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/Analysis/Normed/Group/Seminorm.lean | GroupSeminorm.add_apply | [] | [
290,
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289,
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioi_inter_Ioi | [] | [
1775,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1774,
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Mathlib/Data/Set/Basic.lean | Set.inter_comm | [] | [
926,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
925,
1
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Std/Data/String/Lemmas.lean | String.Pos.lt_iff | [] | [
143,
73
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143,
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Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.testAgainstNN_lipschitz | [
{
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437,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
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Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Embedding.comp_assoc | [] | [
724,
6
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722,
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Std/Data/Int/DivMod.lean | Int.dvd_add | [
{
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}
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Mathlib/Topology/Algebra/GroupWithZero.lean | Continuous.zpow₀ | [] | [
353,
71
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351,
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Mathlib/Order/Filter/Extr.lean | IsMaxOn.sup | [] | [
548,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
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Mathlib/NumberTheory/Padics/PadicVal.lean | padicValNat.div | [
{
"state_after": "no goals",
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"tactic": "rw [padicValNat.div_of_dvd dvd, padicValNat_self]"
}
] | [
422,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
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Mathlib/Order/BoundedOrder.lean | top_ne_bot | [] | [
898,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
897,
1
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.edges_subset_edgeSet | [
{
"state_after": "case head\nV : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v v✝ : V\nh' : Adj G u v✝\np' : Walk G v✝ v\n⊢ Dart.edge { toProd := (u, v✝), is_adj := h' } ∈ edgeSet G\n\ncase tail\nV : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG'... | [
677,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
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Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_smul_left | [] | [
476,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.support_nonempty_iff | [
{
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222,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.ball_disjoint_ball | [] | [
540,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
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Mathlib/Topology/MetricSpace/Infsep.lean | Set.Nontrivial.einfsep_ne_top | [
{
"state_after": "α : Type u_1\nβ : Type ?u.50084\ninst✝ : PseudoMetricSpace α\ns : Set α\nhs : einfsep s = ⊤\n⊢ ¬Set.Nontrivial s",
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"tactic": "contrapose! hs"
},
{
... | [
268,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
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Mathlib/Data/Finset/Pointwise.lean | Finset.card_singleton_mul | [] | [
1888,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1887,
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Mathlib/Order/Filter/Basic.lean | Filter.sup_sets_eq | [] | [
523,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
522,
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_id | [] | [
227,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_norm_mulLeftRight_apply_le | [] | [
1146,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1145,
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Mathlib/MeasureTheory/Function/UniformIntegrable.lean | MeasureTheory.unifIntegrable_of' | [
{
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700,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
638,
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Mathlib/Topology/MetricSpace/Algebra.lean | lipschitz_with_lipschitz_const_mul | [
{
"state_after": "α : Type ?u.2804\nβ : Type u_1\ninst✝³ : PseudoMetricSpace α\ninst✝² : PseudoMetricSpace β\ninst✝¹ : Monoid β\ninst✝ : LipschitzMul β\n⊢ LipschitzWith (LipschitzMul.C β) fun p => p.fst * p.snd",
"state_before": "α : Type ?u.2804\nβ : Type u_1\ninst✝³ : PseudoMetricSpace α\ninst✝² : PseudoM... | [
81,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
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Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.extend_eq | [
{
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}
] | [
1322,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1322,
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Mathlib/Data/Seq/Computation.lean | Computation.results_thinkN | [] | [
595,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
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Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_eq_mul_iff_eq_and_eq_of_pos' | [
{
"state_after": "case inl\nα : Type u_1\na c d : α\ninst✝⁵ : MulZeroClass α\ninst✝⁴ : PartialOrder α\ninst✝³ : PosMulStrictMono α\ninst✝² : MulPosStrictMono α\ninst✝¹ : PosMulMonoRev α\ninst✝ : MulPosMonoRev α\nhbd : c ≤ d\nc0 : 0 < c\nhac : a ≤ a\nb0 : 0 < a\nh : a * c = a * d\n⊢ a = a ∧ c = d\n\ncase inr\nα ... | [
550,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
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Mathlib/Data/Nat/Lattice.lean | Nat.sSup_def | [] | [
42,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
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Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.mem_inv_pointwise_smul_iff | [] | [
349,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
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Mathlib/Data/Seq/Computation.lean | Computation.corec_eq | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nf : β → α ⊕ β\nb : β\n⊢ (match Stream'.corec' (Corec.f f) (Sum.inr b) 0 with\n | none =>\n Sum.inr\n (tail\n { val := Stream'.corec' (Corec.f f) (Sum.inr b),\n property :=\n (_ :\n ∀ (n : ℕ) (a' ... | [
268,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
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Mathlib/Order/LiminfLimsup.lean | Filter.sup_liminf | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.166973\nι : Type ?u.166976\ninst✝ : CompleteDistribLattice α\nf : Filter β\np q : β → Prop\nu : β → α\na : α\n⊢ (a ⊔ ⨆ (s : Set β) (_ : s ∈ f), ⨅ (a : β) (_ : a ∈ s), u a) =\n ⨆ (s : Set β) (_ : s ∈ f), ⨅ (a_1 : β) (_ : a_1 ∈ s), a ⊔ u a_1",
"stat... | [
1006,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1003,
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Mathlib/Combinatorics/Composition.lean | Composition.disjoint_range | [
{
"state_after": "no goals",
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"tactic": "classical\n wlog h' : i₁ < i₂\n exact (this c h.symm (h.lt_or_lt.resolve_left h')).symm\n by_contra d... | [
412,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
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Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.orderIsoRpow_symm_apply | [
{
"state_after": "y : ℝ\nhy : 0 < y\n⊢ OrderIso.symm\n (StrictMono.orderIsoOfRightInverse (fun x => x ^ y) (_ : StrictMono fun x => x ^ y) (fun x => x ^ (1 / y))\n (_ : ∀ (x : ℝ≥0∞), (fun x => x ^ y) ((fun x => x ^ (1 / y)) x) = x)) =\n StrictMono.orderIsoOfRightInverse (fun x => x ^ (1 / y)) (_ ... | [
562,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
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Mathlib/Analysis/InnerProductSpace/Projection.lean | orthogonalProjection_bot | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.555301\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : InnerProductSpace ℝ F\nK : Submodule 𝕜 E\ninst✝ : CompleteSpace { x // x ∈ K }\n⊢ orthog... | [
562,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.map_dfinsupp_sumAddHom | [] | [
1170,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1168,
1
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Mathlib/Algebra/Ring/Semiconj.lean | SemiconjBy.neg_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : Type x\ninst✝¹ : Mul R\ninst✝ : HasDistribNeg R\na x y : R\nh : SemiconjBy a x y\n⊢ SemiconjBy a (-x) (-y)",
"tactic": "simp only [SemiconjBy, h.eq, neg_mul, mul_neg]"
}
] | [
52,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | zero_lt_one_add_norm_sq' | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.74877\n𝕜 : Type ?u.74880\nα : Type ?u.74883\nι : Type ?u.74886\nκ : Type ?u.74889\nE : Type u_1\nF : Type ?u.74895\nG : Type ?u.74898\ninst✝² : SeminormedGroup E\ninst✝¹ : SeminormedGroup F\ninst✝ : SeminormedGroup G\ns : Set E\na a₁ a₂ b b₁ b₂ : E... | [
535,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/GroupTheory/GroupAction/Quotient.lean | MulAction.orbitEquivQuotientStabilizer_symm_apply | [] | [
224,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Basic.lean | GroupWithZero.eq_zero_or_unit | [
{
"state_after": "case pos\nα : Type ?u.16951\nM₀ : Type ?u.16954\nG₀ : Type u_1\nM₀' : Type ?u.16960\nG₀' : Type ?u.16963\nF : Type ?u.16966\nF' : Type ?u.16969\ninst✝¹ : MonoidWithZero M₀\ninst✝ : GroupWithZero G₀\na✝ b a : G₀\nh : a = 0\n⊢ a = 0 ∨ ∃ u, a = ↑u\n\ncase neg\nα : Type ?u.16951\nM₀ : Type ?u.1695... | [
243,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.leInductionOn | [] | [
540,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
] |
Mathlib/Data/MvPolynomial/Supported.lean | MvPolynomial.mem_supported_vars | [
{
"state_after": "no goals",
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"tactic": "rw [mem_supported]"
}
] | [
95,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.of_uncurry_left | [] | [
409,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
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Mathlib/Topology/SubsetProperties.lean | IsClosed.isCompact | [] | [
742,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
741,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.normSq_eq_zero | [
{
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"state_before": "R : Type u_1\ninst✝ : LinearOrderedCommRing R\na : ℍ[R]\n⊢ ↑normSq a = 0 ↔ a = 0",
"tactic": "refine' ⟨fun h => _, fun h => h.symm ▸ normSq.map_zero⟩"
},
{
"state_after": "R :... | [
1270,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1266,
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Mathlib/FieldTheory/SplittingField/IsSplittingField.lean | Polynomial.IsSplittingField.mul | [
{
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111,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Calculus/FDeriv/Mul.lean | DifferentiableAt.mul_const | [] | [
430,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
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Mathlib/GroupTheory/Transfer.lean | MonoidHom.transferSylow_restrict_eq_pow | [] | [
250,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
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Mathlib/Computability/Reduce.lean | oneOneReducible_refl | [
{
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"tactic": "simp"
}
] | [
95,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
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Mathlib/Data/Set/Image.lean | Set.range_comp_subset_range | [
{
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735,
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Mathlib/Analysis/Normed/Group/Quotient.lean | QuotientAddGroup.norm_lift_apply_le | [
{
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"tactic": "cases (... | [
317,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
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Mathlib/Order/Filter/CountableInter.lean | EventuallyLE.countable_bUnion | [
{
"state_after": "ι✝ : Sort ?u.3007\nα : Type u_2\nβ : Type ?u.3013\nl : Filter α\ninst✝ : CountableInterFilter l\nι : Type u_1\nS : Set ι\nhS : Set.Countable S\ns t : (i : ι) → i ∈ S → Set α\nh : ∀ (i : ι) (hi : i ∈ S), s i hi ≤ᶠ[l] t i hi\n⊢ (⋃ (x : ↑S), s ↑x (_ : ↑x ∈ S)) ≤ᶠ[l] ⋃ (x : ↑S), t ↑x (_ : ↑x ∈ S)"... | [
93,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
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Mathlib/MeasureTheory/Measure/OpenPos.lean | MeasureTheory.Measure.eqOn_Icc_of_ae_eq | [] | [
171,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
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Mathlib/CategoryTheory/LiftingProperties/Adjunction.lean | CategoryTheory.CommSq.right_adjoint | [
{
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"state_befo... | [
46,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
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Mathlib/Data/List/Cycle.lean | Cycle.coe_eq_nil | [] | [
498,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
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Mathlib/FieldTheory/PerfectClosure.lean | PerfectClosure.neg_mk | [] | [
299,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
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Mathlib/Data/Finset/NAry.lean | Finset.image₂_union_inter_subset_union | [
{
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534,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
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Mathlib/RingTheory/HahnSeries.lean | HahnSeries.mul_coeff_right' | [
{
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650,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
642,
1
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.edgeSet_subset_edgeSet | [] | [
495,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
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Mathlib/Algebra/GCDMonoid/Basic.lean | normalize_associated | [] | [
119,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
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Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.hom_map_lift | [] | [
280,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
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Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.hom_inv_id_tensor | [
{
"state_after": "no goals",
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"tactic": "rw [... | [
356,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
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Mathlib/Topology/Maps.lean | Embedding.map_nhds_of_mem | [] | [
236,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
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Mathlib/Topology/Instances/Matrix.lean | Continuous.matrix_vecMulVec | [] | [
150,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
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Mathlib/MeasureTheory/Measure/Doubling.lean | IsUnifLocDoublingMeasure.eventually_measure_le_scaling_constant_mul | [
{
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142,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
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Mathlib/CategoryTheory/Preadditive/Opposite.lean | CategoryTheory.op_neg | [] | [
75,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
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Mathlib/Topology/Separation.lean | hasBasis_opens_closure | [] | [
1555,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1554,
1
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Mathlib/CategoryTheory/Grothendieck.lean | CategoryTheory.Grothendieck.ext | [
{
"state_after": "no goals",
"state_before": "C : Type ?u.2075\nD : Type ?u.2078\ninst✝¹ : Category C\ninst✝ : Category D\nF : C ⥤ Cat\nX Y : Grothendieck F\nf g : Hom X Y\nw_base : f.base = g.base\n⊢ (F.map g.base).obj X.fiber = (F.map f.base).obj X.fiber",
"tactic": "rw [w_base]"
},
{
"state_a... | [
87,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
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Mathlib/CategoryTheory/Bicategory/Free.lean | CategoryTheory.FreeBicategory.mk_whisker_right | [] | [
258,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.edgeSet_ssubset_edgeSet | [] | [
500,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.angle_eq_zero_of_angle_eq_pi_left | [
{
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"state_before": "V : Type u_1\nP : Type u_2\ninst✝³ : N... | [
169,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
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Mathlib/Order/Bounded.lean | Set.bounded_le_Icc | [] | [
242,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
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Mathlib/Data/Set/Intervals/SurjOn.lean | surjOn_Iio_of_monotone_surjective | [] | [
76,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
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Mathlib/Algebra/Hom/Freiman.lean | FreimanHom.ext | [] | [
192,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Data/PNat/Factors.lean | PNat.coeNat_factorMultiset | [] | [
256,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Topology/Algebra/ConstMulAction.lean | IsUnit.continuousOn_const_smul_iff | [] | [
418,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
8
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Mathlib/Order/SuccPred/LinearLocallyFinite.lean | toZ_iterate_pred_ge | [
{
"state_after": "case inl\nι : Type u_1\ninst✝³ : LinearOrder ι\ninst✝² : SuccOrder ι\ninst✝¹ : IsSuccArchimedean ι\ninst✝ : PredOrder ι\ni0 i : ι\nn : ℕ\nh : i0 ≤ (pred^[n]) i0\n⊢ -↑n ≤ toZ i0 ((pred^[n]) i0)\n\ncase inr\nι : Type u_1\ninst✝³ : LinearOrder ι\ninst✝² : SuccOrder ι\ninst✝¹ : IsSuccArchimedean ι... | [
254,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
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Mathlib/Topology/Connected.lean | Continuous.connectedComponentsLift_unique | [] | [
1525,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1523,
1
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Mathlib/Topology/PathConnected.lean | pathConnected_subset_basis | [] | [
1237,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1235,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.mono_fun | [] | [
219,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
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Mathlib/Data/Set/Image.lean | Set.preimage_singleton_nonempty | [] | [
1029,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1028,
1
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Mathlib/GroupTheory/Divisible.lean | RootableBy.surjective_pow | [] | [
270,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.coe_curry | [] | [
1987,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1986,
1
] |
Mathlib/Combinatorics/Additive/Behrend.lean | Behrend.lower_bound_le_one' | [
{
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"state_before": "α : Type ?u.840499\nβ : Type ?u.840502\nn d k N : ℕ\nx : Fin n → ℕ\nhN : 2 ≤ N\nhN' : N ≤ 4096\n⊢ ↑N * exp (-4 * Real.sqrt (log ↑N)) ≤ 1",
"tactic": "rw... | [
542,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
1
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Mathlib/CategoryTheory/Limits/ColimitLimit.lean | CategoryTheory.Limits.map_id_left_eq_curry_map | [] | [
47,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
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Mathlib/Topology/MetricSpace/Infsep.lean | Set.einfsep_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1619\ninst✝ : EDist α\nx y : α\ns t : Set α\n⊢ einfsep s = 0 ↔ ∀ (C : ℝ≥0∞), 0 < C → ∃ x x_1 y x_2 _hxy, edist x y < C",
"tactic": "simp_rw [einfsep, ← _root_.bot_eq_zero, iInf_eq_bot, iInf_lt_iff]"
}
] | [
61,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tendsto_cofinite_zero_of_tsum_ne_top | [
{
"state_after": "α✝ : Type ?u.261608\nβ : Type ?u.261611\nγ : Type ?u.261614\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\nf✝ g : α✝ → ℝ≥0∞\nα : Type u_1\nf : α → ℝ≥0∞\nhf : (∑' (x : α), f x) ≠ ⊤\nf_ne_top : ∀ (n : α), f n ≠ ⊤\n⊢ Tendsto f cofinite (𝓝 0)",
"state_before": "α✝ : Type ?u... | [
954,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
948,
1
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Mathlib/Data/Finset/Powerset.lean | Finset.powersetLen_map | [
{
"state_after": "α : Type u_2\ns✝ t✝ : Finset α\nβ : Type u_1\nf : α ↪ β\nn : ℕ\ns : Finset α\nt : Finset β\n⊢ t ⊆ map f s ∧ card t = n ↔ ∃ a, (a ⊆ s ∧ card a = n) ∧ ↑(mapEmbedding f).toEmbedding a = t",
"state_before": "α : Type u_2\ns✝ t✝ : Finset α\nβ : Type u_1\nf : α ↪ β\nn : ℕ\ns : Finset α\nt : Fins... | [
352,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Data/Nat/Size.lean | Nat.size_bit0 | [] | [
93,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.restr_trans | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_3\nγ : Type u_2\nδ : Type ?u.49198\ne : LocalEquiv α β\ne' : LocalEquiv β γ\ns : Set α\n⊢ (LocalEquiv.trans (LocalEquiv.restr e s) e').source = (LocalEquiv.restr (LocalEquiv.trans e e') s).source",
"tactic": "simp [trans_source, inte... | [
773,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
771,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.exists_pow_lt_of_lt_one | [
{
"state_after": "no goals",
"state_before": "a b : ℝ≥0\nha : 0 < a\nhb : b < 1\n⊢ ∃ n, b ^ n < a",
"tactic": "simpa only [← coe_pow, NNReal.coe_lt_coe] using\n exists_pow_lt_of_lt_one (NNReal.coe_pos.2 ha) (NNReal.coe_lt_coe.2 hb)"
}
] | [
732,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
729,
8
] |
Mathlib/Data/List/Func.lean | List.Func.pointwise_nil | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : Inhabited α\ninst✝ : Inhabited β\nf : α → β → γ\na : α\nas : List α\n⊢ pointwise f (a :: as) [] = map (fun a => f a default) (a :: as)",
"tactic": "simp only [pointwise_nil as, pointwise, eq_self_iff_true, and_sel... | [
285,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.TrailingMonic.def | [] | [
74,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Data/Sym/Basic.lean | Sym.attach_map_coe | [] | [
442,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
] |
Mathlib/CategoryTheory/Idempotents/Karoubi.lean | CategoryTheory.Idempotents.Karoubi.decompId_i_toKaroubi | [
{
"state_after": "no goals",
"state_before": "C : Type u_2\ninst✝ : Category C\nX : C\n⊢ decompId_i ((toKaroubi C).obj X) = 𝟙 ((toKaroubi C).obj X)",
"tactic": "rfl"
}
] | [
288,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iio_diff_Iic | [
{
"state_after": "no goals",
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"tactic": "rw [diff_eq, compl_Iic, inter_comm, Ioi_inter_Iio]"
}
] | [
1102,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1101,
1
] |
Mathlib/Computability/Halting.lean | Nat.Partrec'.part_iff₂ | [
{
"state_after": "no goals",
"state_before": "f : ℕ → ℕ →. ℕ\nh : _root_.Partrec fun v => f (Vector.head v) (Vector.head (Vector.tail v))\nv : ℕ × ℕ\n⊢ f (Vector.head (v.fst ::ᵥ v.snd ::ᵥ nil)) (Vector.head (Vector.tail (v.fst ::ᵥ v.snd ::ᵥ nil))) = f v.fst v.snd",
"tactic": "simp only [head_cons, tail_... | [
432,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.union_inter_cancel_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.180770\nγ : Type ?u.180773\ninst✝ : DecidableEq α\ns✝ s₁ s₂ t✝ t₁ t₂ u v : Finset α\na b : α\ns t : Finset α\n⊢ (s ∪ t) ∩ t = t",
"tactic": "rw [← coe_inj, coe_inter, coe_union, Set.union_inter_cancel_right]"
}
] | [
1608,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1607,
1
] |
Std/Data/AssocList.lean | Std.AssocList.eraseP_toList | [
{
"state_after": "case cons\nα : Type u_1\nβ : Type u_2\np : α → β → Bool\nkey✝ : α\nvalue✝ : β\ntail✝ : AssocList α β\ntail_ih✝ :\n toList (eraseP p tail✝) =\n List.eraseP\n (fun x =>\n match x with\n | (a, b) => p a b)\n (toList tail✝)\n⊢ toList\n (match p key✝ value✝ with\n ... | [
176,
63
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
174,
9
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_diff_Ioo_same | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.43065\ninst✝ : PartialOrder α\na b c : α\nh : a < b\n⊢ Ico a b \\ Ioo a b = {a}",
"tactic": "rw [← Ico_diff_left, diff_diff_cancel_left (singleton_subset_iff.2 <| left_mem_Ico.2 h)]"
}
] | [
811,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
810,
1
] |
Mathlib/ModelTheory/LanguageMap.lean | FirstOrder.Language.LHom.sumElim_comp_inr | [] | [
189,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.denom_dvd | [
{
"state_after": "case mp\nK : Type u\ninst✝ : Field K\nx : RatFunc K\nq : K[X]\nhq : q ≠ 0\n⊢ denom x ∣ q → ∃ p, x = ↑(algebraMap K[X] (RatFunc K)) p / ↑(algebraMap K[X] (RatFunc K)) q\n\ncase mpr\nK : Type u\ninst✝ : Field K\nx : RatFunc K\nq : K[X]\nhq : q ≠ 0\n⊢ (∃ p, x = ↑(algebraMap K[X] (RatFunc K)) p / ... | [
1312,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1303,
1
] |
Mathlib/Topology/Algebra/ConstMulAction.lean | Dense.smul | [
{
"state_after": "M : Type ?u.62639\nα : Type u_1\nβ : Type ?u.62645\nG : Type u_2\ninst✝⁴ : TopologicalSpace α\ninst✝³ : Group G\ninst✝² : MulAction G α\ninst✝¹ : ContinuousConstSMul G α\ninst✝ : TopologicalSpace β\nf : β → α\nb : β\ns✝ : Set β\nc : G\ns : Set α\nhs : closure s = univ\n⊢ closure (c • s) = univ... | [
280,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
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