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/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.IsPath.of_cons | [
{
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"tactic": "simp [isPath_def]"
}
] | [
969,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
968,
1
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Mathlib/Data/Real/EReal.lean | EReal.coe_nnreal_ne_top | [] | [
493,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
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Mathlib/Order/Hom/Basic.lean | OrderIso.le_iff_le | [] | [
986,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
985,
1
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Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mul_distrib | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.211564\nι : Type ?u.211567\nG : Type ?u.211570\nM : Type u_2\nN : Type ?u.211576\ninst✝¹ : CommMonoid M\ninst✝ : CommMonoid N\nf g : α → M\na b : α\ns t : Set α\nhf : Set.Finite (mulSupport f)\nhg : Set.Finite (mulSupport g)\n⊢ (∏ᶠ (i :... | [
614,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
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Mathlib/Algebra/Order/Sub/Defs.lean | add_tsub_le_assoc | [
{
"state_after": "α : Type u_1\nβ : Type ?u.7101\ninst✝⁴ : Preorder α\ninst✝³ : AddCommSemigroup α\ninst✝² : Sub α\ninst✝¹ : OrderedSub α\na b c d : α\ninst✝ : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1\n⊢ a + b ≤ a + (c + (b - c))",
"state_before": "α : Type u_1\nβ : Type ?u.7101\ninst✝... | [
138,
38
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Mathlib/LinearAlgebra/Dimension.lean | Basis.card_le_card_of_linearIndependent_aux | [
{
"state_after": "no goals",
"state_before": "K : Type u\nV V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.373329\nR✝ : Type u\ninst✝⁵ : Ring R✝\ninst✝⁴ : StrongRankCondition R✝\nM : Type v\ninst✝³ : AddCommGroup M\ninst✝² : Module R✝ M\nR : Type... | [
761,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
1
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Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.nnnorm_eq_iSup_nnnorm | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.1063529\nα : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : TopologicalSpace α\ninst✝ : SeminormedAddCommGroup β\nf g : α →ᵇ β\nx : α\nC : ℝ\n⊢ (⨆ (x : α), ‖↑f x‖) = ↑(⨆ (x : α), ‖↑f x‖₊)",
"tactic": "simp_rw [val_eq_coe, NNReal.coe_iSup, coe_nnnorm]"
... | [
1029,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1028,
1
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Mathlib/Data/Matrix/Basic.lean | AlgHom.mapMatrix_id | [] | [
1601,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1600,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_nat | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.103317\nβ : Type ?u.103320\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nn : ℕ\n⊢ ENNReal.toReal ↑n = ↑n",
"tactic": "rw [← ENNReal.ofReal_coe_nat n, ENNReal.toReal_ofReal (Nat.cast_nonneg _)]"
}
] | [
705,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
704,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.mul_apply_antidiagonal | [
{
"state_after": "case a\nk : Type u₁\nG : Type u₂\nR : Type ?u.357749\ninst✝¹ : Semiring k\ninst✝ : Mul G\nf g : MonoidAlgebra k G\nx : G\ns : Finset (G × G)\nhs : ∀ {p : G × G}, p ∈ s ↔ p.fst * p.snd = x\nF : G × G → k := fun p => if p.fst * p.snd = x then ↑f p.fst * ↑g p.snd else 0\na✝ : G × G\n⊢ a✝ ∈ Finset... | [
454,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
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Mathlib/Data/Part.lean | Part.getOrElse_none | [] | [
283,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
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Mathlib/Computability/TuringMachine.lean | Turing.TM2to1.addBottom_modifyNth | [
{
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2386,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Order/Filter/Basic.lean | Filter.le_generate_iff | [] | [
358,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
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Mathlib/Data/Multiset/Nodup.lean | Multiset.nodup_map_iff_inj_on | [] | [
150,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.zero_smul_filter_nonpos | [
{
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"state_before": "F : Type ?u.441... | [
1368,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1363,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Concrete.lean | Equiv.Perm.SameCycle.toList_isRotated | [
{
"state_after": "case pos\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx✝ : α\nf : Perm α\nx y : α\nh : SameCycle f x y\nhx : x ∈ support f\n⊢ toList f x ~r toList f y\n\ncase neg\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx✝ : α\nf : Perm α\nx y : α\nh : Sam... | [
337,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
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Mathlib/Topology/Semicontinuous.lean | LowerSemicontinuous.add | [] | [
511,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
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Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Term.realize_liftAt | [] | [
104,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | Class.mem_univ | [] | [
1515,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1514,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.frontier_ball_subset_sphere | [] | [
1886,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1885,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.symm_apply_apply | [] | [
433,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/Algebra/Free.lean | FreeSemigroup.traverse_pure' | [] | [
649,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
1
] |
Mathlib/LinearAlgebra/FreeModule/Finite/Basic.lean | Module.Finite.of_basis | [
{
"state_after": "case intro\nR✝ : Type u\nM✝ : Type v\nN : Type w\ninst✝¹⁰ : CommRing R✝\ninst✝⁹ : AddCommGroup M✝\ninst✝⁸ : Module R✝ M✝\ninst✝⁷ : Free R✝ M✝\ninst✝⁶ : AddCommGroup N\ninst✝⁵ : Module R✝ N\ninst✝⁴ : Free R✝ N\nR : Type u_1\nM : Type u_2\nι : Type u_3\ninst✝³ : CommRing R\ninst✝² : AddCommGroup... | [
61,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
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] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.MutuallySingular.smul_right | [
{
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1238,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1235,
1
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Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.single_le_prod | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.118660\nα : Type u_1\nβ : Type ?u.118666\nγ : Type ?u.118669\ninst✝ : OrderedCommMonoid α\ns t : Multiset α\na : α\nl : List α\nhl : ∀ (x : α), x ∈ Quotient.mk (List.isSetoid α) l → 1 ≤ x\nx : α\nhx : x ∈ Quotient.mk (List.isSetoid α) l\n⊢ x ≤ prod (... | [
375,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.lt_asymm | [] | [
351,
35
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
350,
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] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_eq_two_iff' | [
{
"state_after": "α β : Type u\nx : α\n⊢ (∃ x y, x ≠ y ∧ {x, y} = univ) ↔ ∃! y, y ≠ x",
"state_before": "α β : Type u\nx : α\n⊢ (#α) = 2 ↔ ∃! y, y ≠ x",
"tactic": "rw [mk_eq_two_iff]"
},
{
"state_after": "case mp\nα β : Type u\nx : α\n⊢ (∃ x y, x ≠ y ∧ {x, y} = univ) → ∃! y, y ≠ x\n\ncase mpr\nα... | [
2253,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2246,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.primeSpectrumProd_symm_inl_asIdeal | [
{
"state_after": "case mk\nR : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nasIdeal✝ : Ideal R\nIsPrime✝ : Ideal.IsPrime asIdeal✝\n⊢ (↑(primeSpectrumProd R S).symm (Sum.inl { asIdeal := asIdeal✝, IsPrime := IsPrime✝ })).asIdeal =\n Ideal.prod { asIdeal := asIdeal✝, IsPrime := IsPrime✝ }.asIde... | [
118,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | Wbtw.angle₂₃₁_eq_zero_of_ne | [] | [
363,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.coe_const | [] | [
157,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Order/SuccPred/Limit.lean | Order.isPredLimit_iff | [] | [
410,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | map_extChartAt_symm_nhdsWithin_range' | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_3\nE : Type u_2\nM : Type u_1\nH : Type u_4\nE' : Type ?u.216667\nM' : Type ?u.216670\nH' : Type ?u.216673\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\ninst✝⁷ : TopologicalSpace H\ninst✝⁶ : Topologi... | [
1189,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/RelClasses.lean | not_ssubset_of_subset | [] | [
733,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
733,
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Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_sin_pow_pos | [
{
"state_after": "no goals",
"state_before": "a b : ℝ\nn : ℕ\n⊢ 0 < ∫ (x : ℝ) in 0 ..π, sin x ^ n",
"tactic": "rcases even_or_odd' n with ⟨k, rfl | rfl⟩ <;>\nsimp only [integral_sin_pow_even, integral_sin_pow_odd] <;>\nrefine' mul_pos (by norm_num <;> exact pi_pos) (prod_pos fun n _ => div_pos _ _) <;>\... | [
687,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
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Mathlib/InformationTheory/Hamming.lean | hammingNorm_smul | [
{
"state_after": "no goals",
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232,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/MeasureTheory/Function/UniformIntegrable.lean | MeasureTheory.Memℒp.snorm_indicator_norm_ge_pos_le | [
{
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309,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Combinatorics/Composition.lean | Composition.sum_blocksFun | [
{
"state_after": "no goals",
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"tactic": "conv_rhs => rw [← c.blocks_sum, ← ofFn_blocksFun, sum_ofFn]"
}
] | [
169,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/GroupTheory/Complement.lean | Subgroup.isComplement'_of_card_mul_and_disjoint | [] | [
539,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.dvd_of_mem_normalizedFactors | [
{
"state_after": "case pos\nα : Type u_1\ninst✝³ : CancelCommMonoidWithZero α\ninst✝² : DecidableEq α\ninst✝¹ : NormalizationMonoid α\ninst✝ : UniqueFactorizationMonoid α\na p : α\nH : p ∈ normalizedFactors a\nhcases : a = 0\n⊢ p ∣ a\n\ncase neg\nα : Type u_1\ninst✝³ : CancelCommMonoidWithZero α\ninst✝² : Decid... | [
753,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/Subring/Basic.lean | Subring.map_map | [] | [
613,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
612,
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] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.length_transfer | [
{
"state_after": "no goals",
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"tactic": "induct... | [
1708,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1707,
1
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Mathlib/Analysis/Calculus/ContDiff.lean | ContDiff.pow | [
{
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1450,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1448,
1
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Mathlib/Topology/Algebra/GroupCompletion.lean | UniformSpace.Completion.coe_sub | [] | [
94,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_iUnion_null | [] | [
267,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | HasFDerivAtFilter.neg | [] | [
405,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | borel_eq_generateFrom_Ico | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.658802\nβ : Type ?u.658805\nγ : Type ?u.658808\nγ₂ : Type ?u.658811\nδ : Type ?u.658814\nι : Sort y\ns t u : Set α✝\ninst✝²⁰ : TopologicalSpace α✝\ninst✝¹⁹ : MeasurableSpace α✝\ninst✝¹⁸ : OpensMeasurableSpace α✝\ninst✝¹⁷ : TopologicalSpace β\ninst✝¹... | [
628,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | differentiableOn_fst | [] | [
206,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.eq_C_of_derivative_eq_zero | [] | [
289,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | neg_one_lt_zero | [] | [
1127,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1126,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.Ordered.memP_iff_lowerBound? | [
{
"state_after": "α : Type u_1\ncmp : α → α → Ordering\ncut : α → Ordering\nt : RBNode α\ninst✝¹ : TransCmp cmp\ninst✝ : IsCut cmp cut\nht : Ordered cmp t\nx✝ : ∃ x, x ∈ t ∧ cut x = Ordering.eq\ny : α\nhy : y ∈ t\ney : cut y = Ordering.eq\n⊢ ∃ x, x ∈ lowerBound? cut t none ∧ cut x = Ordering.eq",
"state_bef... | [
313,
75
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
303,
1
] |
Mathlib/Init/Logic.lean | let_value_eq | [] | [
443,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | IsCompact.inv | [
{
"state_after": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝² : TopologicalSpace G\ninst✝¹ : InvolutiveInv G\ninst✝ : ContinuousInv G\ns : Set G\nhs : IsCompact s\n⊢ IsCompact (Inv.inv '' s)",
"state_before": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝² : TopologicalSpace G\ninst✝¹ : I... | [
326,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.restrict_eq_codRestrict_domRestrict | [] | [
249,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Data/Set/Sups.lean | Set.sups_inter_subset_right | [] | [
173,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Topology/Constructions.lean | continuous_uLift_down | [] | [
1581,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1580,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.mapRange_neg' | [] | [
1242,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1240,
1
] |
Mathlib/Data/Set/NAry.lean | Set.forall_image2_iff | [] | [
82,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Data/MvPolynomial/Division.lean | MvPolynomial.monomial_one_dvd_iff_modMonomial_eq_zero | [] | [
152,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.int_div | [] | [
436,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/Algebra/DirectSum/Internal.lean | SetLike.nat_cast_mem_graded | [
{
"state_after": "case zero\nι : Type u_1\nσ : Type u_3\nS : Type ?u.25931\nR : Type u_2\ninst✝⁴ : Zero ι\ninst✝³ : AddMonoidWithOne R\ninst✝² : SetLike σ R\ninst✝¹ : AddSubmonoidClass σ R\nA : ι → σ\ninst✝ : GradedOne A\n⊢ ↑Nat.zero ∈ A 0\n\ncase succ\nι : Type u_1\nσ : Type u_3\nS : Type ?u.25931\nR : Type u_... | [
71,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Order/CompleteBooleanAlgebra.lean | compl_sSup' | [] | [
318,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.log_surjective | [] | [
88,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Analysis/PSeries.lean | sum_Ioc_inv_sq_le_sub | [
{
"state_after": "case refine'_1\nα : Type u_1\ninst✝ : LinearOrderedField α\nk n : ℕ\nhk : k ≠ 0\nh : k ≤ n\n⊢ ∑ i in Ioc k k, (↑(i ^ 2))⁻¹ ≤ (↑k)⁻¹ - (↑k)⁻¹\n\ncase refine'_2\nα : Type u_1\ninst✝ : LinearOrderedField α\nk n : ℕ\nhk : k ≠ 0\nh : k ≤ n\n⊢ ∀ (n : ℕ),\n k ≤ n → ∑ i in Ioc k n, (↑(i ^ 2))⁻¹ ≤ (... | [
313,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/Topology/Algebra/Constructions.lean | MulOpposite.continuous_unop | [] | [
42,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.le_mul_left | [
{
"state_after": "case h.e'_3\na b : Cardinal\nh : b ≠ 0\n⊢ a = 1 * a",
"state_before": "a b : Cardinal\nh : b ≠ 0\n⊢ a ≤ b * a",
"tactic": "convert mul_le_mul_right' (one_le_iff_ne_zero.mpr h) a"
},
{
"state_after": "no goals",
"state_before": "case h.e'_3\na b : Cardinal\nh : b ≠ 0\n⊢ a = ... | [
661,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
659,
1
] |
Mathlib/Data/Nat/Interval.lean | Nat.cauchy_induction | [] | [
368,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.mem_sSup_of_directedOn | [
{
"state_after": "R : Type u\nS✝ : Type v\nT : Type w\ninst✝³ : NonUnitalNonAssocSemiring R\nM : Subsemigroup R\ninst✝² : NonUnitalNonAssocSemiring S✝\ninst✝¹ : NonUnitalNonAssocSemiring T\nF : Type ?u.283475\ninst✝ : NonUnitalRingHomClass F R S✝\nS : Set (NonUnitalSubsemiring R)\nSne : Set.Nonempty S\nhS : Dir... | [
845,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
842,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.mem_cthickening_iff | [] | [
1029,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1028,
1
] |
Mathlib/Order/SymmDiff.lean | bihimp_eq_top | [] | [
259,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Std/Data/List/Lemmas.lean | List.disjoint_nil_left | [] | [
1373,
96
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1373,
9
] |
Mathlib/Data/Finset/Sups.lean | Finset.coe_sups | [] | [
70,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.card_inter_add_card_union | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.33374\ns✝ t✝ : Finset α\nf : α → β\nn : ℕ\ninst✝ : DecidableEq α\ns t : Finset α\n⊢ card (s ∩ t) + card (s ∪ t) = card s + card t",
"tactic": "rw [add_comm, card_union_add_card_inter]"
}
] | [
415,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_subset_Ioc_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.65577\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\nh₁ : a₁ < b₁\n⊢ Ioc a₁ b₁ ⊆ Ioc a₂ b₂ ↔ b₁ ≤ b₂ ∧ a₂ ≤ a₁",
"tactic": "convert @Ico_subset_Ico_iff αᵒᵈ _ b₁ b₂ a₁ a₂ h₁ using 2 <;> exact (@dual_Ico α _ _ _).symm"
}
] | [
1139,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1138,
1
] |
Mathlib/Algebra/Support.lean | Function.mulSupport_one_add' | [] | [
420,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/Data/Rat/NNRat.lean | NNRat.coe_one | [] | [
125,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.QuasiMeasurePreserving.ae_eq | [] | [
2506,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2504,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.op_unop | [] | [
85,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Data/Set/NAry.lean | Set.image2_subset_iff | [] | [
87,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | BoundedContinuousFunction.Lp_norm_le | [] | [
1621,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1618,
1
] |
Mathlib/Topology/Inseparable.lean | Specializes.trans | [] | [
172,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.min_val | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\na : Fin n\n⊢ min (↑a) n = ↑a",
"tactic": "simp"
}
] | [
329,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/Order/Bounds/Basic.lean | bddBelow_Ioo | [] | [
684,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
683,
1
] |
Mathlib/Analysis/Normed/MulAction.lean | norm_smul_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\ninst✝³ : SeminormedAddGroup α\ninst✝² : SeminormedAddGroup β\ninst✝¹ : SMulZeroClass α β\ninst✝ : BoundedSMul α β\nr : α\nx : β\n⊢ ‖r • x‖ ≤ ‖r‖ * ‖x‖",
"tactic": "simpa [smul_zero] using dist_smul_pair r 0 x"
}
] | [
34,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.coprod.inl_map | [] | [
844,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
842,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.floor_one | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.26362\nα : Type u_1\nβ : Type ?u.26368\ninst✝¹ : LinearOrderedSemiring α\ninst✝ : FloorSemiring α\na : α\nn : ℕ\n⊢ ⌊1⌋₊ = 1",
"tactic": "rw [← Nat.cast_one, floor_coe]"
}
] | [
179,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Computability/Partrec.lean | Partrec.bind | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.52270\nσ : Type u_3\ninst✝³ : Primcodable α\ninst✝² : Primcodable β\ninst✝¹ : Primcodable γ\ninst✝ : Primcodable σ\nf : α →. β\ng : α → β →. σ\nhf : Partrec f\nhg : Partrec₂ g\nn : ℕ\n⊢ (Part.bind (Part.bind ↑(decode n) fun y => map (Nat.pair n) (map enc... | [
460,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
11
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.withTopEquiv_top | [] | [
691,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
690,
1
] |
Mathlib/Topology/Filter.lean | Filter.tendsto_nhds_atTop_iff | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.20384\nα : Type u_2\nβ : Type u_1\nX : Type ?u.20393\nY : Type ?u.20396\ninst✝ : Preorder β\nl : Filter α\nf : α → Filter β\n⊢ Tendsto f l (𝓝 atTop) ↔ ∀ (y : β), ∀ᶠ (a : α) in l, Ici y ∈ f a",
"tactic": "simp only [nhds_atTop, tendsto_iInf, tend... | [
194,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
11
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | hasFDerivAt_prod_mk_right | [] | [
94,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.type_fin | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.240894\nβ : Type ?u.240897\nγ : Type ?u.240900\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nn : ℕ\n⊢ (type fun x x_1 => x < x_1) = ↑n",
"tactic": "simp"
}
] | [
1590,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1590,
1
] |
Mathlib/Algebra/Divisibility/Units.lean | Units.coe_dvd | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Monoid α\na b : α\nu : αˣ\n⊢ a = ↑u * (↑u⁻¹ * a)",
"tactic": "simp"
}
] | [
31,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.toReal_sub | [
{
"state_after": "case intro\ny : EReal\nhy : y ≠ ⊤\nh'y : y ≠ ⊥\nx : ℝ\nhx : ↑x ≠ ⊤\nh'x : ↑x ≠ ⊥\n⊢ toReal (↑x - y) = toReal ↑x - toReal y",
"state_before": "x y : EReal\nhx : x ≠ ⊤\nh'x : x ≠ ⊥\nhy : y ≠ ⊤\nh'y : y ≠ ⊥\n⊢ toReal (x - y) = toReal x - toReal y",
"tactic": "lift x to ℝ using ⟨hx, h'x⟩"
... | [
889,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
885,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_prod | [] | [
930,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
928,
1
] |
Mathlib/Order/BoundedOrder.lean | inf_bot_eq | [] | [
518,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.lmul'_comp_includeLeft | [] | [
948,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
947,
1
] |
Mathlib/Algebra/CharZero/Defs.lean | Nat.cast_inj | [] | [
73,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.lean | Real.sin_arctan | [
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ sin (arctan x) = x / sqrt (↑1 + x ^ 2)",
"tactic": "rw_mod_cast [← tan_div_sqrt_one_add_tan_sq (cos_arctan_pos x), tan_arctan]"
}
] | [
149,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biproduct.fromSubtype_π_subtype | [
{
"state_after": "case w\nJ : Type w\nC : Type u\ninst✝³ : Category C\ninst✝² : HasZeroMorphisms C\nf : J → C\ninst✝¹ : HasBiproduct f\np : J → Prop\ninst✝ : HasBiproduct (Subtype.restrict p f)\nj : Subtype p\n⊢ ∀ (j_1 : Subtype p),\n ι (Subtype.restrict p f) j_1 ≫ fromSubtype f p ≫ π f ↑j = ι (Subtype.restr... | [
607,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tendsto_sum_nat_add | [
{
"state_after": "case intro\nα : Type ?u.333832\nβ : Type ?u.333835\nγ : Type ?u.333838\nf : ℕ → ℝ≥0\nhf : (∑' (i : ℕ), (fun i => ↑(f i)) i) ≠ ⊤\n⊢ Tendsto (fun i => ∑' (k : ℕ), (fun i => ↑(f i)) (k + i)) atTop (𝓝 0)",
"state_before": "α : Type ?u.333832\nβ : Type ?u.333835\nγ : Type ?u.333838\nf : ℕ → ℝ≥... | [
1257,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1252,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.Nonempty.mono | [] | [
511,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
] |
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