file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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|---|---|---|---|---|---|---|
Std/Data/Array/Init/Lemmas.lean | Array.toListAppend_eq | [
{
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Mathlib/Data/Rat/Cast.lean | Rat.cast_mul_of_ne_zero | [
{
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150,
49
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Mathlib/Analysis/Calculus/BumpFunctionInner.lean | ContDiffBump.nonneg' | [] | [
396,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
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Mathlib/Data/Matrix/Basic.lean | Matrix.row_mul_col_apply | [] | [
2729,
6
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2727,
1
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Mathlib/Topology/Algebra/InfiniteSum/Real.lean | cauchySeq_of_summable_dist | [] | [
72,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.bddAbove_range | [
{
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{
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28
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.vsub_subset_iff | [] | [
677,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
676,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.one_add_omega | [
{
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"tactic": "re... | [
627,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
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Mathlib/RingTheory/FinitePresentation.lean | Algebra.FinitePresentation.polynomial | [] | [
124,
80
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122,
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Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | LinearMap.SeparatingLeft.toMatrix₂' | [] | [
725,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
723,
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Mathlib/LinearAlgebra/Dual.lean | LinearMap.dualMap_bijective_iff | [
{
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88
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1513,
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_add_le_of_degree_le | [] | [
643,
44
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641,
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Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_neg_Ioi | [
{
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}
] | [
297,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
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Mathlib/Order/Lattice.lean | Monotone.of_map_sup | [] | [
1114,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1112,
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Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.IntegrableOn.mono | [] | [
127,
48
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126,
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Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.IsZero.iff_isSplitEpi_eq_zero | [
{
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225,
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Mathlib/Data/Real/CauSeq.lean | CauSeq.sup_limZero | [
{
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853,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
848,
1
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Mathlib/Order/Partition/Finpartition.lean | Finpartition.card_parts_le_card | [
{
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},
{
"state_after": "... | [
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25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
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Mathlib/Algebra/Category/ModuleCat/Adjunctions.lean | ModuleCat.Free.associativity | [
{
"state_after": "R : Type u\ninst✝ : CommRing R\nX Y Z : Type u\n⊢ ((μ R X Y).hom ⊗ 𝟙 ((free R).obj Z)) ≫ (μ R (X ⊗ Y) Z).hom ≫ map (free R).toPrefunctor.obj (α_ X Y Z).hom =\n (α_ ((free R).obj X) ((free R).obj Y) ((free R).obj Z)).hom ≫\n (𝟙 ((free R).obj X) ⊗ (μ R Y Z).hom) ≫ (μ R X (Y ⊗ Z)).hom",... | [
182,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
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Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.eq_pow_of_pow_eq_one | [
{
"state_after": "case intro\nM : Type ?u.3458904\nN : Type ?u.3458907\nG : Type ?u.3458910\nR : Type u_1\nS : Type ?u.3458916\nF : Type ?u.3458919\ninst✝⁴ : CommMonoid M\ninst✝³ : CommMonoid N\ninst✝² : DivisionCommMonoid G\nk✝ l : ℕ\ninst✝¹ : CommRing R\nζ✝ : Rˣ\nh✝ : IsPrimitiveRoot ζ✝ k✝\ninst✝ : IsDomain R... | [
778,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
770,
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Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.sInf_apply | [
{
"state_after": "no goals",
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"tactic": "simp_rw [sInf_eq_boundedBy_sInfGen, boundedBy_apply, iSup_sInfG... | [
1175,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1172,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.tan_add_pi | [] | [
805,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
804,
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Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.WalkingPair.swap_apply_left | [] | [
66,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
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Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.valuation_p | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\n⊢ valuation ↑p = 1",
"tactic": "simp [valuation]"
}
] | [
394,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
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Mathlib/Data/Nat/Bitwise.lean | Nat.land'_comm | [] | [
181,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
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Mathlib/Data/Real/NNReal.lean | Set.OrdConnected.preimage_real_toNNReal | [] | [
1042,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1041,
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Mathlib/Data/Finset/Sups.lean | Finset.infs_assoc | [] | [
374,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
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Mathlib/Order/Filter/Basic.lean | Filter.frequently_bot | [
{
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"tactic": "simp"
}
] | [
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1386,
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Mathlib/Analysis/Calculus/Deriv/Basic.lean | HasDerivAt.continuousOn | [] | [
728,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
727,
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Mathlib/Data/Finset/Slice.lean | Finset.subset_powersetLen_univ_iff | [
{
"state_after": "no goals",
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"tactic": "rw [mem_powerset_len_univ_iff, mem_coe]"
}
] | [
110,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
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Mathlib/Analysis/Calculus/LHopital.lean | deriv.lhopital_zero_atBot_on_Iio | [
{
"state_after": "a b : ℝ\nhab : a < b\nl : Filter ℝ\nf f' g g' : ℝ → ℝ\nhdf✝ : DifferentiableOn ℝ f (Iio a)\nhg' : ∀ (x : ℝ), x ∈ Iio a → deriv g x ≠ 0\nhfbot : Tendsto f atBot (𝓝 0)\nhgbot : Tendsto g atBot (𝓝 0)\nhdiv : Tendsto (fun x => deriv f x / deriv g x) atBot l\nhdf : ∀ (x : ℝ), x ∈ Iio a → Differen... | [
269,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
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Mathlib/GroupTheory/Subsemigroup/Basic.lean | Subsemigroup.closure_induction | [] | [
359,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
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Mathlib/Algebra/Star/Order.lean | star_mul_self_nonneg | [] | [
157,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_neg_of_base_lt_one | [] | [
302,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
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Mathlib/Data/Set/Basic.lean | Set.inter_self | [] | [
912,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
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Mathlib/Analysis/Convex/Cone/Basic.lean | Submodule.toConvexCone_bot | [] | [
533,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
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Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean | Matrix.SpecialLinearGroup.det_ne_zero | [
{
"state_after": "n : Type u\ninst✝³ : DecidableEq n\ninst✝² : Fintype n\nR : Type v\ninst✝¹ : CommRing R\nA B : SpecialLinearGroup n R\ninst✝ : Nontrivial R\ng : SpecialLinearGroup n R\n⊢ 1 ≠ 0",
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164,
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Mathlib/Order/JordanHolder.lean | CompositionSeries.bot_eraseTop | [] | [
411,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
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Mathlib/GroupTheory/OrderOfElement.lean | inf_eq_bot_of_coprime | [
{
"state_after": "G✝ : Type u\nA : Type v\nx✝ y : G✝\na b : A\nn m : ℕ\ninst✝⁵ : Group G✝\ninst✝⁴ : AddGroup A\ninst✝³ : Fintype G✝\nG : Type u_1\ninst✝² : Group G\nH K : Subgroup G\ninst✝¹ : Fintype { x // x ∈ H }\ninst✝ : Fintype { x // x ∈ K }\nh : coprime (Fintype.card { x // x ∈ H }) (Fintype.card { x // x... | [
1004,
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998,
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Mathlib/Data/Set/Finite.lean | Set.Finite.finite_subsets | [
{
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"tactic": "simpa [← @exists_finite_iff_finset α fun t =>... | [
1000,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
997,
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Mathlib/Topology/Instances/AddCircle.lean | AddCircle.coe_image_Ioc_eq | [
{
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Mathlib/CategoryTheory/Functor/EpiMono.lean | CategoryTheory.Functor.mono_map_iff_mono | [
{
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288,
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Mathlib/NumberTheory/LegendreSymbol/MulCharacter.lean | MulChar.inv_apply_eq_inv | [] | [
339,
21
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338,
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Mathlib/FieldTheory/Finiteness.lean | IsNoetherian.finite_basis_index | [] | [
71,
56
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69,
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Mathlib/CategoryTheory/EssentiallySmall.lean | CategoryTheory.essentiallySmall_iff_of_thin | [
{
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"tactic": "simp [essentiallySmall_iff, CategoryTheory.locallySmall_of_thin]"
}
] | [
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236,
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Mathlib/Algebra/Group/WithOne/Basic.lean | WithOne.map_map | [
{
"state_after": "no goals",
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"tactic": "induction x using WithOne.cases_on <;> rfl"
}
] | [
124,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
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Mathlib/RingTheory/Multiplicity.lean | multiplicity.neg | [
{
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"tactic": "simp only [multiplicity, PartENat.find, dvd_neg]"
},
{
"state_after": "α : Type u_1\ninst✝¹ : Ring α\... | [
428,
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422,
11
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Mathlib/Order/Circular.lean | btw_refl_right | [] | [
311,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/RingTheory/Ideal/LocalRing.lean | LocalRing.ResidueField.lift_comp_residue | [] | [
397,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.Nonempty.of_vsub_right | [] | [
645,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.card_congr | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\ns t✝ : Finset α\nf✝ : α → β\nn : ℕ\nt : Finset β\nf : (a : α) → a ∈ s → β\nh₁ : ∀ (a : α) (ha : a ∈ s), f a ha ∈ t\nh₂ : ∀ (a b : α) (ha : a ∈ s) (hb : b ∈ s), f a ha = f b hb → a = b\nh₃ : ∀ (b : β), b ∈ t → ∃ a ha, f a ha = b\n⊢ car... | [
327,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
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Mathlib/Topology/Algebra/Module/Multilinear.lean | ContinuousMultilinearMap.sum_apply | [] | [
226,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
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Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.limit.isoLimitCone_hom_π | [
{
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"state_before": "J : Type u₁\ninst✝³ : Category J\nK : Type u₂\ninst✝²... | [
257,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
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Mathlib/Data/List/Basic.lean | List.head?_append | [
{
"state_after": "case nil\nι : Type ?u.42760\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ t : List α\nx : α\nh : x ∈ head? []\n⊢ x ∈ head? ([] ++ t)\n\ncase cons\nι : Type ?u.42760\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ t : List α\nx head✝ : α\ntail✝ : List α\nh : x ∈ head? (head✝ :: ... | [
898,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
897,
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Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_one | [
{
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}
] | [
129,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
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Mathlib/GroupTheory/Coset.lean | QuotientGroup.rightRel_r_eq_rightCosetEquivalence | [
{
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"state_before": "α : Type u_1\ninst✝ : Group α\ns : Subgroup α\n⊢ Setoid.r = RightCosetEquivalence ↑s",
"tactic": "ext"
},
{
"state_after": "case h.h.a... | [
399,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
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Mathlib/Algebra/Order/SMul.lean | smul_nonpos_of_nonneg_of_nonpos | [] | [
111,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
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Mathlib/Init/Data/Nat/Bitwise.lean | Nat.ldiff'_bit | [] | [
483,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderEmbedding.isWellOrder | [] | [
682,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
681,
11
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Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.pullback_top | [] | [
469,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
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Mathlib/Data/Matrix/Block.lean | Matrix.blockDiag'_sub | [] | [
906,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
904,
1
] |
Mathlib/Order/Filter/Cofinite.lean | Set.Finite.eventually_cofinite_nmem | [] | [
81,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.nfp_lt_ord | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.35734\nr : α → α → Prop\nf : Ordinal → Ordinal\nc : Ordinal\nhc : ℵ₀ < cof c\nhf : ∀ (i : Ordinal), i < c → f i < c\na : Ordinal\n⊢ Cardinal.lift (#Unit) < cof c",
"tactic": "simpa using Cardinal.one_lt_aleph0.trans hc"
}
] | [
411,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/Algebra/GradedMonoid.lean | GradedMonoid.GMonoid.gnpowRec_zero | [] | [
162,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_neg_atTop_iff | [] | [
859,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
858,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.inv_map_iInf | [] | [
516,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
1
] |
Mathlib/Order/Heyting/Basic.lean | himp_le_himp | [] | [
423,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/Analysis/NormedSpace/ConformalLinearMap.lean | IsConformalMap.injective | [
{
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97,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
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Mathlib/RingTheory/IsTensorProduct.lean | IsBaseChange.equiv_tmul | [] | [
255,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
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Mathlib/NumberTheory/Padics/Hensel.lean | newton_seq_succ_dist | [
{
"state_after": "no goals",
"state_before": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nF : Polynomial ℤ_[p]\na : ℤ_[p]\nhnorm : ‖Polynomial.eval a F‖ < ‖Polynomial.eval a (↑Polynomial.derivative F)‖ ^ 2\nhnsol : Polynomial.eval a F ≠ 0\nn : ℕ\n⊢ ‖Polynomial.eval (newton_seq n) F‖ / ‖Polynomial.eval (newton_seq n)... | [
276,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
9
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Mathlib/GroupTheory/PGroup.lean | IsPGroup.comap_of_injective | [] | [
307,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.two_zsmul_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "θ : Angle\n⊢ 2 • θ = 0 ↔ θ = 0 ∨ θ = ↑π",
"tactic": "simp_rw [two_zsmul, ← two_nsmul, two_nsmul_eq_zero_iff]"
}
] | [
207,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Data/Int/Order/Lemmas.lean | Int.natAbs_lt_iff_mul_self_lt | [
{
"state_after": "a✝ b✝ : ℤ\nn : ℕ\na b : ℤ\n⊢ natAbs a < natAbs b ↔ ↑(natAbs a) < ↑(natAbs b)",
"state_before": "a✝ b✝ : ℤ\nn : ℕ\na b : ℤ\n⊢ natAbs a < natAbs b ↔ a * a < b * b",
"tactic": "rw [← abs_lt_iff_mul_self_lt, abs_eq_natAbs, abs_eq_natAbs]"
},
{
"state_after": "no goals",
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42,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
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Mathlib/Data/Fin/Basic.lean | Fin.castLT_mk | [] | [
1008,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1007,
1
] |
Mathlib/Data/PFunctor/Univariate/Basic.lean | PFunctor.fst_map | [
{
"state_after": "case mk\nP : PFunctor\nα✝ β✝ α β : Type u\nf : α → β\nfst✝ : P.A\nsnd✝ : B P fst✝ → α\n⊢ (f <$> { fst := fst✝, snd := snd✝ }).fst = { fst := fst✝, snd := snd✝ }.fst",
"state_before": "P : PFunctor\nα✝ β✝ α β : Type u\nx : Obj P α\nf : α → β\n⊢ (f <$> x).fst = x.fst",
"tactic": "cases x... | [
143,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Analysis/Normed/Group/HomCompletion.lean | NormedAddGroupHom.completion_comp | [
{
"state_after": "case H\nG : Type u_1\ninst✝² : SeminormedAddCommGroup G\nH : Type u_2\ninst✝¹ : SeminormedAddCommGroup H\nK : Type u_3\ninst✝ : SeminormedAddCommGroup K\nf : NormedAddGroupHom G H\ng : NormedAddGroupHom H K\nx : Completion G\n⊢ ↑(NormedAddGroupHom.comp (completion g) (completion f)) x = ↑(comp... | [
116,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Algebra/Order/Sub/Canonical.lean | lt_of_tsub_lt_tsub_right_of_le | [
{
"state_after": "α : Type u_1\ninst✝⁵ : AddCommSemigroup α\ninst✝⁴ : PartialOrder α\ninst✝³ : ExistsAddOfLE α\ninst✝² : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\na b c d : α\nh : c ≤ b\nh2 : a - c < b - c\n⊢ a ≠ b",
"state_before": "α : Type u_1\n... | [
62,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/MeasureTheory/Lattice.lean | AEMeasurable.sup_const | [] | [
133,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.sign_extendDomain | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝⁴ : DecidableEq α\ninst✝³ : Fintype α\ninst✝² : DecidableEq β\ninst✝¹ : Fintype β\ne : Perm α\np : β → Prop\ninst✝ : DecidablePred p\nf : α ≃ Subtype p\n⊢ ↑sign (extendDomain e f) = ↑sign e",
"tactic": "simp only [Equiv.Perm.exte... | [
794,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
792,
1
] |
Mathlib/Analysis/Convex/Extreme.lean | mem_extremePoints_iff_extreme_singleton | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.5166\nι : Type ?u.5169\nπ : ι → Type ?u.5174\ninst✝² : OrderedSemiring 𝕜\ninst✝¹ : AddCommMonoid E\ninst✝ : SMul 𝕜 E\nA B C : Set E\nx : E\n⊢ x ∈ extremePoints 𝕜 A → IsExtreme 𝕜 A {x}",
"state_before": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.5... | [
148,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/MeasureTheory/Function/LpOrder.lean | MeasureTheory.Memℒp.sup | [] | [
73,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Data/Polynomial/IntegralNormalization.lean | Polynomial.integralNormalization_support | [
{
"state_after": "R : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝ : Semiring R\nf : R[X]\na✝ : ℕ\n⊢ a✝ ∈ support (integralNormalization f) → a✝ ∈ support f",
"state_before": "R : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝ : Semiring R\nf : R[X]\n⊢ support (integralNormalization f) ⊆... | [
62,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | nnnorm_prod_le | [
{
"state_after": "𝓕 : Type ?u.1102940\n𝕜 : Type ?u.1102943\nα : Type ?u.1102946\nι : Type u_1\nκ : Type ?u.1102952\nE : Type u_2\nF : Type ?u.1102958\nG : Type ?u.1102961\ninst✝¹ : SeminormedCommGroup E\ninst✝ : SeminormedCommGroup F\na a₁ a₂ b b₁ b₂ : E\nr r₁ r₂ : ℝ\ns : Finset ι\nf : ι → E\n⊢ ‖∏ a in s, f a... | [
1690,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1687,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_subset_Ioo | [] | [
472,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
1
] |
Mathlib/Algebra/Group/Basic.lean | self_eq_mul_right | [] | [
190,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Data/Sym/Sym2.lean | Sym2.map_pair_eq | [] | [
266,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | Matrix.toLinearMapₛₗ₂'_symm | [] | [
241,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Data/Rat/Order.lean | Rat.num_pos_iff_pos | [
{
"state_after": "no goals",
"state_before": "a✝ b c a : ℚ\n⊢ a.num ≤ 0 ↔ a ≤ 0",
"tactic": "simpa [(by cases a; rfl : (-a).num = -a.num)] using @num_nonneg_iff_zero_le (-a)"
},
{
"state_after": "case mk'\na b c : ℚ\nnum✝ : ℤ\nden✝ : ℕ\nden_nz✝ : den✝ ≠ 0\nreduced✝ : Nat.coprime (Int.natAbs num✝... | [
285,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/GroupTheory/Coset.lean | QuotientGroup.induction_on | [] | [
479,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/Algebra/Group/Basic.lean | eq_one_div_of_mul_eq_one_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.21993\nG : Type ?u.21996\ninst✝ : DivisionMonoid α\na b c : α\nh : b * a = 1\n⊢ b = 1 / a",
"tactic": "rw [eq_inv_of_mul_eq_one_left h, one_div]"
}
] | [
379,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.mapRange_sub' | [] | [
1267,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1264,
1
] |
Mathlib/Algebra/Group/WithOne/Defs.lean | WithZero.coe_pow | [] | [
268,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | dist_self_div_left | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.640919\n𝕜 : Type ?u.640922\nα : Type ?u.640925\nι : Type ?u.640928\nκ : Type ?u.640931\nE : Type u_1\nF : Type ?u.640937\nG : Type ?u.640940\ninst✝¹ : SeminormedCommGroup E\ninst✝ : SeminormedCommGroup F\na✝ a₁ a₂ b✝ b₁ b₂ : E\nr r₁ r₂ : ℝ\na b : E... | [
1423,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1422,
1
] |
Mathlib/Combinatorics/Composition.lean | Composition.eq_ones_iff_le_length | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nc✝ c : Composition n\n⊢ c = ones n ↔ n ≤ length c",
"tactic": "simp [eq_ones_iff_length, le_antisymm_iff, c.length_le]"
}
] | [
566,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
565,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.coe_inf | [] | [
970,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
969,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.im_sq_le_normSq | [] | [
668,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
667,
1
] |
Mathlib/Algebra/Module/Injective.lean | Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd | [
{
"state_after": "R : Type u\ninst✝⁷ : Ring R\nQ : TypeMax\ninst✝⁶ : AddCommGroup Q\ninst✝⁵ : Module R Q\nM N : Type (max u v)\ninst✝⁴ : AddCommGroup M\ninst✝³ : AddCommGroup N\ninst✝² : Module R M\ninst✝¹ : Module R N\ni : M →ₗ[R] N\nf : M →ₗ[R] Q\ninst✝ : Fact (Function.Injective ↑i)\nh : Baer R Q\ny : N\nr r... | [
349,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Independent.lean | AffineIndependent.affineIndependent_of_not_mem_span | [
{
"state_after": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type u_4\np : ι → P\ni : ι\nha : AffineIndependent k fun x => p ↑x\nhi : ¬p i ∈ affineSpan k (p '' {x | x ≠ i})\ns : Finset ι\nw : ι → k\nhw : ∑ i in s,... | [
675,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
633,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.zero_inv | [
{
"state_after": "no goals",
"state_before": "σ : Type u_1\nR : Type ?u.1763981\nk : Type u_2\ninst✝ : Field k\n⊢ 0⁻¹ = 0",
"tactic": "rw [inv_eq_zero, constantCoeff_zero]"
}
] | [
965,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
964,
1
] |
Mathlib/Order/OrdContinuous.lean | LeftOrdContinuous.map_ciSup | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : ConditionallyCompleteLattice α\ninst✝¹ : ConditionallyCompleteLattice β\ninst✝ : Nonempty ι\nf : α → β\nhf : LeftOrdContinuous f\ng : ι → α\nhg : BddAbove (range g)\n⊢ sSup (range (f ∘ g)) = sSup (range fun i => f (g i))",
"state_bef... | [
157,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
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