Filter/Extr.lean | IsExtrOn.neg | [] | [
503,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
1
] |
Mathlib/Order/FixedPoints.lean | OrderHom.le_prevFixed | [] | [
241,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Std/Data/Option/Lemmas.lean | Option.comp_map | [] | [
149,
20
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
148,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.bot_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u\nι : Type ?u.285120\ninst✝ : CommSemiring R\nI J K L : Ideal R\n⊢ ⊥ * I = ⊥",
"tactic": "simp"
}
] | [
748,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
748,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.contDiff_sin | [] | [
588,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
587,
1
] |
Mathlib/Algebra/Group/Commute.lean | Commute.one_left | [] | [
158,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.isBounded_iff | [] | [
72,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.insert_union | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.149642\nγ : Type ?u.149645\ninst✝ : DecidableEq α\ns✝ s₁ s₂ t✝ t₁ t₂ u v : Finset α\na✝ b a : α\ns t : Finset α\n⊢ insert a s ∪ t = insert a (s ∪ t)",
"tactic": "simp only [insert_eq, union_assoc]"
}
] | [
1451,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1450,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.dist_eq | [] | [
355,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
11
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.ofFunction_eq | [] | [
714,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
710,
1
] |
Mathlib/Topology/Instances/EReal.lean | EReal.tendsto_coe_ennreal | [] | [
119,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.relindex_top_right | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝ : Group G\nH K L : Subgroup G\n⊢ relindex H ⊤ = index H",
"tactic": "rw [← relindex_mul_index (show H ≤ ⊤ from le_top), index_top, mul_one]"
}
] | [
250,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.mul_apply | [] | [
278,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.copy_eq | [] | [
222,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.succ_le_succ_iff | [] | [
59,
37
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
58,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.restrict | [] | [
223,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
11
] |
Mathlib/Data/Real/Sqrt.lean | Continuous.sqrt | [] | [
504,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/Algebra/Order/AbsoluteValue.lean | IsAbsoluteValue.abv_div | [] | [
478,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.integralSum_smul | [
{
"state_after": "no goals",
"state_before": "ι : Type u\nE : Type v\nF : Type w\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nI J : Box ι\nπ✝ : TaggedPrepartition I\nc : ℝ\nf : (ι → ℝ) → E\nvol : ι →ᵇᵃ[⊤] E →L[ℝ] F\nπ : TaggedPrepartition ... | [
153,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Std/Data/Int/Lemmas.lean | Int.nonpos_of_neg_nonneg | [
{
"state_after": "no goals",
"state_before": "a : Int\nh : 0 ≤ -a\n⊢ -0 ≤ -a",
"tactic": "rwa [Int.neg_zero]"
}
] | [
873,
48
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
872,
11
] |
Mathlib/Topology/Instances/EReal.lean | EReal.nhds_bot | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.12836\ninst✝ : TopologicalSpace α\n⊢ (⨅ (l : EReal) (_ : ⊥ < l), 𝓟 (Iio l)) = ⨅ (a : EReal) (_ : a ≠ ⊥), 𝓟 (Iio a)",
"tactic": "simp only [bot_lt_iff_ne_bot]"
}
] | [
155,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf_comm | [] | [
427,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
11
] |
Mathlib/Algebra/CharZero/Lemmas.lean | zero_ne_bit0 | [] | [
95,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/CategoryTheory/Monoidal/Preadditive.lean | CategoryTheory.leftDistributor_hom | [
{
"state_after": "case w\nC : Type u_2\ninst✝⁵ : Category C\ninst✝⁴ : Preadditive C\ninst✝³ : MonoidalCategory C\ninst✝² : MonoidalPreadditive C\ninst✝¹ : HasFiniteBiproducts C\nJ : Type\ninst✝ : Fintype J\nX : C\nf : J → C\nj✝ : J\n⊢ (leftDistributor X f).hom ≫ biproduct.π (fun j => X ⊗ f j) j✝ =\n (∑ j : J... | [
152,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.lipschitz_infDist_pt | [] | [
564,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
563,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.conjCle_coe | [] | [
369,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.mem_comap | [] | [
425,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | Padic.padicNormE_lim_le | [
{
"state_after": "case intro\np : ℕ\nhp : Fact (Nat.Prime p)\nf : CauSeq ℚ_[p] norm\na : ℝ\nha : 0 < a\nhf : ∀ (i : ℕ), ‖↑f i‖ ≤ a\nN : ℕ\nhN : ∀ (j : ℕ), j ≥ N → ‖↑(f - const norm (CauSeq.lim f)) j‖ < a\n⊢ ‖CauSeq.lim f‖ ≤ a",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nf : CauSeq ℚ_[p] norm\na : ℝ\nh... | [
1001,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
993,
1
] |
Mathlib/CategoryTheory/Adjunction/AdjointFunctorTheorems.lean | CategoryTheory.Limits.hasLimits_of_hasColimits_of_isSeparating | [] | [
148,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/GroupTheory/GroupAction/Basic.lean | MulAction.orbit_smul | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : Group α\ninst✝ : MulAction α β\na : α\nb : β\n⊢ orbit α b = orbit α (a⁻¹ • a • b)",
"tactic": "rw [inv_smul_smul]"
}
] | [
237,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.mul_single_apply_of_not_exists_mul | [
{
"state_after": "k : Type u₁\nG : Type u₂\nR : Type ?u.506603\ninst✝¹ : Semiring k\ninst✝ : Mul G\nr : k\ng g' : G\nx : MonoidAlgebra k G\nh : ¬∃ d, g' = d * g\n⊢ (sum x fun x v => if x * g = g' then v * r else 0) = 0\n\nk : Type u₁\nG : Type u₂\nR : Type ?u.506603\ninst✝¹ : Semiring k\ninst✝ : Mul G\nr : k\ng... | [
571,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
561,
1
] |
Mathlib/Topology/Basic.lean | isClosed_const | [] | [
206,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.sub_apply | [] | [
1382,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1381,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.add_mem | [] | [
62,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
11
] |
Mathlib/Data/Part.lean | Part.append_get_eq | [
{
"state_after": "α : Type u_1\nβ : Type ?u.80296\nγ : Type ?u.80299\ninst✝ : Append α\na b : Part α\nhab : (a ++ b).Dom\n⊢ get (Part.bind a fun y => map (fun x => y ++ x) b) (_ : (Part.bind a fun y => map (fun x => y ++ x) b).Dom) =\n get a (_ : a.Dom) ++ get b (_ : b.Dom)",
"state_before": "α : Type u_... | [
816,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
814,
1
] |
Mathlib/Algebra/Hom/GroupInstances.lean | AddMonoid.End.int_cast_apply | [] | [
111,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | Submodule.topologicalClosure_mono | [] | [
178,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Data/Set/Function.lean | Set.MapsTo.image_subset | [] | [
408,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.IsOrtho.symm | [] | [
258,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Fintype.prod_unique | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.879170\nβ✝ : Type u\nα✝ : Type v\nγ : Type w\ns s₁ s₂ : Finset α✝\na : α✝\nf✝ g : α✝ → β✝\nα : Type u_1\nβ : Type u_2\ninst✝² : CommMonoid β\ninst✝¹ : Unique α\ninst✝ : Fintype α\nf : α → β\n⊢ ∏ x : α, f x = f default",
"tactic": "rw [univ_unique... | [
2004,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2003,
1
] |
Mathlib/RingTheory/Ideal/AssociatedPrime.lean | IsAssociatedPrime.eq_radical | [
{
"state_after": "case intro.intro\nR : Type u_1\ninst✝⁴ : CommRing R\nI J : Ideal R\nM : Type ?u.74241\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\nM' : Type ?u.74774\ninst✝¹ : AddCommGroup M'\ninst✝ : Module R M'\nf : M →ₗ[R] M'\nhI : Ideal.IsPrimary I\nhJ : Ideal.IsPrime J\nx : R ⧸ I\ne : J = Submodule.ann... | [
161,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.bddAbove_range | [
{
"state_after": "case intro\nα : Type ?u.278295\nβ : Type ?u.278298\nγ : Type ?u.278301\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nι : Type u\nf : ι → Ordinal\ni : ι\n⊢ f i ≤ ord (iSup (succ ∘ card ∘ f))",
"state_before": "α : Type ?u.278295\nβ : Type ?u.278298\nγ : Type ?u.278301\nr : α → α → ... | [
1261,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1257,
1
] |
Mathlib/CategoryTheory/Bicategory/Coherence.lean | CategoryTheory.FreeBicategory.preinclusion_obj | [] | [
93,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | Real.contDiffAt_rpow_of_ne | [
{
"state_after": "case inl\nx y z : ℝ\np : ℝ × ℝ\nhp : p.fst ≠ 0\nn : ℕ∞\nhneg : p.fst < 0\n⊢ ContDiffAt ℝ n (fun p => p.fst ^ p.snd) p\n\ncase inr\nx y z : ℝ\np : ℝ × ℝ\nhp : p.fst ≠ 0\nn : ℕ∞\nhpos : 0 < p.fst\n⊢ ContDiffAt ℝ n (fun p => p.fst ^ p.snd) p",
"state_before": "x y z : ℝ\np : ℝ × ℝ\nhp : p.fst... | [
302,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Algebra/Homology/ShortExact/Preadditive.lean | CategoryTheory.Splitting.section_retraction | [
{
"state_after": "𝒜 : Type u_2\ninst✝² : Category 𝒜\nA B C A' B' C' : 𝒜\nf : A ⟶ B\ng : B ⟶ C\nf' : A' ⟶ B'\ng' : B' ⟶ C'\ninst✝¹ : HasZeroMorphisms 𝒜\ninst✝ : HasBinaryBiproducts 𝒜\nh : Splitting f g\n⊢ (biprod.inr ≫ h.iso.inv) ≫ h.iso.hom ≫ biprod.fst = 0",
"state_before": "𝒜 : Type u_2\ninst✝² : Ca... | [
223,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Data/Fintype/Card.lean | Finset.exists_minimal | [
{
"state_after": "case intro\nα✝ : Type ?u.64966\nβ : Type ?u.64969\nγ : Type ?u.64972\nα : Type u_1\ninst✝ : Preorder α\ns : Finset α\nc : α\nhcs : c ∈ s\n⊢ ∃ m, m ∈ s ∧ ∀ (x : α), x ∈ s → ¬x < m",
"state_before": "α✝ : Type ?u.64966\nβ : Type ?u.64969\nγ : Type ?u.64972\nα : Type u_1\ninst✝ : Preorder α\n... | [
966,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
961,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Independent.lean | affineIndependent_of_ne | [
{
"state_after": "k : Type u_2\nV : Type u_3\nP : Type u_1\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type ?u.410622\np₁ p₂ : P\nh : p₁ ≠ p₂\n⊢ LinearIndependent k fun i => Matrix.vecCons p₁ ![p₂] ↑i -ᵥ Matrix.vecCons p₁ ![p₂] 0",
"state_before": "k ... | [
626,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
614,
1
] |
Mathlib/Topology/Maps.lean | isOpenMap_iff_nhds_le | [] | [
447,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
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