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/Fintype/Basic.lean | Function.Embedding.invFun_restrict | [
{
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546,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Function/EssSup.lean | ae_lt_of_essSup_lt | [] | [
106,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Computability/Primrec.lean | Primrec.decode | [] | [
227,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
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Mathlib/Data/Prod/TProd.lean | List.TProd.ext | [
{
"state_after": "case h₁\nι : Type u\nα : ι → Type v\ni✝ j : ι\nl : List ι\nf : (i : ι) → α i\ninst✝ : DecidableEq ι\ni : ι\nis : List ι\nhl : Nodup (i :: is)\nv w : TProd α (i :: is)\nhvw : ∀ (i_1 : ι) (hi : i_1 ∈ i :: is), TProd.elim v hi = TProd.elim w hi\n⊢ v.fst = w.fst\n\ncase h₂\nι : Type u\nα : ι → Typ... | [
126,
47
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119,
1
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Mathlib/Algebra/Ring/Commute.lean | mul_self_eq_one_iff | [
{
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"tactic": "rw [← (Commute.one_right a).mul_self_eq_mul_self_iff, mul_one]"
}
] | [
166,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
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Mathlib/Algebra/Order/EuclideanAbsoluteValue.lean | AbsoluteValue.IsEuclidean.map_lt_map_iff | [] | [
55,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Homology/HomologicalComplex.lean | HomologicalComplex.Hom.comm_to | [] | [
551,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
550,
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Mathlib/Algebra/Free.lean | Magma.AssocQuotient.lift_comp_of' | [] | [
423,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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src/lean/Init/SimpLemmas.lean | Nat.le_zero_eq | [
{
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}
] | [
155,
78
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
154,
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Mathlib/Analysis/Calculus/FDeriv/Add.lean | DifferentiableWithinAt.add_const | [] | [
199,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
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Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.rootSet_maps_to' | [
{
"state_after": "R : Type u\nS✝ : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝⁸ : CommRing R\ninst✝⁷ : IsDomain R\np✝ q : R[X]\ninst✝⁶ : CommRing T\np : T[X]\nS : Type u_1\nS' : Type u_2\ninst✝⁵ : CommRing S\ninst✝⁴ : IsDomain S\ninst✝³ : Algebra T S\ninst✝² : CommRing S'\ninst✝¹ : IsDomain S'\ninst✝ : Algebra T ... | [
958,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
953,
1
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Mathlib/Order/SuccPred/Basic.lean | Order.le_pred_iff_of_not_isMin | [] | [
641,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
640,
1
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Mathlib/Algebra/Order/Interval.lean | NonemptyInterval.snd_mul | [] | [
189,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Analysis/Convex/Side.lean | Function.Injective.wSameSide_map_iff | [
{
"state_after": "R : Type u_1\nV : Type u_2\nV' : Type u_4\nP : Type u_3\nP' : Type u_5\ninst✝⁶ : StrictOrderedCommRing R\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddTorsor V P\ninst✝² : AddCommGroup V'\ninst✝¹ : Module R V'\ninst✝ : AddTorsor V' P'\ns : AffineSubspace R P\nx y : P\nf : P →ᵃ[R] ... | [
84,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.one_lt_rpow_iff | [
{
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"state_before": "x y z : ℝ\nhx : 0 ≤ x\n⊢ 1 < x ^ y ↔ 1 < x ∧ 0 < y ∨ 0 < x ∧ x < 1 ∧ y < 0",
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574,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
1
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Mathlib/GroupTheory/GroupAction/Defs.lean | AddMonoid.End.smul_def | [] | [
1133,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1132,
1
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Mathlib/Topology/UniformSpace/Basic.lean | Filter.HasBasis.biInter_biUnion_ball | [
{
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"state_before": "α : Type ua\nβ... | [
1079,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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src/lean/Init/Data/Nat/Basic.lean | Nat.lt_eq | [] | [
87,
52
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
87,
9
] |
Mathlib/Data/Fintype/Basic.lean | Set.filter_mem_univ_eq_toFinset | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.98777\nγ : Type ?u.98780\ns✝ t : Set α\ninst✝² : Fintype α\ns : Set α\ninst✝¹ : Fintype ↑s\ninst✝ : DecidablePred fun x => x ∈ s\na✝ : α\n⊢ a✝ ∈ filter (fun x => x ∈ s) Finset.univ ↔ a✝ ∈ toFinset s",
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797,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
793,
1
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Mathlib/Data/Multiset/Sort.lean | Multiset.sort_eq | [] | [
49,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
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Mathlib/Data/Real/Irrational.lean | Irrational.of_int_mul | [
{
"state_after": "no goals",
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}
] | [
360,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
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Mathlib/Data/Set/Intervals/OrdConnectedComponent.lean | Set.ordConnectedComponent_ordConnectedProj | [] | [
125,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
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Mathlib/Data/Set/Intervals/SurjOn.lean | surjOn_Ioi_of_monotone_surjective | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrder α\ninst✝ : PartialOrder β\nf : α → β\nh_mono : Monotone f\nh_surj : Surjective f\na : α\n⊢ SurjOn f (Iic aᶜ) (Ioi (f a)ᶜᶜ)",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrder α\ninst✝ : PartialOrder β\nf : α → β\nh_mono : Mon... | [
71,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Limits/Shapes/Diagonal.lean | CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_snd_snd | [
{
"state_after": "C : Type u_2\ninst✝⁵ : Category C\nX✝ Y✝ Z✝ : C\ninst✝⁴ : HasPullbacks C\nS T : C\nf✝ : X✝ ⟶ T\ng✝ : Y✝ ⟶ T\ni : T ⟶ S\ninst✝³ : HasPullback i i\ninst✝² : HasPullback f✝ g✝\ninst✝¹ : HasPullback (f✝ ≫ i) (g✝ ≫ i)\ninst✝ :\n HasPullback (diagonal i)\n (map (f✝ ≫ i) (g✝ ≫ i) i i f✝ g✝ (𝟙 S)... | [
354,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
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Mathlib/Algebra/ModEq.lean | AddCommGroup.ModEq.add_iff_right | [
{
"state_after": "no goals",
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"tactic": "simp [add_sub_add_comm, hm, ad... | [
198,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
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Mathlib/Data/Dfinsupp/Multiset.lean | Multiset.toDfinsupp_singleton | [
{
"state_after": "no goals",
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"tactic": "rw [← replicate_one, toDfinsupp_replicate]"
}
] | [
80,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Integral/PeakFunction.lean | tendsto_set_integral_pow_smul_of_unique_maximum_of_isCompact_of_measure_nhdsWithin_pos | [
{
"state_after": "α : Type u_1\nE : Type u_2\nι : Type ?u.628948\nhm : MeasurableSpace α\nμ : MeasureTheory.Measure α\ninst✝⁶ : TopologicalSpace α\ninst✝⁵ : BorelSpace α\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ng : α → E\nl : Filter ι\nx₀ : α\ns : Set α\nφ✝ : ι → α → ℝ\ninst✝² : CompleteSpace E... | [
285,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
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Mathlib/Algebra/Order/Hom/Basic.lean | map_eq_zero_iff_eq_one | [
{
"state_after": "ι : Type ?u.52007\nF : Type u_2\nα : Type u_3\nβ : Type u_1\nγ : Type ?u.52019\nδ : Type ?u.52022\ninst✝² : Group α\ninst✝¹ : OrderedAddCommMonoid β\ninst✝ : GroupNormClass F α β\nf : F\n⊢ ↑f 1 = 0",
"state_before": "ι : Type ?u.52007\nF : Type u_2\nα : Type u_3\nβ : Type u_1\nγ : Type ?u.... | [
296,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
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Mathlib/ModelTheory/FinitelyGenerated.lean | FirstOrder.Language.Substructure.cg_closure | [] | [
146,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Finset.coe_infsep_of_offDiag_empty | [
{
"state_after": "α : Type u_1\nβ : Type ?u.77060\ninst✝¹ : PseudoMetricSpace α\nx y z : α\ns✝ t : Set α\ninst✝ : DecidableEq α\ns : Finset α\nhs : ¬Finset.Nonempty (Finset.offDiag s)\n⊢ infsep ↑s = 0",
"state_before": "α : Type u_1\nβ : Type ?u.77060\ninst✝¹ : PseudoMetricSpace α\nx y z : α\ns✝ t : Set α\n... | [
517,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
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Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.eq_re_iff_mem_range_coe | [] | [
688,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
686,
1
] |
Mathlib/LinearAlgebra/Matrix/Charpoly/Basic.lean | charmatrix_apply_eq | [
{
"state_after": "no goals",
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"tactic": "simp only [charmatrix, RingHom.mapMatrix_apply, sub_apply, scalar_apply_eq, map_apply]"
}
] | [
62,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
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Mathlib/Data/Real/EReal.lean | EReal.bot_sub | [] | [
841,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
840,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.integral_Ioi_of_hasDerivAt_of_nonpos' | [] | [
793,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
790,
1
] |
Mathlib/Init/Algebra/Order.lean | le_antisymm_iff | [] | [
197,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.filter_of_true | [
{
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"state_before": "ι : Type u_1\nI J J₁ J₂ : Box ι\nπ π₁ π₂ : Prepartition I\nx :... | [
612,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
610,
1
] |
Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.pow_p_dvd_int_iff | [
{
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"tactic": "rw [← Nat.cast_pow, ← norm_int_le_pow_iff_dvd, norm_le_pow_iff_mem_span_pow,\n Ideal.mem_span_singleton, Nat.cast_pow]"
}
] | [
581,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
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Mathlib/Logic/Basic.lean | forall_apply_eq_imp_iff | [
{
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}
] | [
803,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
802,
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Mathlib/Algebra/Module/LocalizedModule.lean | LocalizedModule.add_smul' | [
{
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... | [
381,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
9
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.sInf_toAddSubgroup | [] | [
753,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
751,
1
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Mathlib/Data/Set/Basic.lean | Set.mem_insert | [] | [
1113,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1112,
1
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Mathlib/Data/Polynomial/Div.lean | Polynomial.div_wf_lemma | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\ninst✝ : Ring R\np q : R[X]\nh : degree q ≤ degree p ∧ p ≠ 0\nhq : Monic q\nhp : leadingCoeff p ≠ 0\nhq0 : q ≠ 0\n⊢ degree q ≤ degree p",
"state_before": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\ninst✝ : ... | [
111,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
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Mathlib/Algebra/Module/Bimodule.lean | Subbimodule.smul_mem | [
{
"state_after": "R : Type u_4\nA : Type u_2\nB : Type u_1\nM : Type u_3\ninst✝¹¹ : CommSemiring R\ninst✝¹⁰ : AddCommMonoid M\ninst✝⁹ : Module R M\ninst✝⁸ : Semiring A\ninst✝⁷ : Semiring B\ninst✝⁶ : Module A M\ninst✝⁵ : Module B M\ninst✝⁴ : Algebra R A\ninst✝³ : Algebra R B\ninst✝² : IsScalarTower R A M\ninst✝¹... | [
100,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
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Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.derivFamily_eq_enumOrd | [
{
"state_after": "ι : Type u\nf : ι → Ordinal → Ordinal\nH : ∀ (i : ι), IsNormal (f i)\n⊢ StrictMono (derivFamily f) ∧ Set.range (derivFamily f) = ⋂ (i : ι), fixedPoints (f i)",
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242,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
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Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_mul_left_Ioo | [
{
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"tactic": "convert image_mul_right_Ioo b c h using 1 <;> simp only [mul_comm _ a]"
}
] | [
759,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
757,
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Mathlib/SetTheory/Game/PGame.lean | PGame.le_trans_aux | [] | [
512,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
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Mathlib/Analysis/NormedSpace/ContinuousAffineMap.lean | ContinuousAffineMap.toConstProdContinuousLinearMap_fst | [] | [
277,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
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Mathlib/Order/Filter/Basic.lean | Filter.eventuallyLE_bind | [] | [
2731,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2729,
1
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Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_le | [] | [
875,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
873,
1
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Mathlib/Topology/Algebra/Monoid.lean | nhds_one_mul_nhds | [] | [
154,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.Memℒp.restrict | [] | [
600,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
599,
1
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Mathlib/LinearAlgebra/AnnihilatingPolynomial.lean | Polynomial.monic_annIdealGenerator | [] | [
129,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
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Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.integrable_prod_mul | [
{
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318,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
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Mathlib/LinearAlgebra/Matrix/Reindex.lean | Matrix.reindexAlgEquiv_refl | [] | [
147,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
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Mathlib/Algebra/Group/Units.lean | Units.val_inv_eq_inv_val | [] | [
407,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
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Mathlib/Data/Part.lean | Part.left_dom_of_union_dom | [] | [
847,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
847,
1
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Mathlib/Order/Circular.lean | Set.mem_cIoo | [] | [
355,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
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Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_neg_eq_arg_sub_pi_iff | [
{
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"state_bef... | [
398,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
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Mathlib/Data/Polynomial/Expand.lean | Polynomial.coe_expand | [] | [
44,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
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Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.SignedMeasure.singularPart_smul_nnreal | [
{
"state_after": "α : Type u_1\nβ : Type ?u.623899\nm : MeasurableSpace α\nμ✝ ν : Measure α\ns✝ t s : SignedMeasure α\nμ : Measure α\nr : ℝ≥0\n⊢ toSignedMeasure (Measure.singularPart (toJordanDecomposition (r • s)).posPart μ) -\n toSignedMeasure (Measure.singularPart (toJordanDecomposition (r • s)).negPart... | [
1089,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1081,
1
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Mathlib/Topology/Instances/ENNReal.lean | Real.diam_Ico | [
{
"state_after": "no goals",
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"tactic": "simp [Metric.diam, ENNReal.toReal_ofReal (sub_nonneg.2 h)]"
}
] | [
1560,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1559,
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Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.top_eq_id | [] | [
233,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
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Mathlib/Order/Interval.lean | Interval.coe_sSubset_coe | [] | [
483,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
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Mathlib/Topology/Bases.lean | TopologicalSpace.isSeparable_univ_iff | [
{
"state_after": "case mp\nα : Type u\nt : TopologicalSpace α\n⊢ IsSeparable univ → SeparableSpace α\n\ncase mpr\nα : Type u\nt : TopologicalSpace α\n⊢ SeparableSpace α → IsSeparable univ",
"state_before": "α : Type u\nt : TopologicalSpace α\n⊢ IsSeparable univ ↔ SeparableSpace α",
"tactic": "constructo... | [
426,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
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Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.constantCoeff_comp_C | [] | [
1544,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1543,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_zpow | [
{
"state_after": "case ofNat\nα : Type ?u.359170\nβ : Type ?u.359173\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nhr : r ≠ 0\nn : ℕ\n⊢ ↑(r ^ Int.ofNat n) = ↑r ^ Int.ofNat n\n\ncase negSucc\nα : Type ?u.359170\nβ : Type ?u.359173\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nhr : r ≠ 0\nn : ℕ\n⊢ ↑(r ^ Int.negSucc n) = ↑r ^ Int.negSucc n",
... | [
1859,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1855,
1
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.snorm_one_le_of_le' | [
{
"state_after": "α : Type u_1\nE : Type ?u.1760021\nF : Type ?u.1760024\n𝕜 : Type ?u.1760027\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : CompleteSpace E\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : SMulCommClass ℝ 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ ... | [
1881,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1877,
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Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.parallelPair_map_left | [] | [
235,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
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Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | Continuous.integral_hasStrictDerivAt | [] | [
685,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
1
] |
Mathlib/Algebra/GradedMonoid.lean | GradedMonoid.mk_pow | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nA : ι → Type u_2\ninst✝¹ : AddMonoid ι\ninst✝ : GMonoid A\ni : ι\na : A i\nn : ℕ\n⊢ mk i a ^ n = mk (n • i) (GMonoid.gnpow n a)",
"tactic": "match n with\n| 0 =>\n rw [pow_zero]\n exact (GMonoid.gnpow_zero' ⟨_, a⟩).symm\n| n+1 =>\n rw [pow_s... | [
222,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_mul | [] | [
2239,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2238,
1
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Mathlib/GroupTheory/GroupAction/Pi.lean | Set.piecewise_smul | [] | [
262,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/GroupTheory/Subgroup/ZPowers.lean | Subgroup.center_eq_infi' | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝² : Group G\nA : Type ?u.41951\ninst✝¹ : AddGroup A\nN : Type ?u.41957\ninst✝ : Group N\ns : Set G\ng : G\nS : Set G\nhS : closure S = ⊤\n⊢ center G = ⨅ (g : ↑S), centralizer (zpowers ↑g)",
"tactic": "rw [center_eq_iInf S hS, ← iInf_subtyp... | [
250,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integral_union_eq_left_of_forall | [] | [
331,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
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Mathlib/Topology/DenseEmbedding.lean | DenseEmbedding.subtype | [
{
"state_after": "case h.mk\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.33913\nδ : Type ?u.33916\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ne : α → β\nde : DenseEmbedding e\np : α → Prop\nx : β\nhx : x ∈ closure (e '' {x | p x})\n⊢ { val := x... | [
292,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
11
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.zpow_toGerm | [] | [
792,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
791,
1
] |
Mathlib/CategoryTheory/Closed/Cartesian.lean | CategoryTheory.CartesianClosed.uncurry_id_eq_ev | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝³ : Category C\nA✝ B X✝ X' Y Y' Z : C\ninst✝² : HasFiniteProducts C\ninst✝¹ : Exponentiable A✝\nA X : C\ninst✝ : Exponentiable A\n⊢ uncurry (𝟙 (A ⟹ X)) = (exp.ev A).app X",
"tactic": "rw [uncurry_eq, prod.map_id_id, id_comp]"
}
] | [
233,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | map_iInf₂ | [
{
"state_after": "no goals",
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144,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_empty | [
{
"state_after": "no goals",
"state_before": "ι : Type u'\nι' : Type ?u.212015\nR : Type u_2\nK : Type ?u.212021\nM : Type u_1\nM' : Type ?u.212027\nM'' : Type ?u.212030\nV : Type u\nV' : Type ?u.212035\nv : ι → M\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : AddCommMonoid M'\ninst✝³ : AddCommMon... | [
415,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/Data/Fintype/Option.lean | univ_option | [] | [
33,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
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Mathlib/Data/List/Pairwise.lean | List.rel_of_pairwise_cons | [] | [
49,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
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Mathlib/MeasureTheory/Function/UniformIntegrable.lean | MeasureTheory.tendsto_Lp_of_tendsto_ae | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nι : Type ?u.487716\nm : MeasurableSpace α\nμ : Measure α\ninst✝¹ : NormedAddCommGroup β\np : ℝ≥0∞\ninst✝ : IsFiniteMeasure μ\nhp : 1 ≤ p\nhp' : p ≠ ⊤\nf : ℕ → α → β\ng : α → β\nhf : ∀ (n : ℕ), AEStronglyMeasurable (f n) μ\nhg : Memℒp g p\nhui : UnifIntegrable f p μ\... | [
574,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
] |
Mathlib/Topology/Sheaves/SheafCondition/PairwiseIntersections.lean | TopCat.Sheaf.objSupIsoProdEqLocus_hom_snd | [] | [
484,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/CategoryTheory/WithTerminal.lean | CategoryTheory.WithTerminal.lift_map_liftStar | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\nD : Type u_1\ninst✝ : Category D\nZ : D\nF : C ⥤ D\nM : (x : C) → F.obj x ⟶ Z\nhM : ∀ (x y : C) (f : x ⟶ y), F.map f ≫ M y = M x\nx : C\n⊢ (lift F M hM).map (Limits.IsTerminal.from starTerminal (incl.obj x)) = M x",
"state_before": "C : Type u\ninst✝¹ : Cat... | [
191,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.one_apply_ne' | [] | [
550,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
1
] |
Mathlib/Topology/Homotopy/Contractible.lean | contractible_iff_id_nullhomotopic | [
{
"state_after": "case mp\nY : Type u_1\ninst✝ : TopologicalSpace Y\n⊢ ContractibleSpace Y → Nullhomotopic (ContinuousMap.id Y)\n\ncase mpr\nY : Type u_1\ninst✝ : TopologicalSpace Y\n⊢ Nullhomotopic (ContinuousMap.id Y) → ContractibleSpace Y",
"state_before": "Y : Type u_1\ninst✝ : TopologicalSpace Y\n⊢ Con... | [
85,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.mul_subset_iff_right | [] | [
438,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.sin_sub_int_mul_two_pi | [] | [
1189,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1188,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.map_equivFun | [] | [
924,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
923,
1
] |
src/lean/Init/Core.lean | HEq.elim | [] | [
619,
20
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
618,
1
] |
Mathlib/Algebra/Lie/IdealOperations.lean | LieSubmodule.lie_comm | [
{
"state_after": "R : Type u\nL : Type v\nM : Type w\nM₂ : Type w₁\ninst✝¹⁰ : CommRing R\ninst✝⁹ : LieRing L\ninst✝⁸ : LieAlgebra R L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCommGroup M₂\ninst✝² : Module R M₂\ninst✝¹ : LieRingModule L M₂\n... | [
123,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Analysis/SpecificLimits/Normed.lean | NormedRing.tsum_geometric_of_norm_lt_1 | [
{
"state_after": "α : Type ?u.1234446\nβ : Type ?u.1234449\nι : Type ?u.1234452\nR : Type u_1\ninst✝¹ : NormedRing R\ninst✝ : CompleteSpace R\nx : R\nh : ‖x‖ < 1\n⊢ ‖x ^ 0 + ∑' (b : ℕ), x ^ (b + 1)‖ ≤ ‖1‖ - 1 + (1 - ‖x‖)⁻¹",
"state_before": "α : Type ?u.1234446\nβ : Type ?u.1234449\nι : Type ?u.1234452\nR :... | [
480,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_ite_index | [] | [
1106,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1104,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_sum_of_nonneg | [
{
"state_after": "α : Type u_1\nβ : Type ?u.204043\na b c d : ℝ≥0∞\nr p q : ℝ≥0\ns : Finset α\nf : α → ℝ\nhf : ∀ (i : α), i ∈ s → 0 ≤ f i\n⊢ Real.toNNReal (∑ i in s, f i) = ∑ a in s, Real.toNNReal (f a)",
"state_before": "α : Type u_1\nβ : Type ?u.204043\na b c d : ℝ≥0∞\nr p q : ℝ≥0\ns : Finset α\nf : α → ℝ... | [
1260,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1257,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.isLimit_add_iff | [
{
"state_after": "case mp\nα : Type ?u.248176\nβ : Type ?u.248179\nγ : Type ?u.248182\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na b : Ordinal\nh : IsLimit (a + b)\n⊢ IsLimit b ∨ b = 0 ∧ IsLimit a\n\ncase mpr\nα : Type ?u.248176\nβ : Type ?u.248179\nγ : Type ?u.248182\nr : α → α → Prop\ns : β → β → ... | [
988,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
976,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.det_smul_inv_vecMul_eq_cramer_transpose | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.364914\nm : Type u\nn : Type u'\nα : Type v\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing α\nA✝ B A : Matrix n n α\nb : n → α\nh : IsUnit (det A)\n⊢ det A • vecMul b A⁻¹ = ↑(cramer Aᵀ) b",
"tactic": "rw [← A⁻¹.transpose_transpose,... | [
615,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
612,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.succ_to_nat | [] | [
299,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.Nondegenerate.congr | [] | [
1301,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1298,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | DoubleQuot.coe_quotLeftToQuotSupₐ | [] | [
690,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
689,
1
] |
Mathlib/Topology/SubsetProperties.lean | IsCompact.ne_univ | [] | [
757,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
756,
1
] |
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