file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | isOpen_extChartAt_source | [] | [
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.refl_trans | [] | [
569,
19
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568,
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Mathlib/Algebra/CharP/Basic.lean | add_pow_prime_eq | [] | [
80,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/PNat/Factors.lean | PrimeMultiset.prod_smul | [
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Mathlib/Data/Complex/Basic.lean | Complex.normSq_I | [
{
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.lsub_const | [] | [
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21
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Mathlib/Data/Multiset/Basic.lean | Multiset.coe_foldr | [] | [
1406,
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.iSup_of_empty | [] | [
1012,
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1011,
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Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isRat_inv_zero | [
{
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497,
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Mathlib/RingTheory/Subring/Basic.lean | Subring.coe_toAddSubgroup | [] | [
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_const_left_of_ne | [
{
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Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.LHom.onTheory_model | [
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Mathlib/Order/Heyting/Basic.lean | toDual_sdiff | [] | [
1152,
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Mathlib/Algebra/Group/Units.lean | Units.inv_mul_eq_iff_eq_mul | [
{
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{
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Mathlib/Algebra/Module/GradedModule.lean | DirectSum.Gmodule.mul_smul' | [
{
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143,
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Mathlib/LinearAlgebra/QuadraticForm/Prod.lean | QuadraticForm.anisotropic_of_prod | [
{
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Mathlib/Algebra/Group/Basic.lean | eq_mul_inv_iff_mul_eq | [
{
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{
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ioc_subset_Ioo_right | [
{
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.SimpleFunc.setToSimpleFunc_indicator | [
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632,
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.nonempty_of_affineSpan_eq_top | [
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Mathlib/Data/Bool/Basic.lean | Bool.not_inj | [
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Mathlib/Data/Finsupp/NeLocus.lean | Finsupp.zipWith_neLocus_eq_right | [
{
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Mathlib/Analysis/Convex/Between.lean | wbtw_const_vsub_iff | [] | [
201,
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Mathlib/Topology/FiberBundle/Basic.lean | FiberPrebundle.continuous_proj | [
{
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Mathlib/Analysis/BoxIntegral/Partition/SubboxInduction.lean | BoxIntegral.Prepartition.iUnion_toSubordinate | [] | [
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Std/Classes/Order.lean | Std.TransCmp.lt_le_trans | [] | [
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Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.linearIsometryBoundedOfCompact_symm_apply | [] | [
319,
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Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.Measure.pi_Iio_ae_eq_pi_Iic | [] | [
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40
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Mathlib/RingTheory/HahnSeries.lean | HahnSeries.ofPowerSeries_apply | [
{
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Mathlib/CategoryTheory/Limits/Preserves/Shapes/Biproducts.lean | CategoryTheory.Limits.biproduct.mapBiproduct_inv_map_desc | [
{
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Mathlib/Algebra/Homology/HomologicalComplex.lean | HomologicalComplex.eqToHom_comp_d | [
{
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Mathlib/Data/Real/EReal.lean | EReal.top_mul_of_pos | [
{
"state_after": "x : EReal\nh : 0 < x\n⊢ x * ⊤ = ⊤",
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{
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Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | ContDiffOn.rpow | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.map_add_left_Ico | [
{
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1055,
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Mathlib/Probability/ProbabilityMassFunction/Basic.lean | Pmf.toMeasure_apply_eq_toOuterMeasure_apply | [] | [
256,
40
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Mathlib/Data/Real/NNReal.lean | NNReal.coe_multiset_prod | [] | [
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Std/Data/Int/DivMod.lean | Int.dvd_trans | [
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Mathlib/CategoryTheory/Groupoid/FreeGroupoid.lean | CategoryTheory.Groupoid.Free.freeGroupoidFunctor_comp | [
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_const_iff_isLittleO_one | [] | [
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Mathlib/Data/Set/Basic.lean | Set.empty_ssubset | [] | [
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70
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Mathlib/Algebra/Lie/Submodule.lean | LieModuleHom.coeSubmodule_range | [] | [
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6
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Mathlib/LinearAlgebra/Matrix/Reindex.lean | Matrix.reindexLinearEquiv_trans | [
{
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Mathlib/GroupTheory/Coset.lean | eq_cosets_of_normal | [
{
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},
{
... | [
254,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.volume_Ici | [
{
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},
{
"state_after": "no goals",
"state_before": "ι : Type ?u.247709\... | [
157,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
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Mathlib/Analysis/NormedSpace/CompactOperator.lean | IsCompactOperator.codRestrict | [] | [
291,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
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Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.set_lintegral_deterministic' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nι : Type ?u.398685\nmα : MeasurableSpace α\nmβ : MeasurableSpace β\nκ : { x // x ∈ kernel α β }\nf : β → ℝ≥0∞\ng : α → β\na : α\nhg : Measurable g\nhf : Measurable f\ns : Set β\nhs : MeasurableSet s\ninst✝ : Decidable (g a ∈ s)\n⊢ (∫⁻... | [
385,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/Order/Bounds/Basic.lean | upperBounds_mono_set | [] | [
192,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Data/Nat/Bitwise.lean | Nat.lxor'_zero | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ lxor' n 0 = n",
"tactic": "simp [lxor']"
}
] | [
194,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.join_append | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nS T : WSeq (WSeq α)\n⊢ ∀ {s t : WSeq α},\n (fun s1 s2 => ∃ s S T, s1 = append s (join (append S T)) ∧ s2 = append s (append (join S) (join T))) s t →\n Computation.LiftRel\n (LiftRelO (fun x x_1 => x = x_1) fun s1 s2 =>\n ∃ s S T, s1 ... | [
1732,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1708,
1
] |
Mathlib/Data/Vector/Mem.lean | Vector.mem_of_mem_tail | [
{
"state_after": "case zero\nα : Type u_1\nβ : Type ?u.2767\nn : ℕ\na a' : α\nv✝ : Vector α n\nha✝ : a ∈ toList (tail v✝)\nv : Vector α Nat.zero\nha : a ∈ toList (tail v)\n⊢ a ∈ toList v\n\ncase succ\nα : Type u_1\nβ : Type ?u.2767\nn✝ : ℕ\na a' : α\nv✝ : Vector α n✝\nha✝ : a ∈ toList (tail v✝)\nn : ℕ\nn_ih✝ : ... | [
76,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Std/Data/Option/Lemmas.lean | Option.ne_none_iff_exists' | [] | [
78,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
77,
1
] |
Mathlib/Data/Int/Basic.lean | Int.sign_negSucc | [] | [
136,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.eq_of_add_eq_of_aleph0_le | [
{
"state_after": "case a\na b c : Cardinal\nh : a + b = c\nha : a < c\nhc : ℵ₀ ≤ c\n⊢ b ≤ c\n\ncase a\na b c : Cardinal\nh : a + b = c\nha : a < c\nhc : ℵ₀ ≤ c\n⊢ c ≤ b",
"state_before": "a b c : Cardinal\nh : a + b = c\nha : a < c\nhc : ℵ₀ ≤ c\n⊢ b = c",
"tactic": "apply le_antisymm"
},
{
"stat... | [
776,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
769,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | ciSup_mono | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type ?u.55772\nγ : Type ?u.55775\nι : Sort u_2\ninst✝ : ConditionallyCompleteLattice α\ns t : Set α\na b : α\nf g : ι → α\nB : BddAbove (range g)\nH : ∀ (x : ι), f x ≤ g x\nh✝ : IsEmpty ι\n⊢ iSup f ≤ iSup g\n\ncase inr\nα : Type u_1\nβ : Type ?u.55772\nγ : Type ?u.5... | [
798,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.mem_map_of_injective | [] | [
1275,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1273,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.card_le_of_finset | [] | [
1337,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1336,
1
] |
Mathlib/LinearAlgebra/Prod.lean | Submodule.sup_eq_range | [
{
"state_after": "no goals",
"state_before": "R : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nM₅ : Type ?u.269908\nM₆ : Type ?u.269911\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid M₂\ninst✝¹ : Module R... | [
545,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
544,
1
] |
Mathlib/Algebra/IsPrimePow.lean | isPrimePow_iff_pow_succ | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : CommMonoidWithZero R\nn p✝ : R\nk✝ : ℕ\nx✝ : ∃ p k, Prime p ∧ 0 < k ∧ p ^ k = n\np : R\nk : ℕ\nhp : Prime p\nhk : 0 < k\nhn : p ^ k = n\n⊢ p ^ (?m.56323 x✝ p k hp hk hn + 1) = n",
"tactic": "rwa [Nat.sub_add_cancel hk]"
}
] | [
38,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.zeroLocus_iSup_ideal | [] | [
255,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.disjoint_one_left | [] | [
72,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.nadd_le_nadd_iff_right | [] | [
431,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/Algebra/Hom/Group.lean | OneHom.ext | [] | [
644,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
643,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.iUnion_single | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nI J J₁ J₂ : Box ι\nπ π₁ π₂ : Prepartition I\nx : ι → ℝ\nh : J ≤ I\n⊢ Prepartition.iUnion (single I J h) = ↑J",
"tactic": "simp [iUnion_def]"
}
] | [
230,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
src/lean/Init/Data/Fin/Basic.lean | Fin.val_ne_of_ne | [] | [
110,
39
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
109,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | closedBall_pi | [
{
"state_after": "case h\nα : Type u\nβ : Type v\nX : Type ?u.403409\nι : Type ?u.403412\ninst✝² : PseudoMetricSpace α\nπ : β → Type u_1\ninst✝¹ : Fintype β\ninst✝ : (b : β) → PseudoMetricSpace (π b)\nx : (b : β) → π b\nr : ℝ\nhr : 0 ≤ r\np : (b : β) → π b\n⊢ p ∈ closedBall x r ↔ p ∈ Set.pi Set.univ fun b => cl... | [
2067,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2064,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.le_total | [
{
"state_after": "d : ℕ\na b : ℤ√↑d\nt : Nonneg (b - a) ∨ Nonneg (-(b - a))\n⊢ a ≤ b ∨ b ≤ a",
"state_before": "d : ℕ\na b : ℤ√↑d\n⊢ a ≤ b ∨ b ≤ a",
"tactic": "have t := (b - a).nonneg_total"
},
{
"state_after": "no goals",
"state_before": "d : ℕ\na b : ℤ√↑d\nt : Nonneg (b - a) ∨ Nonneg (-(b... | [
756,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
754,
11
] |
Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.X.int_coe_snd | [] | [
329,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.mem_cylinder_iff_dist_le | [
{
"state_after": "case inl\nE : ℕ → Type u_1\ny : (n : ℕ) → E n\nn : ℕ\n⊢ y ∈ cylinder y n ↔ dist y y ≤ (1 / 2) ^ n\n\ncase inr\nE : ℕ → Type u_1\nx y : (n : ℕ) → E n\nn : ℕ\nhne : y ≠ x\n⊢ y ∈ cylinder x n ↔ dist y x ≤ (1 / 2) ^ n",
"state_before": "E : ℕ → Type u_1\nx y : (n : ℕ) → E n\nn : ℕ\n⊢ y ∈ cylin... | [
327,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/CategoryTheory/Products/Bifunctor.lean | CategoryTheory.Bifunctor.map_id | [] | [
31,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
29,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.tr_ret_halt | [] | [
1147,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1147,
1
] |
Mathlib/Init/Algebra/Order.lean | le_of_not_lt | [] | [
329,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/Topology/Instances/Matrix.lean | Continuous.matrix_updateRow | [] | [
216,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_eq_inducedOuterMeasure | [] | [
172,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Std/Data/String/Lemmas.lean | String.valid_toSubstring | [] | [
973,
31
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
972,
1
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.dvd_to_int | [
{
"state_after": "α : Type ?u.1071772\nm n : ZNum\nx✝ : ↑m ∣ ↑n\nk : ℤ\ne : ↑n = ↑m * k\n⊢ ↑(↑m * k) = m * ↑k",
"state_before": "α : Type ?u.1071772\nm n : ZNum\nx✝ : ↑m ∣ ↑n\nk : ℤ\ne : ↑n = ↑m * k\n⊢ n = m * ↑k",
"tactic": "rw [← of_to_int n, e]"
},
{
"state_after": "no goals",
"state_befo... | [
1575,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1574,
1
] |
Mathlib/Algebra/Homology/QuasiIso.lean | HomologicalComplex.Hom.from_single₀_exact_f_d_at_zero | [
{
"state_after": "ι : Type ?u.92227\nV : Type u\ninst✝⁸ : Category V\ninst✝⁷ : HasZeroMorphisms V\ninst✝⁶ : HasZeroObject V\ninst✝⁵ : HasEqualizers V\ninst✝⁴ : HasImages V\ninst✝³ : HasImageMaps V\ninst✝² : HasCokernels V\nc : ComplexShape ι\nC D E : HomologicalComplex V c\nW : Type u_2\ninst✝¹ : Category W\nin... | [
193,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Analysis/Calculus/Dslope.lean | dslope_same | [] | [
40,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | Submodule.topologicalClosure_map | [] | [
555,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
550,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.coe_eq_zero_iff_isEmpty | [] | [
115,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Algebra/Lie/OfAssociative.lean | LinearEquiv.lieConj_symm | [] | [
339,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Data/Fintype/Basic.lean | Fin.image_succAbove_univ | [
{
"state_after": "case a\nα : Type ?u.100123\nβ : Type ?u.100126\nγ : Type ?u.100129\nn : ℕ\ni m : Fin (n + 1)\n⊢ m ∈ image (↑(succAbove i)) univ ↔ m ∈ {i}ᶜ",
"state_before": "α : Type ?u.100123\nβ : Type ?u.100126\nγ : Type ?u.100129\nn : ℕ\ni : Fin (n + 1)\n⊢ image (↑(succAbove i)) univ = {i}ᶜ",
"tact... | [
817,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
815,
1
] |
Mathlib/Data/Int/Cast/Basic.lean | Int.cast_negOfNat | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : AddGroupWithOne R\nn : ℕ\n⊢ ↑(negOfNat n) = -↑n",
"tactic": "simp [Int.cast_neg, negOfNat_eq]"
}
] | [
106,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.bounded_range_of_cauchy_map_cofinite | [] | [
2435,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2433,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.lt_inf'_iff | [] | [
1113,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1112,
1
] |
Mathlib/Analysis/InnerProductSpace/GramSchmidtOrtho.lean | gramSchmidtNormed_unit_length_coe | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\nE : Type u_3\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace 𝕜 E\nι : Type u_1\ninst✝² : LinearOrder ι\ninst✝¹ : LocallyFiniteOrderBot ι\ninst✝ : IsWellOrder ι fun x x_1 => x < x_1\nf : ι → E\nn : ι\nh₀ : LinearInde... | [
278,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/Algebra/Lie/Solvable.lean | LieAlgebra.abelian_iff_derived_succ_eq_bot | [
{
"state_after": "no goals",
"state_before": "R : Type u\nL : Type v\nM : Type w\nL' : Type w₁\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\ninst✝¹ : LieRing L'\ninst✝ : LieAlgebra R L'\nI✝ J : LieIdeal R L\nf : L' →ₗ⁅R⁆ L\nI : LieIdeal R L\nk : ℕ\n⊢ IsLieAbelian { x // x ∈ ↑(D k I) } ↔... | [
143,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Order/Bounds/Basic.lean | mem_lowerBounds_image2 | [] | [
1363,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1361,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mem_centralizer_iff_commutator_eq_one | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nG' : Type ?u.412647\ninst✝² : Group G\ninst✝¹ : Group G'\nA : Type ?u.412656\ninst✝ : AddGroup A\nH K : Subgroup G\ng : G\n⊢ g ∈ centralizer H ↔ ∀ (h : G), h ∈ H → h * g * h⁻¹ * g⁻¹ = 1",
"tactic": "simp only [mem_centralizer_iff, mul_inv_eq_if... | [
2288,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2286,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.sUnion_eq_iUnion | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.167312\nγ : Type ?u.167315\nι : Sort ?u.167318\nι' : Sort ?u.167321\nι₂ : Sort ?u.167324\nκ : ι → Sort ?u.167329\nκ₁ : ι → Sort ?u.167334\nκ₂ : ι → Sort ?u.167339\nκ' : ι' → Sort ?u.167344\ns : Set (Set α)\n⊢ ⋃₀ s = ⋃ (i : ↑s), ↑i",
... | [
1322,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1321,
1
] |
Mathlib/Topology/Order/Basic.lean | nhdsWithin_Iio_self_neBot | [] | [
2421,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2420,
1
] |
Mathlib/Data/List/Basic.lean | List.mem_of_mem_head? | [] | [
883,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
882,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.monomial_zero_eq_C_apply | [] | [
378,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.universalHom_unique | [] | [
824,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
822,
1
] |
Mathlib/RingTheory/DiscreteValuationRing/Basic.lean | DiscreteValuationRing.HasUnitMulPowIrreducibleFactorization.of_ufd_of_unique_irreducible | [
{
"state_after": "case intro\nR : Type u_1\ninst✝² : CommRing R\nhR : HasUnitMulPowIrreducibleFactorization R\ninst✝¹ : IsDomain R\ninst✝ : UniqueFactorizationMonoid R\nh₂ : ∀ ⦃p q : R⦄, Irreducible p → Irreducible q → Associated p q\np : R\nhp : Irreducible p\n⊢ HasUnitMulPowIrreducibleFactorization R",
"s... | [
249,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Data/MvPolynomial/PDeriv.lean | MvPolynomial.pderiv_monomial | [
{
"state_after": "R : Type u\nσ : Type v\na a' a₁ a₂ : R\ns : σ →₀ ℕ\ninst✝ : CommSemiring R\ni : σ\n⊢ (sum s fun a_1 b => ↑(monomial (s - single a_1 1)) (a * ↑b) * Pi.single i 1 a_1) =\n ↑(monomial (s - single i 1)) (a * ↑(↑s i))",
"state_before": "R : Type u\nσ : Type v\na a' a₁ a₂ : R\ns : σ →₀ ℕ\nins... | [
82,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/CategoryTheory/Bicategory/Basic.lean | CategoryTheory.Bicategory.inv_hom_whiskerLeft | [
{
"state_after": "no goals",
"state_before": "B : Type u\ninst✝ : Bicategory B\na b c d e : B\nf : a ⟶ b\ng h : b ⟶ c\nη : g ≅ h\n⊢ f ◁ η.inv ≫ f ◁ η.hom = 𝟙 (f ≫ h)",
"tactic": "rw [← whiskerLeft_comp, inv_hom_id, whiskerLeft_id]"
}
] | [
210,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Logic/Relation.lean | Reflexive.ne_imp_iff | [] | [
71,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Data/Set/Image.lean | Set.range_some_inter_none | [] | [
1197,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1196,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.succ_mul_succ_eq | [
{
"state_after": "a b : Nat\n⊢ a * b + b + succ a = a * b + b + a + 1",
"state_before": "a b : Nat\n⊢ succ a * succ b = a * b + a + b + 1",
"tactic": "rw [mul_succ, succ_mul, Nat.add_right_comm _ a]"
},
{
"state_after": "no goals",
"state_before": "a b : Nat\n⊢ a * b + b + succ a = a * b + b... | [
422,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
421,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | differentiableAt_of_deriv_ne_zero | [] | [
248,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
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