file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/Order/Closure.lean | ClosureOperator.closure_iSup₂_closure | [] | [
286,
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283,
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Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.Measure.tprod_cons | [] | [
245,
6
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243,
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Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.root_right_of_root_gcd | [
{
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346,
59
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Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.lintegral_const | [
{
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450,
81
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449,
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Mathlib/Order/WellFounded.lean | WellFounded.has_min | [] | [
53,
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Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.edist_le_mul_of_le | [] | [
139,
44
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Mathlib/Data/Fin/Basic.lean | Fin.succAbove_aux | [] | [
2020,
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Mathlib/GroupTheory/GroupAction/ConjAct.lean | MulAut.conjNormal_apply | [] | [
339,
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337,
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Mathlib/Analysis/InnerProductSpace/Calculus.lean | ContDiffAt.dist | [
{
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Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidWithZeroHom.mul_comp | [] | [
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.infEdist_closure | [
{
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149,
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Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.smul_sup | [] | [
305,
16
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Mathlib/Analysis/Normed/Group/AddTorsor.lean | edist_vadd_vadd_le | [
{
"state_after": "α : Type ?u.26982\nV : Type u_2\nP : Type u_1\nW : Type ?u.26991\nQ : Type ?u.26994\ninst✝⁵ : SeminormedAddCommGroup V\ninst✝⁴ : PseudoMetricSpace P\ninst✝³ : NormedAddTorsor V P\ninst✝² : NormedAddCommGroup W\ninst✝¹ : MetricSpace Q\ninst✝ : NormedAddTorsor W Q\nv v' : V\np p' : P\n⊢ ↑(nndist... | [
199,
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Mathlib/GroupTheory/Congruence.lean | Con.mapOfSurjective_eq_mapGen | [
{
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660,
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658,
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Mathlib/LinearAlgebra/Finrank.lean | FiniteDimensional.finrank_eq_card_finset_basis | [
{
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.of_pow | [
{
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1635,
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Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.Memℒp.induction | [
{
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1020,
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994,
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Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.coeFn_injective | [] | [
154,
24
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153,
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Std/Logic.lean | and_congr_right_eq | [] | [
172,
51
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171,
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Mathlib/RingTheory/Multiplicity.lean | multiplicity.get_multiplicity_self | [
{
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{
"state_after": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : DecidableRel fun x x_... | [
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536,
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Mathlib/Data/Real/ENNReal.lean | ENNReal.add_lt_add_of_le_of_lt | [] | [
790,
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Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.toAlgHom_eq_coe | [] | [
256,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
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Mathlib/CategoryTheory/Limits/ConcreteCategory.lean | CategoryTheory.Limits.Concrete.widePushout_exists_rep | [
{
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320,
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313,
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Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Equivalence.inverse_map_inj_iff | [] | [
751,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
749,
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Std/Data/String/Lemmas.lean | Substring.Valid.dropWhile | [] | [
1076,
66
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | OrderIso.map_csInf' | [] | [
1351,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1349,
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Mathlib/RingTheory/Noetherian.lean | IsNoetherian.injective_of_surjective_endomorphism | [
{
"state_after": "case intro.intro\nR : Type u_1\nM : Type u_2\nP : Type ?u.268814\nN : Type w\ninst✝⁷ : Ring R\ninst✝⁶ : AddCommGroup M\ninst✝⁵ : Module R M\ninst✝⁴ : AddCommGroup N\ninst✝³ : Module R N\ninst✝² : AddCommGroup P\ninst✝¹ : Module R P\ninst✝ : IsNoetherian R M\nf : M →ₗ[R] M\ns : Surjective ↑f\nn... | [
437,
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432,
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Mathlib/Algebra/CubicDiscriminant.lean | Cubic.of_b_eq_zero' | [] | [
153,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
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Mathlib/Data/Set/Intervals/Disjoint.lean | Set.Ici_disjoint_Iic | [
{
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"tactic": "rw [Set.disjoint_iff_inter_eq_empty, Ici_inter_Iic, Icc_eq_empty_iff]"
}
] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.pointwise_smul_toSubmonoid | [] | [
287,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
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Mathlib/Data/ZMod/Basic.lean | ZMod.cast_sub_one | [
{
"state_after": "case inl\nR : Type u_1\ninst✝ : Ring R\nn : ℕ\nk : ZMod n\nhk : k = 0\n⊢ ↑(k - 1) = ↑n - 1\n\ncase inr\nR : Type u_1\ninst✝ : Ring R\nn : ℕ\nk : ZMod n\nhk : ¬k = 0\n⊢ ↑(k - 1) = ↑k - 1",
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526,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
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Mathlib/Algebra/Order/Sub/Canonical.lean | AddLECancellable.tsub_lt_tsub_right_of_le | [
{
"state_after": "α : Type u_1\ninst✝⁵ : AddCommSemigroup α\ninst✝⁴ : PartialOrder α\ninst✝³ : ExistsAddOfLE α\ninst✝² : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\na b c d : α\nhc : AddLECancellable c\nh : c ≤ a\nh2 : a < b\n⊢ c + (a - c) < b",
"sta... | [
175,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
11
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Mathlib/Data/List/Dedup.lean | List.replicate_dedup | [
{
"state_after": "no goals",
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}
] | [
106,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
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Mathlib/Topology/LocallyFinite.lean | locallyFinite_iff_smallSets | [] | [
66,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
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Mathlib/Data/Bool/Basic.lean | Bool.not_and | [
{
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"state_before": "⊢ ∀ (a b : Bool), (!decide ((a && b) = (!a || !b))) = true",
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.toLin_apply | [
{
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605,
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602,
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Mathlib/Topology/PathConnected.lean | Path.continuous_uncurry_iff | [] | [
232,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
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Mathlib/Order/Zorn.lean | zorn_partialOrder₀ | [] | [
177,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
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] |
Mathlib/Order/SuccPred/LinearLocallyFinite.lean | LinearLocallyFiniteOrder.le_succFn | [
{
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},
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
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Mathlib/FieldTheory/IsAlgClosed/Basic.lean | IsAlgClosed.exists_aeval_eq_zero | [] | [
131,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.diam_le_of_subset_closedBall | [
{
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}
] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Over.lean | CategoryTheory.Over.map_obj_left | [] | [
176,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
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Mathlib/Algebra/BigOperators/Finprod.lean | finprod_eq_one_of_forall_eq_one | [
{
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588,
46
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.withDensity_eq_zero | [
{
"state_after": "no goals",
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"tactic": "rw [← lintegral_eq_zero_iff' hf, ← set_lintegral_univ... | [
1672,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1669,
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Std/Data/List/Lemmas.lean | List.eraseP_nil | [] | [
926,
53
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.coe_comap | [] | [
1363,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1362,
1
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Mathlib/CategoryTheory/Abelian/Pseudoelements.lean | CategoryTheory.Abelian.Pseudoelement.pseudoZero_aux | [
{
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"tactic": "simp [comm]"
},
{
... | [
224,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Topology/Order/Hom/Basic.lean | ContinuousOrderHom.comp_id | [] | [
182,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
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Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | Sbtw.angle₃₁₂_eq_zero | [] | [
356,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
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Mathlib/MeasureTheory/Function/UniformIntegrable.lean | MeasureTheory.uniformIntegrable_iff | [] | [
919,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
913,
1
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Mathlib/MeasureTheory/Measure/GiryMonad.lean | MeasureTheory.Measure.measurable_map | [
{
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83,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasFDerivAt.cos | [] | [
930,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
928,
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.SimpleFunc.setToSimpleFunc_add_left | [
{
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410,
42
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406,
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Mathlib/Algebra/Lie/Abelian.lean | LieModule.maxTrivEquiv_of_refl_eq_refl | [
{
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205,
69
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203,
1
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Mathlib/GroupTheory/FreeAbelianGroupFinsupp.lean | FreeAbelianGroup.mem_support_iff | [
{
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},
{
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158,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
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Mathlib/RingTheory/Subsemiring/Pointwise.lean | Subsemiring.mem_inv_pointwise_smul_iff₀ | [] | [
158,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
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Mathlib/Analysis/InnerProductSpace/Calculus.lean | contDiffAt_euclidean | [
{
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345,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
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Mathlib/RingTheory/FiniteType.lean | MonoidAlgebra.finiteType_iff_group_fg | [
{
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}
] | [
623,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
1
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Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_abs | [
{
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}
] | [
60,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.isProbabilityMeasure_map | [
{
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3238,
44
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3236,
1
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Mathlib/Algebra/GeomSum.lean | geom_sum₂_with_one | [
{
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}
] | [
103,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
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Mathlib/LinearAlgebra/Basis.lean | Basis.reindexFinsetRange_repr | [
{
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551,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
1
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Mathlib/Combinatorics/Composition.lean | Composition.single_embedding | [
{
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},
{
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"state_... | [
595,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/Topology/Algebra/Module/Multilinear.lean | ContinuousMultilinearMap.ext_iff | [
{
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117,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
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Mathlib/Algebra/Squarefree.lean | Squarefree.of_mul_left | [] | [
80,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
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Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.isOpen_image_coe | [
{
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"state_before": "X : Type u_1\ninst✝ : TopologicalSpace X\ns✝ : Set (OnePoint X)\nt s : Set X\n⊢ IsOpen (some '' s) ↔ IsOpen s",
"tactic": "rw [isOpen_iff_of_not_mem infty_not_mem_image_coe, preimage_image_eq _ coe_injective]"
}
] | [
240,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Logic/Relation.lean | Relation.TransGen.head' | [] | [
376,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Complex.lean | Complex.inv_cpow | [
{
"state_after": "no goals",
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"tactic": "rw [inv_cpow_eq_ite, if_neg hx]"
}
] | [
190,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.sub_one | [] | [
141,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
141,
11
] |
Mathlib/Data/List/Sublists.lean | List.sublists'_reverse | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nl : List α\n⊢ sublists' (reverse l) = map reverse (sublists l)",
"tactic": "simp only [sublists_eq_sublists', map_map, map_id' reverse_reverse, Function.comp]"
}
] | [
194,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Localization.ind | [] | [
372,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.BlankRel.refl | [] | [
126,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.coe_coeHom | [] | [
71,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | Finset.card_le_card_biUnion_add_card_fiber | [
{
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384,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
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Mathlib/Algebra/Lie/Matrix.lean | Matrix.reindexLieEquiv_apply | [] | [
101,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/FieldTheory/Minpoly/Field.lean | minpoly.sub_algebraMap | [
{
"state_after": "no goals",
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163,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Order/Filter/Cofinite.lean | Filter.eventually_cofinite_ne | [] | [
94,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/RingTheory/MvPolynomial/Ideal.lean | MvPolynomial.mem_ideal_span_X_image | [
{
"state_after": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\nx : MvPolynomial σ R\ns : Set σ\nthis :\n x ∈ Ideal.span ((fun s => ↑(monomial s) 1) '' ((fun i => Finsupp.single i 1) '' s)) ↔\n ∀ (xi : σ →₀ ℕ), xi ∈ support x → ∃ si, si ∈ (fun i => Finsupp.single i 1) '' s ∧ si ≤ xi\n⊢ x ∈ Ideal.span ... | [
57,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | LinearMap.splittingOfFunOnFintypeSurjective_splits | [
{
"state_after": "R : Type u_2\nM : Type u_3\nN : Type ?u.781740\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\ninst✝² : AddCommMonoid N\ninst✝¹ : Module R N\nα : Type u_1\ninst✝ : Fintype α\nf : M →ₗ[R] α → R\ns : Surjective ↑f\nx y : α\n⊢ ↑(comp (comp f (splittingOfFunOnFintypeSurjective... | [
1257,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1250,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.coe_sInf | [] | [
728,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
727,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.prod_coe | [] | [
772,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
771,
1
] |
Mathlib/Order/PFilter.lean | Order.PFilter.mem_principal | [] | [
124,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
9
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.mono | [] | [
456,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
] |
Mathlib/Algebra/Support.lean | Function.support_nat_cast | [] | [
325,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Topology/Order.lean | continuous_top | [] | [
815,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
814,
1
] |
Mathlib/Order/Hom/Lattice.lean | InfTopHom.comp_id | [] | [
968,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
968,
9
] |
Mathlib/Algebra/Order/Field/Basic.lean | StrictMono.div_const | [
{
"state_after": "no goals",
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"tactic": "simpa only [div_e... | [
587,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
1
] |
Mathlib/Data/Bool/Count.lean | List.Chain.count_not | [
{
"state_after": "x : Bool\nl : List Bool\nh : Chain (fun x x_1 => x ≠ x_1) (!x) (x :: l)\n⊢ count (!!x) (x :: l) = count (!x) (x :: l) + length (x :: l) % 2",
"state_before": "b x : Bool\nl : List Bool\nh : Chain (fun x x_1 => x ≠ x_1) b (x :: l)\n⊢ count (!b) (x :: l) = count b (x :: l) + length (x :: l) ... | [
56,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Analysis/Convex/Basic.lean | convex_Ioi | [] | [
291,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | iteratedFDerivWithin_succ_apply_left | [] | [
799,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
] |
Mathlib/Data/Polynomial/Mirror.lean | Polynomial.mirror_natDegree | [
{
"state_after": "case pos\nR : Type u_1\ninst✝ : Semiring R\np q : R[X]\nhp : p = 0\n⊢ natDegree (mirror p) = natDegree p\n\ncase neg\nR : Type u_1\ninst✝ : Semiring R\np q : R[X]\nhp : ¬p = 0\n⊢ natDegree (mirror p) = natDegree p",
"state_before": "R : Type u_1\ninst✝ : Semiring R\np q : R[X]\n⊢ natDegree... | [
75,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup_singleton'' | [
{
"state_after": "case a\nF : Type ?u.416774\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.416783\nι : Type ?u.416786\nκ : Type ?u.416789\ninst✝ : DecidableEq α\ns : Finset β\nf : β → α\na : α\n⊢ (a ∈ sup s fun b => {f b}) ↔ a ∈ image f s",
"state_before": "F : Type ?u.416774\nα : Type u_1\nβ : Type u_2\nγ : Typ... | [
1798,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1794,
1
] |
Mathlib/Data/Set/Basic.lean | Set.not_nonempty_iff_eq_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns✝ s₁ s₂ t t₁ t₂ u s : Set α\n⊢ ¬Set.Nonempty s ↔ s = ∅",
"tactic": "simp only [Set.Nonempty, not_exists, eq_empty_iff_forall_not_mem]"
}
] | [
604,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
] |
Mathlib/Data/Real/Pi/Wallis.lean | Real.tendsto_prod_pi_div_two | [] | [
130,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/RingTheory/Noetherian.lean | isNoetherian_of_injective | [] | [
147,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.map_mul_right_ae | [] | [
308,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Topology/Order/Basic.lean | mem_nhdsWithin_Ici_iff_exists_Ico_subset' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : TopologicalSpace α\ninst✝¹ : LinearOrder α\ninst✝ : OrderTopology α\na u' : α\ns : Set α\nhu' : a < u'\n⊢ List.get?\n [s ∈ 𝓝[Ici a] a, s ∈ 𝓝[Icc a u'] a, s ∈ 𝓝[Ico a u'] a, ∃ u, u ∈ Ioc a u' ∧ Ico a u ⊆ s,\n ... | [
1765,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1763,
1
] |
Mathlib/Order/SymmDiff.lean | bot_symmDiff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.18813\nα : Type u_1\nβ : Type ?u.18819\nπ : ι → Type ?u.18824\ninst✝ : GeneralizedCoheytingAlgebra α\na b c d : α\n⊢ ⊥ ∆ a = a",
"tactic": "rw [symmDiff_comm, symmDiff_bot]"
}
] | [
133,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Std/Data/List/Lemmas.lean | List.dropLast_nil | [] | [
485,
58
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
485,
9
] |
Mathlib/Topology/Sequences.lean | tendsto_nhds_iff_seq_tendsto | [
{
"state_after": "X : Type u_1\nY : Type u_2\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : FrechetUrysohnSpace X\nf : X → Y\na : X\nb : Y\nh : ∀ (u : ℕ → X), Tendsto u atTop (𝓝 a) → Tendsto (f ∘ u) atTop (𝓝 b)\n⊢ ∀ (ib : Set Y), ¬b ∈ ib ∧ IsClosed ib → ∃ ia, (¬a ∈ ia ∧ IsClosed ia) ∧ ∀ (x... | [
155,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
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