file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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values | start list |
|---|---|---|---|---|---|---|
Mathlib/Order/Filter/Germ.lean | Filter.Germ.coe_nonneg | [] | [
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Mathlib/Data/Set/Basic.lean | Set.empty_subset | [] | [
573,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Finsupp/Multiset.lean | Multiset.toFinsupp_support | [
{
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153,
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Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.norm_le_of_forall_le | [
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Mathlib/Topology/Maps.lean | isOpenMap_iff_interior | [
{
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Mathlib/Data/PFun.lean | PFun.mem_prodMap | [
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684,
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Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.mem_vanishingIdeal | [
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.sin_coe | [] | [
312,
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Mathlib/Data/Finset/NAry.lean | Finset.image₂_subset_iff_left | [
{
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Mathlib/Topology/LocalExtr.lean | Filter.EventuallyEq.isLocalMaxOn_iff | [] | [
565,
51
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563,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.isFiniteMeasure_map | [
{
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Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | Ideal.IsHomogeneous.toIdeal_homogeneousHull_eq_self | [
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Mathlib/Analysis/Convex/Normed.lean | bounded_convexHull | [
{
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}
] | [
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_extend_by_one | [] | [
1037,
42
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1035,
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Mathlib/FieldTheory/SplittingField/IsSplittingField.lean | Polynomial.IsSplittingField.adjoin_roots | [] | [
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16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Algebra/Basic.lean | Module.End_isUnit_apply_inv_apply_of_isUnit | [
{
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] | [
646,
38
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644,
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Mathlib/Algebra/Ring/Basic.lean | AddMonoidHom.coe_mulRight | [] | [
85,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Fin/Tuple/Basic.lean | Fin.cons_injective_of_injective | [
{
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187,
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Mathlib/RingTheory/PrincipalIdealDomain.lean | Irreducible.dvd_iff_not_coprime | [] | [
448,
40
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447,
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Mathlib/Algebra/Invertible.lean | invOf_eq_inv | [] | [
384,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
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Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.isCaratheodory_sum | [
{
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"tactic": "simp [Nat.not_lt_zero, ... | [
1003,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
995,
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Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.lift_of_comp | [] | [
528,
55
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526,
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Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_add_left | [] | [
461,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
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Mathlib/Topology/MetricSpace/Basic.lean | IsComplete.nonempty_iInter_of_nonempty_biInter | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.540098\nι : Type ?u.540101\ninst✝ : PseudoMetricSpace α\ns✝ : Set α\nx y z : α\ns : ℕ → Set α\nh0 : IsComplete (s 0)\nhs : ∀ (n : ℕ), IsClosed (s n)\nh's : ∀ (n : ℕ), Bounded (s n)\nh : ∀ (N : ℕ), Set.Nonempty (⋂ (n : ℕ) (_ : n ≤ N), s n)\nh' : Tendsto (fun ... | [
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2735,
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Mathlib/Data/MvPolynomial/Equiv.lean | MvPolynomial.natDegree_finSuccEquiv | [
{
"state_after": "case pos\nR : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type ?u.1366622\na a' a₁ a₂ : R\ne : ℕ\ns : σ →₀ ℕ\ninst✝ : CommSemiring R\nn : ℕ\nf : MvPolynomial (Fin (n + 1)) R\nc : f = 0\n⊢ natDegree (↑(finSuccEquiv R n) f) = degreeOf 0 f\n\ncase neg\nR : Type u\nS₁ : Type v\nS₂ : Type w\... | [
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Mathlib/Data/Complex/Exponential.lean | Real.exp_neg | [
{
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"tactic": "simp [exp_neg]"
}
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40
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1168,
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Mathlib/InformationTheory/Hamming.lean | hammingNorm_pos_iff | [] | [
203,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Image.lean | Set.range_const | [] | [
1002,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
999,
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Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.eq_reflection_of_eq_subspace | [
{
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552,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
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Mathlib/Combinatorics/Quiver/Path.lean | Prefunctor.mapPath_comp | [
{
"state_after": "V : Type u₁\ninst✝¹ : Quiver V\nW : Type u₂\ninst✝ : Quiver W\nF : V ⥤q W\na b : V\np : Path a b\nc b✝ : V\nq : Path b b✝\ne : b✝ ⟶ c\n⊢ Path.cons (mapPath F (Path.comp p q)) (F.map e) = Path.cons (Path.comp (mapPath F p) (mapPath F q)) (F.map e)",
"state_before": "V : Type u₁\ninst✝¹ : Qu... | [
234,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
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Std/Logic.lean | forall_prop_of_true | [] | [
488,
28
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
487,
1
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Mathlib/Data/Polynomial/Monic.lean | Polynomial.Monic.natDegree_pow | [
{
"state_after": "case zero\nR : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝ : Semiring R\np q r : R[X]\nhp : Monic p\n⊢ natDegree (p ^ Nat.zero) = Nat.zero * natDegree p\n\ncase succ\nR : Type u\nS : Type v\na b : R\nm n✝ : ℕ\nι : Type y\ninst✝ : Semiring R\np q r : R[X]\nhp : Monic p\nn : ℕ\nhn : ... | [
236,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Filter/Basic.lean | Filter.diff_mem | [] | [
168,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_of_div_tendsto_nhds | [] | [
2010,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2007,
1
] |
Mathlib/CategoryTheory/LiftingProperties/Adjunction.lean | CategoryTheory.CommSq.left_adjoint_hasLift_iff | [
{
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118,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
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Mathlib/Order/SymmDiff.lean | bihimp_himp_eq_inf | [] | [
302,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.closure_ball_subset_closedBall | [] | [
1882,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1881,
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Mathlib/Algebra/BigOperators/Finprod.lean | finprod_cond_eq_prod_of_cond_iff | [
{
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452,
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442,
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Mathlib/Data/Fin/Basic.lean | Fin.range_castSucc | [] | [
1323,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1321,
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Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_const_add_uIcc | [
{
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"tactic": "simp [add_comm]"
}
] | [
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101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
456,
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Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableEmbedding.comp | [
{
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1091,
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Mathlib/Order/Filter/Lift.lean | Filter.lift'_principal | [] | [
320,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
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Mathlib/Order/SuccPred/LinearLocallyFinite.lean | iterate_succ_toZ | [
{
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"state_before": "ι : Type u_1\ninst✝³ : LinearOrder ι\ninst✝² : SuccOrder ι\ninst✝¹ : IsSuccArc... | [
218,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
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Mathlib/Algebra/Group/Basic.lean | div_div_cancel_left | [
{
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"tactic": "simp"
}
] | [
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67
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Mathlib/GroupTheory/GroupAction/Defs.lean | SMul.comp.smulCommClass' | [] | [
398,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
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Mathlib/Dynamics/PeriodicPts.lean | Function.IsPeriodicPt.iterate_mod_apply | [
{
"state_after": "no goals",
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"tactic": "conv_rhs => rw [← Nat.mod_add_div m n, iterate_add_apply, (h.mul_const _).eq]"
}
] | [
161,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
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Mathlib/Topology/Algebra/UniformGroup.lean | uniformity_eq_comap_nhds_one' | [] | [
581,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
1
] |
Mathlib/Algebra/Regular/Basic.lean | IsRightRegular.subsingleton | [] | [
199,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.IsFundamentalDomain.integrableOn_iff | [] | [
399,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
11
] |
Mathlib/Data/PEquiv.lean | PEquiv.trans_assoc | [] | [
147,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Order/SymmDiff.lean | sdiff_symmDiff_left | [
{
"state_after": "no goals",
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"tactic": "simp [sdiff_symmDiff]"
}
] | [
433,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/Data/Bitvec/Lemmas.lean | Bitvec.addLsb_div_two | [
{
"state_after": "case true\nx : ℕ\n⊢ x + 1 / 2 = x",
"state_before": "x : ℕ\nb : Bool\n⊢ addLsb x b / 2 = x",
"tactic": "cases b <;>\n simp only [Nat.add_mul_div_left, addLsb, ← two_mul, add_comm, Nat.succ_pos',\n Nat.mul_div_right, gt_iff_lt, zero_add, cond]"
},
{
"state_after": "no go... | [
119,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Data/List/Permutation.lean | List.mem_permutationsAux2' | [
{
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167,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
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Mathlib/Topology/Algebra/Valuation.lean | Valued.cauchy_iff | [
{
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170,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
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Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.BoundedFormula.induction_on_all_ex | [
{
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623,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
610,
1
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Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.exists_degree_lt | [
{
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"st... | [
769,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
758,
1
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Mathlib/Data/Nat/Factorization/Basic.lean | Nat.factorization_gcd | [
{
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"tactic... | [
689,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
667,
1
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Mathlib/Algebra/Module/Torsion.lean | Submodule.torsion_isTorsion | [] | [
661,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.refl_coe | [] | [
619,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
1
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Mathlib/Analysis/Convex/Quasiconvex.lean | quasilinearOn_iff_monotoneOn_or_antitoneOn | [] | [
250,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
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Mathlib/Algebra/BigOperators/Order.lean | WithTop.sum_lt_top_iff | [
{
"state_after": "no goals",
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727,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
725,
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Mathlib/Topology/Order/Basic.lean | right_nhdsWithin_Ioo_neBot | [] | [
2442,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2441,
1
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Mathlib/Algebra/GroupPower/Order.lean | pow_bit1_neg | [
{
"state_after": "β : Type ?u.235419\nA : Type ?u.235422\nG : Type ?u.235425\nM : Type ?u.235428\nR : Type u_1\ninst✝ : StrictOrderedRing R\na : R\nha : a < 0\nn : ℕ\n⊢ a * a ^ bit0 n < 0",
"state_before": "β : Type ?u.235419\nA : Type ?u.235422\nG : Type ?u.235425\nM : Type ?u.235428\nR : Type u_1\ninst✝ :... | [
551,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
1
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Mathlib/Analysis/Calculus/Deriv/Mul.lean | HasDerivWithinAt.clm_comp | [
{
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362,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
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Mathlib/Algebra/Order/Sub/WithTop.lean | WithTop.map_sub | [
{
"state_after": "no goals",
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"tactic": "simp only [h₀, sub_top, WithTop.m... | [
61,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.subtypePerm_inv | [] | [
391,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/Algebra/Hom/Ring.lean | RingHom.mul_def | [] | [
734,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
733,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.exists_le_of_tendsto_atBot | [] | [
523,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Std/Data/RBMap/WF.lean | Std.RBNode.Balanced.balLeft | [
{
"state_after": "α✝ : Type u_1\nl : RBNode α✝\nv : α✝\nr : RBNode α✝\ncr : RBColor\nn : Nat\nhl : RedRed True l n\nhr : Balanced r cr (n + 1)\n⊢ RedRed (cr = red)\n (match l with\n | node red a x b => node red (node black a x b) v r\n | l =>\n match r with\n | node black a y b => balance2 l ... | [
267,
95
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
253,
11
] |
Mathlib/Order/Bounds/Basic.lean | BddBelow.insert | [] | [
943,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
941,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | norm_iteratedFDerivWithin_smul_le | [] | [
2489,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2482,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | HasDerivWithinAt.hasDerivAt | [] | [
424,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieModuleEquiv.toEquiv_mk | [] | [
1009,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1007,
1
] |
Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.X.ωb_mul_ω | [
{
"state_after": "no goals",
"state_before": "q✝ q : ℕ+\n⊢ ωb * ω = 1",
"tactic": "rw [mul_comm, ω_mul_ωb]"
}
] | [
375,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.multiplicity_eq_factorization | [
{
"state_after": "no goals",
"state_before": "n p : ℕ\npp : Prime p\nhn : n ≠ 0\n⊢ multiplicity p n = ↑(↑(factorization n) p)",
"tactic": "simp [factorization, pp, padicValNat_def' pp.ne_one hn.bot_lt]"
}
] | [
99,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_eq_iff_natDegree_eq | [
{
"state_after": "R : Type u\nS : Type v\na b c d : R\nn✝ m : ℕ\ninst✝ : Semiring R\np✝ q r p : R[X]\nn : ℕ\nhp : p ≠ 0\n⊢ ↑(natDegree p) = ↑n ↔ natDegree p = n",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn✝ m : ℕ\ninst✝ : Semiring R\np✝ q r p : R[X]\nn : ℕ\nhp : p ≠ 0\n⊢ degree p = ↑n ↔ natDegr... | [
136,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
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Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | HasStrictFDerivAt.exp | [] | [
289,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.norm_sq_eq_of_L2 | [
{
"state_after": "p : ℝ≥0∞\n𝕜 : Type ?u.285404\n𝕜' : Type ?u.285407\nι : Type u_2\nα : ι → Type ?u.285415\nβ✝ : ι → Type ?u.285420\ninst✝² : Fintype ι\ninst✝¹ : Fact (1 ≤ p)\nβ : ι → Type u_1\ninst✝ : (i : ι) → SeminormedAddCommGroup (β i)\nx : PiLp 2 β\n⊢ ‖x‖₊ ^ 2 = ∑ i : ι, ‖x i‖₊ ^ 2",
"state_before": ... | [
600,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
596,
1
] |
Mathlib/Init/Algebra/Classes.lean | lt_of_incomp_of_lt | [] | [
406,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | VectorBundleCore.mem_localTriv_target | [] | [
713,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
711,
1
] |
Mathlib/Analysis/NormedSpace/Star/Basic.lean | starₗᵢ_apply | [] | [
308,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Analysis/Normed/Group/AddTorsor.lean | dist_vsub_vsub_le | [
{
"state_after": "α : Type ?u.24677\nV : Type u_1\nP : Type u_2\nW : Type ?u.24686\nQ : Type ?u.24689\ninst✝⁵ : SeminormedAddCommGroup V\ninst✝⁴ : PseudoMetricSpace P\ninst✝³ : NormedAddTorsor V P\ninst✝² : NormedAddCommGroup W\ninst✝¹ : MetricSpace Q\ninst✝ : NormedAddTorsor W Q\np₁ p₂ p₃ p₄ : P\n⊢ ‖p₁ -ᵥ p₃ -... | [
186,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/ModelTheory/Skolem.lean | FirstOrder.Language.Substructure.skolem₁_reduct_isElementary | [
{
"state_after": "L : Language\nM : Type w\ninst✝¹ : Nonempty M\ninst✝ : Structure L M\nS : Substructure (Language.sum L (skolem₁ L)) M\n⊢ ∀ (n : ℕ) (φ : BoundedFormula L Empty (n + 1)) (x : Fin n → { x // x ∈ ↑(LHom.substructureReduct LHom.sumInl) S })\n (a : M),\n BoundedFormula.Realize φ default (Fin.s... | [
98,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.ne_of_mem_sphere | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.32596\nι : Type ?u.32599\ninst✝ : PseudoMetricSpace α\nx y z : α\nδ ε ε₁ ε₂ : ℝ\ns : Set α\nh : y ∈ sphere x ε\nhε : ε ≠ 0\n⊢ ¬x ∈ sphere x ε",
"tactic": "simpa using hε.symm"
}
] | [
498,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Equivalence.unit_inverse_comp | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\ne : C ≌ D\nY : D\n⊢ (unit e).app (e.inverse.obj Y) ≫\n (e.inverse.map ((counitInv e).app (e.functor.obj (e.inverse.obj Y))) ≫\n e.inverse.map (e.functor.map ((unitInv e).app (e.inverse.obj Y)))) ≫\n e.inver... | [
204,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Order/Filter/Partial.lean | Filter.mem_pmap | [] | [
219,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/NumberTheory/LegendreSymbol/MulCharacter.lean | MulChar.IsNontrivial.sum_eq_zero | [
{
"state_after": "case intro\nR : Type u\ninst✝⁴ : CommRing R\nR' : Type v\ninst✝³ : CommRing R'\nR'' : Type w\ninst✝² : CommRing R''\ninst✝¹ : Fintype R\ninst✝ : IsDomain R'\nχ : MulChar R R'\nb : Rˣ\nhb : ↑χ ↑b ≠ 1\n⊢ ∑ a : R, ↑χ a = 0",
"state_before": "R : Type u\ninst✝⁴ : CommRing R\nR' : Type v\ninst✝... | [
545,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
] |
Mathlib/Data/List/Infix.lean | List.insert_nil | [] | [
471,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/Order/OrdContinuous.lean | RightOrdContinuous.le_iff | [] | [
209,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Topology/GDelta.lean | Finset.isGδ_compl | [] | [
158,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Algebra/Parity.lean | isSquare_op_iff | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.311\nα : Type u_1\nβ : Type ?u.317\nR : Type ?u.320\ninst✝ : Mul α\na : α\nx✝ : IsSquare (op a)\nc : αᵐᵒᵖ\nhc : op a = c * c\n⊢ a = unop c * unop c",
"tactic": "rw [← unop_mul, ← hc, unop_op]"
},
{
"state_after": "no goals",
"state_be... | [
65,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/GroupTheory/Subgroup/ZPowers.lean | Subgroup.zpowers_eq_bot | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝² : Group G\nA : Type ?u.38880\ninst✝¹ : AddGroup A\nN : Type ?u.38886\ninst✝ : Group N\ns : Set G\ng✝ g : G\n⊢ zpowers g = ⊥ ↔ g = 1",
"tactic": "rw [eq_bot_iff, zpowers_le, mem_bot]"
}
] | [
213,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.ofLE_map | [
{
"state_after": "case mk\nα : Type ?u.32610\nX : Type u_1\nY : Type u_2\nZ : Type ?u.32619\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\nS : DiscreteQuotient X\nf : C(X, Y)\nA A' : DiscreteQuotient X\nB B' : DiscreteQuotient Y\ng : C(Y, Z)\nC : DiscreteQuotient Z\ncond ... | [
343,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Algebra/Order/SMul.lean | lowerBounds_smul_of_pos | [] | [
281,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.comap_equiv_symm | [] | [
2542,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2541,
1
] |
Mathlib/CategoryTheory/Sites/Canonical.lean | CategoryTheory.Sheaf.isSheafFor_trans | [
{
"state_after": "C : Type u\ninst✝ : Category C\nP✝ : Cᵒᵖ ⥤ Type v\nX Y : C\nS✝ : Sieve X\nR✝ : Presieve X\nJ J₂ : GrothendieckTopology C\nP : Cᵒᵖ ⥤ Type v\nR S : Sieve X\nhR : Presieve.IsSheafFor P R.arrows\nhR' : ∀ ⦃Y : C⦄ ⦃f : Y ⟶ X⦄, S.arrows f → Presieve.IsSeparatedFor P (Sieve.pullback f R).arrows\nhS : ... | [
156,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | isClosedMap_div_right | [] | [
1191,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1190,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.coe_linear | [] | [
134,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.ext_fun_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nι : Type ?u.364824\nmα : MeasurableSpace α\nmβ : MeasurableSpace β\nκ η : { x // x ∈ kernel α β }\nh : κ = η\na : α\nf : β → ℝ≥0∞\nx✝ : Measurable f\n⊢ (∫⁻ (b : β), f b ∂↑κ a) = ∫⁻ (b : β), f b ∂↑η a",
"tactic": "rw [h]"
}
] | [
205,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/GroupTheory/Perm/List.lean | List.formPerm_eq_head_iff_eq_getLast | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.671041\ninst✝ : DecidableEq α\nl : List α\nx✝ x y : α\n⊢ ↑(formPerm (y :: l)) x = y ↔ ↑(formPerm (y :: l)) x = ↑(formPerm (y :: l)) (getLast (y :: l) (_ : y :: l ≠ []))",
"tactic": "rw [formPerm_apply_getLast]"
}
] | [
165,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
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