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/Data/List/MinMax.lean | List.le_of_mem_argmin | [] | [
181,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | mul_zpow_self | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.129303\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : Group G\nb : G\nm : ℤ\n⊢ b ^ m * b ^ 1 = b ^ (m + 1)",
"tactic": "rw [← zpow_add, add_comm]"
}
] | [
239,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
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Mathlib/Data/Analysis/Filter.lean | Filter.Realizer.bot_F | [] | [
208,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
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Mathlib/RingTheory/HahnSeries.lean | HahnSeries.neg_coeff | [] | [
458,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
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Mathlib/Data/List/Func.lean | List.Func.nil_pointwise | [
{
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"tactic": "simp only [nil_pointwise bs, pointwise, eq_self_iff_true, and_self_iff, map]... | [
279,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
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Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesOnBall.isBigO_image_sub_image_sub_deriv_principal | [
{
"state_after": "case intro\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.738043\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf g : E →... | [
779,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
716,
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | Filter.EventuallyEq.fderiv_within' | [] | [
952,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Inseparable.lean | Filter.HasBasis.specializes_iff | [] | [
159,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.cyclotomic'_eq_X_pow_sub_one_div | [
{
"state_after": "K✝ : Type ?u.243517\ninst✝² : Field K✝\nK : Type u_1\ninst✝¹ : CommRing K\ninst✝ : IsDomain K\nζ : K\nn : ℕ\nhpos : 0 < n\nh : IsPrimitiveRoot ζ n\n⊢ cyclotomic' n K =\n (cyclotomic' n K * ∏ x in Nat.properDivisors n, cyclotomic' x K) /ₘ ∏ i in Nat.properDivisors n, cyclotomic' i K",
"s... | [
197,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
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Mathlib/Data/Finset/Fold.lean | Finset.le_fold_min | [] | [
219,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
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Mathlib/Algebra/Order/Ring/Lemmas.lean | Left.one_le_mul_of_le_of_le | [] | [
781,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
779,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.succ_strictMono | [] | [
358,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | exp_units_conj' | [] | [
536,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_toPartENat_eq_coe_card | [
{
"state_after": "no goals",
"state_before": "α β : Type u\ninst✝ : Fintype α\n⊢ ↑toPartENat (#α) = ↑(Fintype.card α)",
"tactic": "simp"
}
] | [
1883,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1883,
1
] |
Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.unitCoeff_spec | [
{
"state_after": "case a\np : ℕ\nhp : Fact (Nat.Prime p)\nx : ℤ_[p]\nhx : x ≠ 0\n⊢ (fun a => ↑a) x = (fun a => ↑a) (↑(unitCoeff hx) * ↑p ^ Int.natAbs (valuation x))",
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"tactic":... | [
509,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
500,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.map_lift_equalizerComparison | [
{
"state_after": "no goals",
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"tactic": ... | [
1136,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1131,
1
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Mathlib/Data/Set/Basic.lean | Set.mem_def | [] | [
289,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
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Mathlib/Algebra/Module/LocalizedModule.lean | IsLocalizedModule.mk'_one | [
{
"state_after": "R : Type u_2\ninst✝⁷ : CommRing R\nS : Submonoid R\nM : Type u_3\nM' : Type u_1\nM'' : Type ?u.826565\ninst✝⁶ : AddCommMonoid M\ninst✝⁵ : AddCommMonoid M'\ninst✝⁴ : AddCommMonoid M''\ninst✝³ : Module R M\ninst✝² : Module R M'\ninst✝¹ : Module R M''\nf : M →ₗ[R] M'\ng : M →ₗ[R] M''\ninst✝ : IsL... | [
943,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
940,
1
] |
Mathlib/InformationTheory/Hamming.lean | hammingNorm_lt_one | [] | [
208,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_nat_mul_two_pi | [] | [
346,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Topology/Order.lean | Equiv.induced_symm | [
{
"state_after": "case h.a.h.a\nα✝ : Type ?u.26688\nβ✝ : Type ?u.26691\nγ : Type ?u.26694\nt✝ t₁ t₂ : TopologicalSpace α✝\nt' : TopologicalSpace β✝\nf : α✝ → β✝\ng : β✝ → α✝\nα : Type u_1\nβ : Type u_2\ne : α ≃ β\nt : TopologicalSpace α\nU : Set β\n⊢ IsOpen U ↔ IsOpen U",
"state_before": "α✝ : Type ?u.26688... | [
494,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/Combinatorics/SetFamily/Compression/UV.lean | UV.compress_of_disjoint_of_le | [] | [
107,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieHom.congr_fun | [] | [
395,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/Topology/Basic.lean | IsOpen.frontier_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns✝ s₁ s₂ t : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\ns : Set α\nhs : IsOpen s\n⊢ frontier s = closure s \\ s",
"tactic": "rw [frontier, hs.interior_eq]"
}
] | [
761,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
760,
1
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Mathlib/Data/Set/Pointwise/Finite.lean | Set.finite_one | [] | [
29,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
28,
1
] |
Mathlib/Topology/Inseparable.lean | SeparationQuotient.tendsto_lift₂_nhds | [
{
"state_after": "X : Type u_1\nY : Type u_2\nZ : Type ?u.106593\nα : Type u_3\nι : Type ?u.106599\nπ : ι → Type ?u.106604\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace Y\ninst✝¹ : TopologicalSpace Z\ninst✝ : (i : ι) → TopologicalSpace (π i)\nx✝ y✝ z : X\ns : Set X\nf✝ : X → Y\nt : Set (SeparationQuot... | [
595,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
591,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.nonempty | [] | [
292,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
11
] |
Mathlib/GroupTheory/GroupAction/Pi.lean | Function.extend_smul | [
{
"state_after": "I : Type u\nf✝ : I → Type v\nx✝ y : (i : I) → f✝ i\ni : I\nR : Type u_1\nα : Type u_2\nβ : Type u_3\nγ : Type u_4\ninst✝ : SMul R γ\nr : R\nf : α → β\ng : α → γ\ne : β → γ\nx : β\nthis : Decidable (∃ a, f a = x)\n⊢ extend f (r • g) (r • e) x = (r • extend f g e) x",
"state_before": "I : Ty... | [
278,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Complex.lean | Complex.eq_zero_cpow_iff | [
{
"state_after": "no goals",
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"tactic": "rw [← zero_cpow_eq_iff, eq_comm]"
}
] | [
79,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.comap_lt_comap_of_surjective | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nG' : Type ?u.577797\ninst✝³ : Group G\ninst✝² : Group G'\nA : Type ?u.577806\ninst✝¹ : AddGroup A\nN : Type u_2\ninst✝ : Group N\nf✝ f : G →* N\nK L : Subgroup N\nhf : Surjective ↑f\n⊢ comap f K < comap f L ↔ K < L",
"tactic": "simp_rw [lt_iff_... | [
3052,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3051,
1
] |
Mathlib/Data/Quot.lean | Quot.eq | [] | [
296,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Topology/UniformSpace/Separation.lean | UniformSpace.SeparationQuotient.map_id | [] | [
414,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Algebra/Module/Submodule/Lattice.lean | Submodule.bot_coe | [] | [
56,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.exists_isOpen_measure_lt_top | [
{
"state_after": "no goals",
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3908,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3905,
1
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Mathlib/Order/Bounds/Basic.lean | IsGreatest.mono | [] | [
246,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/AlgebraicTopology/SimplexCategory.lean | SimplexCategory.eq_id_of_epi | [
{
"state_after": "x : SimplexCategory\ni : x ⟶ x\ninst✝ : Epi i\n⊢ IsIso i",
"state_before": "x : SimplexCategory\ni : x ⟶ x\ninst✝ : Epi i\n⊢ i = 𝟙 x",
"tactic": "suffices IsIso i by\n haveI := this\n apply eq_id_of_isIso"
},
{
"state_after": "case hf\nx : SimplexCategory\ni : x ⟶ x\ninst✝ :... | [
731,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
723,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_neg_Ioo | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\n⊢ Neg.neg '' Ioo a b = Ioo (-b) (-a)",
"tactic": "simp"
}
] | [
312,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Analysis/Normed/Group/HomCompletion.lean | NormedAddGroupHom.completion_sub | [] | [
131,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/CategoryTheory/Shift/Basic.lean | CategoryTheory.shiftComm_hom_comp | [
{
"state_after": "no goals",
"state_before": "C : Type u\nA : Type u_1\ninst✝² : Category C\ninst✝¹ : AddCommMonoid A\ninst✝ : HasShift C A\nX Y : C\nf : X ⟶ Y\ni j : A\n⊢ (shiftComm X i j).hom ≫ (shiftFunctor C i).map ((shiftFunctor C j).map f) =\n (shiftFunctor C j).map ((shiftFunctor C i).map f) ≫ (sh... | [
616,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
614,
1
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Mathlib/Computability/Primrec.lean | Primrec.subtype_val | [
{
"state_after": "α : Type u_1\nβ : Type ?u.353649\nγ : Type ?u.353652\nσ : Type ?u.353655\ninst✝⁴ : Primcodable α\ninst✝³ : Primcodable β\ninst✝² : Primcodable γ\ninst✝¹ : Primcodable σ\np : α → Prop\ninst✝ : DecidablePred p\nhp : PrimrecPred p\nthis : Primcodable (Subtype p) := Primcodable.subtype hp\n⊢ Primr... | [
1231,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1226,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_at_nat_cast | [
{
"state_after": "case h.e'_2.h.e'_6\nR : 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]\nx : R\nS : Type u_1\ninst✝ : Semiring S\nf : R →+* S\nn : ℕ\n⊢ ↑n = ↑f ↑n",
"state_before": "R : Type u\nS✝ : Type v\nT : Type w\nι : Type y\na b : R\nm n✝ : ℕ\ninst✝¹... | [
348,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.closure_iUnion | [] | [
780,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
779,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.length_reverse | [
{
"state_after": "no goals",
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"tactic": "simp [reverse]"
}
] | [
422,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.mem_verts_toSubgraph | [
{
"state_after": "case nil\nV : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v w u✝ : V\n⊢ w ∈ (Walk.toSubgraph nil).verts ↔ w ∈ support nil\n\ncase cons\nV : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\n... | [
2235,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2230,
1
] |
Mathlib/Order/Disjoint.lean | Codisjoint.dual | [] | [
411,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.Nonempty.of_vsub_left | [] | [
641,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
640,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.geom_sum_X_comp_X_add_one_eq_sum | [
{
"state_after": "case a\nR : Type u\nS : Type ?u.49481\ninst✝ : Semiring R\nn i : ℕ\n⊢ coeff (comp (∑ i in range n, X ^ i) (X + 1)) i = coeff (∑ i in range n, ↑(Nat.choose n (i + 1)) * X ^ i) i",
"state_before": "R : Type u\nS : Type ?u.49481\ninst✝ : Semiring R\nn : ℕ\n⊢ comp (∑ i in range n, X ^ i) (X + ... | [
227,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.Icc_pred_right | [] | [
751,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
750,
1
] |
Mathlib/RingTheory/Finiteness.lean | Submodule.FG.map | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nM : Type u_2\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\nP : Type u_3\ninst✝¹ : AddCommMonoid P\ninst✝ : Module R P\nf : M →ₗ[R] P\nN : Submodule R M\nhs : FG N\nt : Set M\nht : Set.Finite t ∧ span R t = N\n⊢ span R (↑f '' ... | [
209,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Order/Hom/Bounded.lean | BotHom.coe_bot | [] | [
505,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.BinaryBiproduct.bicone_inr | [] | [
1321,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1320,
1
] |
Std/Data/List/Lemmas.lean | List.modifyNthTail_id | [] | [
720,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
717,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.monomial_add | [] | [
443,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.add_factorial_succ_le_factorial_add_succ | [
{
"state_after": "case inl\nm n✝ i n : ℕ\nh✝ : 2 ≤ i\n⊢ i + (n + 1)! ≤ (i + (n + 1))!\n\ncase inr\nm n✝ i n : ℕ\nh✝ : i < 2\n⊢ i + (n + 1)! ≤ (i + (n + 1))!",
"state_before": "m n✝ i n : ℕ\n⊢ i + (n + 1)! ≤ (i + (n + 1))!",
"tactic": "cases (le_or_lt (2 : ℕ) i)"
},
{
"state_after": "case inl\nm ... | [
200,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Data/Nat/Parity.lean | Nat.one_add_div_two_mul_two_of_odd | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\nh : Odd n\n⊢ 1 + n / 2 * 2 = n",
"tactic": "rw [← odd_iff.mp h, mod_add_div']"
}
] | [
239,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.map_eq_zero_iff | [] | [
998,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
997,
1
] |
Mathlib/Topology/UniformSpace/Equicontinuity.lean | Equicontinuous.closure | [] | [
416,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.tan_add_nat_mul_pi | [] | [
1035,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1034,
1
] |
Mathlib/CategoryTheory/Whiskering.lean | CategoryTheory.Functor.triangle | [
{
"state_after": "no goals",
"state_before": "A : Type u₁\ninst✝³ : Category A\nB : Type u₂\ninst✝² : Category B\nC : Type u₃\ninst✝¹ : Category C\nD : Type u₄\ninst✝ : Category D\nF : A ⥤ B\nG : B ⥤ C\n⊢ (associator F (𝟭 B) G).hom ≫ whiskerLeft F (leftUnitor G).hom = whiskerRight (rightUnitor F).hom G",
... | [
281,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Logic/Relation.lean | swap_eq_iff | [] | [
97,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Data/Int/Interval.lean | Int.Icc_eq_finset_map | [] | [
86,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/RingTheory/Ideal/LocalRing.lean | LocalRing.mem_maximalIdeal | [] | [
146,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iInf_eq_dif | [] | [
260,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | LipschitzWith.norm_div_le_of_le | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.196007\n𝕜 : Type ?u.196010\nα : Type ?u.196013\nι : Type ?u.196016\nκ : Type ?u.196019\nE : Type u_1\nF : Type u_2\nG : Type ?u.196028\ninst✝² : SeminormedGroup E\ninst✝¹ : SeminormedGroup F\ninst✝ : SeminormedGroup G\ns : Set E\na a₁ a₂ b b₁ b₂ : ... | [
834,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
832,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_eq_coe | [] | [
327,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
20
] |
Mathlib/Order/SuccPred/Basic.lean | Order.succ_le_of_lt | [] | [
225,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Topology/Separation.lean | Dense.diff_singleton | [] | [
712,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
710,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | HomogeneousLocalization.NumDenSameDeg.num_pow | [] | [
249,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Combinatorics/Additive/SalemSpencer.lean | rothNumberNat_def | [] | [
470,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
469,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | IsUnit.pow | [] | [
63,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | IsLinearMap.isLinearMap_smul | [
{
"state_after": "R✝ : Type ?u.325967\nR₁ : Type ?u.325970\nR₂ : Type ?u.325973\nR₃ : Type ?u.325976\nk : Type ?u.325979\nS : Type ?u.325982\nS₃ : Type ?u.325985\nT : Type ?u.325988\nM✝ : Type ?u.325991\nM₁ : Type ?u.325994\nM₂ : Type ?u.325997\nM₃ : Type ?u.326000\nN₁ : Type ?u.326003\nN₂ : Type ?u.326006\nN₃ ... | [
696,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
1
] |
Mathlib/Order/WithBot.lean | WithTop.toDual_apply_coe | [] | [
685,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
684,
1
] |
Mathlib/LinearAlgebra/Ray.lean | sameRay_neg_smul_right_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝³ : LinearOrderedCommRing R\nM : Type u_2\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\ninst✝ : NoZeroSMulDivisors R M\nv : M\nr : R\n⊢ SameRay R (-v) (r • v) ↔ r ≤ 0 ∨ v = 0",
"tactic": "rw [← sameRay_neg_iff, neg_neg, ← neg_smul, sameRa... | [
559,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf_congr | [
{
"state_after": "F : Type ?u.108630\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.108639\nι : Type ?u.108642\nκ : Type ?u.108645\ninst✝¹ : SemilatticeInf α\ninst✝ : OrderTop α\ns s₁ : Finset β\nf✝ g✝ : β → α\na : α\nf g : β → α\nhfg : ∀ (a : β), a ∈ s₁ → f a = g a\n⊢ inf s₁ f = inf s₁ g",
"state_before": "F : T... | [
368,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.ext_abs_arg_iff | [] | [
131,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/LinearAlgebra/Finrank.lean | Subalgebra.rank_toSubmodule | [] | [
531,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/GroupTheory/GroupAction/Defs.lean | ofMul_vadd | [] | [
1180,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1179,
1
] |
Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingHom.coe_RingHom_id | [] | [
288,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Data/List/MinMax.lean | List.minimum_cons | [] | [
380,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.sum_nil | [] | [
831,
48
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
831,
9
] |
Mathlib/Data/Set/Sups.lean | Set.sups_nonempty | [] | [
116,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Analysis/Convex/Strict.lean | StrictConvex.linear_preimage | [
{
"state_after": "𝕜 : Type u_2\n𝕝 : Type ?u.28655\nE : Type u_3\nF : Type u_1\nβ : Type ?u.28664\ninst✝⁶ : OrderedSemiring 𝕜\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : TopologicalSpace F\ninst✝³ : AddCommMonoid E\ninst✝² : AddCommMonoid F\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\ns✝ : Set E\ns : Set F\nhs : St... | [
149,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | Basis.le_span'' | [
{
"state_after": "case f\nK : Type u\nV V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι✝ : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.301145\nR : Type u\ninst✝⁵ : Ring R\ninst✝⁴ : RankCondition R\nM : Type v\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\nι : Type u_1\ninst✝¹ : Fintype ι\nb : Bas... | [
599,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
590,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.QuasiMeasurePreserving.tendsto_ae | [] | [
2496,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2495,
1
] |
Mathlib/ModelTheory/FinitelyGenerated.lean | FirstOrder.Language.Structure.FG.range | [
{
"state_after": "L : Language\nM : Type u_4\ninst✝¹ : Structure L M\nN : Type u_1\ninst✝ : Structure L N\nh : FG L M\nf : M →[L] N\n⊢ Substructure.FG (map f ⊤)",
"state_before": "L : Language\nM : Type u_4\ninst✝¹ : Structure L M\nN : Type u_1\ninst✝ : Structure L N\nh : FG L M\nf : M →[L] N\n⊢ Substructur... | [
219,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Algebra/CharP/Algebra.lean | IsFractionRing.charZero_of_isFractionRing | [] | [
144,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Data/MvPolynomial/Rename.lean | MvPolynomial.rename_C | [] | [
65,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Std/Data/Int/DivMod.lean | Int.ediv_self | [
{
"state_after": "a : Int\nH : a ≠ 0\nthis : 1 * a / a = 1\n⊢ a / a = 1",
"state_before": "a : Int\nH : a ≠ 0\n⊢ a / a = 1",
"tactic": "have := Int.mul_ediv_cancel 1 H"
},
{
"state_after": "no goals",
"state_before": "a : Int\nH : a ≠ 0\nthis : 1 * a / a = 1\n⊢ a / a = 1",
"tactic": "rwa... | [
229,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
228,
19
] |
Mathlib/Data/Set/Basic.lean | Set.nontrivial_of_univ_nontrivial | [] | [
2562,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2560,
1
] |
Mathlib/Data/String/Basic.lean | String.toList_inj | [] | [
124,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/CategoryTheory/Limits/MonoCoprod.lean | CategoryTheory.Limits.MonoCoprod.mono_inl_iff | [
{
"state_after": "C : Type u_2\ninst✝ : Category C\nA B : C\nc₁ c₂ : BinaryCofan A B\nhc₁ : IsColimit c₁\nhc₂ : IsColimit c₂\n⊢ ∀ (c₁ c₂ : BinaryCofan A B), IsColimit c₁ → IsColimit c₂ → Mono (BinaryCofan.inl c₁) → Mono (BinaryCofan.inl c₂)",
"state_before": "C : Type u_2\ninst✝ : Category C\nA B : C\nc₁ c₂... | [
85,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.IsPath.reverse | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V\np : Walk G u v\nh : IsPath p\n⊢ IsPath (Walk.reverse p)",
"tactic": "simpa [isPath_def] using h"
}
] | [
984,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
983,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Structure.funMap_apply₀ | [] | [
423,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.sq_eq_neg_normSq | [
{
"state_after": "R : Type u_1\ninst✝ : LinearOrderedCommRing R\na : ℍ[R]\n⊢ a ^ 2 = -↑(↑normSq a) ↔ star a = -a",
"state_before": "R : Type u_1\ninst✝ : LinearOrderedCommRing R\na : ℍ[R]\n⊢ a ^ 2 = -↑(↑normSq a) ↔ a.re = 0",
"tactic": "simp_rw [← star_eq_neg]"
},
{
"state_after": "case inl\nR :... | [
1306,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1302,
1
] |
Mathlib/CategoryTheory/Preadditive/Basic.lean | CategoryTheory.Preadditive.comp_sum | [] | [
188,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.vsub_union | [] | [
689,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
688,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasurableEmbedding.map_comap | [
{
"state_after": "case h\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.911558\nδ : Type ?u.911561\nι : Type ?u.911564\nR : Type ?u.911567\nR' : Type ?u.911570\nm0 : MeasurableSpace α\nm1 : MeasurableSpace β\nf : α → β\nhf : MeasurableEmbedding f\nμ : MeasureTheory.Measure β\nt : Set β\nht : MeasurableSet t\n⊢ ↑↑(Mea... | [
4196,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4193,
1
] |
Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsLimit.lift_self | [] | [
96,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.mem_lift' | [] | [
250,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.toFinset_eq_empty | [] | [
282,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
11
] |
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