file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.sigma_sum | [
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Mathlib/Analysis/MeanInequalities.lean | Real.arith_mean_weighted_of_constant | [
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Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_nonneg_iff | [
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Mathlib/Order/Filter/NAry.lean | Filter.map₂_neBot_iff | [
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.comap_inclusion_subgroupOf | [] | [
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Mathlib/RingTheory/Multiplicity.lean | multiplicity.pow_dvd_of_le_multiplicity | [
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Mathlib/Algebra/Category/GroupCat/EpiMono.lean | GroupCat.SurjectiveOfEpiAuxs.g_ne_h | [
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Mathlib/Analysis/Convex/Independent.lean | ConvexIndependent.comp_embedding | [
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.withDensity_one | [
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Mathlib/RingTheory/HahnSeries.lean | HahnSeries.isPwo_support | [] | [
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Mathlib/Data/Set/Lattice.lean | Set.iUnion_or | [] | [
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Mathlib/Topology/Algebra/Order/ProjIcc.lean | Continuous.IccExtend | [] | [
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Mathlib/Data/Real/Basic.lean | Real.le_sSup_iff | [
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Mathlib/RingTheory/Adjoin/PowerBasis.lean | PowerBasis.toMatrix_isIntegral | [
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Mathlib/RingTheory/HahnSeries.lean | HahnSeries.single_zero_one | [] | [
603,
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Mathlib/Data/Polynomial/EraseLead.lean | Polynomial.eraseLead_degree_le | [] | [
184,
22
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183,
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Mathlib/Topology/CompactOpen.lean | ContinuousMap.continuous_uncurry | [
{
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409,
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Mathlib/Data/Real/Irrational.lean | Irrational.of_sub_nat | [] | [
320,
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319,
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Mathlib/Data/Int/Basic.lean | Int.neg_succ | [] | [
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.neg_pi_lt_toReal | [
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] | [
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Mathlib/Algebra/BigOperators/Basic.lean | MonoidHom.map_prod | [] | [
219,
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Mathlib/Data/Polynomial/Taylor.lean | Polynomial.taylor_eval_sub | [
{
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] | [
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Mathlib/Logic/Lemmas.lean | dite_ite_distrib_left | [] | [
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Mathlib/Data/Fin/Basic.lean | Fin.cast_mk | [
{
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... | [
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Iic_diff_Iio | [
{
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Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.count_pow | [
{
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Mathlib/Topology/Sheaves/PresheafOfFunctions.lean | TopCat.presheafToType_map | [] | [
102,
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100,
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Mathlib/Topology/Maps.lean | closedEmbedding_id | [] | [
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46
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688,
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Mathlib/Order/LiminfLimsup.lean | Filter.liminf_compl | [
{
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"tactic": "simp only [limsup_eq_iInf_iSup, compl_iInf, compl_iSup, liminf_eq_iSup_iInf, Func... | [
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Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.toSeq_ofSeq | [
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Mathlib/Algebra/Polynomial/GroupRingAction.lean | prodXSubSmul.monic | [] | [
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74
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Mathlib/Analysis/Convex/Slope.lean | StrictConcaveOn.secant_strict_mono | [
{
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Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.ofLEMk_comp_ofMkLEMk | [
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Mathlib/Data/Set/Basic.lean | Set.univ_nonempty | [] | [
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.mk_uniformity_basis | [
{
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Mathlib/Data/Real/EReal.lean | EReal.top_sub_bot | [] | [
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Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.coe_sInf | [] | [
152,
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Mathlib/CategoryTheory/Monoidal/End.lean | CategoryTheory.obj_zero_map_μ_app | [
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Mathlib/Logic/Relation.lean | Relation.reflTransGen_iff_eq | [
{
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Mathlib/CategoryTheory/Monoidal/Functor.lean | CategoryTheory.LaxMonoidalFunctor.left_unitality_inv | [
{
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"tactic": "rw [Is... | [
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Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.pullback_pushforward_le | [] | [
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Mathlib/Dynamics/PeriodicPts.lean | Function.minimalPeriod_eq_one_iff_isFixedPt | [
{
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79
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373,
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Std/Data/List/Lemmas.lean | List.filterMap_filter | [
{
"state_after": "α : Type u_1\nβ : Type u_2\np : α → Bool\nf : α → Option β\nl : List α\n⊢ filterMap (fun x => Option.bind (Option.guard (fun x => p x = true) x) f) l =\n filterMap (fun x => if p x = true then f x else none) l",
"state_before": "α : Type u_1\nβ : Type u_2\np : α → Bool\nf : α → Option β... | [
1198,
63
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1195,
1
] |
Mathlib/CategoryTheory/Preadditive/Generator.lean | CategoryTheory.isSeparator_iff_faithful_preadditiveCoyoneda | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : Preadditive C\nG : C\n⊢ Faithful (preadditiveCoyoneda.obj G.op ⋙ forget AddCommGroupCat) ↔ Faithful (preadditiveCoyoneda.obj G.op)",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : Preadditive C\nG : C\n⊢ IsSeparator G ↔ Faithful (preaddit... | [
61,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.periodicOrbit_apply_iterate_eq | [
{
"state_after": "α : Type u_1\nβ : Type ?u.32376\nf fa : α → α\nfb : β → β\nx y : α\nm n✝ : ℕ\nhx : x ∈ periodicPts f\nn : ℕ\n⊢ List.length (List.rotate (List.map (fun n => (f^[n]) x) (List.range (minimalPeriod f x))) n) =\n List.length (List.map (fun n_1 => (f^[n_1]) ((f^[n]) x)) (List.range (minimalPeriod... | [
553,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
] |
Mathlib/Deprecated/Subgroup.lean | IsSubgroup.trivial_normal | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nH : Type ?u.28279\nA : Type ?u.28282\na a₁ a₂ b c : G\ninst✝ : Group G\n⊢ IsNormalSubgroup (trivial G)",
"tactic": "refine' { .. } <;> simp (config := { contextual := true }) [trivial]"
}
] | [
248,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | AbsoluteValue.map_prod | [] | [
755,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
752,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | InnerProductGeometry.norm_add_sq_eq_norm_sq_add_norm_sq' | [] | [
59,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Data/Set/Basic.lean | Set.insert_eq_of_mem | [] | [
1139,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1138,
1
] |
Mathlib/Analysis/Convex/Slope.lean | StrictConvexOn.slope_strict_mono_adjacent | [
{
"state_after": "𝕜 : Type u_1\ninst✝ : LinearOrderedField 𝕜\ns : Set 𝕜\nf : 𝕜 → 𝕜\nhf : StrictConvexOn 𝕜 s f\nx y z : 𝕜\nhx : x ∈ s\nhz : z ∈ s\nhxy : x < y\nhyz : y < z\nhxz : x < z\n⊢ (f y - f x) / (y - x) < (f z - f y) / (z - y)",
"state_before": "𝕜 : Type u_1\ninst✝ : LinearOrderedField 𝕜\ns :... | [
91,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Computability/Reduce.lean | OneOneEquiv.of_equiv | [] | [
235,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_range_succ' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.434314\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ninst✝ : CommMonoid β\nf : ℕ → β\nn : ℕ\n⊢ ∏ k in range (n + 1 + 1), f k = (∏ k in range (n + 1), f (k + 1)) * f 0",
"tactic": "rw [prod_range_succ _ n, mul_right... | [
1228,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1225,
1
] |
Mathlib/Data/PFunctor/Univariate/M.lean | PFunctor.M.head_mk | [
{
"state_after": "no goals",
"state_before": "F : PFunctor\nX : Type ?u.26443\nf : X → Obj F X\nx : Obj F (M F)\n⊢ x.fst = (dest (M.mk x)).fst",
"tactic": "rw [dest_mk]"
},
{
"state_after": "no goals",
"state_before": "F : PFunctor\nX : Type ?u.26443\nf : X → Obj F X\nx : Obj F (M F)\n⊢ (des... | [
541,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.ncard_diff | [
{
"state_after": "no goals",
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"tactic": "rw [← ncard_diff_add_ncard_eq_ncard h ht, add_tsub_cancel_right]"
}
] | [
505,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.nnnorm_def | [] | [
267,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.image_eq_preimage | [] | [
2117,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2116,
11
] |
Mathlib/CategoryTheory/CommSq.lean | CategoryTheory.CommSq.fac_left | [] | [
230,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Order/BoundedOrder.lean | ne_top_of_lt | [] | [
124,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/CategoryTheory/Idempotents/Basic.lean | CategoryTheory.Idempotents.Equivalence.isIdempotentComplete | [
{
"state_after": "C : Type u_4\ninst✝¹ : Category C\nD : Type u_1\ninst✝ : Category D\nε : C ≌ D\nh : IsIdempotentComplete C\n⊢ ∀ (X : D) (p : X ⟶ X), p ≫ p = p → ∃ Y i e, i ≫ e = 𝟙 Y ∧ e ≫ i = p",
"state_before": "C : Type u_4\ninst✝¹ : Category C\nD : Type u_1\ninst✝ : Category D\nε : C ≌ D\nh : IsIdempo... | [
175,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.coe_zero_iff_zero | [] | [
181,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Topology/CompactOpen.lean | ContinuousMap.coe_const' | [] | [
419,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coeIdeal_bot | [] | [
297,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.Ioo_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\na b c : α\n⊢ Ioo a a = 0",
"tactic": "rw [Ioo, Finset.Ioo_self, Finset.empty_val]"
}
] | [
112,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Topology/UniformSpace/UniformEmbedding.lean | UniformEmbedding.prod | [] | [
272,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.norm_mk_le | [] | [
1429,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1428,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.min'_eq_inf' | [] | [
1386,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1385,
1
] |
Mathlib/Analysis/Convex/Between.lean | Sbtw.right_mem_affineSpan | [] | [
734,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
733,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.to_average | [
{
"state_after": "case inl\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.851862\nδ : Type ?u.851865\nm : MeasurableSpace α\nν : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\nf : α → β\nh : Integrable f\n⊢ Integrable f\n\ncase inr\nα : Type u_2\nβ : Type u_1\nγ : ... | [
586,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
582,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.choice_mem_aux | [
{
"state_after": "no goals",
"state_before": "x : ZFSet\nh : ¬∅ ∈ x\ny : ZFSet\nyx : y ∈ x\nn : ¬∃ y_1, y_1 ∈ y\n⊢ ∅ ∈ x",
"tactic": "rwa [← (eq_empty y).2 fun z zx => n ⟨z, zx⟩]"
}
] | [
1810,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1807,
1
] |
Mathlib/GroupTheory/Sylow.lean | IsPGroup.sylow_mem_fixedPoints_iff | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nG : Type u_1\ninst✝ : Group G\nP : Subgroup G\nhP : IsPGroup p { x // x ∈ P }\nQ : Sylow p G\n⊢ Q ∈ fixedPoints { x // x ∈ P } (Sylow p G) ↔ P ≤ ↑Q",
"tactic": "rw [P.sylow_mem_fixedPoints_iff, ← inf_eq_left, hP.inf_normalizer_sylow, inf_eq_left]"
}... | [
293,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/Analysis/Convex/Jensen.lean | ConvexOn.exists_ge_of_mem_convexHull | [
{
"state_after": "𝕜 : Type u\nE : Type v\nF : Type ?u.65372\nβ : Type u_1\nι : Type ?u.65378\ninst✝⁵ : LinearOrderedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : LinearOrderedAddCommGroup β\ninst✝² : Module 𝕜 E\ninst✝¹ : Module 𝕜 β\ninst✝ : OrderedSMul 𝕜 β\ns : Set E\nf : E → β\nt : Finset ι\nw : ι → 𝕜\np : ... | [
138,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.coe_degree | [
{
"state_after": "ι : Sort ?u.202740\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : Subgraph G\na b : V\nG' : Subgraph G\nv : ↑G'.verts\ninst✝¹ : Fintype ↑(SimpleGraph.neighborSet (Subgraph.coe G') v)\ninst✝ : Fintype ↑(neighborSet G' ↑v)\n⊢ Fintype.card ↑(SimpleGraph.neighborSet (Subgraph.coe G') v) = deg... | [
822,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
819,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.rpow_le_rpow_of_exponent_le | [
{
"state_after": "case none\ny z : ℝ\nhyz : y ≤ z\nhx : 1 ≤ none\n⊢ none ^ y ≤ none ^ z\n\ncase some\ny z : ℝ\nhyz : y ≤ z\nval✝ : ℝ≥0\nhx : 1 ≤ Option.some val✝\n⊢ Option.some val✝ ^ y ≤ Option.some val✝ ^ z",
"state_before": "x : ℝ≥0∞\ny z : ℝ\nhx : 1 ≤ x\nhyz : y ≤ z\n⊢ x ^ y ≤ x ^ z",
"tactic": "cas... | [
616,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
1
] |
Mathlib/Algebra/Order/Archimedean.lean | exists_mem_Ioc_zpow | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : LinearOrderedField α\ninst✝ : Archimedean α\nx y ε : α\nhx : 0 < x\nhy : 1 < y\nm : ℤ\nhle : y ^ m ≤ x⁻¹\nhlt : x⁻¹ < y ^ (m + 1)\nhyp : 0 < y\n⊢ y ^ (-(m + 1)) < x",
"tactic": "rwa [zpow_neg, inv_lt (zpow_pos_of_pos hyp _) hx]"
},
... | [
228,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.uncurry_curryRight | [
{
"state_after": "case H\nR : Type u\nι : Type u'\nn : ℕ\nM : Fin (Nat.succ n) → Type v\nM₁ : ι → Type v₁\nM₂ : Type v₂\nM₃ : Type v₃\nM' : Type v'\ninst✝⁶ : CommSemiring R\ninst✝⁵ : (i : Fin (Nat.succ n)) → AddCommMonoid (M i)\ninst✝⁴ : AddCommMonoid M'\ninst✝³ : AddCommMonoid M₂\ninst✝² : (i : Fin (Nat.succ n... | [
1402,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1399,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | orthogonalProjection_orthogonalProjection_of_le | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.841108\ninst✝⁶ : IsROrC 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : InnerProductSpace ℝ F\nK U V : Submodule 𝕜 E\ninst✝¹ : CompleteSpace { x // x ∈ U }\nins... | [
878,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
872,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_unique | [] | [
230,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Topology/Algebra/Monoid.lean | exists_open_nhds_one_split | [
{
"state_after": "ι : Type ?u.155162\nα : Type ?u.155165\nX : Type ?u.155168\nM : Type u_1\nN : Type ?u.155174\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace M\ninst✝¹ : Monoid M\ninst✝ : ContinuousMul M\ns : Set M\nhs : s ∈ 𝓝 1\nthis : (fun a => a.fst * a.snd) ⁻¹' s ∈ 𝓝 (1, 1)\n⊢ ∃ V, IsOpen V ∧ 1 ∈... | [
481,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/CategoryTheory/Limits/ConcreteCategory.lean | CategoryTheory.Limits.cokernel_funext | [
{
"state_after": "case h\nC : Type u_1\ninst✝³ : Category C\ninst✝² : HasZeroMorphisms C\ninst✝¹ : ConcreteCategory C\nM N K : C\nf : M ⟶ N\ninst✝ : HasCokernel f\ng h : cokernel f ⟶ K\nw :\n ∀ (n : (forget C).obj N),\n (forget C).map g ((forget C).map (cokernel.π f) n) = (forget C).map h ((forget C).map (c... | [
169,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | MulLECancellable.inj_left | [] | [
1626,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1623,
11
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.inducedOuterMeasure_preimage | [
{
"state_after": "α : Type u_1\nP : Set α → Prop\nm : (s : Set α) → P s → ℝ≥0∞\nP0 : P ∅\nm0 : m ∅ P0 = 0\nPU : ∀ ⦃f : ℕ → Set α⦄, (∀ (i : ℕ), P (f i)) → P (⋃ (i : ℕ), f i)\nmU :\n ∀ ⦃f : ℕ → Set α⦄ (hm : ∀ (i : ℕ), P (f i)),\n Pairwise (Disjoint on f) → m (⋃ (i : ℕ), f i) (_ : P (⋃ (i : ℕ), f i)) = ∑' (i :... | [
1499,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1492,
1
] |
Mathlib/Order/SymmDiff.lean | symmDiff_top' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.53407\nα : Type u_1\nβ : Type ?u.53413\nπ : ι → Type ?u.53418\ninst✝ : CoheytingAlgebra α\na : α\n⊢ a ∆ ⊤ = ￢a",
"tactic": "simp [symmDiff]"
}
] | [
341,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.disjoint_image | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.112000\ninst✝ : DecidableEq β\nf✝ g : α → β\ns✝ : Finset α\nt✝ : Finset β\na : α\nb c : β\ns t : Finset α\nf : α → β\nhf : Injective f\n⊢ _root_.Disjoint (image f s) (image f t) ↔\n _root_.Disjoint (map { toFun := f, inj' := hf } s) (map { toFun := f,... | [
611,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
1
] |
Mathlib/Dynamics/FixedPoints/Basic.lean | Function.invOn_fixedPoints_comp | [] | [
167,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | LiouvilleWith.int_mul | [] | [
165,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.Prime.dvd_of_dvd_pow | [
{
"state_after": "case zero\np m n : ℕ\npp : Prime p\nh✝ : p ∣ m ^ n\nh : p ∣ m ^ zero\n⊢ p ∣ m\n\ncase succ\np m n✝ : ℕ\npp : Prime p\nh✝ : p ∣ m ^ n✝\nn : ℕ\nIH : p ∣ m ^ n → p ∣ m\nh : p ∣ m ^ succ n\n⊢ p ∣ m",
"state_before": "p m n : ℕ\npp : Prime p\nh : p ∣ m ^ n\n⊢ p ∣ m",
"tactic": "induction' n... | [
591,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
587,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | PadicSeq.norm_eq_norm_app_of_nonzero | [
{
"state_after": "no goals",
"state_before": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nf : PadicSeq p\nhf : ¬f ≈ 0\n⊢ norm f = padicNorm p (↑f (stationaryPoint hf))",
"tactic": "simp [norm, hf]"
},
{
"state_after": "no goals",
"state_before": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nf : PadicSeq p\nhf ... | [
162,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | norm_mul_le_of_le | [] | [
476,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | MulPosReflectLT.toMulPosMono | [] | [
308,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.exists_dist_lt_of_hausdorffDist_lt | [
{
"state_after": "ι : Sort ?u.78581\nα : Type u\nβ : Type v\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\ns t u : Set α\nx y : α\nΦ : α → β\nr : ℝ\nh : x ∈ s\nH : hausdorffDist s t < r\nfin : hausdorffEdist s t ≠ ⊤\nr0 : 0 < r\n⊢ ∃ y, y ∈ t ∧ dist x y < r",
"state_before": "ι : Sort ?u.78581\n... | [
810,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
802,
1
] |
Mathlib/Data/Finset/Basic.lean | List.toFinset_inter | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.476415\nγ : Type ?u.476418\ninst✝ : DecidableEq α\nl✝ l'✝ : List α\na : α\nl l' : List α\na✝ : α\n⊢ a✝ ∈ toFinset (l ∩ l') ↔ a✝ ∈ toFinset l ∩ toFinset l'",
"state_before": "α : Type u_1\nβ : Type ?u.476415\nγ : Type ?u.476418\ninst✝ : DecidableEq α\nl✝ l'... | [
3329,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3327,
1
] |
Mathlib/Algebra/Free.lean | FreeMagma.traverse_mul | [] | [
252,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Metrizable.lean | measurable_of_tendsto_metrizable' | [
{
"state_after": "α : Type u_2\nβ : Type u_3\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : TopologicalSpace β\ninst✝⁴ : PseudoMetrizableSpace β\ninst✝³ : MeasurableSpace β\ninst✝² : BorelSpace β\nι : Type u_1\nf : ι → α → β\ng : α → β\nu : Filter ι\ninst✝¹ : NeBot u\ninst✝ : IsCountablyGenerated u\nhf : ∀ (i : ι), Meas... | [
85,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Topology/MetricSpace/Gluing.lean | Metric.le_glueDist_inr_inl | [
{
"state_after": "X : Type u\nY : Type v\nZ : Type w\ninst✝¹ : MetricSpace X\ninst✝ : MetricSpace Y\nΦ✝ : Z → X\nΨ✝ : Z → Y\nε✝ : ℝ\nΦ : Z → X\nΨ : Z → Y\nε : ℝ\nx : Y\ny : X\n⊢ ε ≤ glueDist Φ Ψ ε (Sum.inl y) (Sum.inr x)",
"state_before": "X : Type u\nY : Type v\nZ : Type w\ninst✝¹ : MetricSpace X\ninst✝ : ... | [
113,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.coe_iInf | [
{
"state_after": "no goals",
"state_before": "L : Language\nM : Type w\nN : Type ?u.19468\nP : Type ?u.19471\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nS✝ : Substructure L M\nι : Sort u_1\nS : ι → Substructure L M\n⊢ ↑(⨅ (i : ι), S i) = ⋂ (i : ι), ↑(S i)",
"tactic": "simp on... | [
233,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/RingTheory/Localization/AtPrime.lean | Localization.localRingHom_mk' | [] | [
237,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Data/Int/GCD.lean | Int.gcd_dvd_gcd_of_dvd_right | [] | [
342,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/Data/List/Intervals.lean | List.Ico.filter_le_of_bot | [
{
"state_after": "n m : ℕ\nhnm : n < m\n⊢ filter (fun x => decide (x ≤ n)) (Ico n m) = filter (fun x => decide (x < n + 1)) (Ico n m)",
"state_before": "n m : ℕ\nhnm : n < m\n⊢ filter (fun x => decide (x ≤ n)) (Ico n m) = [n]",
"tactic": "rw [← filter_lt_of_succ_bot hnm]"
},
{
"state_after": "no... | [
226,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Presieve.is_compatible_of_exists_amalgamation | [
{
"state_after": "case intro\nC : Type u₁\ninst✝ : Category C\nP Q U : Cᵒᵖ ⥤ Type w\nX Y : C\nS : Sieve X\nR : Presieve X\nJ J₂ : GrothendieckTopology C\nx : FamilyOfElements P R\nt : P.obj X.op\nht : FamilyOfElements.IsAmalgamation x t\n⊢ FamilyOfElements.Compatible x",
"state_before": "C : Type u₁\ninst✝ ... | [
396,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | Part.eq_of_chain | [
{
"state_after": "case intro\nα : Type u\nβ : Type v\nγ : Type ?u.13795\nc : Chain (Part α)\na b : α\nhb : some b ∈ c\ni : ℕ\nha : some a = ↑c i\n⊢ a = b",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.13795\nc : Chain (Part α)\na b : α\nha : some a ∈ c\nhb : some b ∈ c\n⊢ a = b",
"tactic": "case... | [
320,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
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