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/Topology/Instances/ENNReal.lean | ENNReal.tsum_biUnion_le_tsum | [
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1008,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/TensorAlgebra/Basic.lean | TensorAlgebra.lift_unique | [
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144,
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Mathlib/Data/Pi/Algebra.lean | Pi.mulSingle_inj | [] | [
331,
38
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330,
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Mathlib/MeasureTheory/Measure/AEMeasurable.lean | AEMeasurable.mono_measure | [] | [
50,
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Mathlib/Data/Complex/Exponential.lean | Real.exp_injective | [] | [
1529,
27
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1528,
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Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.enum_zero_le | [
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Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.mem_mk | [] | [
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10
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Mathlib/Analysis/Calculus/FDeriv/Prod.lean | fderiv_pi | [] | [
462,
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Mathlib/GroupTheory/Perm/List.lean | List.formPerm_apply_nthLe_zero | [
{
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158,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.congr | [] | [
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44
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Mathlib/MeasureTheory/PiSystem.lean | generateFrom_piiUnionInter_measurableSet | [
{
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Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_inf | [] | [
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pushout.condition | [] | [
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Mathlib/Computability/Primrec.lean | Primrec.option_getD | [
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Mathlib/Analysis/Calculus/ContDiffDef.lean | Set.EqOn.iteratedFDerivWithin | [] | [
915,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
913,
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Std/Data/Option/Lemmas.lean | Option.bind_eq_none | [
{
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"tactic": "simp only [eq_none_iff_forall_not_mem, not_exists, not_and, mem_def, bind_eq_some]"
}
] | [
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] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/Logic/Function/Basic.lean | InvImage.equivalence | [] | [
1064,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.spanPoints_subset_coe_of_subset_coe | [
{
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519,
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Mathlib/Algebra/Support.lean | Function.support_prod | [
{
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Mathlib/CategoryTheory/Limits/Shapes/Diagonal.lean | CategoryTheory.Limits.pullback.diagonal_isKernelPair | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Generator.lean | CategoryTheory.isSeparator_sigma_of_isSeparator | [
{
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"tactic": "simp"
}
] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Order/Monoid/Lemmas.lean | Antitone.mul_const' | [] | [
1326,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1325,
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | edist_pi_const | [] | [
498,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
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Mathlib/Analysis/NormedSpace/RieszLemma.lean | riesz_lemma | [
{
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Mathlib/LinearAlgebra/Basic.lean | Submodule.map_add_le | [
{
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Mathlib/Analysis/SpecificLimits/Normed.lean | tendsto_pow_const_mul_const_pow_of_abs_lt_one | [
{
"state_after": "case pos\nα : Type ?u.120365\nβ : Type ?u.120368\nι : Type ?u.120371\nk : ℕ\nr : ℝ\nhr : abs r < 1\nh0 : r = 0\n⊢ Tendsto (fun n => ↑n ^ k * r ^ n) atTop (𝓝 0)\n\ncase neg\nα : Type ?u.120365\nβ : Type ?u.120368\nι : Type ?u.120371\nk : ℕ\nr : ℝ\nhr : abs r < 1\nh0 : ¬r = 0\n⊢ Tendsto (fun n ... | [
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Mathlib/FieldTheory/PerfectClosure.lean | PerfectClosure.induction_on | [] | [
184,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
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Mathlib/CategoryTheory/Preadditive/Biproducts.lean | CategoryTheory.Limits.biproduct.total | [] | [
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42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/List/Sublists.lean | List.sublists'_map | [
{
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},
{
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Mathlib/Data/Set/Sups.lean | Set.sup_mem_sups | [] | [
82,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
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Mathlib/Init/Data/Nat/Lemmas.lean | Nat.bit1_ne | [] | [
144,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
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Mathlib/MeasureTheory/MeasurableSpace.lean | isCountablySpanning_measurableSet | [] | [
1763,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1761,
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Mathlib/Order/Filter/Basic.lean | Filter.mem_sup | [] | [
559,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
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Std/Data/RBMap/Lemmas.lean | Std.RBNode.foldr_cons | [
{
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"tactic": "unfold toList"
},
{
"state_after": "... | [
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] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
329,
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Mathlib/AlgebraicGeometry/PresheafedSpace/HasColimits.lean | AlgebraicGeometry.PresheafedSpace.ColimitCoconeIsColimit.desc_fac | [
{
"state_after": "case w\nJ : Type u'\ninst✝⁴ : Category J\nC : Type u\ninst✝³ : Category C\ninst✝² : HasColimitsOfShape J TopCat\ninst✝¹ : ∀ (X : TopCat), HasLimitsOfShape Jᵒᵖ (Presheaf C X)\ninst✝ : HasLimitsOfShape Jᵒᵖ C\nF : J ⥤ PresheafedSpace C\ns : Cocone F\nj : J\n⊢ ((colimitCocone F).ι.app j ≫ desc F s... | [
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Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.subtype_comp_inclusion | [] | [
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6
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188,
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Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.total_eq_fintype_total | [] | [
1083,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1080,
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Mathlib/ModelTheory/ElementaryMaps.lean | FirstOrder.Language.ElementaryEmbedding.map_formula | [
{
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Mathlib/Data/Matrix/DMatrix.lean | AddMonoidHom.mapDMatrix_apply | [] | [
190,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
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Mathlib/Topology/Maps.lean | Function.LeftInverse.embedding | [] | [
226,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Fourier/FourierTransform.lean | Real.fourierIntegral_def | [] | [
270,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_comp_div_add | [
{
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777,
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Mathlib/Algebra/Order/Monoid/Lemmas.lean | one_lt_of_lt_mul_left | [
{
"state_after": "no goals",
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"tactic": "simpa only [one_mul]"
}
] | [
492,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
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Mathlib/Order/Filter/Pointwise.lean | Filter.pure_div_pure | [] | [
507,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
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Mathlib/Order/Hom/Lattice.lean | LatticeHom.coe_comp_inf_hom | [] | [
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6
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1133,
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Mathlib/Algebra/GroupPower/Order.lean | sq_pos_of_ne_zero | [] | [
662,
19
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661,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_add_diff | [
{
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Mathlib/Order/Lattice.lean | eq_of_inf_eq_sup_eq | [] | [
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64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Order/Monoid/Lemmas.lean | StrictAntiOn.mul_antitone' | [] | [
1548,
73
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1546,
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Mathlib/Algebra/Lie/Basic.lean | LieModuleHom.coe_zsmul | [] | [
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6
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922,
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Mathlib/Probability/Independence/ZeroOne.lean | ProbabilityTheory.measure_eq_zero_or_one_of_indepSetCat_self | [
{
"state_after": "Ω : Type u_1\nι : Type ?u.108607\nm m0 : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\ninst✝ : IsFiniteMeasure μ\nt : Set Ω\nh_indep : IndepSet t t\nh_0_1_top : ↑↑μ t = 0 ∨ ↑↑μ t = 1 ∨ ↑↑μ t = ⊤\n⊢ ↑↑μ t = 0 ∨ ↑↑μ t = 1",
"state_before": "Ω : Type u_1\nι : Type ?u.108607\nm m0 : Measurab... | [
50,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/RingTheory/WittVector/WittPolynomial.lean | xInTermsOfW_vars_subset | [] | [
288,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Data/Nat/Choose/Cast.lean | Nat.cast_choose | [
{
"state_after": "K : Type u_1\ninst✝¹ : DivisionRing K\ninst✝ : CharZero K\na b : ℕ\nh : a ≤ b\nthis : ∀ {n : ℕ}, ↑n ! ≠ 0\n⊢ ↑(choose b a) = ↑b ! / (↑a ! * ↑(b - a)!)",
"state_before": "K : Type u_1\ninst✝¹ : DivisionRing K\ninst✝ : CharZero K\na b : ℕ\nh : a ≤ b\n⊢ ↑(choose b a) = ↑b ! / (↑a ! * ↑(b - a)... | [
31,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
28,
1
] |
Mathlib/Control/Traversable/Instances.lean | Sum.map_traverse | [
{
"state_after": "no goals",
"state_before": "σ : Type u\nF G : Type u → Type u\ninst✝³ : Applicative F\ninst✝² : Applicative G\ninst✝¹ : LawfulApplicative F\ninst✝ : LawfulApplicative G\nα : Type u_1\nβ γ : Type u\ng : α → G β\nf : β → γ\nx : σ ⊕ α\n⊢ (fun x x_1 => x <$> x_1) f <$> Sum.traverse g x = Sum.t... | [
184,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
11
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.destruct_flatten | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nc : Computation (WSeq α)\n⊢ Computation.IsBisimulation fun c1 c2 => c1 = c2 ∨ ∃ c, c1 = destruct (flatten c) ∧ c2 = Computation.bind c destruct",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nc : Computation (WSeq α)\n⊢ destruct (flatten c) = c >>... | [
698,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
686,
1
] |
Mathlib/Analysis/Convex/Between.lean | wbtw_lineMap_iff | [
{
"state_after": "case pos\nR : Type u_1\nV : Type u_2\nV' : Type ?u.236526\nP : Type u_3\nP' : Type ?u.236532\ninst✝⁷ : OrderedRing R\ninst✝⁶ : AddCommGroup V\ninst✝⁵ : Module R V\ninst✝⁴ : AddTorsor V P\ninst✝³ : AddCommGroup V'\ninst✝² : Module R V'\ninst✝¹ : AddTorsor V' P'\ninst✝ : NoZeroSMulDivisors R V\n... | [
421,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.factors_decreasing | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\na b : α\ninst✝² : CommSemiring α\nI : Ideal α\ninst✝¹ : CommRing β\ninst✝ : IsDomain β\nb₁ b₂ : β\nh₁ : b₁ ≠ 0\nh₂ : ¬IsUnit b₂\nh : span {b₁} ≤ span {b₁ * b₂}\n⊢ b₁ * b₂ ∣ b₁ * 1",
"tactic": "rwa [mul_one, ← Ideal.span_singleton_le_s... | [
560,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/Topology/MetricSpace/Equicontinuity.lean | Metric.equicontinuousAt_iff_pair | [
{
"state_after": "α : Type u_3\nβ : Type u_2\nι✝ : Type ?u.1103\ninst✝¹ : PseudoMetricSpace α\nι : Type u_1\ninst✝ : TopologicalSpace β\nF : ι → β → α\nx₀ : β\n⊢ (∀ (U : Set (α × α)), U ∈ 𝓤 α → ∃ V, V ∈ 𝓝 x₀ ∧ ∀ (x : β), x ∈ V → ∀ (y : β), y ∈ V → ∀ (i : ι), (F i x, F i y) ∈ U) ↔\n ∀ (ε : ℝ), ε > 0 → ∃ U, ... | [
72,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
11
] |
Mathlib/Data/Real/Sqrt.lean | Real.sqrt_one | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ sqrt 1 = 1",
"tactic": "simp [sqrt]"
}
] | [
258,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Order/Category/NonemptyFinLinOrdCat.lean | NonemptyFinLinOrdCat.epi_iff_surjective | [
{
"state_after": "case mp\nA B : NonemptyFinLinOrdCat\nf : A ⟶ B\n⊢ Epi f → Function.Surjective ↑f\n\ncase mpr\nA B : NonemptyFinLinOrdCat\nf : A ⟶ B\n⊢ Function.Surjective ↑f → Epi f",
"state_before": "A B : NonemptyFinLinOrdCat\nf : A ⟶ B\n⊢ Epi f ↔ Function.Surjective ↑f",
"tactic": "constructor"
}... | [
208,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.dist_eq_of_ne | [
{
"state_after": "no goals",
"state_before": "E : ℕ → Type u_1\nx y : (n : ℕ) → E n\nh : x ≠ y\n⊢ dist x y = (1 / 2) ^ firstDiff x y",
"tactic": "simp [dist, h]"
}
] | [
277,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Analysis/Quaternion.lean | Quaternion.summable_coe | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nf : α → ℝ\n⊢ (Summable fun a => ↑(f a)) ↔ Summable f",
"tactic": "simpa only using\n Summable.map_iff_of_leftInverse (algebraMap ℝ ℍ) (show ℍ →ₗ[ℝ] ℝ from QuaternionAlgebra.reₗ _ _)\n (continuous_algebraMap _ _) continuous_re coe_re"
}
] | [
251,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/CategoryTheory/Limits/Creates.lean | CategoryTheory.hasColimit_of_created | [] | [
204,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurableSet_Ici | [] | [
438,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | UniformOnFun.hasBasis_uniformity_of_basis_aux₂ | [] | [
653,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
11
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.add_lt_add_of_lt_of_le | [] | [
794,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
793,
11
] |
Mathlib/Data/Nat/Parity.lean | Nat.two_mul_div_two_of_even | [] | [
223,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Topology/Algebra/Module/Multilinear.lean | ContinuousMultilinearMap.pi_apply | [] | [
270,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.reduce.min | [
{
"state_after": "case refl\nα : Type u\nL L₁ L₂ L₃ L₄ : List (α × Bool)\ninst✝ : DecidableEq α\n⊢ reduce L₁ = reduce L₁\n\ncase tail\nα : Type u\nL L₁ L₂ L₃ L₄ : List (α × Bool)\ninst✝ : DecidableEq α\nL1 L' : List (α × Bool)\nL2 : ReflTransGen Red.Step (reduce L₁) L1\nH1 : Red.Step L1 L'\nH2 : reduce L₁ = L1\... | [
1197,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1193,
1
] |
Mathlib/Logic/Basic.lean | Ne.ite_ne_right_iff | [] | [
1205,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1204,
11
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.mk'_mem_incidenceSet_left_iff | [] | [
839,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
838,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.isSuccLimit_aleph0 | [
{
"state_after": "case intro\nα β : Type u\nn : ℕ\nha : ↑n < ℵ₀\n⊢ succ ↑n < ℵ₀",
"state_before": "α β : Type u\na : Cardinal\nha : a < ℵ₀\n⊢ succ a < ℵ₀",
"tactic": "rcases lt_aleph0.1 ha with ⟨n, rfl⟩"
},
{
"state_after": "case intro\nα β : Type u\nn : ℕ\nha : ↑n < ℵ₀\n⊢ ↑(Nat.succ n) < ℵ₀",
... | [
1444,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1440,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.sum_apply | [] | [
524,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.m_neg_part_def | [] | [
162,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Analysis/NormedSpace/AddTorsorBases.lean | IsOpen.exists_subset_affineIndependent_span_eq_top | [
{
"state_after": "case intro\nV : Type u_2\nP : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : NormedSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nu : Set P\nhu : IsOpen u\nx : P\nhx : x ∈ u\n⊢ ∃ s x, AffineIndependent ℝ Subtype.val ∧ affineSpan ℝ s = ⊤",
"state_before": "V : Type u_2\n... | [
127,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Algebra/Module/Basic.lean | inv_int_cast_smul_eq | [] | [
522,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
] |
Mathlib/Topology/Instances/Rat.lean | Rat.continuous_coe_real | [] | [
56,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.totallyBounded_iff' | [] | [
772,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
767,
1
] |
Mathlib/Data/Matrix/Hadamard.lean | Matrix.add_hadamard | [] | [
82,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Topology/Order/Basic.lean | comap_coe_nhdsWithin_Ioi_of_Ioo_subset | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na b : α\ns : Set α\nha : s ⊆ Ioi a\nhs : Set.Nonempty s → ∃ b, b > a ∧ Ioo a b ⊆ s\nh : Set.Nonempty (↑ofDual ⁻¹' s)\n⊢ ∃... | [
2466,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2463,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.norm_eq_zero_iff | [] | [
333,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Std/Logic.lean | or_and_left | [] | [
331,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
329,
1
] |
Mathlib/Topology/IsLocallyHomeomorph.lean | IsLocallyHomeomorphOn.continuousAt | [] | [
68,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
11
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.normalClosure_mono | [] | [
2498,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2497,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | rank_zero_iff | [] | [
517,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | IsMax.Ici_eq | [] | [
953,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
952,
1
] |
Mathlib/Algebra/Group/Basic.lean | div_eq_inv_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.30968\nG : Type ?u.30971\ninst✝ : DivisionCommMonoid α\na b c d : α\n⊢ a / b = b⁻¹ * a",
"tactic": "simp"
}
] | [
505,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/CategoryTheory/Localization/Predicate.lean | CategoryTheory.Localization.liftNatTrans_app | [] | [
349,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Topology/Algebra/UniformGroup.lean | CauchySeq.mul_const | [] | [
449,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Data/Polynomial/Expand.lean | Polynomial.coeff_contract | [
{
"state_after": "R : Type u\ninst✝¹ : CommSemiring R\nS : Type v\ninst✝ : CommSemiring S\np✝ q p : ℕ\nhp : p ≠ 0\nf : R[X]\nn : ℕ\n⊢ natDegree f + 1 ≤ n → 0 = coeff f (n * p)",
"state_before": "R : Type u\ninst✝¹ : CommSemiring R\nS : Type v\ninst✝ : CommSemiring S\np✝ q p : ℕ\nhp : p ≠ 0\nf : R[X]\nn : ℕ\... | [
217,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/GroupTheory/Finiteness.lean | Group.fg_def | [] | [
297,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Algebra/Parity.lean | Dvd.dvd.even | [] | [
261,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/CategoryTheory/Limits/ConeCategory.lean | CategoryTheory.Limits.hasLimitsOfShape_iff_isLeftAdjoint_const | [] | [
104,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.subset_iUnion_of_subset | [] | [
346,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | tendsto_dist_right_cocompact_atTop | [] | [
2153,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2150,
1
] |
Mathlib/Analysis/NormedSpace/Pointwise.lean | affinity_unitClosedBall | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.1782138\nE : Type u_1\ninst✝³ : NormedField 𝕜\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : NormedSpace ℝ E\nr : ℝ\nhr : 0 ≤ r\nx : E\n⊢ x +ᵥ r • closedBall 0 1 = closedBall x r",
"tactic": "rw [smul_closedUnitBall, Real.no... | [
444,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.mulVec_add | [
{
"state_after": "case h\nl : Type ?u.856313\nm : Type u_2\nn : Type u_1\no : Type ?u.856322\nm' : o → Type ?u.856327\nn' : o → Type ?u.856332\nR : Type ?u.856335\nS : Type ?u.856338\nα : Type v\nβ : Type w\nγ : Type ?u.856345\ninst✝¹ : NonUnitalNonAssocSemiring α\ninst✝ : Fintype n\nA : Matrix m n α\nx y : n →... | [
1751,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1748,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_univ | [] | [
612,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
611,
1
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.coe_finset_sum | [] | [
103,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | ofAdd_nsmul | [] | [
449,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
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