file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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values | start list |
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Mathlib/Algebra/Algebra/Unitization.lean | Unitization.snd_zero | [] | [
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Mathlib/FieldTheory/Finite/Basic.lean | FiniteField.isSquare_iff | [
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Mathlib/Order/Filter/Basic.lean | Filter.eventuallyEq_of_left_inv_of_right_inv | [] | [
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Mathlib/Analysis/Convex/Star.lean | starConvex_zero_iff | [
{
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Mathlib/Init/Algebra/Classes.lean | not_lt_of_lt | [] | [
432,
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Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.lift_spec_mul_add | [
{
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Mathlib/Data/Finset/Lattice.lean | Finset.sup_sdiff_left | [
{
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Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_const_mul_Iic | [] | [
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37
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Mathlib/RingTheory/IntegralClosure.lean | isIntegral_zero | [] | [
481,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
480,
1
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Mathlib/Topology/MetricSpace/GromovHausdorffRealized.lean | GromovHausdorff.maxVar_bound | [
{
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Mathlib/Data/List/AList.lean | AList.insertRec_insert | [
{
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387,
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Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.iUnion_ofWithBot | [
{
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431,
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Mathlib/Order/Filter/Germ.lean | Filter.const_eventuallyEq | [] | [
67,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
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Mathlib/Data/Int/Cast/Lemmas.lean | Int.cast_natAbs | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Star/Subalgebra.lean | Subalgebra.coe_star | [] | [
368,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/FreeAlgebra.lean | FreeAlgebra.liftAux_eq | [
{
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328,
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Mathlib/Data/Finset/Fold.lean | Finset.fold_insert | [
{
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58,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.centralizer_le | [] | [
541,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
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Mathlib/Order/RelClasses.lean | wellFoundedLT_dual_iff | [] | [
374,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
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Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.angle_zero_right | [
{
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"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y x : V\n⊢ angle x 0 = π / 2",
"tactic": "unfold angle"
... | [
129,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
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src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Poly.denote_le_cancel_eq | [] | [
506,
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] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
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Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.isLocalization_iff_of_base_ringEquiv | [
{
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818,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Data/PairingHeap.lean | Std.PairingHeapImp.Heap.noSibling_merge | [
{
"state_after": "α : Type u_1\nle : α → α → Bool\ns₁ s₂ : Heap α\n⊢ NoSibling\n (match s₁, s₂ with\n | nil, nil => nil\n | nil, node a₂ c₂ sibling => node a₂ c₂ nil\n | node a₁ c₁ sibling, nil => node a₁ c₁ nil\n | node a₁ c₁ sibling, node a₂ c₂ sibling_1 =>\n if le a₁ a₂ = true then node a... | [
94,
40
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/RingTheory/NonZeroDivisors.lean | prod_zero_iff_exists_zero | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/SymmDiff.lean | symmDiff_sdiff_eq_sup | [
{
"state_after": "ι : Type ?u.32022\nα : Type u_1\nβ : Type ?u.32028\nπ : ι → Type ?u.32033\ninst✝ : GeneralizedCoheytingAlgebra α\na b c d : α\n⊢ a \\ (b \\ a) ⊔ b \\ a = a ⊔ b",
"state_before": "ι : Type ?u.32022\nα : Type u_1\nβ : Type ?u.32028\nπ : ι → Type ?u.32033\ninst✝ : GeneralizedCoheytingAlgebra ... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
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Mathlib/Data/Subtype.lean | Subtype.forall' | [] | [
53,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
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Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.BinaryCofan.mk_inr | [] | [
336,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/Topology/Filter.lean | Filter.sInter_nhds | [] | [
152,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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] |
Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.coeff_zero_eq_aeval_zero | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurableSet_interior | [] | [
311,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
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Mathlib/Algebra/Order/Hom/Monoid.lean | monotone_iff_map_nonneg | [
{
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"state_before": "F : Type u_3\nα : Type u_1\nβ : Type u_2... | [
243,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
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Mathlib/Analysis/NormedSpace/Exponential.lean | expSeries_div_summable_of_mem_ball | [] | [
347,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
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Mathlib/Topology/MetricSpace/GromovHausdorffRealized.lean | GromovHausdorff.HD_lipschitz_aux3 | [] | [
409,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
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Mathlib/Topology/SubsetProperties.lean | isPreirreducible_singleton | [] | [
1712,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1711,
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Std/Logic.lean | Decidable.or_iff_not_and_not | [
{
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"tactic": "rw [← not_or, not_not]"
}
] | [
606,
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1
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Mathlib/Analysis/Calculus/MeanValue.lean | StrictMonoOn.strictConvexOn_of_deriv | [
{
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68
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src/lean/Init/SimpLemmas.lean | false_iff | [] | [
96,
94
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
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Mathlib/Data/Set/Lattice.lean | Set.iUnion_prod_of_monotone | [
{
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Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_union_ne_top | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/InnerProductSpace/Basic.lean | real_inner_div_norm_mul_norm_eq_neg_one_of_ne_zero_of_neg_mul | [
{
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71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.cast_toNat_of_aleph0_le | [
{
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}
] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1689,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.add_le_add_iff_left | [] | [
774,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
773,
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Mathlib/Analysis/Convex/Between.lean | wbtw_smul_vadd_smul_vadd_of_nonneg_of_le | [
{
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... | [
771,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integral_Icc_eq_integral_Ioc' | [] | [
612,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
610,
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Mathlib/Computability/Halting.lean | Nat.Partrec'.to_part | [
{
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306,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/Analysis/NormedSpace/ContinuousAffineMap.lean | ContinuousAffineMap.neg_contLinear | [] | [
148,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/GroupTheory/SpecificGroups/Dihedral.lean | DihedralGroup.card | [
{
"state_after": "no goals",
"state_before": "n : ℕ\ninst✝ : NeZero n\n⊢ Fintype.card (DihedralGroup n) = 2 * n",
"tactic": "rw [← Fintype.card_eq.mpr ⟨fintypeHelper⟩, Fintype.card_sum, ZMod.card, two_mul]"
}
] | [
126,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/RingTheory/Polynomial/RationalRoot.lean | den_dvd_of_is_root | [
{
"state_after": "A : Type u_1\nK : Type u_2\ninst✝⁵ : CommRing A\ninst✝⁴ : IsDomain A\ninst✝³ : UniqueFactorizationMonoid A\ninst✝² : Field K\ninst✝¹ : Algebra A K\ninst✝ : IsFractionRing A K\np : A[X]\nr : K\nhr : ↑(aeval r) p = 0\n⊢ ↑(den A r) ∣ leadingCoeff p * num A r ^ natDegree p",
"state_before": "A... | [
118,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | List.stronglyMeasurable_prod | [
{
"state_after": "no goals",
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556,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
1
] |
Mathlib/Topology/Partial.lean | pcontinuous_iff' | [
{
"state_after": "case mp\nα : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α →. β\n⊢ PContinuous f → ∀ {x : α} {y : β}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)\n\ncase mpr\nα : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α →. β\n⊢ (∀ ... | [
86,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.bmex_le_blsub | [] | [
2103,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2101,
1
] |
Mathlib/Data/Nat/Dist.lean | Nat.dist_eq_sub_of_le_right | [
{
"state_after": "n m : ℕ\nh : m ≤ n\n⊢ dist m n = n - m",
"state_before": "n m : ℕ\nh : m ≤ n\n⊢ dist n m = n - m",
"tactic": "rw [dist_comm]"
},
{
"state_after": "no goals",
"state_before": "n m : ℕ\nh : m ≤ n\n⊢ dist m n = n - m",
"tactic": "apply dist_eq_sub_of_le h"
}
] | [
54,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.trans_apply | [] | [
2032,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2030,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidWithZeroHom.coe_comp | [] | [
1108,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1107,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.isIso_colimit_cocone_parallelPair_of_eq | [] | [
1051,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1049,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.reachable_deleteEdges_iff_exists_cycle.aux | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\ninst✝ : DecidableEq V\nu v w : V\nhb : ∀ (p : Walk G v w), Quotient.mk (Sym2.Rel.setoid V) (v, w) ∈ Walk.edges p\nc : Walk G u u\nhc : Walk.IsTrail c\nhe : Quotient.mk (Sym2.Rel.setoid V) (v, ... | [
2495,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2471,
1
] |
Mathlib/Order/Basic.lean | exists_ge_of_linear | [] | [
496,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.relindex_eq_zero_of_le_right | [] | [
387,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Data/Subtype.lean | Subtype.coind_surjective | [] | [
193,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.cos_add_int_mul_two_pi | [] | [
1244,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1243,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Localization.mk_le_mk | [] | [
1947,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1946,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieModuleHom.mem_range | [] | [
1222,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1221,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEFinStronglyMeasurable.neg | [] | [
1888,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1886,
11
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.map_mul_left | [
{
"state_after": "no goals",
"state_before": "M : Type u_2\ninst✝³ : CommMonoid M\nS : Submonoid M\nN : Type u_4\ninst✝² : CommMonoid N\nP : Type u_3\ninst✝¹ : CommMonoid P\nf : LocalizationMap S N\ng : M →* P\nhg : ∀ (y : { x // x ∈ S }), IsUnit (↑g ↑y)\nT : Submonoid P\nhy : ∀ (y : { x // x ∈ S }), ↑g ↑y ... | [
1198,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1197,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.not_mem_empty | [] | [
828,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
827,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.rpow_one_div_le_iff | [
{
"state_after": "x y : ℝ≥0∞\nz : ℝ\nhz : 0 < z\n⊢ x ^ (1 / z) ≤ y ^ 1 ↔ x ≤ y ^ z",
"state_before": "x y : ℝ≥0∞\nz : ℝ\nhz : 0 < z\n⊢ x ^ (1 / z) ≤ y ↔ x ≤ y ^ z",
"tactic": "nth_rw 1 [← ENNReal.rpow_one y]"
},
{
"state_after": "x y : ℝ≥0∞\nz : ℝ\nhz : 0 < z\n⊢ x ^ (1 / z) ≤ y ^ (z * z⁻¹) ↔ x ≤... | [
596,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.nthHom_zero | [
{
"state_after": "p : ℕ\nhp_prime : Fact (Nat.Prime p)\nR : Type u_1\ninst✝ : NonAssocSemiring R\nf : (k : ℕ) → R →+* ZMod (p ^ k)\nf_compat : ∀ (k1 k2 : ℕ) (hk : k1 ≤ k2), RingHom.comp (ZMod.castHom (_ : p ^ k1 ∣ p ^ k2) (ZMod (p ^ k1))) (f k2) = f k1\n⊢ (fun n => 0) = 0",
"state_before": "p : ℕ\nhp_prime ... | [
495,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
495,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.invFun_eq_symm | [] | [
344,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/CategoryTheory/Abelian/Pseudoelements.lean | CategoryTheory.Abelian.Pseudoelement.pseudo_exact_of_exact | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : Abelian C\nP Q R : C\nf : P ⟶ Q\ng : Q ⟶ R\nh : Exact f g\na : Pseudoelement P\n⊢ pseudoApply 0 a = 0",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : Abelian C\nP Q R : C\nf : P ⟶ Q\ng : Q ⟶ R\nh : Exact f g\na : Pseudoelement P\n⊢ pseud... | [
389,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Data/Finmap.lean | Finmap.lookup_erase | [] | [
450,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
1
] |
Mathlib/Topology/Algebra/Polynomial.lean | Polynomial.continuousWithinAt_aeval | [] | [
93,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
11
] |
Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.divByMonic_eq_div | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝ : Field R\np✝ q p : R[X]\nhq : Monic q\n⊢ p /ₘ q = ↑C (leadingCoeff q)⁻¹ * (p /ₘ (q * ↑C (leadingCoeff q)⁻¹))",
"tactic": "simp only [Monic.def.1 hq, inv_one, C_1, one_mul, mul_one]"
}
] | [
207,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.cosh_sub_sinh | [
{
"state_after": "x y : ℝ\n⊢ ↑(cosh x - sinh x) = ↑(exp (-x))",
"state_before": "x y : ℝ\n⊢ cosh x - sinh x = exp (-x)",
"tactic": "rw [← ofReal_inj]"
},
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ ↑(cosh x - sinh x) = ↑(exp (-x))",
"tactic": "simp"
}
] | [
1423,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1421,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.nthRoots_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np q : R[X]\nr : R\n⊢ nthRoots 0 r = 0",
"tactic": "simp only [empty_eq_zero, pow_zero, nthRoots, ← C_1, ← C_sub, roots_C]"
}
] | [
786,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
785,
1
] |
Mathlib/Order/Lattice.lean | Prod.sup_def | [] | [
1298,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1297,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_indicator_const | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.952854\nγ : Type ?u.952857\nδ : Type ?u.952860\nm : MeasurableSpace α\nμ ν : Measure α\ns : Set α\nhs : MeasurableSet s\nc : ℝ≥0∞\n⊢ (∫⁻ (a : α), indicator s (fun x => c) a ∂μ) = c * ↑↑μ s",
"tactic": "rw [lintegral_indicator _ hs, ... | [
793,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
791,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.multiplicity_lt_iff_neg_dvd | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : Monoid α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\na b : α\nk : ℕ\n⊢ multiplicity a b < ↑k ↔ ¬a ^ k ∣ b",
"tactic": "rw [pow_dvd_iff_le_multiplicity, not_le]"
}
] | [
155,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/MeasureTheory/Measure/Stieltjes.lean | StieltjesFunction.id_leftLim | [] | [
266,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/RingTheory/Artinian.lean | IsArtinianRing.localization_surjective | [
{
"state_after": "R : Type u_1\ninst✝⁴ : CommRing R\ninst✝³ : IsArtinianRing R\nS : Submonoid R\nL : Type u_2\ninst✝² : CommRing L\ninst✝¹ : Algebra R L\ninst✝ : IsLocalization S L\nr' : L\n⊢ ∃ a, ↑(algebraMap R L) a = r'",
"state_before": "R : Type u_1\ninst✝⁴ : CommRing R\ninst✝³ : IsArtinianRing R\nS : S... | [
441,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.Ordered.mem_find? | [
{
"state_after": "α : Type u_1\ncmp : α → α → Ordering\ncut : α → Ordering\nt : RBNode α\nx : α\ninst✝¹ : TransCmp cmp\ninst✝ : IsStrictCut cmp cut\nht : Ordered cmp t\nx✝ : x ∈ t ∧ cut x = Ordering.eq\nhx : x ∈ t\ne : cut x = Ordering.eq\n⊢ x ∈ find? cut t",
"state_before": "α : Type u_1\ncmp : α → α → Ord... | [
212,
98
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
208,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.leadingCoeff_divByMonic_X_sub_C | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\na✝ b : R\nn : ℕ\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\np✝ q p : R[X]\nhp : degree p ≠ 0\na : R\ninst✝ : Nontrivial R\n⊢ leadingCoeff (p /ₘ (X - ↑C a)) = leadingCoeff p",
"state_before": "R : Type u\nS : Type v\nT : Type w\na✝ b : R\nn : ℕ\ninst✝¹ : C... | [
1023,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1017,
1
] |
Mathlib/Analysis/LocallyConvex/Basic.lean | Set.Finite.absorbs_iUnion | [
{
"state_after": "case intro\n𝕜 : Type u_3\n𝕝 : Type ?u.5168\nE : Type u_2\nι✝ : Sort ?u.5174\nκ : ι✝ → Sort ?u.5179\ninst✝¹ : SeminormedRing 𝕜\ninst✝ : SMul 𝕜 E\ns✝ t✝ u v A B : Set E\nι : Type u_1\ns : Set E\nf : ι → Set E\nt : Finset ι\n⊢ Absorbs 𝕜 s (⋃ (i : ι) (_ : i ∈ ↑t), f i) ↔ ∀ (i : ι), i ∈ ↑t → A... | [
119,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.toAddSubmonoid_closure | [] | [
109,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/RingTheory/ClassGroup.lean | ClassGroup.mk_eq_one_iff | [
{
"state_after": "R : Type u_2\nK : Type u_1\nL : Type ?u.1775691\ninst✝¹⁰ : CommRing R\ninst✝⁹ : Field K\ninst✝⁸ : Field L\ninst✝⁷ : DecidableEq L\ninst✝⁶ : Algebra R K\ninst✝⁵ : IsFractionRing R K\ninst✝⁴ : Algebra K L\ninst✝³ : FiniteDimensional K L\ninst✝² : Algebra R L\ninst✝¹ : IsScalarTower R K L\ninst✝ ... | [
381,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/Algebra/Regular/SMul.lean | isLeftRegular_iff | [] | [
48,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | mul_nonneg_iff_left_nonneg_of_pos | [] | [
935,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
934,
1
] |
Mathlib/Analysis/Calculus/ParametricIntegral.lean | hasFDerivAt_integral_of_dominated_loc_of_lip' | [
{
"state_after": "α : Type u_4\ninst✝⁷ : MeasurableSpace α\nμ : MeasureTheory.Measure α\n𝕜 : Type u_1\ninst✝⁶ : IsROrC 𝕜\nE : Type u_3\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : CompleteSpace E\nH : Type u_2\ninst✝¹ : NormedAddCommGroup H\ninst✝ : NormedSpace... | [
147,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.PullbackCone.mk_fst | [] | [
601,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
600,
1
] |
Mathlib/Analysis/Calculus/FormalMultilinearSeries.lean | FormalMultilinearSeries.ext | [] | [
83,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
11
] |
Mathlib/Order/UpperLower/Hom.lean | UpperSet.coe_iciSupHom | [] | [
39,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/Data/List/MinMax.lean | List.le_minimum_of_mem' | [] | [
367,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.subset_closure | [] | [
807,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
807,
1
] |
Mathlib/Topology/Semicontinuous.lean | UpperSemicontinuousOn.add' | [] | [
919,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
915,
1
] |
Mathlib/Algebra/Module/Submodule/Pointwise.lean | Submodule.coe_set_neg | [] | [
68,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
src/lean/Init/Data/Nat/Div.lean | Nat.div_rec_lemma | [] | [
13,
65
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
12,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.lt_ceil | [] | [
283,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.map_id | [] | [
229,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
8
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.subtypeDomain_smul | [] | [
517,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup_mono_fun | [] | [
151,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.abs_exp_ofReal | [
{
"state_after": "x : ℝ\n⊢ ↑abs ↑(Real.exp x) = Real.exp x",
"state_before": "x : ℝ\n⊢ ↑abs (exp ↑x) = Real.exp x",
"tactic": "rw [← ofReal_exp]"
},
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ ↑abs ↑(Real.exp x) = Real.exp x",
"tactic": "exact abs_of_nonneg (le_of_lt (Real.exp... | [
2032,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2030,
1
] |
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