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 |
|---|---|---|---|---|---|---|
Std/Data/List/Basic.lean | List.scanlTR_go_eq | [
{
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"tactic": "simp [scanlTR.go, scanl]"
},
{
"state_after": "no goals",
"state_before": "α✝¹ : Type u_1\nα✝ : Type u_2\... | [
642,
59
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Mathlib/Analysis/Calculus/FDeriv/Add.lean | Differentiable.sub_const | [] | [
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69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.Measure.pi_ball | [
{
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407,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.as_sum_support_C_mul_X_pow | [
{
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"tactic": "simp only [C_mul_X_pow_eq_monomial]"
}
] | [
391,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.map_le | [] | [
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23
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Mathlib/Data/Finset/LocallyFinite.lean | BddAbove.finite | [] | [
494,
17
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493,
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Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.cos_angle_mul_norm_mul_norm | [
{
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"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y✝ x y : V\n⊢ cos (angle x y) * (‖x‖ * ‖y‖) = inner x y",
"tactic... | [
185,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | WithTop.isLUB_sSup' | [
{
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1110,
1
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Mathlib/Data/Fin/Basic.lean | Fin.heq_fun_iff | [
{
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"state_before": "n m : ℕ\nα : Sort u_1\nk l : ℕ\nh : k = l\nf : Fin k → α\ng : Fin l → α\n⊢ HEq f g ↔ ∀ (i : Fin k), f i = g { val := ↑i, isLt := (_ : ↑i < l) }",
"ta... | [
237,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
11
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.eraseMin.valid | [
{
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1412,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1410,
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Mathlib/Data/Finsupp/Order.lean | Finsupp.tsub_apply | [] | [
199,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.le_measure_diff | [] | [
249,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
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Mathlib/Algebra/GroupPower/Lemmas.lean | zsmul_eq_mul' | [
{
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"tactic": "rw [zsmul_eq_mul, (n.cast_commute a).eq]"
}
] | [
597,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Constructions.lean | ContinuousAt.prod_map | [] | [
608,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
606,
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Mathlib/GroupTheory/Index.lean | Subgroup.relindex_dvd_of_le_left | [] | [
176,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
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Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.mem_mk | [] | [
74,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Stream/Init.lean | Stream'.get?_take_succ | [] | [
607,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
605,
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.ofFinsupp_erase | [
{
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1031,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1028,
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_bij' | [
{
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577,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
566,
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Mathlib/FieldTheory/RatFunc.lean | RatFunc.lift_on_condition_of_lift_on'_condition | [
{
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"tactic": "rw [h,... | [
181,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
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Mathlib/CategoryTheory/Monoidal/Limits.lean | CategoryTheory.Limits.limitFunctorial_map | [] | [
47,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
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Mathlib/Order/Monotone/Basic.lean | Antitone.comp_monotone | [] | [
649,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
1
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Mathlib/Order/UpperLower/Basic.lean | UpperSet.Ici_bot | [] | [
1128,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1127,
8
] |
Mathlib/GroupTheory/PGroup.lean | IsPGroup.to_sup_of_normal_left' | [] | [
340,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/InverseDeriv.lean | Real.differentiableOn_arcsin | [] | [
122,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
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Mathlib/Algebra/Module/Zlattice.lean | Zspan.fract_fract | [
{
"state_after": "no goals",
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127,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
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Mathlib/Analysis/Normed/Group/Basic.lean | norm_pow_le_mul_norm | [
{
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Mathlib/Topology/Separation.lean | Continuous.isClosedMap | [] | [
1332,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1331,
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Mathlib/Order/Atoms.lean | GaloisCoinsertion.isAtom_iff | [] | [
794,
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791,
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Mathlib/Combinatorics/Derangements/Finite.lean | numDerangements_add_two | [] | [
88,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
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Mathlib/Topology/Instances/ENNReal.lean | Real.tsum_le_of_sum_range_le | [] | [
1358,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1356,
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Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.translationNumber_eq_of_tendsto₀' | [
{
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"tactic": "exact_mod_cast h"
}
] | [
665,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
663,
1
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Mathlib/Order/Hom/Basic.lean | OrderIso.funUnique_symm_apply | [] | [
1110,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1108,
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Mathlib/Data/Dfinsupp/WellFounded.lean | Dfinsupp.wellFoundedLT | [
{
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235,
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218,
11
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Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.symm_trans | [] | [
849,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
847,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.mono | [] | [
448,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
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Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | UniformFun.hasBasis_nhds_of_basis | [] | [
333,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
11
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Mathlib/Geometry/Euclidean/Sphere/Basic.lean | EuclideanGeometry.Sphere.mem_coe' | [] | [
96,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
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Std/Logic.lean | imp.swap | [] | [
126,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
126,
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Iso.symm_apply_reachable | [
{
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"tactic": "rw [← Iso.reachable... | [
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52
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1913,
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Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPushout.of_iso_pushout | [] | [
447,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
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Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_mul_top | [
{
"state_after": "no goals",
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"tactic": "rw [toReal_mul, top_toReal, mul_zero]"
}
] | [
2259,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2258,
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Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isNat_eq_false | [
{
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"tactic": "simp"
},
{
"st... | [
681,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
679,
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Mathlib/Topology/LocallyConstant/Basic.lean | IsLocallyConstant.apply_eq_of_isPreconnected | [
{
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"state_before": "X : Type u_1\nY : Type u_2\nZ : Type ... | [
162,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
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Mathlib/Analysis/Complex/LocallyUniformLimit.lean | Complex.cderiv_eq_deriv | [] | [
51,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
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Mathlib/Logic/Equiv/Defs.lean | Equiv.cast_apply | [] | [
312,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
9
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Mathlib/Topology/Algebra/Order/IntermediateValue.lean | isPreconnected_Iio | [] | [
446,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
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Mathlib/Analysis/Calculus/FDerivAnalytic.lean | HasFPowerSeriesAt.hasStrictDerivAt | [] | [
174,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
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] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.real_toNNReal | [] | [
1487,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1485,
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Mathlib/Topology/Sheaves/Presheaf.lean | TopCat.Presheaf.Pullback.id_inv_app | [
{
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"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : HasColimits C\nX Y : TopCat\nℱ : Presheaf C Y\nU : Opens ↑Y\n⊢ (Functor.op (Opens.map (𝟙 Y))).obj U.op = U.op",
"tactic": "simp"
},
{
"state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : HasColimits C\nX ... | [
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37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
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] |
Mathlib/Algebra/Polynomial/GroupRingAction.lean | Polynomial.eval_smul' | [
{
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"state_before": "M : Type ?u.43976\ninst✝⁶ : Monoid M\nR : Type ?u.43982\ninst✝⁵ : Semiring R\ninst✝⁴ : MulSemiringAction M R\nS : Type u_2\ninst✝³ : CommSemiring S\ninst✝² : MulSemiringAction M S\nG : Type u_1\ninst✝¹ : Group G\ninst✝ : MulSemiringAction G S\ng : G\nf : S[X]\nx... | [
79,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.finset_card_neighborSet_eq_degree | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.200590\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : Subgraph G\na b : V\nG' : Subgraph G\nv : V\ninst✝ : Fintype ↑(neighborSet G' v)\n⊢ Finset.card (Set.toFinset (neighborSet G' v)) = degree G' v",
"tactic": "rw [degree, Set.toFinset_card]... | [
804,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
802,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_set_neg | [
{
"state_after": "no goals",
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"tactic": "simp_rw [← image_smul, ← image_neg, image_image, smul_neg]... | [
1079,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1078,
1
] |
Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.is_left_invariant_haarContent | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝³ : Group G\ninst✝² : TopologicalSpace G\ninst✝¹ : TopologicalGroup G\ninst✝ : T2Space G\nK₀ : PositiveCompacts G\ng : G\nK : Compacts G\n⊢ (fun s => ↑(Content.toFun (haarContent K₀) s)) (Compacts.map (fun b => g * b) (_ : Continuous fun b => ... | [
576,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
1
] |
Mathlib/Data/Set/Intervals/OrdConnected.lean | Set.ordConnected_uIcc | [] | [
249,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Order/SymmDiff.lean | symmDiff_bot | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.18260\nα : Type u_1\nβ : Type ?u.18266\nπ : ι → Type ?u.18271\ninst✝ : GeneralizedCoheytingAlgebra α\na b c d : α\n⊢ a ∆ ⊥ = a",
"tactic": "rw [symmDiff, sdiff_bot, bot_sdiff, sup_bot_eq]"
}
] | [
129,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Data/Real/CauSeq.lean | exists_forall_ge_and | [] | [
46,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.ball_subset_closedBall | [] | [
553,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.inv_trans_self | [] | [
167,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.range_le_ker_iff | [
{
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1426,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1423,
1
] |
Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.transpose_le_iff | [
{
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"state_before": "μ ν : YoungDiagram\nh : transpose μ ≤ transpose ν\n⊢ μ ≤ ν",
"tactic": "convert YoungDiagram.le_of_transpose_le h"
},
{
"state_after": "no goals",
"state_before"... | [
254,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Data/PNat/Xgcd.lean | PNat.XgcdType.isReduced_iff | [] | [
177,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.OpenNhdsOf.basis_nhds | [] | [
467,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.mapRange_def | [
{
"state_after": "case h\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝⁴ : (i : ι) → Zero (β i)\ninst✝³ : (i : ι) → (x : β i) → Decidable (x ≠ 0)\ninst✝² : (i : ι) → Zero (β₁ i)\ninst✝¹ : (i : ι) → Zero (β₂ i)\ninst✝ : (i : ι) → (x : β₁ i) → Decidable (x ... | [
1180,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1176,
1
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Mathlib/Topology/MetricSpace/Basic.lean | totallyBounded_Ioc | [] | [
1428,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1427,
1
] |
Mathlib/GroupTheory/Congruence.lean | Con.ext'_iff | [] | [
218,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Analysis/NormedSpace/Basic.lean | nnnorm_algebraMap | [] | [
507,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Mathlib/RingTheory/WittVector/IsPoly.lean | WittVector.bind₁_zero_wittPolynomial | [
{
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"state_before": "p : ℕ\nR S : Type u\nσ : Type ?u.653400\nidx : Type ?u.653403\ninst✝² : CommRing R\ninst✝¹ : CommRing S\ninst✝ : Fact (Nat.Prime p)\nn : ℕ\n⊢ ↑(bind₁ 0) (wittPolynomial p R n) = 0",
"tactic": "rw [← aeval_eq_bind₁, aeval_zero, constantCoeff_wittPolynomial, R... | [
498,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
] |
Mathlib/Analysis/NormedSpace/Basic.lean | norm_algebraMap | [
{
"state_after": "α : Type ?u.431038\nβ : Type ?u.431041\nγ : Type ?u.431044\nι : Type ?u.431047\n𝕜 : Type u_2\n𝕜' : Type u_1\ninst✝² : NormedField 𝕜\ninst✝¹ : SeminormedRing 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nx : 𝕜\n⊢ ‖x • 1‖ = ‖x‖ * ‖1‖",
"state_before": "α : Type ?u.431038\nβ : Type ?u.431041\nγ : Ty... | [
503,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/GroupTheory/Transfer.lean | Subgroup.leftTransversals.diff_mul_diff | [
{
"state_after": "no goals",
"state_before": "G : Type u_2\ninst✝² : Group G\nH : Subgroup G\nA : Type u_1\ninst✝¹ : CommGroup A\nϕ : { x // x ∈ H } →* A\nR S T : ↑(leftTransversals ↑H)\ninst✝ : FiniteIndex H\nq : G ⧸ H\nx✝ : q ∈ univ\n⊢ {\n val :=\n (↑(↑(MemLeftTransversals.toEquiv (_ : ↑R ... | [
66,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Differentiable.csin | [] | [
404,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/AlgebraicGeometry/SheafedSpace.lean | AlgebraicGeometry.SheafedSpace.mk_coe | [] | [
75,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.add_ofNat' | [
{
"state_after": "α : Type ?u.188122\nm n : ℕ\nthis : ∀ {n : ℕ}, ofNat' (Nat.succ n) = ofNat' n + 1\n⊢ ofNat' (m + n) = ofNat' m + ofNat' n",
"state_before": "α : Type ?u.188122\nm n : ℕ\n⊢ ofNat' (m + n) = ofNat' m + ofNat' n",
"tactic": "have : ∀ {n}, ofNat' n.succ = ofNat' n + 1 := ofNat'_succ"
},
... | [
270,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Std/Data/String/Lemmas.lean | String.mk_length | [] | [
24,
83
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
24,
9
] |
Mathlib/Topology/Sober.lean | IsGenericPoint.mem_closed_set_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.2539\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nx y : α\nS U Z : Set α\nh : IsGenericPoint x S\nhZ : IsClosed Z\n⊢ x ∈ Z ↔ S ⊆ Z",
"tactic": "rw [← h.def, hZ.closure_subset_iff, singleton_subset_iff]"
}
] | [
100,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.divInt_mul_divInt_cancel | [
{
"state_after": "case pos\na b c : ℚ\nx : ℤ\nhx : x ≠ 0\nn d : ℤ\nhd : d = 0\n⊢ n /. x * (x /. d) = n /. d\n\ncase neg\na b c : ℚ\nx : ℤ\nhx : x ≠ 0\nn d : ℤ\nhd : ¬d = 0\n⊢ n /. x * (x /. d) = n /. d",
"state_before": "a b c : ℚ\nx : ℤ\nhx : x ≠ 0\nn d : ℤ\n⊢ n /. x * (x /. d) = n /. d",
"tactic": "by... | [
490,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.mem_eqLocus | [] | [
1269,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1268,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | stronglyMeasurable_iff_measurable_separable | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.136321\nι : Type ?u.136324\ninst✝⁴ : Countable ι\nf g : α → β\nm : MeasurableSpace α\ninst✝³ : TopologicalSpace β\ninst✝² : PseudoMetrizableSpace β\ninst✝¹ : MeasurableSpace β\ninst✝ : BorelSpace β\n⊢ Measurable f ∧ IsSeparable (range f) → StronglyMeasur... | [
672,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
650,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.Disjoint.symm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nf g h : Perm α\n⊢ Disjoint f g → Disjoint g f",
"tactic": "simp only [Disjoint, or_comm, imp_self]"
}
] | [
47,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.inr_sum | [] | [
380,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | orderOf_dvd_card_univ | [
{
"state_after": "no goals",
"state_before": "G : Type u\nA : Type v\nx y : G\na b : A\nn m : ℕ\ninst✝² : Group G\ninst✝¹ : AddGroup A\ninst✝ : Fintype G\n⊢ orderOf x ∣ Fintype.card G",
"tactic": "classical\n have ft_prod : Fintype ((G ⧸ zpowers x) × zpowers x) :=\n Fintype.ofEquiv G groupEquivQuoti... | [
922,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
901,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | CategoryTheory.Limits.IsInitial.mono_from | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\ninst✝ : InitialMonoClass C\nI X : C\nhI : IsInitial I\nf : I ⟶ X\n⊢ Mono (to hI X)",
"state_before": "C : Type u₁\ninst✝¹ : Category C\ninst✝ : InitialMonoClass C\nI X : C\nhI : IsInitial I\nf : I ⟶ X\n⊢ Mono f",
"tactic": "rw [hI.hom_ext f (hI.to X)]"... | [
514,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
1
] |
Mathlib/Order/Basic.lean | Subtype.mk_lt_mk | [] | [
1140,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1138,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.comp_isOpenMap_iff | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type ?u.72267\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nh : α ≃ₜ β\nf : γ → α\n⊢ IsOpenMap (↑h ∘ f) → IsOpenMap f",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ... | [
439,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.ofBijective.symm_eq | [] | [
249,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.normSq_smul | [
{
"state_after": "no goals",
"state_before": "S : Type ?u.864368\nT : Type ?u.864371\nR : Type u_1\ninst✝ : CommRing R\nr✝ x y z : R\na b c : ℍ[R]\nr : R\nq : ℍ[R]\n⊢ ↑normSq (r • q) = r ^ 2 * ↑normSq q",
"tactic": "simp only [normSq_def', smul_re, smul_imI, smul_imJ, smul_imK, mul_pow, mul_add, smul_eq... | [
1243,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1242,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.finMeasSupp_iff_support | [] | [
1189,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1188,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.rpow_lt_one_of_one_lt_of_neg | [
{
"state_after": "case none\nz : ℝ\nhz : z < 0\nhx : 1 < none\n⊢ none ^ z < 1\n\ncase some\nz : ℝ\nhz : z < 0\nval✝ : ℝ≥0\nhx : 1 < Option.some val✝\n⊢ Option.some val✝ ^ z < 1",
"state_before": "x : ℝ≥0∞\nz : ℝ\nhx : 1 < x\nhz : z < 0\n⊢ x ^ z < 1",
"tactic": "cases x"
},
{
"state_after": "no g... | [
682,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
677,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.mem_bot | [] | [
405,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Topology/PathConnected.lean | pathComponent_symm | [] | [
917,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
916,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.coeSubmodule_comap | [] | [
730,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
728,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.le_toNNReal_of_coe_le | [] | [
928,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
927,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_finset_product_right | [
{
"state_after": "ι : Type ?u.318416\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ninst✝ : CommMonoid β\nr : Finset (α × γ)\ns : Finset γ\nt : γ → Finset α\nh : ∀ (p : α × γ), p ∈ r ↔ p.snd ∈ s ∧ p.fst ∈ t p.snd\nf : α × γ → β\n⊢ ∏ p in r, f p = ∏ x in Finset.sigma s t, f (x.snd... | [
626,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
619,
1
] |
Mathlib/Data/List/Basic.lean | List.append_eq_cons_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.10352\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ a b c : List α\nx : α\n⊢ a ++ b = x :: c ↔ a = [] ∧ b = x :: c ∨ ∃ a', a = x :: a' ∧ c = a' ++ b",
"tactic": "cases a <;>\n simp only [and_assoc, @eq_comm _ c, nil_append, cons_append,... | [
374,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.self_mul_star | [
{
"state_after": "no goals",
"state_before": "S : Type ?u.725571\nT : Type ?u.725574\nR : Type u_1\ninst✝ : CommRing R\nr x y z : R\na b c : ℍ[R]\n⊢ a * star a = ↑(↑normSq a)",
"tactic": "rw [mul_star_eq_coe, normSq_def]"
}
] | [
1228,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1228,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.prod_target | [] | [
947,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
945,
1
] |
Mathlib/Topology/DenseEmbedding.lean | DenseInducing.comap_nhds_neBot | [
{
"state_after": "case intro.intro.intro\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.5500\nδ : Type ?u.5503\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ni : α → β\ndi✝ : DenseInducing i\ninst✝ : TopologicalSpace δ\nf : γ → α\ng : γ → δ\nh : δ → β\ndi : DenseInducing i\nb : β\ns : Set β\nhs : s ∈ 𝓝 b... | [
138,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.domain_mkSpanSingleton | [] | [
153,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Topology/PartitionOfUnity.lean | BumpCovering.toPartitionOfUnity_apply | [] | [
458,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Mathlib/GroupTheory/Abelianization.lean | abelianizationCongr_symm | [] | [
238,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
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