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 |
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Mathlib/RingTheory/Valuation/Basic.lean | Valuation.isEquiv_tfae | [
{
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14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean | Matrix.SpecialLinearGroup.toLin'_to_linearMap | [] | [
201,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/FiberBundle/Trivialization.lean | Pretrivialization.apply_mk_symm | [
{
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291,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.ofReal_ratCast | [] | [
678,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
677,
1
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Mathlib/Order/Bounds/Basic.lean | Antitone.mem_upperBounds_image | [] | [
1310,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1309,
1
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Mathlib/Algebra/Order/Floor.lean | Nat.floor_eq_zero | [
{
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"state_before": "F : Type ?u.36275\nα : Type u_1\nβ : Type ?u.36281\ninst✝¹ : LinearOrderedSemiring α\ninst✝ : FloorSemiring α\na : α\nn : ℕ\n⊢... | [
237,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
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Std/Data/List/Lemmas.lean | List.exists_mem_nil | [] | [
213,
67
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
213,
1
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Mathlib/Algebra/Module/LocalizedModule.lean | IsLocalizedModule.fromLocalizedModule.bij | [] | [
800,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
799,
1
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Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.StronglyMeasurable.integral_prod_right | [
{
"state_after": "α : Type u_2\nα' : Type ?u.2296206\nβ : Type u_1\nβ' : Type ?u.2296212\nγ : Type ?u.2296215\nE : Type u_3\ninst✝⁸ : MeasurableSpace α\ninst✝⁷ : MeasurableSpace α'\ninst✝⁶ : MeasurableSpace β\ninst✝⁵ : MeasurableSpace β'\ninst✝⁴ : MeasurableSpace γ\nμ μ' : Measure α\nν ν' : Measure β\nτ : Measu... | [
123,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
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Mathlib/MeasureTheory/CardMeasurableSpace.lean | MeasurableSpace.empty_mem_generateMeasurableRec | [
{
"state_after": "α : Type u\ns : Set (Set α)\ni : (Quotient.out (ord (aleph 1))).α\n⊢ ∅ ∈\n let i := i;\n let S := ⋃ (j : ↑(Iio i)), generateMeasurableRec s ↑j;\n s ∪ {∅} ∪ compl '' S ∪ range fun f => ⋃ (n : ℕ), ↑(f n)",
"state_before": "α : Type u\ns : Set (Set α)\ni : (Quotient.out (ord (aleph 1... | [
68,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.mk_uniformity_basis | [
{
"state_after": "α : Type u\nβ✝ : Type v\nX : Type ?u.16479\ninst✝ : PseudoEMetricSpace α\nβ : Type u_1\np : β → Prop\nf : β → ℝ≥0∞\nhf₀ : ∀ (x : β), p x → 0 < f x\nhf : ∀ (ε : ℝ≥0∞), 0 < ε → ∃ x, p x ∧ f x ≤ ε\ns : Set (α × α)\n⊢ (∃ i, 0 < i ∧ {p | edist p.fst p.snd < i} ⊆ s) ↔ ∃ i, p i ∧ {p | edist p.fst p.s... | [
199,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
11
] |
Mathlib/ModelTheory/Order.lean | FirstOrder.Language.realize_noTopOrder | [] | [
245,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
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Mathlib/LinearAlgebra/Dimension.lean | rank_self | [
{
"state_after": "no goals",
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907,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
906,
1
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Mathlib/Logic/Function/Basic.lean | Function.update_injective | [
{
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"state_before": "α : Sort u\nβ ... | [
574,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
572,
1
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Mathlib/Data/Fintype/Basic.lean | Fintype.coe_image_univ | [
{
"state_after": "case h\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.120186\ninst✝¹ : Fintype α\ninst✝ : DecidableEq β\nf : α → β\nx : β\n⊢ x ∈ ↑(image f univ) ↔ x ∈ Set.range f",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.120186\ninst✝¹ : Fintype α\ninst✝ : DecidableEq β\nf : α → β\n⊢ ↑(image f ... | [
963,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
960,
1
] |
Mathlib/Computability/Ackermann.lean | ack_mono_left | [] | [
225,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.piPremeasure_pi | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nι' : Type ?u.1293941\nα : ι → Type u_1\ninst✝ : Fintype ι\nm : (i : ι) → OuterMeasure (α i)\ns : (i : ι) → Set (α i)\nhs : Set.Nonempty (Set.pi univ s)\n⊢ piPremeasure m (Set.pi univ s) = ∏ i : ι, ↑(m i) (s i)",
"tactic": "simp [hs, piPremeasur... | [
167,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
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Mathlib/Logic/Equiv/Basic.lean | Equiv.sumCongr_symm | [] | [
288,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
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Mathlib/SetTheory/ZFC/Basic.lean | PSet.mem_asymm | [] | [
337,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/Computability/Primrec.lean | Nat.Primrec.pow | [
{
"state_after": "p : ℕ\n⊢ Nat.rec 1 (fun y IH => IH * (unpair p).fst) (unpair p).snd = (unpair p).fst ^ (unpair p).snd",
"state_before": "p : ℕ\n⊢ unpaired\n (fun z n =>\n Nat.rec 1\n (fun y IH =>\n unpaired (fun x x_1 => x * x_1)\n (Nat.pair (unpair (unpair (Na... | [
150,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.addCases_left | [
{
"state_after": "case mk\nn✝ m✝ m n : ℕ\nC : Fin (m + n) → Sort u_1\nhleft : (i : Fin m) → C (↑(castAdd n) i)\nhright : (i : Fin n) → C (↑(natAdd m) i)\ni : ℕ\nhi : i < m\n⊢ addCases hleft hright (↑(castAdd n) { val := i, isLt := hi }) = hleft { val := i, isLt := hi }",
"state_before": "n✝ m✝ m n : ℕ\nC : ... | [
1853,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1848,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.map_id | [] | [
637,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
635,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_nat_cast_map | [
{
"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✝¹ : Semiring R\np✝ q r : R[X]\ninst✝ : Semiring S\nf✝ f : R →+* S\np : R[X]\nn : ℕ\n⊢ eval (↑n) (map f p) = ↑f (eval (↑n) p)",
"tactic": "induction p using Polynomial.induction_on' with\... | [
980,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
973,
1
] |
Mathlib/Order/Monotone/Basic.lean | monotone_nat_of_le_succ | [] | [
991,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
990,
1
] |
Mathlib/CategoryTheory/Types.lean | CategoryTheory.ofTypeFunctor_obj | [] | [
293,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Topology/LocallyConstant/Basic.lean | LocallyConstant.map_apply | [] | [
410,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.radical_le_radical_iff | [] | [
900,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
899,
1
] |
Mathlib/Order/Monotone/Basic.lean | StrictAnti.comp | [] | [
683,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
11
] |
Mathlib/Data/List/Palindrome.lean | List.Palindrome.iff_reverse_eq | [] | [
68,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.union_subset_left | [] | [
1416,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1415,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.coe_imI | [] | [
834,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
834,
1
] |
Mathlib/Init/Data/Fin/Basic.lean | Fin.vne_of_ne | [] | [
22,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
22,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.WalkingPair.equivBool_symm_apply_true | [] | [
107,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Data/Fin/Interval.lean | Fin.map_valEmbedding_Iic | [
{
"state_after": "no goals",
"state_before": "n : ℕ\na b : Fin n\n⊢ map valEmbedding (Iic b) = Iic ↑b",
"tactic": "simp [Iic_eq_finset_subtype, Finset.fin, Finset.map_map, Iic_filter_lt_of_lt_right]"
}
] | [
166,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.dual_eraseMax | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nt : Ordnode α\n⊢ dual (eraseMax t) = eraseMin (dual t)",
"tactic": "rw [← dual_dual (eraseMin _), dual_eraseMin, dual_dual]"
}
] | [
606,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
605,
1
] |
Mathlib/Data/Real/NNReal.lean | Real.toNNReal_lt_toNNReal_iff' | [] | [
641,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
640,
1
] |
Std/Data/List/Lemmas.lean | List.Subset.refl | [] | [
233,
65
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
233,
9
] |
Mathlib/Algebra/Order/Interval.lean | Interval.bot_div | [] | [
456,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.epic_of_localizationMap | [
{
"state_after": "M : Type u_3\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type u_1\ninst✝¹ : CommMonoid N\nP : Type u_2\ninst✝ : CommMonoid P\nf : LocalizationMap S N\ng : M →* P\nhg : ∀ (y : { x // x ∈ S }), IsUnit (↑g ↑y)\nj k : N →* P\nh : ∀ (a : M), ↑(MonoidHom.comp j (toMap f)) a = ↑(MonoidHom.comp k (to... | [
1040,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1037,
1
] |
Mathlib/Control/LawfulFix.lean | Part.fix_le | [
{
"state_after": "α✝ : Type u_2\nβ : α✝ → Type u_1\nα : Type ?u.12565\nf : ((a : α✝) → Part (β a)) →o (a : α✝) → Part (β a)\nX : (a : α✝) → Part (β a)\nhX : ↑f X ≤ X\n⊢ ωSup (approxChain f) ≤ X",
"state_before": "α✝ : Type u_2\nβ : α✝ → Type u_1\nα : Type ?u.12565\nf : ((a : α✝) → Part (β a)) →o (a : α✝) → ... | [
173,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.mul_const_inv | [] | [
154,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Order/Hom/Lattice.lean | BoundedLatticeHom.comp_apply | [] | [
1299,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1297,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.empty_pow | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.440630\nα : Type u_1\nβ : Type ?u.440636\nγ : Type ?u.440639\ninst✝² : DecidableEq α\ninst✝¹ : DecidableEq β\ninst✝ : Monoid α\ns t : Finset α\na : α\nm n : ℕ\nhn : n ≠ 0\n⊢ ∅ ^ n = ∅",
"tactic": "rw [← tsub_add_cancel_of_le (Nat.succ_le_of_lt <|... | [
930,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
929,
1
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | cauchySeq_of_edist_le_geometric | [
{
"state_after": "α : Type u_1\nβ : Type ?u.430769\nι : Type ?u.430772\ninst✝ : PseudoEMetricSpace α\nr C : ℝ≥0∞\nhr : r < 1\nhC : C ≠ ⊤\nf : ℕ → α\nhu : ∀ (n : ℕ), edist (f n) (f (n + 1)) ≤ C * r ^ n\n⊢ (∑' (n : ℕ), C * r ^ n) ≠ ⊤",
"state_before": "α : Type u_1\nβ : Type ?u.430769\nι : Type ?u.430772\nins... | [
317,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
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Mathlib/RingTheory/Adjoin/FG.lean | Subalgebra.fg_of_noetherian | [] | [
123,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.coeff_update_same | [
{
"state_after": "no goals",
"state_before": "R : Type u\na✝ b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np✝ q p : R[X]\nn : ℕ\na : R\n⊢ coeff (update p n a) n = a",
"tactic": "rw [p.coeff_update_apply, if_pos rfl]"
}
] | [
1098,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1097,
1
] |
Mathlib/Algebra/GroupRingAction/Basic.lean | smul_inv'' | [] | [
103,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Data/Rat/Cast.lean | Rat.cast_hom_rat | [] | [
430,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.equiv_neg | [] | [
802,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
801,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_union_Ico' | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.114474\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\nh₁ : c ≤ b\nh₂ : a ≤ d\nx : α\n⊢ x ∈ Ico a b ∪ Ico c d ↔ x ∈ Ico (min a c) (max b d)",
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43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1513,
1
] |
Mathlib/InformationTheory/Hamming.lean | Hamming.nnnorm_eq_hammingNorm | [] | [
477,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
] |
Mathlib/Algebra/Order/Module.lean | smul_inv_lt_iff_of_neg | [
{
"state_after": "no goals",
"state_before": "k : Type u_1\nM : Type u_2\nN : Type ?u.102476\ninst✝³ : LinearOrderedField k\ninst✝² : OrderedAddCommGroup M\ninst✝¹ : Module k M\ninst✝ : OrderedSMul k M\na b : M\nc : k\nh : c < 0\n⊢ a < c⁻¹ • b ↔ b < c • a",
"tactic": "rw [← smul_lt_smul_iff_of_neg h, sm... | [
179,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Topology/SubsetProperties.lean | CompactExhaustion.find_shiftr | [] | [
1498,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1497,
1
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Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.Monic.irreducible_of_irreducible_map | [
{
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1264,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1252,
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Mathlib/GroupTheory/Submonoid/Basic.lean | MonoidHom.eq_of_eqOn_denseM | [] | [
616,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
614,
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Mathlib/CategoryTheory/Subobject/FactorThru.lean | CategoryTheory.Subobject.factorThru_self | [
{
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132,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
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Mathlib/Data/Set/Image.lean | Set.subset_image_diff | [
{
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433,
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431,
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Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_surjective | [] | [
119,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.map_fst_darts | [
{
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"tactic": "simpa! using congr_arg List.dropLast (map_fst_darts_... | [
736,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
1
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src/lean/Init/Data/Array/DecidableEq.lean | Array.eq_of_isEqv | [
{
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32,
59
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25,
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Mathlib/LinearAlgebra/AffineSpace/Basis.lean | AffineBasis.coord_apply_ne | [
{
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... | [
182,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.append_reverseAux | [
{
"state_after": "no goals",
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"tactic": "inducti... | [
339,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
11
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | stronglyMeasurable_of_restrict_of_restrict_compl | [] | [
807,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
802,
1
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.iSup_add_iSup | [
{
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622,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
615,
1
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Mathlib/MeasureTheory/Function/SpecialFunctions/Basic.lean | Measurable.cexp | [] | [
186,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
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Mathlib/Data/Set/Basic.lean | Set.inter_diff_distrib_right | [] | [
1617,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1616,
1
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Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_lt_logb | [
{
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},
{
"state_after": "no goals",
"state_before": "b x y : ℝ\n... | [
154,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
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Mathlib/GroupTheory/Subsemigroup/Membership.lean | Subsemigroup.mem_sSup_of_directed_on | [
{
"state_after": "no goals",
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"tactic": "simp only [sSup_eq_iSup', mem_iSup_of_directed hS.dir... | [
71,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
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Mathlib/Topology/NoetherianSpace.lean | TopologicalSpace.NoetherianSpace.exists_finite_set_isClosed_irreducible | [
{
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204,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
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Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.d_pos | [] | [
888,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
887,
1
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Mathlib/Data/Finset/Fold.lean | Finset.fold_const | [
{
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95,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
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Mathlib/CategoryTheory/Monoidal/Free/Coherence.lean | CategoryTheory.FreeMonoidalCategory.normalizeObj_unitor | [] | [
99,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
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Mathlib/Data/Fin/Basic.lean | Fin.succRecOn_zero | [
{
"state_after": "no goals",
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"tactic": "cases n <;> rfl"
}
] | [
1671,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1669,
1
] |
Mathlib/Algebra/Category/GroupCat/EpiMono.lean | GroupCat.SurjectiveOfEpiAuxs.h_apply_infinity | [
{
"state_after": "A B : GroupCat\nf : A ⟶ B\nx : ↑B\nhx : x ∈ MonoidHom.range f\n⊢ ↑((τ.symm.trans (↑g x)).trans τ) ∞ = ∞",
"state_before": "A B : GroupCat\nf : A ⟶ B\nx : ↑B\nhx : x ∈ MonoidHom.range f\n⊢ ↑(↑h x) ∞ = ∞",
"tactic": "change ((τ).symm.trans (g x)).trans τ _ = _"
},
{
"state_after"... | [
264,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.L1.norm_Integral_le_one | [] | [
733,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
732,
1
] |
Mathlib/Data/Finmap.lean | Multiset.coe_nodupKeys | [] | [
47,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/Data/Set/Intervals/Instances.lean | Set.Icc.one_sub_nonneg | [
{
"state_after": "no goals",
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"tactic": "simpa using x.2.2"
}
] | [
175,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Topology/Connected.lean | isPreconnected_of_forall_constant | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.145858\nπ : ι → Type ?u.145863\ninst✝ : TopologicalSpace α\ns✝ t u v s : Set α\nhs : ∀ (f : α → Bool), ContinuousOn f s → ∀ (x : α), x ∈ s → ∀ (y : α), y ∈ s → f x = f y\n⊢ ∀ (u v : Set α),\n IsOpen u → IsOpen v → s ⊆ u ∪ v → Set.Nonempty (s ∩ u) → Set.No... | [
1590,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1577,
1
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Mathlib/Tactic/LinearCombination.lean | Mathlib.Tactic.LinearCombination.c_mul_pf | [] | [
45,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Analysis/Normed/Order/Lattice.lean | norm_abs_eq_norm | [] | [
118,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Algebra/ContinuedFractions/Translations.lean | GeneralizedContinuedFraction.first_continuant_eq | [
{
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"state_before": "K : Type u_1\ng : GeneralizedContinuedFraction K\nn : ℕ\ninst✝... | [
160,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
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Mathlib/Order/GaloisConnection.lean | GaloisInsertion.strictMono_u | [] | [
598,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
1
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Mathlib/Data/Set/Sigma.lean | Set.empty_sigma | [] | [
99,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/ModelTheory/LanguageMap.lean | FirstOrder.Language.LHom.Injective.isExpansionOn_default | [
{
"state_after": "L : Language\nL' : Language\nM✝ : Type w\ninst✝⁴ : Structure L M✝\nϕ✝ : L →ᴸ L'\nL'' : Language\nϕ : L →ᴸ L'\ninst✝³ : (n : ℕ) → (f : Functions L' n) → Decidable (f ∈ Set.range fun f => LHom.onFunction ϕ f)\ninst✝² : (n : ℕ) → (r : Relations L' n) → Decidable (r ∈ Set.range fun r => LHom.onRel... | [
336,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Topology/Algebra/ConstMulAction.lean | HasCompactSupport.comp_smul | [] | [
390,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.isPwo_singleton | [] | [
450,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
9
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_iInter_eq_iInf | [
{
"state_after": "case intro\nα : Type u_2\nβ : Type ?u.53347\nγ : Type ?u.53350\nδ : Type ?u.53353\nι : Type u_1\nR : Type ?u.53359\nR' : Type ?u.53362\nm : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns✝ s₁ s₂ t : Set α\ninst✝ : Countable ι\ns : ι → Set α\nh : ∀ (i : ι), MeasurableSet (s i)\nhd : Directed (fun x x... | [
513,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
495,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.support_nil | [] | [
531,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/Order/Filter/NAry.lean | Filter.map₂_assoc | [
{
"state_after": "no goals",
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305,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/CategoryTheory/Monoidal/Types/Basic.lean | CategoryTheory.associator_hom_apply | [] | [
66,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.support_mono | [] | [
602,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
601,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.ne_empty_of_mem | [] | [
566,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
565,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | StrictMono.mul_monotone' | [] | [
1521,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1519,
1
] |
Mathlib/Data/Set/Image.lean | Subtype.forall_set_subtype | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nt : Set α\np : Set α → Prop\n⊢ (∀ (s : Set ↑t), p (val '' s)) ↔ ∀ (s : Set α), s ⊆ t → p s",
"tactic": "rw [← forall_subset_range_iff, range_coe]"
}
] | [
1463,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1461,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coeIdeal_eq_one | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁸ : CommRing R\nS : Submonoid R\nP : Type ?u.1120670\ninst✝⁷ : CommRing P\ninst✝⁶ : Algebra R P\nloc : IsLocalization S P\nK : Type u_2\nK' : Type ?u.1121134\ninst✝⁵ : Field K\ninst✝⁴ : Field K'\ninst✝³ : Algebra R K\ninst✝² : IsFractionRing R... | [
1021,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1020,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.inductionOn₃ | [] | [
141,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Data/Polynomial/Laurent.lean | LaurentPolynomial.algebraMap_eq_toLaurent | [] | [
590,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
589,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Presieve.pullback_singleton | [
{
"state_after": "case h\nC : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nF : C ⥤ D\nX Y Z : C\nf : Y ⟶ X\ninst✝ : HasPullbacks C\ng : Z ⟶ X\nW : C\n⊢ pullbackArrows f (singleton g) = singleton pullback.snd",
"state_before": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Catego... | [
128,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Data/Int/Parity.lean | Int.ne_of_odd_add | [
{
"state_after": "no goals",
"state_before": "m n : ℤ\nh : Odd (m + n)\nhnot : m = n\n⊢ False",
"tactic": "simp [hnot, parity_simps] at h"
}
] | [
184,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.nilFun_comp | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nα₀ : TypeVec 0\nf₀ : α₀ ⟹ Fin2.elim0\nx : Fin2 0\n⊢ (nilFun ⊚ f₀) x = f₀ x",
"tactic": "apply Fin2.elim0 x"
}
] | [
276,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
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