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/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.continuous_iff_surjective | [] | [
557,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
1
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Mathlib/AlgebraicTopology/SimplexCategory.lean | SimplexCategory.δ_comp_σ_of_le | [
{
"state_after": "case mk\nn : ℕ\nj : Fin (n + 1)\ni : ℕ\nhi : i < n + 2\nH : { val := i, isLt := hi } ≤ ↑Fin.castSucc j\n⊢ δ (↑Fin.castSucc { val := i, isLt := hi }) ≫ σ (Fin.succ j) = σ j ≫ δ { val := i, isLt := hi }",
"state_before": "n : ℕ\ni : Fin (n + 2)\nj : Fin (n + 1)\nH : i ≤ ↑Fin.castSucc j\n⊢ δ ... | [
270,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
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Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.add_pf_add_gt | [
{
"state_after": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na b₂ b₁ : R\n⊢ a + (b₁ + b₂) = b₁ + (a + b₂)",
"state_before": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na b₂ c b₁ : R\nx✝ : a + b₂ = c\n⊢ ... | [
324,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
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Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.single_smul | [
{
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1033,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Algebra/GroupWithZero.lean | HasContinuousInv₀.of_nhds_one | [
{
"state_after": "α : Type ?u.61226\nβ : Type ?u.61229\nG₀ : Type u_1\ninst✝² : TopologicalSpace G₀\ninst✝¹ : GroupWithZero G₀\ninst✝ : ContinuousMul G₀\na : G₀\nh : Tendsto Inv.inv (𝓝 1) (𝓝 1)\nx : G₀\nhx : x ≠ 0\nhx' : x⁻¹ ≠ 0\n⊢ ContinuousAt Inv.inv x",
"state_before": "α : Type ?u.61226\nβ : Type ?u.6... | [
308,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.single_mul_apply_aux | [] | [
1642,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1640,
1
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Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.restrictDom_apply | [] | [
250,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Std/Data/Int/Lemmas.lean | Int.ofNat_mul_subNatNat | [
{
"state_after": "no goals",
"state_before": "m n k : Nat\n⊢ ↑m * subNatNat n k = subNatNat (m * n) (m * k)",
"tactic": "cases m with\n| zero => simp [ofNat_zero, Int.zero_mul, Nat.zero_mul]\n| succ m => cases n.lt_or_ge k with\n | inl h =>\n have h' : succ m * n < succ m * k := Nat.mul_lt_mul_of_po... | [
424,
77
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
412,
1
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Mathlib/Topology/Order/Basic.lean | nhdsWithin_Iio_self_neBot' | [] | [
2416,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2415,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.tailings_disjoint_tailing | [] | [
987,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
985,
1
] |
Mathlib/Topology/Algebra/ConstMulAction.lean | isOpenMap_quotient_mk'_mul | [
{
"state_after": "M : Type ?u.142323\nα : Type ?u.142326\nβ : Type ?u.142329\nΓ : Type u_1\ninst✝³ : Group Γ\nT : Type u_2\ninst✝² : TopologicalSpace T\ninst✝¹ : MulAction Γ T\ninst✝ : ContinuousConstSMul Γ T\nU : Set T\nhU : IsOpen U\n⊢ IsOpen (⋃ (a : Γ), (fun x x_1 => x • x_1) a '' U)",
"state_before": "M... | [
490,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
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Mathlib/Algebra/Star/SelfAdjoint.lean | isSelfAdjoint_intCast | [] | [
224,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/GroupTheory/Perm/List.lean | List.formPerm_apply_getLast | [
{
"state_after": "no goals",
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"tactic": "induction' xs using List.reverseRecOn with xs y _ generalizing x <;> simp"
}
] | [
138,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
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Mathlib/Algebra/Category/Ring/Colimits.lean | CommRingCat.Colimits.quot_neg | [] | [
223,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Algebra/Category/ModuleCat/Monoidal/Basic.lean | ModuleCat.MonoidalCategory.tensor_id | [
{
"state_after": "case H\nR : Type u\ninst✝ : CommRing R\nM : ModuleCat R\nN : ModuleCat R\n⊢ LinearMap.compr₂ (TensorProduct.mk R ↑M ↑N) (tensorHom (𝟙 M) (𝟙 N)) =\n LinearMap.compr₂ (TensorProduct.mk R ↑M ↑N) (𝟙 (of R (↑M ⊗[R] ↑N)))",
"state_before": "R : Type u\ninst✝ : CommRing R\nM : ModuleCat R\n... | [
70,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Order/WithBot.lean | WithTop.strictMono_iff | [] | [
1141,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1136,
1
] |
Mathlib/Algebra/Associated.lean | associated_one_of_mul_eq_one | [] | [
445,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
Mathlib/CategoryTheory/Sites/Plus.lean | CategoryTheory.GrothendieckTopology.isoToPlus_inv | [
{
"state_after": "case hγ\nC : Type u\ninst✝³ : Category C\nJ : GrothendieckTopology C\nD : Type w\ninst✝² : Category D\ninst✝¹ : ∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : Cover J X), HasMultiequalizer (Cover.index S P)\nP : Cᵒᵖ ⥤ D\ninst✝ : ∀ (X : C), HasColimitsOfShape (Cover J X)ᵒᵖ D\nhP : Presheaf.IsSheaf J P\n⊢ toPlus ... | [
347,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Embedding.coe_injective | [
{
"state_after": "case mk\nL : Language\nL' : Language\nM : Type w\nN : Type w'\ninst✝³ : Structure L M\ninst✝² : Structure L N\nP : Type ?u.138427\ninst✝¹ : Structure L P\nQ : Type ?u.138435\ninst✝ : Structure L Q\ng : M ↪[L] N\ntoEmbedding✝ : M ↪ N\nmap_fun'✝ :\n ∀ {n : ℕ} (f : Functions L n) (x : Fin n → M)... | [
652,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
646,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.Parallel.vectorSpan_eq | [
{
"state_after": "k : Type u_2\nV : Type u_3\nP : Type u_1\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\ns₁ s₂ : Set P\nh : affineSpan k s₁ ∥ affineSpan k s₂\n⊢ direction (affineSpan k s₁) = direction (affineSpan k s₂)",
"state_before": "k : Type u_2\nV : Type u_3\... | [
1789,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1786,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/ContinuousLinearMap.lean | AEMeasurable.apply_continuousLinearMap | [] | [
95,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | LinearEquiv.coe_ofInjectiveEndo | [] | [
981,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
979,
1
] |
Mathlib/MeasureTheory/Function/EssSup.lean | essSup_le_of_ae_le | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nm : MeasurableSpace α\nμ ν : MeasureTheory.Measure α\ninst✝ : CompleteLattice β\nf : α → β\nc : β\nhf : f ≤ᵐ[μ] fun x => c\n⊢ essSup (fun x => c) μ ≤ c",
"state_before": "α : Type u_1\nβ : Type u_2\nm : MeasurableSpace α\nμ ν : MeasureTheory.Measure α\ninst✝ : C... | [
171,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.div_eq_empty | [] | [
589,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
Mathlib/Data/FinEnum.lean | FinEnum.pi.mem_enum | [
{
"state_after": "α : Type u\nβ✝ : α → Type v\nβ : α → Type (max u v)\ninst✝¹ : FinEnum α\ninst✝ : (a : α) → FinEnum (β a)\nf : (a : α) → β a\n⊢ ∃ a, (a ∈ pi (toList α) fun x => toList (β x)) ∧ (fun x => a x (_ : x ∈ toList α)) = f",
"state_before": "α : Type u\nβ✝ : α → Type v\nβ : α → Type (max u v)\ninst... | [
257,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | edist_le_of_edist_le_geometric_two_of_tendsto | [
{
"state_after": "α : Type u_1\nβ : Type ?u.441500\nι : Type ?u.441503\ninst✝ : PseudoEMetricSpace α\nC : ℝ≥0∞\nhC : C ≠ ⊤\nf : ℕ → α\na : α\nha : Tendsto f atTop (𝓝 a)\nn : ℕ\nhu : ∀ (n : ℕ), edist (f n) (f (n + 1)) ≤ C * 2⁻¹ ^ n\n⊢ edist (f n) a ≤ 2 * C * 2⁻¹ ^ n",
"state_before": "α : Type u_1\nβ : Type... | [
355,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/Topology/MetricSpace/Baire.lean | dense_biUnion_interior_of_closed | [] | [
335,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/RingTheory/IsTensorProduct.lean | IsTensorProduct.lift_eq | [
{
"state_after": "R : Type u_1\ninst✝¹⁴ : CommRing R\nM₁ : Type u_2\nM₂ : Type u_3\nM : Type u_4\nM' : Type u_5\ninst✝¹³ : AddCommMonoid M₁\ninst✝¹² : AddCommMonoid M₂\ninst✝¹¹ : AddCommMonoid M\ninst✝¹⁰ : AddCommMonoid M'\ninst✝⁹ : Module R M₁\ninst✝⁸ : Module R M₂\ninst✝⁷ : Module R M\ninst✝⁶ : Module R M'\nf... | [
110,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Data/Set/Image.lean | Set.image_symm_diff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.48465\nι : Sort ?u.48468\nι' : Sort ?u.48471\nf : α → β\ns✝ t✝ : Set α\nhf : Injective f\ns t : Set α\n⊢ f '' s ∆ t = (f '' s) ∆ (f '' t)",
"tactic": "simp_rw [Set.symmDiff_def, image_union, image_diff hf]"
}
] | [
448,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.secondCountableTopology | [] | [
258,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
11
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | AntitoneOn.intervalIntegrable | [] | [
389,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Topology/Constructions.lean | nhds_swap | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type ?u.39611\nδ : Type ?u.39614\nε : Type ?u.39617\nζ : Type ?u.39620\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⊢ map (... | [
586,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
1
] |
Mathlib/Combinatorics/SimpleGraph/Density.lean | SimpleGraph.mk_mem_interedges_comm | [] | [
426,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Data/Matrix/Notation.lean | Matrix.empty_mulVec | [] | [
302,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/CategoryTheory/Functor/FullyFaithful.lean | CategoryTheory.Functor.image_preimage | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nX✝ Y✝ : C\nF : C ⥤ D\ninst✝ : Full F\nX Y : C\nf : F.obj X ⟶ F.obj Y\n⊢ F.map (Full.preimage f) = f",
"state_before": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nX✝ Y✝ : C\nF : C ⥤ D\ninst✝ : Full ... | [
95,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.coe_pi_add_coe_pi | [
{
"state_after": "no goals",
"state_before": "⊢ ↑π + ↑π = 0",
"tactic": "rw [← two_nsmul, two_nsmul_coe_pi]"
}
] | [
173,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.IsPrime.prod_le | [] | [
1066,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1064,
1
] |
Mathlib/Algebra/Group/TypeTags.lean | ofAdd_add | [] | [
152,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Data/Dfinsupp/NeLocus.lean | Dfinsupp.nonempty_neLocus_iff | [] | [
67,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Analysis/NormedSpace/ENorm.lean | ENorm.finite_dist_eq | [] | [
222,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Topology/ContinuousOn.lean | ContinuousOn.mono_dom | [] | [
634,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
631,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.insert_subset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.112523\nγ : Type ?u.112526\ninst✝ : DecidableEq α\ns t u v : Finset α\na b : α\n⊢ insert a s ⊆ t ↔ a ∈ t ∧ s ⊆ t",
"tactic": "simp only [subset_iff, mem_insert, forall_eq, or_imp, forall_and]"
}
] | [
1161,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1160,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.map_div_right_divisors | [
{
"state_after": "case a.mk\nn d nd : ℕ\n⊢ (d, nd) ∈\n map\n { toFun := fun d => (d, n / d),\n inj' :=\n (_ :\n ∀ (p₁ p₂ : ℕ),\n (fun d => (d, n / d)) p₁ = (fun d => (d, n / d)) p₂ →\n ((fun d => (d, n / d)) p₁).fst = ((fun d => (d, n ... | [
274,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/Analysis/Complex/UnitDisc/Basic.lean | Complex.UnitDisc.conj_conj | [] | [
228,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/MeasureTheory/Covering/OneDim.lean | Real.Icc_mem_vitaliFamily_at_right | [
{
"state_after": "x y : ℝ\nhxy : x < y\n⊢ Metric.closedBall ((x + y) / 2) ((y - x) / 2) ∈ VitaliFamily.setsAt (vitaliFamily volume 1) x",
"state_before": "x y : ℝ\nhxy : x < y\n⊢ Icc x y ∈ VitaliFamily.setsAt (vitaliFamily volume 1) x",
"tactic": "rw [Icc_eq_closedBall]"
},
{
"state_after": "x y... | [
33,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
29,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.subset_pointwise_smul_iff | [] | [
362,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | real_inner_add_add_self | [
{
"state_after": "𝕜 : Type ?u.1806744\nE : Type ?u.1806747\nF : Type u_1\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx y : F\nthis : inner y x = inner x y\n⊢ inner (x + y) (x + y) = inn... | [
674,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
670,
1
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_indicator_ge_of_bdd_below | [
{
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Mathlib/GroupTheory/GroupAction/Opposite.lean | MulOpposite.smul_eq_mul_unop | [] | [
105,
6
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104,
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Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.snorm_indicator_const_le | [
{
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629,
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616,
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Mathlib/Order/Hom/CompleteLattice.lean | CompleteLatticeHom.toFun_eq_coe | [] | [
689,
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688,
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Mathlib/LinearAlgebra/Basic.lean | LinearMap.range_comp | [] | [
1231,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1229,
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Mathlib/Algebra/Order/Group/Defs.lean | Right.one_le_inv_iff | [
{
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228,
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226,
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Mathlib/Combinatorics/SetFamily/Compression/Down.lean | Finset.memberSubfamily_nonMemberSubfamily | [
{
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125,
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Mathlib/Analysis/Complex/PhragmenLindelof.lean | PhragmenLindelof.eqOn_vertical_strip | [] | [
346,
84
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337,
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Mathlib/Data/List/BigOperators/Lemmas.lean | MonoidHom.unop_map_list_prod | [] | [
174,
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172,
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Mathlib/Order/SuccPred/Basic.lean | Order.le_pred_iff | [] | [
706,
42
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705,
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Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.cokernelIsoOfEq_inv_comp_desc | [
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849,
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846,
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Mathlib/Data/Set/Prod.lean | Set.update_preimage_pi | [
{
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857,
22
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848,
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Mathlib/Algebra/Category/ModuleCat/EpiMono.lean | ModuleCat.epi_iff_surjective | [
{
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] | [
60,
52
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Mathlib/Data/Finset/Basic.lean | Finset.biUnion_insert | [
{
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3553,
22
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Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_mul_cpow_one_add_sq | [
{
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589,
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560,
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Mathlib/Topology/PartitionOfUnity.lean | PartitionOfUnity.exists_finset_nhd_support_subset | [] | [
214,
18
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207,
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Mathlib/Logic/Equiv/Defs.lean | Equiv.trans_refl | [
{
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341,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
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Mathlib/Order/Max.lean | IsBot.isMin | [] | [
225,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
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Mathlib/Data/Matrix/Basic.lean | Matrix.conjTranspose_map | [] | [
2252,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2250,
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Mathlib/Data/Fintype/Pi.lean | Fintype.piFinset_subset | [] | [
57,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
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Mathlib/Data/List/Nodup.lean | List.Nodup.set | [] | [
411,
52
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403,
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.le_normalizer | [
{
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"tactic": "rw [H.mul_mem_cancel_right (H.inv_mem xH), H.mul_mem_cancel_lef... | [
2173,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2172,
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Mathlib/CategoryTheory/Limits/Shapes/Diagonal.lean | CategoryTheory.Limits.pullbackDiagonalMapIso_inv_fst | [
{
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172,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
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Mathlib/Order/Hom/Basic.lean | OrderIso.prodComm_symm | [] | [
944,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
943,
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Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesAt.analyticAt | [] | [
420,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
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Mathlib/ModelTheory/FinitelyGenerated.lean | FirstOrder.Language.Substructure.fg_iff_exists_fin_generating_family | [
{
"state_after": "L : Language\nM : Type u_3\ninst✝ : Structure L M\nN : Substructure L M\n⊢ (∃ S, Set.Finite S ∧ LowerAdjoint.toFun (closure L) S = N) ↔ ∃ n s, LowerAdjoint.toFun (closure L) (range s) = N",
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63,
42
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55,
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Mathlib/Algebra/ModEq.lean | AddCommGroup.zsmul_modEq_zsmul | [
{
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"tactic": "rw [← smul_sub, smul_comm, smul_right_inj hn]"
}
] | [
172,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
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Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.coe_moebius_mul_coe_zeta | [
{
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"tactic": "rw [← coe_coe, ← intCoe_mul, moebius_mul_coe_zeta, intCoe_one]"
}
] | [
1051,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1050,
1
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Mathlib/Order/Minimal.lean | maximals_mono | [
{
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138,
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133,
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Mathlib/Order/Minimal.lean | IsAntichain.max_maximals | [
{
"state_after": "α : Type u_1\nr r₁ r₂ : α → α → Prop\ns t : Set α\na✝ b : α\nht : IsAntichain r t\nh : maximals r s ⊆ t\nhs : ∀ ⦃a : α⦄, a ∈ t → ∃ b, b ∈ maximals r s ∧ r b a\na : α\nha : a ∈ t\n⊢ a ∈ maximals r s",
"state_before": "α : Type u_1\nr r₁ r₂ : α → α → Prop\ns t : Set α\na b : α\nht : IsAntich... | [
203,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | LiouvilleWith.add_nat | [] | [
241,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | Matrix.toLinearMapₛₗ₂'_aux_eq | [] | [
194,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Analysis/Convex/Hull.lean | Convex.convexHull_eq | [] | [
89,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.mem_nhds_iff | [] | [
945,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
944,
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Mathlib/Data/Multiset/Basic.lean | Multiset.card_add | [] | [
735,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
734,
1
] |
Mathlib/Order/Heyting/Basic.lean | hnot_top | [
{
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"tactic": "rw [← top_sdiff', sdiff_self]"
}
] | [
1076,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1076,
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Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.vanishingIdeal_strict_anti_mono_iff | [
{
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"tactic": "rw [Set.ssubset_def, vanishingIdeal_anti_mono_iff hs, vanishingIdeal_an... | [
498,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
495,
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Mathlib/Topology/Basic.lean | mem_closure_iff_nhds_neBot | [] | [
1295,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1294,
1
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Mathlib/Data/Set/Finite.lean | Set.Finite.image | [
{
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"tactic": "cases hs"
},
{
... | [
854,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
852,
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Mathlib/LinearAlgebra/Matrix/Block.lean | Matrix.blockTriangular_blockDiagonal | [
{
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123,
10
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119,
1
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.aestronglyMeasurable_uIoc_iff | [
{
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1729,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1724,
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Mathlib/Algebra/Order/Field/Power.lean | zpow_bit0_abs | [] | [
221,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
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Mathlib/MeasureTheory/Measure/GiryMonad.lean | MeasureTheory.Measure.join_map_join | [
{
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227,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
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Mathlib/Data/Real/ENNReal.lean | ENNReal.lt_inv_iff_lt_inv | [
{
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"tactic": "simpa only [inv_inv] using @ENNReal.inv_lt_inv a⁻¹ b"
}
] | [
1487,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1486,
1
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Mathlib/Order/Filter/Basic.lean | Filter.not_le | [
{
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"tactic": "simp_rw [le_def, not_forall, exists_prop]"
}
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336,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
11
] |
Mathlib/Analysis/Convex/Slope.lean | concaveOn_iff_slope_anti_adjacent | [] | [
213,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.floor_int_add | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.133790\nα : Type u_1\nβ : Type ?u.133796\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz✝ : ℤ\na✝ : α\nz : ℤ\na : α\n⊢ ⌊↑z + a⌋ = z + ⌊a⌋",
"tactic": "simpa only [add_comm] using floor_add_int a z"
}
] | [
748,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
747,
1
] |
Std/Data/Int/Lemmas.lean | Int.lt_of_neg_lt_neg | [] | [
885,
51
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
884,
11
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Int.addRight_one_isCycle | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.3068304\nα : Type ?u.3068307\nβ : Type ?u.3068310\ninst✝ : DecidableEq α\nn : ℤ\nx✝ : ↑(Equiv.addRight 1) n ≠ n\n⊢ ↑(Equiv.addRight 1 ^ n) 0 = n",
"tactic": "simp"
}
] | [
1864,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1863,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.aeval_modByMonic_eq_self_of_root | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝² : CommRing R\np✝ q✝ : R[X]\ninst✝¹ : Ring S\ninst✝ : Algebra R S\np q : R[X]\nhq : Monic q\nx : S\nhx : ↑(aeval x) q = 0\n⊢ ↑(aeval x) (p %ₘ q) = ↑(aeval x) p",
"tactic": "rw [modByMonic_eq_sub_mul_d... | [
119,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.op_smul_set_mul_eq_mul_smul_set | [] | [
855,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
853,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.enumOrd_mem | [] | [
2178,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2177,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | Ideal.quotientMap_injective | [] | [
411,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
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