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/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.mem_fundamentalFrontier | [
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"tactic": "simp [fundamentalFrontier]"
}
] | [
557,
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Mathlib/LinearAlgebra/Span.lean | LinearMap.map_le_map_iff | [
{
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889,
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Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.rootSet_def | [] | [
894,
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892,
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Std/Data/RBMap/Lemmas.lean | Std.RBNode.Path.rootOrdered_iff | [
{
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"tactic": "induction p with\n (simp [All_def] at hp; simp [*, and_assoc,... | [
461,
72
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456,
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Mathlib/GroupTheory/GroupAction/Pi.lean | Pi.faithfulSMul_at | [
{
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"state_before": "I : Type u\nf : I → Type v\nx y : (i : I) → f i\ni✝ : I\nα : Type u_1\ninst✝² : (i : I) → SMul α (f i)\ninst✝¹ : ∀ (i : I), Nonempty (f i)\ni : I\ninst✝ : FaithfulSMul α (f i)\nm₁✝ m₂✝ : α\nh : ∀ (a : (i : I) → f i), m₁✝ • a = m₂✝ • a\na : f i\n⊢ m₁✝ • a = m₂✝ •... | [
118,
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Mathlib/Data/Opposite.lean | Opposite.op_unop | [] | [
67,
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Mathlib/Topology/UnitInterval.lean | unitInterval.le_one' | [] | [
166,
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165,
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Mathlib/CategoryTheory/Sites/Grothendieck.lean | CategoryTheory.GrothendieckTopology.covers_iff | [] | [
186,
10
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185,
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Mathlib/Topology/ContinuousOn.lean | Filter.EventuallyEq.eq_of_nhdsWithin | [] | [
474,
28
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472,
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Mathlib/Algebra/DirectSum/Ring.lean | DirectSum.of_zero_pow | [
{
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"tactic": "rw [pow_zero, pow_zero, DirectSum.of_zero_one]"
},
{
... | [
468,
70
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Mathlib/RingTheory/Polynomial/Vieta.lean | Multiset.prod_X_add_C_coeff | [
{
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"state_before": "R : Type u_1\ninst✝ : CommSemiring R\ns : Multiset R\nk : ℕ\nh : k ≤ ↑card... | [
74,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
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Mathlib/GroupTheory/GroupAction/SubMulAction/Pointwise.lean | SubMulAction.mem_one | [] | [
45,
10
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44,
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Mathlib/Data/List/Basic.lean | List.nthLe_cons_length | [
{
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}
] | [
1370,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1369,
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Mathlib/RingTheory/PowerSeries/Basic.lean | Polynomial.coe_one | [
{
"state_after": "σ : Type ?u.4306859\nR : Type u_1\ninst✝ : CommSemiring R\nφ ψ : R[X]\nthis : ↑(↑(monomial 0) 1) = ↑(PowerSeries.monomial R 0) 1\n⊢ ↑1 = 1",
"state_before": "σ : Type ?u.4306859\nR : Type u_1\ninst✝ : CommSemiring R\nφ ψ : R[X]\n⊢ ↑1 = 1",
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}... | [
2563,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | HomogeneousIdeal.ext | [] | [
98,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
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Mathlib/Topology/PathConnected.lean | Path.coe_reparam | [] | [
731,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
729,
1
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Mathlib/Topology/Sheaves/SheafCondition/PairwiseIntersections.lean | TopCat.Presheaf.isSheaf_iff_isSheafPairwiseIntersections | [
{
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"state_before": "C : Type u\ninst✝ : Category C\nX : TopCat\nF : Presheaf C X\n⊢ IsSheaf F ↔ IsSheafPairwiseIntersections F",
"tactic": "rw [isSheaf_iff_isSheafOpensLeCover,\n isSheafOpensLeCover_iff_isSheafPairwiseIntersections]"
}
] | [
286,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
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Mathlib/Algebra/Lie/Subalgebra.lean | LieEquiv.ofEq_apply | [] | [
791,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
789,
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Mathlib/Data/PNat/Factors.lean | PrimeMultiset.factorMultiset_prod | [
{
"state_after": "case a\nv : PrimeMultiset\n⊢ Coe.coe (PNat.factorMultiset (prod v)) = Coe.coe v",
"state_before": "v : PrimeMultiset\n⊢ PNat.factorMultiset (prod v) = v",
"tactic": "apply PrimeMultiset.coeNat_injective"
},
{
"state_after": "case a\nv : PrimeMultiset\n⊢ toNatMultiset (PNat.fact... | [
277,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
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Mathlib/Topology/UnitInterval.lean | unitInterval.nonneg | [] | [
142,
8
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141,
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Mathlib/Topology/Sequences.lean | tendsto_subseq_of_bounded | [] | [
433,
69
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431,
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Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.functorPullback_union | [] | [
696,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
694,
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Mathlib/Analysis/Normed/Group/Seminorm.lean | NonarchAddGroupSeminorm.add_bddBelow_range_add | [
{
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611,
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Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | Ideal.IsHomogeneous.top | [
{
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Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | HasDerivWithinAt.const_cpow | [] | [
201,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
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Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.lintegral_restrict | [
{
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Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.map_mul | [] | [
226,
19
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225,
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Mathlib/Data/Polynomial/Mirror.lean | Polynomial.mirror_leadingCoeff | [
{
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}
] | [
161,
64
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Mathlib/Data/Fin/Basic.lean | Fin.prop | [] | [
141,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Finset/Basic.lean | List.toFinset_cons | [
{
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"tactic": "by_cases h : a ∈ l <;> simp [Finset.insert_val', Multiset.dedup_cons, h]"
}
] | [
3267,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3266,
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Mathlib/Data/Set/Basic.lean | Set.diff_singleton_sSubset | [
{
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}
] | [
2050,
65
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Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.ElementarilyEquivalent.infinite | [] | [
1142,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1141,
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Mathlib/MeasureTheory/Decomposition/Jordan.lean | MeasureTheory.JordanDecomposition.coe_smul | [
{
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"tactic": "rw [real_smul_def, if_pos (NNReal.coe_nonneg r), Real.toNNReal_coe]"
}
] | [
140,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
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Mathlib/Combinatorics/SimpleGraph/Density.lean | SimpleGraph.interedges_biUnion_right | [] | [
368,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
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Mathlib/Algebra/FreeAlgebra.lean | FreeAlgebra.ι_inj | [] | [
450,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
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Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.canonicalEquiv_flip | [
{
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57
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925,
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Mathlib/Analysis/Seminorm.lean | Seminorm.continuousAt_zero | [] | [
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84
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1128,
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Mathlib/Algebra/Lie/Free.lean | FreeLieAlgebra.of_comp_lift | [] | [
251,
78
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251,
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Mathlib/Order/SymmDiff.lean | top_bihimp | [
{
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"tactic": "rw [bihimp_comm, bihimp_top]"
}
] | [
254,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
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Mathlib/Analysis/NormedSpace/WeakDual.lean | WeakDual.isCompact_of_bounded_of_closed | [] | [
224,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.vsub_iUnion₂ | [] | [
731,
29
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729,
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Mathlib/LinearAlgebra/Prod.lean | Submodule.fst_inf_snd | [
{
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689,
41
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685,
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | WithTop.coe_iSup | [
{
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125,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/Matrix/ToLin.lean | Algebra.leftMulMatrix_injective | [
{
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25
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909,
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Mathlib/Order/Bounds/Basic.lean | mem_upperBounds_image2_of_mem_lowerBounds | [] | [
1459,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1457,
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Mathlib/Algebra/Group/Basic.lean | mul_mul_inv_cancel'_right | [
{
"state_after": "no goals",
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"tactic": "rw [← div_eq_mul_inv, mul_div_cancel'_right a b]"
}
] | [
983,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
982,
1
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Mathlib/Order/Disjoint.lean | IsCompl.of_eq | [] | [
494,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
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Mathlib/Order/Filter/AtTopBot.lean | Filter.eventually_atTop | [] | [
176,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/CategoryTheory/Sites/Grothendieck.lean | CategoryTheory.GrothendieckTopology.right_ore_of_pullbacks | [] | [
380,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
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Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mk_list_eq_aleph0 | [] | [
1004,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1003,
1
] |
Mathlib/Analysis/Calculus/FDerivAnalytic.lean | AnalyticOn.differentiableOn | [] | [
75,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/RingTheory/Ideal/LocalRing.lean | LocalRing.ResidueField.residue_smul | [] | [
495,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
] |
Mathlib/Data/Set/Intervals/Group.lean | Set.inv_mem_Ioo_iff | [] | [
51,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.piecewise_insert_of_ne | [
{
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2481,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2480,
1
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Mathlib/Topology/Algebra/Module/LinearPMap.lean | LinearPMap.closure_def' | [
{
"state_after": "no goals",
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116,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_self_const_mul' | [] | [
1474,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1471,
1
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Mathlib/Algebra/CharP/Basic.lean | isSquare_of_charTwo' | [
{
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459,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/NumberTheory/SumFourSquares.lean | Int.exists_sq_add_sq_add_one_eq_k | [
{
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}
] | [
109,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/LinearAlgebra/Eigenspace/IsAlgClosed.lean | Module.End.iSup_generalizedEigenspace_eq_top | [
{
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114,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
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Mathlib/Data/List/Cycle.lean | List.prev_singleton | [] | [
155,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.get_natCast' | [
{
"state_after": "no goals",
"state_before": "x : ℕ\nh : (↑x).Dom\n⊢ Part.get (↑x) h = x",
"tactic": "rw [← natCast_inj, natCast_get]"
}
] | [
177,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Order/Filter/IndicatorFunction.lean | indicator_eventuallyLE_indicator | [] | [
59,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
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Mathlib/Topology/Order/LowerTopology.lean | LowerTopology.isClosed_Ici | [] | [
177,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/CategoryTheory/Simple.lean | CategoryTheory.indecomposable_of_simple | [
{
"state_after": "C : Type u\ninst✝³ : Category C\ninst✝² : Preadditive C\ninst✝¹ : HasBinaryBiproducts C\nX : C\ninst✝ : Simple X\nY Z : C\ni : X ≅ Y ⊞ Z\nh : ¬IsZero Y\n⊢ IsZero Z",
"state_before": "C : Type u\ninst✝³ : Category C\ninst✝² : Preadditive C\ninst✝¹ : HasBinaryBiproducts C\nX : C\ninst✝ : Sim... | [
216,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | Commute.units_zpow_right | [] | [
1139,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1137,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.coe_openToLocalization | [] | [
518,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
1
] |
Std/Logic.lean | subsingleton_of_forall_eq | [] | [
753,
31
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
752,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.ofReal_integral_eq_lintegral_ofReal | [
{
"state_after": "α : Type u_1\nE : Type ?u.1079546\nF : Type ?u.1079549\n𝕜 : Type ?u.1079552\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace ℝ E\ninst✝⁸ : CompleteSpace E\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : SMulCommClass ℝ 𝕜 E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³... | [
1184,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1176,
1
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Mathlib/Topology/SubsetProperties.lean | Filter.mem_coclosed_compact' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Type ?u.52679\nπ : ι → Type ?u.52684\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t : Set α\n⊢ s ∈ coclosedCompact α ↔ ∃ t, IsClosed t ∧ IsCompact t ∧ sᶜ ⊆ t",
"tactic": "simp only [mem_coclosedCompact, compl_subset... | [
603,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | HomogeneousLocalization.NumDenSameDeg.den_neg | [] | [
223,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Data/Sum/Interval.lean | Sum.Ioo_inr_inr | [] | [
210,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Logic/Denumerable.lean | Denumerable.decode_isSome | [] | [
49,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Topology/UniformSpace/Separation.lean | UniformSpace.SeparationQuotient.map_comp | [
{
"state_after": "no goals",
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419,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/NumberTheory/VonMangoldt.lean | Nat.ArithmeticFunction.vonMangoldt_apply | [] | [
74,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Logic/Encodable/Basic.lean | ULower.ext | [] | [
545,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
544,
11
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | exists_dvd_and_dvd_of_dvd_mul | [
{
"state_after": "case pos\nα : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : GCDMonoid α\nm n k : α\nH : k ∣ m * n\nh0 : gcd k m = 0\n⊢ ∃ d₁ d₂, d₁ ∣ m ∧ d₂ ∣ n ∧ k = d₁ * d₂\n\ncase neg\nα : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : GCDMonoid α\nm n k : α\nH : k ∣ m * n\nh0 : ¬gcd k m = ... | [
543,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
528,
1
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.succ_ascFactorial | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ (n + 1) * ascFactorial (succ n) 0 = (n + 0 + 1) * ascFactorial n 0",
"tactic": "rw [add_zero, ascFactorial_zero, ascFactorial_zero]"
},
{
"state_after": "no goals",
"state_before": "n k : ℕ\n⊢ (n + 1) * ascFactorial (succ n) (k + 1) = (n... | [
256,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Algebra/Lie/OfAssociative.lean | LieAlgebra.ad_eq_lmul_left_sub_lmul_right | [
{
"state_after": "case h.h\nR : Type u\nL : Type v\nM : Type w\ninst✝⁸ : CommRing R\ninst✝⁷ : LieRing L\ninst✝⁶ : LieAlgebra R L\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\ninst✝³ : LieRingModule L M\ninst✝² : LieModule R L M\nA : Type v\ninst✝¹ : Ring A\ninst✝ : Algebra R A\na b : A\n⊢ ↑(↑(ad R A) a) b = ↑(... | [
291,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | ContinuousLinearEquiv.comp_right_differentiableWithinAt_iff | [
{
"state_after": "𝕜 : Type u_2\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_1\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type u_4\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.157911\ninst✝... | [
182,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.map_roots | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nS : Type u_1\nF : Type ?u.681619\nK : Type ?u.681622\nP : Cubic R\ninst✝² : CommRing R\ninst✝¹ : CommRing S\nφ : R →+* S\ninst✝ : IsDomain S\n⊢ roots (map φ P) = Polynomial.roots (Polynomial.map φ (toPoly P))",
"tactic": "rw [roots, map_toPoly]... | [
486,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.hausdorffDist_zero_iff_closure_eq_closure | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.87629\nα : Type u\nβ : Type v\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\ns t u : Set α\nx y : α\nΦ : α → β\nfin : hausdorffEdist s t ≠ ⊤\n⊢ hausdorffDist s t = 0 ↔ closure s = closure t",
"tactic": "simp [← hausdorffEdist_zero_if... | [
882,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
879,
1
] |
Mathlib/Topology/Algebra/ConstMulAction.lean | continuous_const_smul_iff₀ | [] | [
320,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Algebra/Jordan/Basic.lean | commute_lmul_rmul_sq | [] | [
153,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | ContinuousLinearEquiv.comp_right_hasFDerivWithinAt_iff' | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_1\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type u_4\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace ... | [
229,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.liftMonoidWithZeroHom_apply_div | [
{
"state_after": "case inl\nK : Type u\ninst✝² : CommRing K\ninst✝¹ : IsDomain K\nL : Type u_1\ninst✝ : CommGroupWithZero L\nφ : K[X] →*₀ L\nhφ : K[X]⁰ ≤ Submonoid.comap φ L⁰\np : K[X]\n⊢ ↑(liftMonoidWithZeroHom φ hφ) (↑(algebraMap K[X] (RatFunc K)) p / ↑(algebraMap K[X] (RatFunc K)) 0) = ↑φ p / ↑φ 0\n\ncase in... | [
886,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
880,
1
] |
Mathlib/Algebra/Group/Units.lean | Units.mul_inv_cancel_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Monoid α\na✝ b✝ c u : αˣ\na : α\nb : αˣ\n⊢ a * ↑b * ↑b⁻¹ = a",
"tactic": "rw [mul_assoc, mul_inv, mul_one]"
}
] | [
297,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.tendstoUniformlyOn_iff | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.80494\nι✝ : Type ?u.80497\ninst✝ : PseudoMetricSpace α\nx y z : α\nδ ε ε₁ ε₂ : ℝ\ns✝ : Set α\nι : Type u_1\nF : ι → β → α\nf : β → α\np : Filter ι\ns : Set β\nH : ∀ (ε : ℝ), ε > 0 → ∀ᶠ (n : ι) in p, ∀ (x : β), x ∈ s → dist (f x) (F n x) < ε\nu : Set (α × α)\... | [
916,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
912,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | uniformContinuous₂_def | [] | [
1708,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1706,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.ofSeq_lt_ofSeq | [] | [
156,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.sub_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.77999\nf g : α → β\nc c₁ c₂ x✝ : α\ninst✝ : AddGroup α\nh : Periodic f c\nx : α\n⊢ f (x - c) = f x",
"tactic": "simpa only [sub_add_cancel] using (h (x - c)).symm"
}
] | [
166,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Std/Data/Int/DivMod.lean | Int.dvd_add_right | [
{
"state_after": "no goals",
"state_before": "a b c : Int\nH : a ∣ b\n⊢ a ∣ b + c ↔ a ∣ c",
"tactic": "rw [Int.add_comm, Int.dvd_add_left H]"
}
] | [
625,
40
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
624,
11
] |
Mathlib/Dynamics/OmegaLimit.lean | omegaLimit_preimage_subset | [] | [
121,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Std/Logic.lean | and_self_right | [] | [
229,
54
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
228,
9
] |
Mathlib/LinearAlgebra/Determinant.lean | LinearMap.det_toMatrix' | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.466824\ninst✝¹¹ : CommRing R\nM : Type ?u.466830\ninst✝¹⁰ : AddCommGroup M\ninst✝⁹ : Module R M\nM' : Type ?u.467415\ninst✝⁸ : AddCommGroup M'\ninst✝⁷ : Module R M'\nι✝ : Type ?u.467957\ninst✝⁶ : DecidableEq ι✝\ninst✝⁵ : Fintype ι✝\ne : Basis ι✝ R M\... | [
221,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Algebra/Associated.lean | Associates.mul_mono | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.297556\nγ : Type ?u.297559\nδ : Type ?u.297562\ninst✝ : CommMonoid α\na b c d : Associates α\nh₁ : a ≤ b\nh₂ : c ≤ d\nx : Associates α\nhx : b = a * x\ny : Associates α\nhy : d = c * y\n⊢ b * d = a * c * (x * y)",
"tactic": "simp [h... | [
905,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
902,
1
] |
Mathlib/Order/Hom/Bounded.lean | BoundedOrderHom.dual_id | [] | [
810,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
809,
1
] |
Mathlib/LinearAlgebra/Matrix/Charpoly/Basic.lean | matPolyEquiv_charmatrix | [
{
"state_after": "case a.a.h\nR : Type u\ninst✝² : CommRing R\nn : Type w\ninst✝¹ : DecidableEq n\ninst✝ : Fintype n\nM : Matrix n n R\nk : ℕ\ni j : n\n⊢ coeff (↑matPolyEquiv (charmatrix M)) k i j = coeff (X - ↑C M) k i j",
"state_before": "R : Type u\ninst✝² : CommRing R\nn : Type w\ninst✝¹ : DecidableEq n... | [
82,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_mul_distrib' | [
{
"state_after": "α : Type u_1\nβ : Type ?u.217456\nι : Type ?u.217459\nG : Type ?u.217462\nM : Type u_2\nN : Type ?u.217468\ninst✝¹ : CommMonoid M\ninst✝ : CommMonoid N\nf g : α → M\na b : α\ns t : Set α\nhf : Set.Finite (mulSupport (mulIndicator s f))\nhg : Set.Finite (mulSupport (mulIndicator s g))\n⊢ (∏ᶠ (i... | [
638,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
635,
1
] |
Mathlib/CategoryTheory/Sums/Basic.lean | CategoryTheory.NatTrans.sum_app_inl | [] | [
237,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearEquiv.coord_norm | [
{
"state_after": "𝕜 : Type u_2\n𝕜₂ : Type ?u.3824025\n𝕜₃ : Type ?u.3824028\nE : Type u_1\nEₗ : Type ?u.3824034\nF : Type ?u.3824037\nFₗ : Type ?u.3824040\nG : Type ?u.3824043\nGₗ : Type ?u.3824046\n𝓕 : Type ?u.3824049\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NormedAddCommGro... | [
1991,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1987,
1
] |
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