file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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|---|---|---|---|---|---|---|
Mathlib/LinearAlgebra/Projection.lean | Submodule.coe_isComplEquivProj_apply | [] | [
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76
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358,
1
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Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingIso.coe_ringEquiv_refl | [] | [
447,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
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Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.toLocalizationMap_toMap | [] | [
173,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
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Mathlib/RingTheory/Bezout.lean | IsBezout.TFAE | [
{
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146,
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121,
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Mathlib/Algebra/MonoidAlgebra/Division.lean | AddMonoidAlgebra.of'_dvd_iff_modOf_eq_zero | [
{
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203,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.enumOrd_def'_nonempty | [] | [
2169,
28
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2167,
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Mathlib/Analysis/Convex/SimplicialComplex/Basic.lean | Geometry.SimplicialComplex.mem_vertices | [] | [
154,
65
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154,
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_finset_of_fintype | [
{
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}
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1323,
17
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1322,
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.natCast_inj | [] | [
1368,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1367,
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Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_insert' | [
{
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Mathlib/Algebra/Order/Field/Basic.lean | one_le_div | [
{
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"tactic": "rw [le_div_iff hb, one_mul]"
}
] | [
424,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
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Mathlib/Topology/Instances/Real.lean | Function.Periodic.compact_of_continuous' | [] | [
213,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
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Mathlib/FieldTheory/RatFunc.lean | RatFunc.denom_ne_zero | [] | [
1207,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1206,
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Mathlib/Analysis/Calculus/Deriv/Add.lean | hasDerivAt_neg' | [] | [
255,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
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Mathlib/Data/Rel.lean | Set.image_eq | [
{
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"tactic": "simp [Set.image, Function.graph, Rel.image]"
}
] | [
275,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.FiniteAtFilter.inf_ae_iff | [
{
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4118,
69
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4114,
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Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_real_mul | [
{
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},
{
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... | [
185,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
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Mathlib/Analysis/Calculus/IteratedDeriv.lean | iteratedFDerivWithin_eq_equiv_comp | [
{
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100,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
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Mathlib/NumberTheory/Padics/PadicNumbers.lean | padicNormE.norm_p_pow | [
{
"state_after": "no goals",
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}
] | [
862,
33
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861,
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Mathlib/Topology/Instances/AddCircle.lean | AddCircle.coe_zsmul | [] | [
159,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
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Mathlib/Algebra/Invertible.lean | invOf_mul_self_assoc | [
{
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}
] | [
123,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
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Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.Lp.simpleFunc.denseRange | [] | [
796,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
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Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_unique_iff | [
{
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1121,
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1116,
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Mathlib/Topology/Algebra/Order/IntermediateValue.lean | Set.OrdConnected.isPreconnected | [] | [
430,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
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Mathlib/Topology/LocalExtr.lean | Filter.EventuallyEq.isLocalExtrOn_iff | [] | [
590,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
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Mathlib/Data/Num/Lemmas.lean | PosNum.cast_to_int | [
{
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"state_before": "α : Type u_1\ninst✝ : AddGroupWithOne α\nn : PosNum\n⊢ ↑↑n = ↑n",
"tactic": "rw [← to_nat_to_int, Int.cast_ofNat, cast_to_nat]"
}
] | [
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52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/ZMod/Basic.lean | RingHom.ext_zmod | [
{
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"tactic": "ext a"
},
{
"state_after": "case a.intro\nn : ℕ\nR : Type u_1\ninst✝ : Semiring R\... | [
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1139,
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Mathlib/Data/Set/Lattice.lean | Set.sSup_eq_sUnion | [] | [
120,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
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Mathlib/Data/Complex/Basic.lean | Complex.isCauSeq_re | [
{
"state_after": "no goals",
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"tactic": "simpa using abs_re_le_abs (f j - f i)"
}
] | [
1240,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/QuotientPi.lean | Submodule.quotientPi_aux.map_add | [] | [
118,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
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Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.exists_mem_normalizedFactors | [
{
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646,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
642,
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_le_of_forall_fin_meas_le_of_measurable | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1825244\nγ : Type ?u.1825247\nδ : Type ?u.1825250\nm m0 : MeasurableSpace α\nE : Type ?u.1825259\ninst✝³ : NormedAddCommGroup E\ninst✝² : MeasurableSpace E\ninst✝¹ : OpensMeasurableSpace E\nμ : Measure α\nhm : m ≤ m0\ninst✝ : SigmaFinite (Measure.trim μ hm)\nC : ℝ≥0∞\... | [
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Mathlib/Data/List/Basic.lean | List.length_modifyNth | [] | [
1556,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1555,
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Mathlib/Logic/Encodable/Basic.lean | Encodable.surjective_decode_iget | [
{
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}
] | [
83,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.ne_zero_of_ortho | [] | [
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77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
611,
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Mathlib/Topology/SubsetProperties.lean | IsCompact.finite | [] | [
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96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
922,
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Std/Data/List/Lemmas.lean | List.getLast?_eq_getLast | [] | [
481,
19
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
479,
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Mathlib/LinearAlgebra/Matrix/Transvection.lean | Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_row | [
{
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519,
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | aemeasurable_biSup | [
{
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Mathlib/Analysis/Calculus/FDeriv/Bilinear.lean | ContinuousLinearMap.fderiv_of_bilinear | [] | [
155,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
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Mathlib/Data/Nat/Log.lean | Nat.clog_pos | [
{
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},
{
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.filter_apply_pos | [] | [
914,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
914,
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Mathlib/Data/Nat/Choose/Sum.lean | Int.alternating_sum_range_choose_of_ne | [
{
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"tactic": "rw [Int.alternating_sum_range_choose, if_neg h0]"
}
] | [
150,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
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Mathlib/RingTheory/Coprime/Lemmas.lean | IsCoprime.prod_left_iff | [
{
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},
{
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86
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64,
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Mathlib/Algebra/Order/Rearrangement.lean | Monovary.sum_mul_comp_perm_le_sum_mul | [] | [
457,
37
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455,
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Mathlib/Computability/Partrec.lean | Nat.Partrec.some | [] | [
203,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
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Mathlib/Algebra/Module/Injective.lean | Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd' | [
{
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340,
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Mathlib/Analysis/Convex/Function.lean | ConcaveOn.left_lt_of_lt_right' | [] | [
787,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/WittVector/Defs.lean | WittVector.wittSub_zero | [
{
"state_after": "case a\np : ℕ\nR : Type ?u.60999\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\n⊢ ↑(map (Int.castRingHom ℚ)) (wittSub p 0) = ↑(map (Int.castRingHom ℚ)) (X (0, 0) - X (1, 0))",
"state_before": "p : ℕ\nR : Type ?u.60999\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\n⊢ wittSub p 0 = X (0, 0) - ... | [
276,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.inf_def | [] | [
571,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.Nonempty.of_smul_right | [] | [
147,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup₂_le | [] | [
825,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
824,
1
] |
Mathlib/Data/Set/Basic.lean | Set.diff_diff_cancel_left | [] | [
2074,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2073,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.tr_eval | [
{
"state_after": "case intro.intro\nc : Code\nv : List ℕ\ni : Cfg'\nh₁ : TrCfg (stepNormal c Cont.halt v) i\nh₂ : Reaches₁ (TM2.step tr) (init c v) i\n⊢ eval (TM2.step tr) (init c v) = halt <$> Code.eval c v",
"state_before": "c : Code\nv : List ℕ\n⊢ eval (TM2.step tr) (init c v) = halt <$> Code.eval c v",
... | [
1719,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1706,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.lt_bsup_of_limit | [] | [
1541,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1538,
1
] |
Mathlib/Topology/ContinuousOn.lean | nhds_bind_nhdsWithin | [] | [
43,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.neg_of_one_le | [] | [
514,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | isCoprime_one_left | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : CommSemiring R\nx y z : R\n⊢ 1 * 1 + 0 * x = 1",
"tactic": "rw [one_mul, zero_mul, add_zero]"
}
] | [
83,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_C | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝¹ : Semiring R\np q r : R[X]\ninst✝ : Semiring S\nf : R →+* S\nx : S\n⊢ eval₂ f x (↑C a) = ↑f a",
"tactic": "simp [eval₂_eq_sum]"
}
] | [
73,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Topology/SubsetProperties.lean | isClopen_range_inl | [] | [
1644,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1643,
1
] |
Mathlib/NumberTheory/Padics/PadicVal.lean | padicValNat.one | [
{
"state_after": "p : ℕ\n⊢ (if h : p ≠ 1 ∧ 0 < 1 then Part.get (multiplicity p 1) (_ : multiplicity.Finite p 1) else 0) = 0",
"state_before": "p : ℕ\n⊢ padicValNat p 1 = 0",
"tactic": "unfold padicValNat"
},
{
"state_after": "case inl\np : ℕ\nh✝ : p ≠ 1 ∧ 0 < 1\n⊢ Part.get (multiplicity p 1) (_ ... | [
77,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
11
] |
Mathlib/Algebra/Ring/Defs.lean | sub_one_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : Type x\ninst✝ : NonAssocRing α\na b : α\n⊢ (a - 1) * b = a * b - b",
"tactic": "rw [sub_mul, one_mul]"
}
] | [
410,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
Mathlib/Algebra/Category/ModuleCat/Monoidal/Symmetric.lean | ModuleCat.MonoidalCategory.hexagon_reverse | [
{
"state_after": "R : Type u\ninst✝ : CommRing R\nX Y Z : ModuleCat R\n⊢ (α_ X Y Z).hom ≫ (α_ X Y Z).inv ≫ (braiding (X ⊗ Y) Z).hom ≫ (α_ Z X Y).inv =\n (α_ X Y Z).hom ≫ (𝟙 X ⊗ (braiding Y Z).hom) ≫ (α_ X Z Y).inv ≫ ((braiding X Z).hom ⊗ 𝟙 Y)",
"state_before": "R : Type u\ninst✝ : CommRing R\nX Y Z : M... | [
61,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Order/Atoms.lean | IsSimpleOrder.bot_ne_top | [
{
"state_after": "case intro.intro\nα : Type u_1\nβ : Type ?u.23015\ninst✝² : LE α\ninst✝¹ : BoundedOrder α\ninst✝ : IsSimpleOrder α\na b : α\nh : a ≠ b\n⊢ ⊥ ≠ ⊤",
"state_before": "α : Type u_1\nβ : Type ?u.23015\ninst✝² : LE α\ninst✝¹ : BoundedOrder α\ninst✝ : IsSimpleOrder α\n⊢ ⊥ ≠ ⊤",
"tactic": "obta... | [
448,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
Mathlib/CategoryTheory/Sites/Types.lean | CategoryTheory.eval_typesGlue | [
{
"state_after": "case h\nS : Type uᵒᵖ ⥤ Type u\nhs : IsSheaf typesGrothendieckTopology S\nα : Type u\nf : α → S.obj PUnit.op\nx : α\n⊢ eval S α (typesGlue S hs α f) x = f x",
"state_before": "S : Type uᵒᵖ ⥤ Type u\nhs : IsSheaf typesGrothendieckTopology S\nα : Type u\nf : α → S.obj PUnit.op\n⊢ eval S α (ty... | [
108,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalMinOn.sup | [] | [
461,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
8
] |
Mathlib/Data/LazyList/Basic.lean | LazyList.append_bind | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nxs : LazyList α\nys : Thunk (LazyList α)\nf : α → LazyList β\n⊢ LazyList.bind (append xs ys) f = append (LazyList.bind xs f) { fn := fun x => LazyList.bind (Thunk.get ys) f }",
"tactic": "match xs with\n| LazyList.nil => rfl\n| La... | [
190,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Order/Bounded.lean | Set.Unbounded.mono | [] | [
34,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/Probability/Independence/ZeroOne.lean | ProbabilityTheory.indep_limsup_atTop_self | [
{
"state_after": "Ω : Type u_1\nι : Type u_2\nm m0 : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\ninst✝³ : IsProbabilityMeasure μ\ns : ι → MeasurableSpace Ω\ninst✝² : SemilatticeSup ι\ninst✝¹ : NoMaxOrder ι\ninst✝ : Nonempty ι\nh_le : ∀ (n : ι), s n ≤ m0\nh_indep : iIndep s\nns : ι → Set ι := Set.Iic\n⊢ Inde... | [
145,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Algebra/DirectLimit.lean | AddCommGroup.DirectLimit.induction_on | [] | [
316,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
11
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | derivWithin_inter | [
{
"state_after": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type w\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL L₁ L₂ : Filter 𝕜\nht : t ∈ 𝓝 x\n⊢ ↑(fder... | [
519,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.ball_subset_closedBall | [] | [
677,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
676,
1
] |
Mathlib/LinearAlgebra/UnitaryGroup.lean | Matrix.UnitaryGroup.ext | [] | [
110,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | Left.inv_lt_one_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Group α\ninst✝¹ : LT α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x < x_1\na b c : α\n⊢ a⁻¹ < 1 ↔ 1 < a",
"tactic": "rw [← mul_lt_mul_iff_left a, mul_inv_self, mul_one]"
}
] | [
169,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/GroupTheory/Commutator.lean | Subgroup.commutator_comm | [] | [
128,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | tendsto_inv_nhdsWithin_Ici_inv | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝⁶ : TopologicalSpace G\ninst✝⁵ : Group G\ninst✝⁴ : TopologicalGroup G\ninst✝³ : TopologicalSpace α\nf : α → G\ns : Set α\nx : α\ninst✝² : TopologicalSpace H\ninst✝¹ : OrderedCommGroup H\ninst✝ : ContinuousInv ... | [
597,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
596,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderIso.complementedLattice_iff | [
{
"state_after": "F : Type ?u.129007\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.129016\nδ : Type ?u.129019\ninst✝³ : Lattice α\ninst✝² : Lattice β\ninst✝¹ : BoundedOrder α\ninst✝ : BoundedOrder β\nf : α ≃o β\na✝ : ComplementedLattice α\n⊢ ComplementedLattice β",
"state_before": "F : Type ?u.129007\nα : Type u... | [
1385,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1383,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ioo_filter_lt | [
{
"state_after": "case a\nι : Type ?u.141256\nα : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : LocallyFiniteOrder α\na✝¹ b✝ a b c a✝ : α\n⊢ a✝ ∈ filter (fun x => x < c) (Ioo a b) ↔ a✝ ∈ Ioo a (min b c)",
"state_before": "ι : Type ?u.141256\nα : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : LocallyFiniteOrder α\na✝... | [
804,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
802,
1
] |
Mathlib/CategoryTheory/Monoidal/Opposite.lean | CategoryTheory.unmop_inj | [] | [
110,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Order/Filter/ENNReal.lean | ENNReal.eventually_le_limsup | [] | [
28,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
26,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_plift_up | [] | [
230,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.le_sSup | [
{
"state_after": "case f\nC : Type u₁\ninst✝⁴ : Category C\nX Y Z : C\nD : Type u₂\ninst✝³ : Category D\ninst✝² : WellPowered C\ninst✝¹ : HasCoproducts C\ninst✝ : HasImages C\nA : C\ns : Set (Subobject A)\nf : Subobject A\nhf : f ∈ s\n⊢ underlying.obj f ⟶ underlying.obj (sSup s)\n\ncase w\nC : Type u₁\ninst✝⁴ :... | [
693,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
688,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.isOption_neg_neg | [
{
"state_after": "no goals",
"state_before": "x y : PGame\n⊢ IsOption (-x) (-y) ↔ IsOption x y",
"tactic": "rw [isOption_neg, neg_neg]"
}
] | [
1238,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1237,
1
] |
Mathlib/Topology/Constructions.lean | nhds_prod_eq | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type ?u.32917\nδ : Type ?u.32920\nε : Type ?u.32923\nζ : Type ?u.32926\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : TopologicalSpace β\ninst✝³ : TopologicalSpace γ\ninst✝² : TopologicalSpace δ\ninst✝¹ : TopologicalSpace ε\ninst✝ : TopologicalSpace ζ\na : α\nb : β\n⊢ 𝓝 (a... | [
514,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
1
] |
Mathlib/Topology/Constructions.lean | induced_to_pi | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type ?u.512017\nδ : Type ?u.512020\nε : Type ?u.512023\nζ : Type ?u.512026\nι : Type u_2\nπ : ι → Type u_3\nκ : Type ?u.512037\ninst✝¹ : TopologicalSpace α\ninst✝ : (i : ι) → TopologicalSpace (π i)\nf✝ : α → (i : ι) → π i\nX : Type u_1\nf : X → (i : ι) → π i\n⊢ (⨅ (... | [
1415,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1411,
1
] |
Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.iUnion_cylinder_update | [
{
"state_after": "case h\nE : ℕ → Type u_1\nx : (n : ℕ) → E n\nn : ℕ\ny : (n : ℕ) → E n\n⊢ (y ∈ ⋃ (k : E n), cylinder (update x n k) (n + 1)) ↔ y ∈ cylinder x n",
"state_before": "E : ℕ → Type u_1\nx : (n : ℕ) → E n\nn : ℕ\n⊢ (⋃ (k : E n), cylinder (update x n k) (n + 1)) = cylinder x n",
"tactic": "ext... | [
188,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.normSq_add_mul_I | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ ↑normSq (↑x + ↑y * I) = x ^ 2 + y ^ 2",
"tactic": "rw [← mk_eq_add_mul_I, normSq_mk, sq, sq]"
}
] | [
598,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.mem_closedBall_zero | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.818815\nR' : Type ?u.818818\n𝕜 : Type u_2\n𝕜₂ : Type ?u.818824\n𝕜₃ : Type ?u.818827\n𝕝 : Type ?u.818830\nE : Type u_1\nE₂ : Type ?u.818836\nE₃ : Type ?u.818839\nF : Type ?u.818842\nG : Type ?u.818845\nι : Type ?u.818848\ninst✝² : SeminormedRing �... | [
665,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
665,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | DifferentiableWithinAt.smul | [] | [
199,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Topology/Algebra/UniformRing.lean | UniformSpace.Completion.continuous_mul | [
{
"state_after": "α : Type u_1\ninst✝³ : Ring α\ninst✝² : UniformSpace α\ninst✝¹ : TopologicalRing α\ninst✝ : UniformAddGroup α\nm : α →+ α →+ Completion α := AddMonoidHom.compr₂ AddMonoidHom.mul toCompl\n⊢ Continuous fun p => p.fst * p.snd",
"state_before": "α : Type u_1\ninst✝³ : Ring α\ninst✝² : UniformS... | [
85,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Topology/Order/Basic.lean | Icc_mem_nhdsWithin_Ioi | [] | [
425,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/Data/Rat/NNRat.lean | NNRat.ext_iff | [] | [
86,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/RingTheory/IsTensorProduct.lean | IsBaseChange.lift_eq | [
{
"state_after": "R : Type u_1\nM : Type v₁\nN : Type v₂\nS : Type v₃\ninst✝¹⁴ : AddCommMonoid M\ninst✝¹³ : AddCommMonoid N\ninst✝¹² : CommRing R\ninst✝¹¹ : CommRing S\ninst✝¹⁰ : Algebra R S\ninst✝⁹ : Module R M\ninst✝⁸ : Module R N\ninst✝⁷ : Module S N\ninst✝⁶ : IsScalarTower R S N\nf : M →ₗ[R] N\nh : IsBaseCh... | [
192,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
8
] |
Mathlib/Analysis/Calculus/FDeriv/Bilinear.lean | ContinuousLinearMap.fderivWithin_of_bilinear | [] | [
148,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Order/SuccPred/LinearLocallyFinite.lean | injective_toZ | [] | [
363,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/RepresentationTheory/Action.lean | Action.associator_hom_hom | [
{
"state_after": "V : Type (u + 1)\ninst✝¹ : LargeCategory V\nG : MonCat\ninst✝ : MonoidalCategory V\nX Y Z : Action V G\n⊢ (𝟙 (X.V ⊗ Y.V) ⊗ 𝟙 Z.V) ≫ (α_ X.V Y.V Z.V).hom ≫ (𝟙 X.V ⊗ 𝟙 (Y.V ⊗ Z.V)) = (α_ X.V Y.V Z.V).hom",
"state_before": "V : Type (u + 1)\ninst✝¹ : LargeCategory V\nG : MonCat\ninst✝ : M... | [
514,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.comap_cocompact | [] | [
273,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Data/Nat/Interval.lean | Nat.image_Ico_mod | [
{
"state_after": "case inl\na b c n : ℕ\n⊢ image (fun x => x % 0) (Ico n (n + 0)) = range 0\n\ncase inr\na✝ b c n a : ℕ\nha : a ≠ 0\n⊢ image (fun x => x % a) (Ico n (n + a)) = range a",
"state_before": "a✝ b c n a : ℕ\n⊢ image (fun x => x % a) (Ico n (n + a)) = range a",
"tactic": "obtain rfl | ha := eq... | [
307,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Topology/MetricSpace/Kuratowski.lean | kuratowskiEmbedding.isometry | [] | [
123,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
11
] |
Mathlib/Topology/MetricSpace/Antilipschitz.lean | AntilipschitzWith.to_rightInvOn' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.8961\ninst✝² : PseudoEMetricSpace α\ninst✝¹ : PseudoEMetricSpace β\ninst✝ : PseudoEMetricSpace γ\nK : ℝ≥0\nf : α → β\ns : Set α\nhf : AntilipschitzWith K (Set.restrict s f)\ng : β → α\nt : Set β\ng_maps : MapsTo g t s\ng_i... | [
151,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
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