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/Data/Nat/GCD/Basic.lean | Nat.gcd_add_self_left | [
{
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"tactic": "rw [gcd_comm, gcd_add_self_right, gcd_comm]"
}
] | [
82,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
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Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.mul_eq_one_comm | [
{
"state_after": "l : Type ?u.57544\nm : Type u\nn : Type u'\nα : Type v\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing α\nA✝ B✝ A B : Matrix n n α\nh : A ⬝ B = 1\nthis : Invertible (det B) := detInvertibleOfLeftInverse B A h\n⊢ B ⬝ A = 1",
"state_before": "l : Type ?u.57544\nm : Type u\nn : ... | [
161,
37
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152,
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Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | limsSup_eq_of_le_nhds | [] | [
194,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
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Mathlib/Data/Multiset/Dedup.lean | Multiset.subset_dedup' | [] | [
75,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Data/Int/Interval.lean | Int.card_fintype_Ico | [
{
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"state_before": "a b : ℤ\n⊢ Fintype.card ↑(Set.Ico a b) = toNat (b - a)",
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}
] | [
153,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.continuousOn_mul | [
{
"state_after": "ι : Type ?u.6487579\n𝕜 : Type ?u.6487582\nE : Type ?u.6487585\nF : Type ?u.6487588\nA : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedRing A\nf✝ g✝ : ℝ → E\na b : ℝ\nμ : MeasureTheory.Measure ℝ\nf g : ℝ → A\nhf : IntegrableOn f (Ι a b)\nhg : ContinuousOn g [[a, b]]\n⊢ IntegrableOn (f... | [
273,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
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Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.coe_map | [] | [
300,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
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src/lean/Init/Core.lean | Setoid.symm | [] | [
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17
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Mathlib/Data/Part.lean | Part.right_dom_of_append_dom | [] | [
810,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
810,
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Mathlib/Topology/Connected.lean | isPreconnected_iff_subset_of_fully_disjoint_closed | [
{
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986,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/CategoryTheory/Limits/Preserves/Shapes/Kernels.lean | CategoryTheory.Limits.PreservesCokernel.iso_inv | [
{
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214,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
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Mathlib/RingTheory/Algebraic.lean | isAlgebraic_of_larger_base | [] | [
245,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
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Mathlib/Order/BoundedOrder.lean | top_eq_true | [] | [
920,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
919,
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_eq_setToFun | [
{
"state_after": "α : Type u_2\nE : Type u_1\nF : Type ?u.812425\n𝕜 : Type ?u.812428\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : CompleteSpace E\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : SMulCommClass ℝ 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedS... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Convex/Basic.lean | Convex.smul_mem_of_zero_mem | [
{
"state_after": "no goals",
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472,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
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Mathlib/Algebra/Category/Ring/Adjunctions.lean | CommRingCat.free_obj_coe | [] | [
47,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
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Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidWithZeroHom.comp_assoc | [] | [
704,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
702,
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Std/Data/List/Init/Lemmas.lean | List.foldrM_append | [
{
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"tactic": "induction l <;> simp [*]"
}
] | [
194,
27
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
192,
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Mathlib/Algebra/Category/ModuleCat/Images.lean | ModuleCat.image.lift_fac | [
{
"state_after": "case h\nR : Type u\ninst✝ : Ring R\nG H : ModuleCat R\nf : G ⟶ H\nF' : MonoFactorisation f\nx : ↑(image f)\n⊢ ↑(lift F' ≫ F'.m) x = ↑(ι f) x",
"state_before": "R : Type u\ninst✝ : Ring R\nG H : ModuleCat R\nf : G ⟶ H\nF' : MonoFactorisation f\n⊢ lift F' ≫ F'.m = ι f",
"tactic": "ext x"... | [
87,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | differentiableOn_congr | [] | [
928,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
925,
1
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Mathlib/Topology/Instances/ENNReal.lean | Real.diam_Ioo | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.565531\nβ : Type ?u.565534\nγ : Type ?u.565537\ninst✝ : PseudoEMetricSpace α\na b : ℝ\nh : a ≤ b\n⊢ Metric.diam (Ioo a b) = b - a",
"tactic": "simp [Metric.diam, ENNReal.toReal_ofReal (sub_nonneg.2 h)]"
}
] | [
1568,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1567,
1
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Mathlib/GroupTheory/Index.lean | Subgroup.index_dvd_card | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝¹ : Group G\nH K L : Subgroup G\ninst✝ : Fintype G\n⊢ index H ∣ Fintype.card G",
"tactic": "classical exact ⟨Fintype.card H, H.index_mul_card.symm⟩"
},
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝¹ : Group ... | [
373,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
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Mathlib/Data/Finset/Sups.lean | Finset.infs_union_left | [] | [
338,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
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Mathlib/Data/String/Basic.lean | String.toList_nonempty | [
{
"state_after": "case nil\nh : { data := [] } ≠ \"\"\n⊢ toList { data := [] } = head { data := [] } :: toList (drop { data := [] } 1)\n\ncase cons\nhead✝ : Char\ntail✝ : List Char\nh : { data := head✝ :: tail✝ } ≠ \"\"\n⊢ toList { data := head✝ :: tail✝ } = head { data := head✝ :: tail✝ } :: toList (drop { dat... | [
148,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Data/Set/Basic.lean | Set.eq_of_not_mem_of_mem_insert | [] | [
1129,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1128,
1
] |
Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.mul_assoc | [
{
"state_after": "R : Type u\ninst✝⁴ : CommSemiring R\nA : Type v₁\ninst✝³ : Semiring A\ninst✝² : Algebra R A\nB : Type v₂\ninst✝¹ : Semiring B\ninst✝ : Algebra R B\nx y z : A ⊗[R] B\na₁✝ a₂✝ a₃✝ : A\nb₁✝ b₂✝ b₃✝ : B\n⊢ ↑(↑mul (↑(↑mul (a₁✝ ⊗ₜ[R] b₁✝)) (a₂✝ ⊗ₜ[R] b₂✝))) (a₃✝ ⊗ₜ[R] b₃✝) =\n ↑(↑mul (a₁✝ ⊗ₜ[R] b... | [
421,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
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Mathlib/Data/Multiset/FinsetOps.lean | Multiset.le_ndinter | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns✝ s t u : Multiset α\n⊢ s ≤ ndinter t u ↔ s ≤ t ∧ s ⊆ u",
"tactic": "simp [ndinter, le_filter, subset_iff]"
}
] | [
253,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
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Mathlib/Analysis/InnerProductSpace/PiL2.lean | OrthonormalBasis.coe_toBasis | [
{
"state_after": "ι : Type u_1\nι' : Type ?u.788937\n𝕜 : Type u_2\ninst✝⁹ : IsROrC 𝕜\nE : Type u_3\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : InnerProductSpace 𝕜 E\nE' : Type ?u.788966\ninst✝⁶ : NormedAddCommGroup E'\ninst✝⁵ : InnerProductSpace 𝕜 E'\nF : Type ?u.788984\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ :... | [
423,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
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Mathlib/AlgebraicGeometry/RingedSpace.lean | AlgebraicGeometry.RingedSpace.isUnit_res_basicOpen | [
{
"state_after": "case h\nX : RingedSpace\nU : Opens ↑↑X.toPresheafedSpace\nf : ↑(X.presheaf.obj U.op)\n⊢ ∀ (x : { x // x ∈ basicOpen X f }),\n IsUnit (↑(germ X.presheaf x) (↑(X.presheaf.map (homOfLE (_ : basicOpen X f ≤ U)).op) f))",
"state_before": "X : RingedSpace\nU : Opens ↑↑X.toPresheafedSpace\nf :... | [
193,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
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Mathlib/GroupTheory/MonoidLocalization.lean | Localization.mulEquivOfQuotient_symm_mk' | [] | [
1717,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1715,
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Mathlib/Data/Real/ENNReal.lean | ENNReal.sub_sub_cancel | [] | [
1189,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1188,
1
] |
Mathlib/Data/String/Basic.lean | String.asString_inv_toList | [] | [
137,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Topology/List.lean | List.tendsto_insertNth' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.13544\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\na : α\nn : ℕ\n⊢ Tendsto (fun p => insertNth (n + 1) p.fst p.snd) (𝓝 a ×ˢ 𝓝 []) (𝓝 (insertNth (n + 1) a []))",
"tactic": "simp"
},
{
"state_after": "α : Type ... | [
138,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.IsTrail.takeUntil | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\ninst✝ : DecidableEq V\nu v w : V\np : Walk G v w\nhc : IsTrail p\nh : u ∈ support p\n⊢ IsTrail (append (takeUntil p u h) (?m.255284 hc h))",
"tactic": "rwa ... | [
1183,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1181,
11
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | volume_regionBetween_eq_lintegral | [
{
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580,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_sdiff_div_prod_sdiff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.856258\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nf g : α → β\ninst✝¹ : CommGroup β\ninst✝ : DecidableEq α\n⊢ (∏ x in s₂ \\ s₁, f x) / ∏ x in s₁ \\ s₂, f x = (∏ x in s₂, f x) / ∏ x in s₁, f x",
"tactic": "simp [← Finset.prod_... | [
1839,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1837,
1
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Mathlib/Data/Finset/NAry.lean | Finset.image₂_subset_iff | [] | [
109,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/RingTheory/Derivation/Basic.lean | Derivation.map_sum | [] | [
133,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | LinearMap.mkContinuous₂_norm_le' | [] | [
763,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
761,
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] |
Mathlib/Order/Closure.lean | ClosureOperator.closure_is_closed | [] | [
187,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Data/MvPolynomial/Division.lean | MvPolynomial.mul_X_divMonomial | [] | [
179,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalMin.comp_antitone | [] | [
233,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
8
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.ContinuousHom.apply_mono | [] | [
619,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
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Mathlib/Topology/MetricSpace/Basic.lean | dist_pi_const_le | [] | [
2020,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2019,
1
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Mathlib/Topology/Constructions.lean | Embedding.codRestrict | [] | [
1120,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1118,
1
] |
Mathlib/GroupTheory/Exponent.lean | Monoid.exponent_pos_of_exists | [
{
"state_after": "G : Type u\ninst✝ : Monoid G\nn : ℕ\nhpos : 0 < n\nhG : ∀ (g : G), g ^ n = 1\nh : ∃ n, 0 < n ∧ ∀ (g : G), g ^ n = 1\n⊢ 0 < exponent G",
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"tactic": "have h : ∃ n, 0 < n ∧ ∀ g... | [
125,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Quot.lean | Quotient.map'_mk'' | [] | [
750,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
748,
1
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Mathlib/Topology/PathConnected.lean | Path.truncate_zero_zero | [
{
"state_after": "no goals",
"state_before": "X✝ : Type ?u.473740\nY : Type ?u.473743\ninst✝² : TopologicalSpace X✝\ninst✝¹ : TopologicalSpace Y\nx y z : X✝\nι : Type ?u.473758\nγ✝ : Path x y\nX : Type ?u.473807\ninst✝ : TopologicalSpace X\na b : X\nγ : Path a b\n⊢ extend γ (min 0 0) = a",
"tactic": "rw... | [
696,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
694,
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Mathlib/RingTheory/IntegrallyClosed.lean | isIntegrallyClosed_iff | [
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Mathlib/RepresentationTheory/Maschke.lean | MonoidAlgebra.exists_leftInverse_of_injective | [
{
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Mathlib/Data/Finmap.lean | Finmap.disjoint_union_right | [
{
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679,
92
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Mathlib/Control/Basic.lean | seq_bind_eq | [] | [
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106,
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Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | UniformFun.mono | [] | [
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Std/Data/RBMap/Lemmas.lean | Std.RBNode.Ordered.memP_iff_find? | [
{
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Mathlib/Order/Cover.lean | AntisymmRel.wcovby | [] | [
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29
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Mathlib/GroupTheory/Finiteness.lean | Subgroup.fg_iff | [
{
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Mathlib/Topology/Sets/Closeds.lean | TopologicalSpace.Closeds.gc | [] | [
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Mathlib/CategoryTheory/Sites/CompatiblePlus.lean | CategoryTheory.GrothendieckTopology.diagramCompIso_hom_ι | [
{
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69,
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Mathlib/Analysis/NormedSpace/CompactOperator.lean | IsCompactOperator.neg | [] | [
230,
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Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.star_im | [] | [
674,
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674,
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Mathlib/Topology/MetricSpace/Basic.lean | ULift.nndist_up_up | [] | [
1729,
92
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Mathlib/Data/Finset/MulAntidiagonal.lean | Finset.support_mulAntidiagonal_subset_mul | [
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Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_eq_add_fract_mul | [
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.sum_range_measure_preimage_singleton | [
{
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Mathlib/CategoryTheory/Sites/Grothendieck.lean | CategoryTheory.GrothendieckTopology.Cover.Arrow.to_middle_condition | [] | [
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Mathlib/LinearAlgebra/Span.lean | Submodule.coe_iSup_of_directed | [
{
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Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Equiv.coe_injective | [] | [
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Mathlib/Algebra/MonoidAlgebra/Division.lean | AddMonoidAlgebra.of'_mul_modOf | [
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Mathlib/Data/List/OfFn.lean | List.ofFn_eq_nil_iff | [
{
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Mathlib/Analysis/InnerProductSpace/Basic.lean | real_inner_smul_left | [] | [
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24
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Mathlib/Topology/SubsetProperties.lean | IsCompact.disjoint_nhdsSet_right | [
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Std/Data/Nat/Lemmas.lean | Nat.sub_add_lt_sub | [] | [
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Mathlib/Order/SymmDiff.lean | bihimp_himp_right | [] | [
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Mathlib/Topology/PathConnected.lean | Path.map_map | [
{
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Mathlib/Algebra/Hom/GroupInstances.lean | AddMonoidHom.coe_flip_mul | [] | [
323,
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Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.preimage_comap_zeroLocus_aux | [
{
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.coe_toHomeomorph | [] | [
466,
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465,
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.mem_commonNeighbors | [] | [
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1016,
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Mathlib/AlgebraicTopology/DoldKan/FunctorGamma.lean | AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_id | [
{
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Mathlib/Data/PEquiv.lean | PEquiv.single_trans_of_eq_none | [] | [
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48
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Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Formula.realize_bot | [] | [
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10
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Mathlib/LinearAlgebra/Basis.lean | Basis.coe_sumCoords_eq_finsum | [
{
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242,
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Mathlib/Analysis/Asymptotics/SuperpolynomialDecay.lean | Asymptotics.SuperpolynomialDecay.mul_const | [
{
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99,
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Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.nonneg_smul | [
{
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Mathlib/Data/List/TFAE.lean | List.tfae_cons_of_mem | [
{
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Mathlib/LinearAlgebra/Dimension.lean | LinearMap.le_rank_iff_exists_linearIndependent_finset | [
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Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.liftPropWithinAt_indep_chart | [] | [
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Mathlib/Computability/TuringMachine.lean | Turing.TM2to1.trStmts₁_run | [
{
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Mathlib/LinearAlgebra/Pi.lean | LinearMap.pi_comp | [] | [
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Mathlib/LinearAlgebra/Basic.lean | Submodule.comap_smul | [
{
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src/lean/Init/Control/Lawful.lean | bind_congr | [
{
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Mathlib/Order/Bounds/Basic.lean | isLUB_univ | [] | [
816,
24
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Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffWithinAt.prod | [
{
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527,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
] |
Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean | Matrix.SpecialLinearGroup.toLin'_injective | [] | [
216,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.IsMaximal.coprime_of_ne | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝ : Semiring α\nI : Ideal α\na b : α\nM M' : Ideal α\nhM : IsMaximal M\nhM' : IsMaximal M'\nh : M ⊔ M' ≠ ⊤\n⊢ M = M'",
"state_before": "α : Type u\nβ : Type v\ninst✝ : Semiring α\nI : Ideal α\na b : α\nM M' : Ideal α\nhM : IsMaximal M\nhM' : IsMaximal M'\nhne : ... | [
328,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/MeasureTheory/Integral/DivergenceTheorem.lean | MeasureTheory.integral_eq_of_has_deriv_within_at_off_countable | [
{
"state_after": "case inl\nE : Type u\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nf f' : ℝ → E\na b : ℝ\ns : Set ℝ\nhs : Set.Countable s\nHc : ContinuousOn f [[a, b]]\nHd : ∀ (x : ℝ), x ∈ Set.Ioo (min a b) (max a b) \\ s → HasDerivAt f (f' x) x\nHi : IntervalIntegrable f'... | [
430,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | Convex.subset_toCone | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.172872\nG : Type ?u.172875\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\ns : Set E\nhs : Convex 𝕜 s\nx✝ x : E\nhx : x ∈ s\n⊢ 1 • x ∈ s",
"tactic": "rwa [one_smul]"
}
] | [
673,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.mem_prod_principal | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.2996\nδ : Type ?u.2999\nι : Sort ?u.3002\ns✝ : Set α\nt✝ : Set β\nf✝ : Filter α\ng : Filter β\nf : Filter α\ns : Set (α × β)\nt : Set β\n⊢ (∃ t₁, t₁ ∈ f ∧ ∃ t₂, t₂ ∈ 𝓟 t ∧ t₁ ×ˢ t₂ ⊆ s) ↔ ∃ t_1, t_1 ∈ f ∧ t_1 ⊆ {a | ∀ (b : β), b ∈ t → (a, b) ∈ s}",
... | [
97,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.add_lt_add | [
{
"state_after": "case intro\nα : Type ?u.138661\nβ : Type ?u.138664\nb c d : ℝ≥0∞\nr p q : ℝ≥0\nbd : b < d\na : ℝ≥0\nac : ↑a < c\n⊢ ↑a + b < c + d",
"state_before": "α : Type ?u.138661\nβ : Type ?u.138664\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nac : a < c\nbd : b < d\n⊢ a + b < c + d",
"tactic": "lift a to ℝ≥0 u... | [
909,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
903,
11
] |
Mathlib/Data/Set/Intervals/OrderIso.lean | OrderIso.image_Icc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ne : α ≃o β\na b : α\n⊢ ↑e '' Icc a b = Icc (↑e a) (↑e b)",
"tactic": "rw [e.image_eq_preimage, e.symm.preimage_Icc, e.symm_symm]"
}
] | [
106,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
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