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 |
|---|---|---|---|---|---|---|
Mathlib/Control/Applicative.lean | Functor.Comp.seq_assoc | [] | [
106,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_subset_iff | [] | [
189,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.bddAbove_of_small | [] | [
1388,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1387,
1
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Mathlib/GroupTheory/Exponent.lean | Monoid.exp_eq_one_of_subsingleton | [
{
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"state_before": "G : Type u\ninst✝¹ : Monoid G\ninst✝ : Subsingleton G\n⊢ exponent G = 1",
"tactic": "apply le_antisymm"
... | [
153,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.fst_prod_snd | [] | [
1101,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1100,
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Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | MvPolynomial.weightedTotalDegree'_zero | [
{
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"tactic": "simp only [weightedTotalDegree', support_zero, Finset.sup_empty]"
}
] | [
91,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Intervals/Group.lean | Set.inv_mem_Ico_iff | [] | [
39,
46
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Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.BinaryBicone.binary_fan_fst_toCone | [] | [
1012,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1012,
1
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Mathlib/Data/List/Perm.lean | List.cons_perm_iff_perm_erase | [] | [
866,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
861,
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Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.isHenstock_biUnionTagged | [] | [
233,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
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Mathlib/LinearAlgebra/UnitaryGroup.lean | Matrix.UnitaryGroup.ext_iff | [] | [
105,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
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Mathlib/Analysis/Calculus/FDeriv/Add.lean | differentiableAt_const_add_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.265379\ninst✝³ : NormedAddCommGroup G\ninst✝² : Normed... | [
291,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.succ_zero | [
{
"state_after": "no goals",
"state_before": "α β : Type u\n⊢ succ 0 = 1",
"tactic": "norm_cast"
}
] | [
1381,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1381,
1
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Mathlib/Analysis/MeanInequalities.lean | Real.geom_mean_weighted_of_constant | [
{
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"state_before": "ι : Type u\ns : Finset ι\nw z : ι → ℝ\nx : ℝ\nhw :... | [
157,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
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Mathlib/Init/Data/Nat/Bitwise.lean | Nat.lxor'_bit | [] | [
488,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
1
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Mathlib/Data/Finsupp/WellFounded.lean | Finsupp.wellFoundedLT | [] | [
77,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
11
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | ContDiffAt.rpow_const_of_ne | [] | [
527,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.ball_eq_empty_iff | [] | [
606,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
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Mathlib/Analysis/NormedSpace/FiniteDimension.lean | LinearMap.exists_antilipschitzWith | [
{
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232,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
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Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.walkingParallelPairOpEquiv_unitIso_one | [] | [
191,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
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Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.ComplexMeasure.integrable_rnDeriv | [
{
"state_after": "α : Type u_1\nβ : Type ?u.660001\nm : MeasurableSpace α\nμ✝ ν : Measure α\nc✝ c : ComplexMeasure α\nμ : Measure α\n⊢ Memℒp (fun x => ↑IsROrC.re (rnDeriv c μ x)) 1 ∧ Memℒp (fun x => ↑IsROrC.im (rnDeriv c μ x)) 1",
"state_before": "α : Type u_1\nβ : Type ?u.660001\nm : MeasurableSpace α\nμ✝ ... | [
1223,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1219,
1
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Mathlib/Data/Bool/Basic.lean | Bool.toNat_le_toNat | [
{
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},
{
"state_after": "case inl\nb₁ : Bool\n⊢ toNat false ≤ toNat b₁",
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396,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
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Mathlib/Order/WithBot.lean | WithTop.recTopCoe_top | [] | [
624,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
1
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Mathlib/Algebra/Order/Ring/Defs.lean | cmp_mul_pos_right | [] | [
965,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
964,
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Mathlib/Data/Vector/Basic.lean | Vector.scanl_get | [
{
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393,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
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Mathlib/CategoryTheory/Preadditive/FunctorCategory.lean | CategoryTheory.NatTrans.app_zsmul | [] | [
112,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
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Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.mul_inv_cancel_left_of_invertible | [] | [
361,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
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Mathlib/Data/Seq/Computation.lean | Computation.mem_unique | [
{
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"tactic": "injection\n (le_stable s (le_max_left m n) ha.symm).symm... | [
341,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
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Mathlib/Topology/ContinuousOn.lean | nhdsWithin_iUnion | [
{
"state_after": "no goals",
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"tactic": "rw [← sUnion_range, nhdsWithin_sUnion (finite... | [
258,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
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Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.lift_card_closure_le_card_term | [
{
"state_after": "L : Language\nM : Type w\nN : Type ?u.34066\nP : Type ?u.34069\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nS : Substructure L M\ns : Set M\n⊢ lift (#↑(range (Term.realize Subtype.val))) ≤ (#Term L ↑s)",
"state_before": "L : Language\nM : Type w\nN : Type ?u.3406... | [
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323,
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Mathlib/Data/Set/Intervals/Instances.lean | Set.Icc.coe_pow | [] | [
132,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
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Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | MeasureTheory.locallyIntegrable_map_homeomorph | [
{
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237,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
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Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_rel_mulIndicator | [
{
"state_after": "α : Type u_2\nβ : Type ?u.42764\nι : Type ?u.42767\nM : Type u_1\nN : Type ?u.42773\ninst✝¹ : One M\ninst✝ : One N\ns t : Set α\nf g : α → M\na : α\nr : M → M → Prop\nh1 : r 1 1\nha : a ∈ s → r (f a) (g a)\n⊢ r (if a ∈ s then f a else 1) (if a ∈ s then g a else 1)",
"state_before": "α : Ty... | [
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22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
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Mathlib/RingTheory/Polynomial/Tower.lean | Subalgebra.aeval_coe | [] | [
90,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
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Mathlib/LinearAlgebra/Trace.lean | LinearMap.trace_eq_contract_of_basis | [
{
"state_after": "case intro\nR : Type u_2\ninst✝⁵ : CommRing R\nM : Type u_3\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\nN : Type ?u.321532\ninst✝² : AddCommGroup N\ninst✝¹ : Module R N\nι : Type u_1\ninst✝ : Finite ι\nb : Basis ι R M\nval✝ : Fintype ι\n⊢ comp (trace R M) (dualTensorHom R M M) = contractLef... | [
151,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.SimpleFunc.setToL1S_add_left | [] | [
736,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
734,
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Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.map_le_iff_le_comap | [] | [
659,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
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Mathlib/Topology/Inseparable.lean | specializes_refl | [] | [
167,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Topology/List.lean | List.tendsto_cons_iff | [
{
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96,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
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Mathlib/Algebra/Algebra/Tower.lean | Submodule.restrictScalars_span | [
{
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.sub_apply | [] | [
266,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
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Mathlib/Order/BooleanAlgebra.lean | sup_lt_of_lt_sdiff_left | [
{
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"tactic": "r... | [
478,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
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Mathlib/Order/Filter/AtTopBot.lean | Filter.mem_atBot | [] | [
68,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/IsPrimePow.lean | IsPrimePow.ne_one | [] | [
74,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
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Mathlib/Data/MvPolynomial/Equiv.lean | MvPolynomial.finSuccEquiv_eq | [
{
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Mathlib/Algebra/Group/Defs.lean | zpow_negSucc | [
{
"state_after": "G : Type u_1\ninst✝ : DivInvMonoid G\na✝ b a : G\nn : ℕ\n⊢ a ^ Int.negSucc n = (a ^ ↑(n + 1))⁻¹",
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"tactic": "rw [← zpow_ofNat]"
},
{
"state_after": "no goals",
... | [
937,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
935,
1
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Mathlib/Data/Polynomial/Laurent.lean | Polynomial.toLaurentAlg_apply | [] | [
121,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
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Mathlib/Data/Fin/Tuple/Basic.lean | Fin.exists_fin_succ_pi | [] | [
216,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
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Mathlib/Order/Heyting/Regular.lean | Heyting.Regular.coe_toRegular | [] | [
200,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
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Mathlib/Topology/Constructions.lean | Continuous.fin_insertNth | [] | [
1280,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/WellFoundedSet.lean | Set.WellFoundedOn.mono | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
11
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Mathlib/Data/ZMod/Basic.lean | ZMod.neg_eq_self_mod_two | [
{
"state_after": "no goals",
"state_before": "a : ZMod 2\n⊢ -a = a",
"tactic": "fin_cases a <;> apply Fin.ext <;> simp [Fin.coe_neg, Int.natMod]"
}
] | [
828,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
827,
1
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Mathlib/Order/Bounds/Basic.lean | IsLUB.upperBounds_eq | [] | [
287,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
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Mathlib/Topology/Instances/Nat.lean | Nat.closedEmbedding_coe_real | [] | [
47,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Data/Finset/Lattice.lean | Finset.iSup_insert_update | [
{
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1979,
61
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1976,
1
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Mathlib/Analysis/Calculus/Deriv/Mul.lean | deriv_const_mul_field' | [] | [
284,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
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Mathlib/Analysis/Asymptotics/SuperpolynomialDecay.lean | Asymptotics.SuperpolynomialDecay.inv_param_mul | [
{
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"tactic": "simpa ... | [
274,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
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Mathlib/Dynamics/PeriodicPts.lean | Function.isPeriodicPt_minimalPeriod | [
{
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281,
32
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277,
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Mathlib/Combinatorics/Configuration.lean | Configuration.HasPoints.lineCount_eq_pointCount | [] | [
318,
86
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315,
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Mathlib/Analysis/Convex/Between.lean | wbtw_vsub_const_iff | [] | [
207,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
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Mathlib/Data/List/Infix.lean | List.dropWhile_suffix | [] | [
167,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
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Mathlib/Analysis/Calculus/Deriv/Comp.lean | deriv.comp | [] | [
201,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
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Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.basisFun_eq_pi_basisFun | [] | [
986,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
984,
1
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Mathlib/Logic/Basic.lean | exists_or_eq_right' | [] | [
799,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
799,
9
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Mathlib/Data/List/Sublists.lean | List.length_sublists' | [
{
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"tactic": "simp_arith only [sublists'_cons, length_append, length_sublists' l,\n length_map, length, Nat.pow_succ', mul_succ, mul_zero, zero_add]"
... | [
103,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
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Mathlib/RingTheory/DedekindDomain/Ideal.lean | idealFactorsFunOfQuotHom_id | [
{
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1081,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1074,
1
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Mathlib/Algebra/Hom/Units.lean | IsUnit.div_eq_div_iff | [
{
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"tactic": "rw [← (hb.mul hd).mul_left_inj, ← mul_assoc, hb.di... | [
499,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
11
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Mathlib/Dynamics/Ergodic/MeasurePreserving.lean | MeasureTheory.MeasurePreserving.comp_left_iff | [
{
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109,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.map_eq_nil_iff | [
{
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}
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1495,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1495,
1
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Mathlib/CategoryTheory/Subobject/FactorThru.lean | CategoryTheory.Subobject.mk_factors_self | [
{
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"tactic": "simp"
}
] | [
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17
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Mathlib/Data/List/Zip.lean | List.zipWith_same | [] | [
294,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_cancels_of_partition_cancels | [
{
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1603,
19
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Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | MvPolynomial.sum_weightedHomogeneousComponent | [
{
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420,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
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Mathlib/Order/SuccPred/Basic.lean | Order.pred_eq_pred_iff | [
{
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"tactic": "simp_rw [eq_iff_le_not_lt, pred_le_pred_iff, pred_lt_pred_iff]"
}
] | [
827,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/InnerProductSpace/Calculus.lean | hasStrictFDerivAt_norm_sq | [
{
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229,
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224,
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Mathlib/Data/List/Forall2.lean | List.rel_map | [] | [
248,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
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Mathlib/Topology/Algebra/Order/IntermediateValue.lean | IsClosed.Icc_subset_of_forall_exists_gt | [
{
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375,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
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Mathlib/Topology/Homotopy/HomotopyGroup.lean | joined_genLoopZeroEquiv_iff | [
{
"state_after": "no goals",
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"tactic": "rw [← homotopic_genLoopZeroEquiv_symm_iff, Equiv.symm_apply_apply, Equiv.symm_apply_apply]"
}... | [
240,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
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Mathlib/Order/Filter/Basic.lean | Filter.tendsto_congr | [] | [
2900,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2898,
1
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Mathlib/Order/Hom/Lattice.lean | InfTopHom.coe_toTopHom | [] | [
899,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
898,
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Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.Lp.simpleFunc.uniformInducing | [] | [
767,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
766,
11
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Mathlib/Analysis/Asymptotics/SpecificAsymptotics.lean | Filter.IsBoundedUnder.isLittleO_sub_self_inv | [
{
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"state_before": "𝕜 : Type u_1\nE : Type u_2\ninst✝¹ : NormedField 𝕜\nins... | [
35,
66
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Mathlib/NumberTheory/Padics/PadicNorm.lean | padicNorm.padicNorm_p_lt_one_of_prime | [] | [
120,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.leadingCoeff_mul | [
{
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1544,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1538,
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Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.prod_add_index_of_disjoint | [
{
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589,
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579,
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Mathlib/Data/Option/NAry.lean | Option.map₂_map_left | [
{
"state_after": "no goals",
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"tactic": "cases a <;> rfl"
}
] | [
98,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
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Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.polar_comp | [
{
"state_after": "no goals",
"state_before": "S : Type u_2\nR : Type u_3\nR₁ : Type ?u.15005\nM : Type u_4\ninst✝⁴ : Ring R\ninst✝³ : CommRing R₁\ninst✝² : AddCommGroup M\nF : Type u_1\ninst✝¹ : Ring S\ninst✝ : AddMonoidHomClass F R S\nf : M → R\ng : F\nx y : M\n⊢ polar (↑g ∘ f) x y = ↑g (polar f x y)",
... | [
124,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
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Mathlib/Data/Set/Intervals/Basic.lean | IsTop.Iic_eq | [] | [
699,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
698,
1
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Mathlib/Data/Nat/Digits.lean | Nat.modEq_nine_digits_sum | [
{
"state_after": "no goals",
"state_before": "n✝ n : ℕ\n⊢ 10 % 9 = 1",
"tactic": "norm_num"
}
] | [
556,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/Topology/Homotopy/HomotopyGroup.lean | genLoopOneEquivPathSelf_symm_homotopic_iff | [
{
"state_after": "X : Type u\ninst✝ : TopologicalSpace X\nn : ℕ\nx : X\nf g : Path x x\n⊢ Path.Homotopic f g → GenLoop.Homotopic (↑genLoopOneEquivPathSelf.symm f) (↑genLoopOneEquivPathSelf.symm g)",
"state_before": "X : Type u\ninst✝ : TopologicalSpace X\nn : ℕ\nx : X\nf g : Path x x\n⊢ GenLoop.Homotopic (↑... | [
273,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.conjTranspose_add | [
{
"state_after": "no goals",
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2151,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2149,
1
] |
Mathlib/RingTheory/Polynomial/Quotient.lean | Ideal.polynomialQuotientEquivQuotientPolynomial_symm_mk | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : CommRing R\nI : Ideal R\nf : R[X]\n⊢ ↑(RingEquiv.symm (polynomialQuotientEquivQuotientPolynomial I)) (↑(Quotient.mk (map C I)) f) =\n Polynomial.map (Quotient.mk I) f",
"tactic": "rw [polynomialQuotientEquivQuotientPolynomial, RingEq... | [
146,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Algebra/Ring/Idempotents.lean | IsIdempotentElem.eq | [] | [
52,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Algebra/CharP/Basic.lean | Commute.add_pow_prime_eq | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\np : ℕ\nx y : R\nhp : Nat.Prime p\nh : Commute x y\n⊢ (x + y) ^ p = x ^ p + y ^ p + ↑p * ∑ k in Ioo 0 p, x ^ k * y ^ (p - k) * ↑(Nat.choose p k / p)",
"tactic": "simpa using h.add_pow_prime_pow_eq hp 1"
}
] | [
51,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
11
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.lt_of_lt_of_eq | [
{
"state_after": "case h.e'_3\nα : Type u_1\ninst✝ : LinearOrderedField α\nf g h : CauSeq α abs\nfg : f < g\ngh : g ≈ h\n⊢ h - f = g - f + -(g - h)",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\nf g h : CauSeq α abs\nfg : f < g\ngh : g ≈ h\n⊢ Pos (h - f)",
"tactic": "convert pos_add_limZ... | [
730,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
727,
1
] |
Mathlib/RepresentationTheory/Action.lean | Action.tensor_v | [] | [
494,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.lt_iff_sub_pos | [] | [
1826,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1818,
1
] |
Mathlib/Order/Heyting/Basic.lean | LE.le.codisjoint_hnot_right | [] | [
1049,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1048,
1
] |
Mathlib/Data/List/Infix.lean | List.nth_le_tails | [
{
"state_after": "case nil\nα : Type u_1\nβ : Type ?u.49282\nl✝ l₁ l₂ l₃ : List α\na b : α\nm n✝¹ : ℕ\nl : List α\nn✝ : ℕ\nhn✝ : n✝ < length (tails l)\nn : ℕ\nhn : n < length (tails [])\n⊢ nthLe (tails []) n hn = drop n []\n\ncase cons\nα : Type u_1\nβ : Type ?u.49282\nl✝¹ l₁ l₂ l₃ : List α\na b : α\nm n✝¹ : ℕ\... | [
446,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/Algebra/BigOperators/RingEquiv.lean | RingEquiv.map_multiset_sum | [] | [
46,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
11
] |
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