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/LinearAlgebra/Finsupp.lean | Finsupp.span_eq_range_total | [
{
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655,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
654,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | HasStrictFDerivAt.hasStrictDerivAt | [] | [
209,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
11
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Mathlib/Algebra/Order/Group/Defs.lean | inv_le_inv' | [] | [
1247,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1245,
1
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Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | coplanar_triple | [] | [
751,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
750,
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Mathlib/Analysis/Calculus/Series.lean | iteratedFDeriv_tsum | [
{
"state_after": "case zero\nα : Type u_4\nβ : Type ?u.65025\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : CompleteSpace F\nu : α → ℝ\ninst✝ : NormedSpace 𝕜 F\nf : α → E → F\nf' : α → E → E →L[𝕜... | [
215,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
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Mathlib/Data/Finset/Sum.lean | Finset.disjSum_mono_right | [] | [
94,
37
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93,
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.single_add_single_eq_single_add_single | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.473549\nγ : Type ?u.473552\nι : Type ?u.473555\nM : Type u_1\nM' : Type ?u.473561\nN : Type ?u.473564\nP : Type ?u.473567\nG : Type ?u.473570\nH : Type ?u.473573\nR : Type ?u.473576\nS : Type ?u.473579\ninst✝ : AddCommMonoid M\nk l m n ... | [
1291,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1285,
1
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Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.StableUnderInverse.unop | [] | [
132,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
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Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Equiv.apply_symm_apply | [] | [
781,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
780,
1
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Mathlib/Topology/ContinuousFunction/Algebra.lean | ContinuousMap.coe_prod | [] | [
382,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
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Mathlib/Data/Set/Basic.lean | Set.union_union_union_comm | [] | [
1090,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1089,
1
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Mathlib/Algebra/Star/SelfAdjoint.lean | IsSelfAdjoint.neg | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nA : Type ?u.8541\ninst✝¹ : AddGroup R\ninst✝ : StarAddMonoid R\nx : R\nhx : IsSelfAdjoint x\n⊢ IsSelfAdjoint (-x)",
"tactic": "simp only [isSelfAdjoint_iff, star_neg, hx.star_eq]"
}
] | [
132,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
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Mathlib/Topology/UniformSpace/Basic.lean | Dense.biUnion_uniformity_ball | [
{
"state_after": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.92331\ninst✝ : UniformSpace α\ns : Set α\nU : Set (α × α)\nhs : Dense s\nhU : U ∈ 𝓤 α\ny : α\n⊢ ∃ i j, y ∈ ball i U",
"state_before": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.92331\ninst✝ : UniformSpac... | [
1025,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1021,
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Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.map_id | [] | [
214,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.single_apply | [
{
"state_after": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝ : (i : ι) → Zero (β i)\ns : Finset ι\nx : (i : ↑↑s) → β ↑i\ni✝ i i' : ι\nb : β i\n⊢ (if h : i' = i then (_ : i = i') ▸ b else OfNat.ofNat 0 i') = if h : i = i' then Eq.recOn h b else 0",
... | [
644,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
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Mathlib/MeasureTheory/Measure/Stieltjes.lean | StieltjesFunction.measure_Icc | [
{
"state_after": "case inl\nf : StieltjesFunction\na b : ℝ\nhab : a ≤ b\n⊢ ↑↑(StieltjesFunction.measure f) (Icc a b) = ofReal (↑f b - leftLim (↑f) a)\n\ncase inr\nf : StieltjesFunction\na b : ℝ\nhab : b < a\n⊢ ↑↑(StieltjesFunction.measure f) (Icc a b) = ofReal (↑f b - leftLim (↑f) a)",
"state_before": "f : ... | [
555,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | tendstoUniformlyOn_iff_tendstoUniformly_comp_coe | [
{
"state_after": "no goals",
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155,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisConnection.u_top | [] | [
245,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/CategoryTheory/Idempotents/Karoubi.lean | CategoryTheory.Idempotents.Karoubi.sum_hom | [] | [
209,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.le_restrict_univ_iff_le | [
{
"state_after": "case mp\nα : Type u_1\nβ : Type ?u.546843\nm : MeasurableSpace α\nM : Type u_2\ninst✝² : TopologicalSpace M\ninst✝¹ : AddCommMonoid M\ninst✝ : PartialOrder M\nv w : VectorMeasure α M\n⊢ restrict v Set.univ ≤ restrict w Set.univ → v ≤ w\n\ncase mpr\nα : Type u_1\nβ : Type ?u.546843\nm : Measura... | [
914,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
905,
1
] |
Mathlib/Order/Monotone/Basic.lean | injective_of_lt_imp_ne | [
{
"state_after": "ι : Type ?u.16131\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.16140\nπ : ι → Type ?u.16145\nr : α → α → Prop\ninst✝ : LinearOrder α\nf : α → β\nh : ∀ (x y : α), x < y → f x ≠ f y\nx y : α\nhf : f x = f y\n⊢ x = y",
"state_before": "ι : Type ?u.16131\nα : Type u\nβ : Type v\nγ : Type w... | [
558,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
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Mathlib/Order/Filter/Extr.lean | IsMinFilter.min | [] | [
589,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
586,
1
] |
Mathlib/Data/Set/Function.lean | Set.eqOn_empty | [] | [
188,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
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] |
Mathlib/Computability/Primrec.lean | Primrec₂.nat_iff' | [] | [
547,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
544,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.smul_eq_map | [] | [
681,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | Filter.Tendsto.rpow | [] | [
279,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/MeasureTheory/Covering/DensityTheorem.lean | IsUnifLocDoublingMeasure.tendsto_closedBall_filterAt | [
{
"state_after": "case refine'_1\nα : Type u_2\ninst✝⁵ : MetricSpace α\ninst✝⁴ : MeasurableSpace α\nμ : MeasureTheory.Measure α\ninst✝³ : IsUnifLocDoublingMeasure μ\ninst✝² : SecondCountableTopology α\ninst✝¹ : BorelSpace α\ninst✝ : IsLocallyFiniteMeasure μ\nK : ℝ\nx : α\nι : Type u_1\nl : Filter ι\nw : ι → α\n... | [
135,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
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Mathlib/Data/Set/Sups.lean | Set.infs_inter_subset_left | [] | [
324,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
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Mathlib/Algebra/DirectSum/Basic.lean | DirectSum.of_eq_same | [] | [
126,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_restrict_iUnion_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.559207\nγ : Type ?u.559210\nδ : Type ?u.559213\nι : Type u_1\nR : Type ?u.559219\nR' : Type ?u.559222\nm0 : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t : Set α\ni... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Lattice.lean | Set.compl_iUnion₂ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.67630\nγ : Type ?u.67633\nι : Sort u_2\nι' : Sort ?u.67639\nι₂ : Sort ?u.67642\nκ : ι → Sort u_3\nκ₁ : ι → Sort ?u.67652\nκ₂ : ι → Sort ?u.67657\nκ' : ι' → Sort ?u.67662\ns : (i : ι) → κ i → Set α\n⊢ (⋃ (i : ι) (j : κ i), s i j)ᶜ = ⋂ (i... | [
497,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
] |
Mathlib/RingTheory/PowerSeries/WellKnown.lean | PowerSeries.exp_mul_exp_neg_eq_one | [
{
"state_after": "no goals",
"state_before": "A : Type u_1\ninst✝¹ : CommRing A\ninst✝ : Algebra ℚ A\n⊢ exp A * ↑evalNegHom (exp A) = 1",
"tactic": "convert exp_mul_exp_eq_exp_add (1 : A) (-1) <;> simp"
}
] | [
188,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Algebra/Free.lean | Magma.AssocQuotient.hom_ext | [] | [
397,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
] |
Mathlib/Data/Real/Pointwise.lean | Real.iInf_mul_of_nonpos | [
{
"state_after": "no goals",
"state_before": "ι : Sort u_1\nα : Type ?u.16734\ninst✝ : LinearOrderedField α\nr : ℝ\nha : r ≤ 0\nf : ι → ℝ\n⊢ (⨅ (i : ι), f i) * r = ⨆ (i : ι), f i * r",
"tactic": "simp only [Real.mul_iInf_of_nonpos ha, mul_comm]"
}
] | [
143,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.adjoin_induction₂ | [
{
"state_after": "case refine'_1\nR : Type u\nA : Type v\nB : Type w\ninst✝⁴ : CommSemiring R\ninst✝³ : Semiring A\ninst✝² : Semiring B\ninst✝¹ : Algebra R A\ninst✝ : Algebra R B\ns t : Set A\np : A → A → Prop\na b : A\nha : a ∈ adjoin R s\nhb : b ∈ adjoin R s\nHs : ∀ (x : A), x ∈ s → ∀ (y : A), y ∈ s → p x y\n... | [
112,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
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Mathlib/Analysis/Calculus/MeanValue.lean | eq_of_has_deriv_right_eq | [
{
"state_after": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type ?u.52033\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : ℝ → E\na b : ℝ\nf' g : ℝ → E\nderivf : ∀ (x : ℝ), x ∈ Ico a b → HasDerivWithinAt f (f' x) (Ici x) x\nderivg : ∀ (x : ℝ), x ∈ Ico a b → HasDerivW... | [
421,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
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] |
Mathlib/Data/Real/NNReal.lean | NNReal.iSup_mul_le | [
{
"state_after": "ι : Sort u_1\nf : ι → ℝ≥0\na : ℝ≥0\ng : ι → ℝ≥0\nh : ℝ≥0\nH : ∀ (i : ι), g i * h ≤ a\n⊢ (⨆ (i : ι), g i * h) ≤ a",
"state_before": "ι : Sort u_1\nf : ι → ℝ≥0\na : ℝ≥0\ng : ι → ℝ≥0\nh : ℝ≥0\nH : ∀ (i : ι), g i * h ≤ a\n⊢ iSup g * h ≤ a",
"tactic": "rw [iSup_mul]"
},
{
"state_aft... | [
985,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
983,
1
] |
Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.factorThruImageSubobject_comp_self | [
{
"state_after": "case h\nC : Type u\ninst✝¹ : Category C\nX Y Z : C\nf : X ⟶ Y\ninst✝ : HasImage f\nW : C\nk : W ⟶ X\nh : Factors (imageSubobject f) (k ≫ f)\n⊢ factorThru (imageSubobject f) (k ≫ f) h ≫ arrow (imageSubobject f) =\n (k ≫ factorThruImageSubobject f) ≫ arrow (imageSubobject f)",
"state_befo... | [
349,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
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] |
Mathlib/Data/Finset/Sups.lean | Finset.Nonempty.of_sups_left | [] | [
127,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.imClm_coe | [] | [
287,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | abs_sq | [
{
"state_after": "no goals",
"state_before": "β : Type ?u.256337\nA : Type ?u.256340\nG : Type ?u.256343\nM : Type ?u.256346\nR : Type u_1\ninst✝ : LinearOrderedRing R\nx✝ y x : R\n⊢ abs (x ^ 2) = x ^ 2",
"tactic": "simpa only [sq] using abs_mul_self x"
}
] | [
688,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
688,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | continuousAt_const_cpow' | [
{
"state_after": "case pos\nα : Type ?u.292640\na b : ℂ\nh : b ≠ 0\nha : a = 0\n⊢ ContinuousAt (fun x => a ^ x) b\n\ncase neg\nα : Type ?u.292640\na b : ℂ\nh : b ≠ 0\nha : ¬a = 0\n⊢ ContinuousAt (fun x => a ^ x) b",
"state_before": "α : Type ?u.292640\na b : ℂ\nh : b ≠ 0\n⊢ ContinuousAt (fun x => a ^ x) b",... | [
85,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/MeasureTheory/Measure/Stieltjes.lean | StieltjesFunction.countable_leftLim_ne | [
{
"state_after": "f✝ f : StieltjesFunction\n⊢ {x | leftLim (↑f) x ≠ ↑f x} ⊆ {x | ¬ContinuousAt (↑f) x}",
"state_before": "f✝ f : StieltjesFunction\n⊢ Set.Countable {x | leftLim (↑f) x ≠ ↑f x}",
"tactic": "refine Countable.mono ?_ f.mono.countable_not_continuousAt"
},
{
"state_after": "f✝ f : Sti... | [
304,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.zero_le | [
{
"state_after": "x : PGame\n⊢ ((∀ (i : LeftMoves 0), (∃ i', moveLeft 0 i ≤ moveLeft x i') ∨ ∃ j, moveRight (moveLeft 0 i) j ≤ x) ∧\n ∀ (j : RightMoves x), (∃ i, 0 ≤ moveLeft (moveRight x j) i) ∨ ∃ j', moveRight 0 j' ≤ moveRight x j) ↔\n ∀ (j : RightMoves x), ∃ i, 0 ≤ moveLeft (moveRight x j) i",
"s... | [
669,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
667,
1
] |
Mathlib/Data/SetLike/Basic.lean | SetLike.lt_iff_le_and_exists | [
{
"state_after": "no goals",
"state_before": "A : Type u_1\nB : Type u_2\ni : SetLike A B\np q : A\n⊢ p < q ↔ p ≤ q ∧ ∃ x, x ∈ q ∧ ¬x ∈ p",
"tactic": "rw [lt_iff_le_not_le, not_le_iff_exists]"
}
] | [
219,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Algebra/GroupWithZero/Defs.lean | mul_left_cancel₀ | [] | [
66,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_le_mk_of_subset | [] | [
2117,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2116,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | iUnion_Icc_add_zsmul | [
{
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"tactic": "simpa only [iUnion_Ioc_add_zsmul hp a, univ_subset_iff] using\n iUnion_mono fun n : ℤ =... | [
1071,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1069,
1
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Mathlib/Algebra/CovariantAndContravariant.lean | act_rel_act_of_rel_of_rel | [] | [
215,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
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Mathlib/Data/Nat/Bits.lean | Nat.bit_cases_on_inj | [] | [
150,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
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Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.nullMeasurableSet_univ | [] | [
117,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
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Mathlib/Data/ZMod/Basic.lean | ZMod.cast_eq_val | [
{
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"state_before": "n : ℕ\nR : Type u_1\nins... | [
171,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
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Mathlib/Analysis/InnerProductSpace/PiL2.lean | EuclideanSpace.norm_eq | [
{
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128,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
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Mathlib/Data/Complex/Exponential.lean | isCauSeq_series_of_abv_le_of_isCauSeq | [
{
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117,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
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Mathlib/Order/Filter/Prod.lean | Filter.coprod_neBot_right | [] | [
514,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
1
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Mathlib/Data/Fintype/Card.lean | Fintype.card_eq_one_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.20214\nγ : Type ?u.20217\ninst✝¹ : Fintype α\ninst✝ : Fintype β\n⊢ Nonempty (α ≃ Unit) ↔ ∃ x, ∀ (y : α), y = x",
"state_before": "α : Type u_1\nβ : Type ?u.20214\nγ : Type ?u.20217\ninst✝¹ : Fintype α\ninst✝ : Fintype β\n⊢ card α = 1 ↔ ∃ x, ∀ (y : α), y = x",
... | [
514,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
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Mathlib/Data/Set/Lattice.lean | Set.iInter_subtype | [] | [
913,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
1
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Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.map_neg | [] | [
569,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
11
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Mathlib/Analysis/Normed/Group/Basic.lean | LipschitzWith.div | [
{
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1876,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1874,
1
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Mathlib/Data/Set/Semiring.lean | SetSemiring.down_subset_down | [] | [
87,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
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Mathlib/Data/Num/Lemmas.lean | Num.cast_succ | [] | [
726,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
725,
1
] |
Mathlib/Data/Rat/Lemmas.lean | Rat.coe_int_div | [
{
"state_after": "case intro\nb c : ℤ\n⊢ ↑(b * c / b) = ↑(b * c) / ↑b",
"state_before": "a b : ℤ\nh : b ∣ a\n⊢ ↑(a / b) = ↑a / ↑b",
"tactic": "rcases h with ⟨c, rfl⟩"
},
{
"state_after": "no goals",
"state_before": "case intro\nb c : ℤ\n⊢ ↑(b * c / b) = ↑(b * c) / ↑b",
"tactic": "rw [mul... | [
249,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
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Mathlib/Order/Circular.lean | sbtw_irrefl_left_right | [] | [
257,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.image_subset_iff | [
{
"state_after": "no goals",
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"tactic": "norm_cast"
}
] | [
447,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
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Mathlib/Data/List/Perm.lean | List.length_permutations | [] | [
1235,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1234,
1
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Mathlib/GroupTheory/Finiteness.lean | Subgroup.rank_congr | [
{
"state_after": "M : Type ?u.114054\nN : Type ?u.114057\ninst✝⁵ : Monoid M\ninst✝⁴ : AddMonoid N\nG : Type u_1\nH✝ : Type ?u.114069\ninst✝³ : Group G\ninst✝² : AddGroup H✝\nH : Subgroup G\ninst✝¹ inst✝ : Group.FG { x // x ∈ H }\n⊢ Group.rank { x // x ∈ H } = Group.rank { x // x ∈ H }",
"state_before": "M :... | [
436,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/Dynamics/Flow.lean | Flow.continuous_toFun | [
{
"state_after": "τ : Type u_2\ninst✝³ : AddCommGroup τ\ninst✝² : TopologicalSpace τ\ninst✝¹ : TopologicalAddGroup τ\nα : Type u_1\ninst✝ : TopologicalSpace α\nϕ : Flow τ α\nt : τ\n⊢ Continuous (curry (uncurry ϕ.toFun) t)",
"state_before": "τ : Type u_2\ninst✝³ : AddCommGroup τ\ninst✝² : TopologicalSpace τ\... | [
185,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Data/Set/Image.lean | Set.image_compl_preimage | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.91374\nι : Sort ?u.91377\nι' : Sort ?u.91380\nf✝ : ι → α\ns✝ t : Set α\nf : α → β\ns : Set β\n⊢ f '' (f ⁻¹' s)ᶜ = range f \\ s",
"tactic": "rw [compl_eq_univ_diff, image_diff_preimage, image_univ]"
}
] | [
1041,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1040,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | LinearMap.mk_coe | [] | [
321,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.top_eq_last | [] | [
556,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/Analysis/NormedSpace/FiniteDimension.lean | isClosedMap_smul_left | [
{
"state_after": "case pos\n𝕜 : Type u\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type v\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\nF : Type w\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace 𝕜 F\nF' : Type x\ninst✝⁵ : AddCommGroup F'\ninst✝⁴ : Module 𝕜 F'\ninst✝³ : TopologicalSpace F'\ni... | [
543,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
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Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.map_inf_comap_of_surjective | [] | [
632,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.Integrable.cauchy_map_integralSum_toFilteriUnion | [
{
"state_after": "ι : Type u\nE : Type v\nF : Type w\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\nI J : Box ι\nπ : TaggedPrepartition I\ninst✝ : Fintype ι\nl : IntegrationParams\nf g : (ι → ℝ) → E\nvol : ι →ᵇᵃ[⊤] E →L[ℝ] F\ny y' : F\nc c₁ c₂ ... | [
524,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
src/lean/Init/Core.lean | Quotient.exists_rep | [] | [
1374,
20
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1373,
1
] |
Mathlib/CategoryTheory/Abelian/Pseudoelements.lean | CategoryTheory.Abelian.Pseudoelement.zero_of_map_zero | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : Abelian C\nP Q : C\nf : P ⟶ Q\nh : Function.Injective (pseudoApply f)\na : Pseudoelement P\nha : pseudoApply f a = pseudoApply f 0\n⊢ a = 0",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : Abelian C\nP Q : C\nf : P ⟶ Q\nh : Function.Injec... | [
319,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/LinearAlgebra/Matrix/InvariantBasisNumber.lean | Matrix.square_of_invertible | [] | [
27,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
25,
1
] |
Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.aeval_bind₁ | [] | [
313,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.mem_restrict | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nI J J₁ J₂ : Box ι\nπ π₁ π₂ : Prepartition I\nx : ι → ℝ\nπi πi₁ πi₂ : (J : Box ι) → Prepartition J\n⊢ J₁ ∈ restrict π J ↔ ∃ J', J' ∈ π ∧ ↑J₁ = ↑J ⊓ ↑J'",
"tactic": "simp [restrict, eq_comm]"
}
] | [
490,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | DoubleQuot.quotQuotEquivQuotOfLE_comp_quotQuotMkₐ | [] | [
853,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
851,
1
] |
Mathlib/Data/Num/Lemmas.lean | PosNum.pred'_succ' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.327018\nn : Num\n⊢ ↑(pred' (succ' n)) = ↑n",
"tactic": "rw [pred'_to_nat, succ'_to_nat, Nat.add_one, Nat.pred_succ]"
}
] | [
550,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_mul_const_uIcc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\na : α\nha : a ≠ 0\nb c : α\nh : a < 0\n⊢ (fun x => x * a) ⁻¹' [[b, c]] = [[b / a, c / a]]",
"tactic": "simp [← Icc_min_max, h, h.le, min_div_div_right_of_nonpos, max_div_div_right_of_nonpos]"
},
{
"state_af... | [
694,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
689,
1
] |
Mathlib/Analysis/NormedSpace/Units.lean | Units.nhds | [] | [
90,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
11
] |
Mathlib/Order/Monotone/Monovary.lean | AntitoneOn.monovaryOn | [] | [
347,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
11
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csInf_le_iff | [] | [
480,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/Data/List/Perm.lean | List.perm_permutations_iff | [] | [
1344,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1342,
1
] |
Mathlib/Algebra/MonoidAlgebra/Grading.lean | AddMonoidAlgebra.decomposeAux_single | [
{
"state_after": "M : Type u_1\nι : Type u_2\nR : Type u_3\ninst✝⁴ : DecidableEq M\ninst✝³ : AddMonoid M\ninst✝² : DecidableEq ι\ninst✝¹ : AddMonoid ι\ninst✝ : CommSemiring R\nf : M →+ ι\nm : M\nr : R\n⊢ r •\n ↑{\n toOneHom :=\n {\n toFun := fun m =>\n ... | [
157,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/CategoryTheory/Preadditive/Opposite.lean | CategoryTheory.unop_add | [] | [
45,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integral_Ici_eq_integral_Ioi | [] | [
672,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
671,
1
] |
Mathlib/Algebra/Hom/GroupAction.lean | DistribMulActionHom.toFun_eq_coe | [] | [
267,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.mem_bind | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.20373\nδ : Type ?u.20376\na : α\ns✝ t : Multiset α\nf✝ g : α → Multiset β\nb : β\ns : Multiset α\nf : α → Multiset β\n⊢ b ∈ bind s f ↔ ∃ a, a ∈ s ∧ b ∈ f a",
"tactic": "simp [bind]"
}
] | [
144,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/RingTheory/Localization/NumDen.lean | IsFractionRing.isInteger_of_isUnit_den | [
{
"state_after": "case intro\nR : Type ?u.153107\ninst✝⁹ : CommRing R\nM : Submonoid R\nS : Type ?u.153313\ninst✝⁸ : CommRing S\ninst✝⁷ : Algebra R S\nP : Type ?u.153567\ninst✝⁶ : CommRing P\nA : Type u_1\ninst✝⁵ : CommRing A\ninst✝⁴ : IsDomain A\ninst✝³ : UniqueFactorizationMonoid A\nK : Type u_2\ninst✝² : Fie... | [
110,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Data/List/Sort.lean | List.rel_of_sorted_cons | [] | [
70,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableEmbedding.exists_measurable_extend | [] | [
1133,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1129,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.coe_image | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.74073\ninst✝ : DecidableEq β\nf✝ g : α → β\ns : Finset α\nt : Finset β\na : α\nb c : β\nf : α → β\n⊢ ∀ (x : β), x ∈ ↑(image f s) ↔ x ∈ f '' ↑s",
"tactic": "simp only [mem_coe, mem_image, Set.mem_image, implies_true]"
... | [
386,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integrableOn_deriv_of_nonneg | [] | [
1293,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1290,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | fderivWithin_add | [] | [
169,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.uncurry0_curry0 | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\nι : Type v\nι' : Type v'\nn : ℕ\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nEi : Fin (Nat.succ n) → Type wEi\nG : Type wG\nG' : Type wG'\ninst✝¹⁴ : Fintype ι\ninst✝¹³ : Fintype ι'\ninst✝¹² : NontriviallyNormedField 𝕜\ninst✝¹¹ : (i : ι)... | [
1653,
66
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1652,
1
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.ContinuousHom.ωSup_apply_ωSup | [
{
"state_after": "no goals",
"state_before": "α : Type u\nα' : Type ?u.73638\nβ : Type v\nβ' : Type ?u.73643\nγ : Type ?u.73646\nφ : Type ?u.73649\ninst✝⁵ : OmegaCompletePartialOrder α\ninst✝⁴ : OmegaCompletePartialOrder β\ninst✝³ : OmegaCompletePartialOrder γ\ninst✝² : OmegaCompletePartialOrder φ\ninst✝¹ :... | [
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99
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844,
1
] |
Mathlib/Data/PNat/Basic.lean | PNat.bit1_le_bit1 | [] | [
225,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
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Mathlib/Combinatorics/SimpleGraph/Clique.lean | SimpleGraph.not_cliqueFree_card_of_top_embedding | [
{
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"state_before": "α : Type u_1\nG H : SimpleGraph α\nm n : ℕ\ns : Finset α\ninst✝ : Fintype α\nf : ⊤ ↪g G\n⊢ ¬CliqueFree G (Fintype.card α)",
"tactic": "rw [not_cliqueFree_iff]... | [
207,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
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