file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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values | start list |
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Mathlib/Analysis/SpecificLimits/Basic.lean | ENNReal.tendsto_pow_atTop_nhds_0_of_lt_1 | [
{
"state_after": "case intro.intro\nα : Type ?u.42152\nβ : Type ?u.42155\nι : Type ?u.42158\nr : ℝ≥0\nhr' : ↑r < 1\nhr : ↑r < 1\n⊢ Tendsto (fun n => ↑r ^ n) atTop (𝓝 0)",
"state_before": "α : Type ?u.42152\nβ : Type ?u.42155\nι : Type ?u.42158\nr : ℝ≥0∞\nhr : r < 1\n⊢ Tendsto (fun n => r ^ n) atTop (𝓝 0)"... | [
174,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
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Mathlib/Algebra/Order/Group/Abs.lean | le_abs | [] | [
57,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
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Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.coe_injective | [
{
"state_after": "R : Type u\nι : Type u'\nn : ℕ\nM : Fin (Nat.succ n) → Type v\nM₁ : ι → Type v₁\nM₂ : Type v₂\nM₃ : Type v₃\nM' : Type v'\ninst✝¹⁰ : Semiring R\ninst✝⁹ : (i : Fin (Nat.succ n)) → AddCommMonoid (M i)\ninst✝⁸ : (i : ι) → AddCommMonoid (M₁ i)\ninst✝⁷ : AddCommMonoid M₂\ninst✝⁶ : AddCommMonoid M₃\... | [
145,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
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Mathlib/Order/Max.lean | isMax_iff_forall_not_lt | [] | [
336,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
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Mathlib/FieldTheory/RatFunc.lean | RatFunc.coe_def | [] | [
1681,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1680,
1
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Mathlib/Algebra/Quaternion.lean | Quaternion.coe_inj | [] | [
1030,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1029,
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Mathlib/Algebra/Module/LinearMap.lean | LinearMap.toAddMonoidHom_coe | [] | [
435,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
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Mathlib/Analysis/SpecificLimits/Normed.lean | NormedRing.summable_geometric_of_norm_lt_1 | [
{
"state_after": "α : Type ?u.1232352\nβ : Type ?u.1232355\nι : Type ?u.1232358\nR : Type u_1\ninst✝¹ : NormedRing R\ninst✝ : CompleteSpace R\nx : R\nh : ‖x‖ < 1\nh1 : Summable fun n => ‖x‖ ^ n\n⊢ Summable fun n => x ^ n",
"state_before": "α : Type ?u.1232352\nβ : Type ?u.1232355\nι : Type ?u.1232358\nR : T... | [
466,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
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Mathlib/Order/CompleteLattice.lean | sInf_le_sInf_of_forall_exists_le | [
{
"state_after": "α : Type u_1\nβ : Type ?u.39374\nβ₂ : Type ?u.39377\nγ : Type ?u.39380\nι : Sort ?u.39383\nι' : Sort ?u.39386\nκ : ι → Sort ?u.39391\nκ' : ι' → Sort ?u.39396\ninst✝ : CompleteSemilatticeInf α\ns t : Set α\na b : α\nh : ∀ (x : α), x ∈ s → ∃ y, y ∈ t ∧ y ≤ x\n⊢ ∀ (c : α), (∀ (b : α), b ∈ t → c ≤... | [
250,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
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Mathlib/Analysis/Calculus/Deriv/Prod.lean | hasDerivAt_pi | [] | [
101,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
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Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.lift_apply | [
{
"state_after": "no goals",
"state_before": "k : Type u₁\nG : Type u₂\nR : Type ?u.2579273\ninst✝⁵ : CommSemiring k\ninst✝⁴ : AddMonoid G\nA : Type u₃\ninst✝³ : Semiring A\ninst✝² : Algebra k A\nB : Type ?u.2579310\ninst✝¹ : Semiring B\ninst✝ : Algebra k B\nF : Multiplicative G →* A\nf : MonoidAlgebra k G\... | [
1974,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1972,
1
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Mathlib/Topology/Constructions.lean | isClosedMap_toAdd | [] | [
127,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
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Mathlib/LinearAlgebra/Determinant.lean | LinearMap.isUnit_det | [
{
"state_after": "case intro\nR : Type ?u.1057928\ninst✝¹¹ : CommRing R\nM : Type u_2\ninst✝¹⁰ : AddCommGroup M\ninst✝⁹ : Module R M\nM' : Type ?u.1058519\ninst✝⁸ : AddCommGroup M'\ninst✝⁷ : Module R M'\nι : Type ?u.1059061\ninst✝⁶ : DecidableEq ι\ninst✝⁵ : Fintype ι\ne : Basis ι R M\nA✝ : Type ?u.1059539\ninst... | [
337,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
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Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.mem_of_mem_dropn | [] | [
986,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
984,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Complex.hasDerivAt_sin | [] | [
49,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
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Mathlib/Topology/PathConnected.lean | Path.symm_continuous_family | [] | [
490,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_norm_flip | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\n𝕜₂ : Type u_6\n𝕜₃ : Type u_2\nE : Type u_3\nEₗ : Type ?u.1114653\nF : Type u_5\nFₗ : Type ?u.1114659\nG : Type u_4\nGₗ : Type ?u.1114665\n𝓕 : Type ?u.1114668\ninst✝¹⁷ : SeminormedAddCommGroup E\ninst✝¹⁶ : SeminormedAddCommGroup Eₗ\ninst✝¹⁵ : Se... | [
810,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
809,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.aestronglyMeasurable_one | [] | [
1158,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1156,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.to_subtype | [] | [
98,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
11
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean | Real.hasDerivAt_tan_of_mem_Ioo | [] | [
79,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Analysis/NormedSpace/FiniteDimension.lean | FiniteDimensional.proper | [
{
"state_after": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type v\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : ProperSpace 𝕜\ninst✝ : FiniteDimensional 𝕜 E\ne : E ≃L[𝕜] Fin (finrank 𝕜 E) → 𝕜 :=\n ContinuousLinearEquiv.ofFinrankEq (_ : finrank 𝕜 E = finrank 𝕜 (Fin (fin... | [
606,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
604,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.castPred_castSucc | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\ni : Fin (n + 1)\n⊢ castPred (↑castSucc i) = i",
"tactic": "simp [castPred, predAbove, not_lt.mpr (le_last i)]"
}
] | [
2453,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2452,
1
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_mul | [] | [
1053,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1052,
1
] |
Std/Data/List/Lemmas.lean | List.eq_of_mem_singleton | [] | [
73,
20
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
72,
1
] |
Mathlib/Analysis/Calculus/Deriv/Inverse.lean | HasDerivAt.hasFDerivAt_equiv | [] | [
61,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
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Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.Measure.inv_inv | [] | [
408,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
11
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_norm_norm | [] | [
842,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
1
] |
Mathlib/Data/Real/Sqrt.lean | Real.lt_sqrt | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\nhx : 0 ≤ x\n⊢ x < sqrt y ↔ x ^ 2 < y",
"tactic": "rw [← sqrt_lt_sqrt_iff (sq_nonneg _), sqrt_sq hx]"
}
] | [
433,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.smul_pure | [] | [
1025,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1024,
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] |
Mathlib/MeasureTheory/Function/Jacobian.lean | MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_image | [
{
"state_after": "E : Type u_1\nF : Type ?u.837957\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : FiniteDimensional ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ns : Set E\nf : E → E\nf' : E → E →L[ℝ] E\ninst✝² : MeasurableSpace E\ninst✝¹ : BorelSpace E\nμ : Measure E\ninst✝ ... | [
1099,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1060,
1
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Mathlib/Algebra/Order/UpperLower.lean | lowerClosure_smul | [] | [
283,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
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Mathlib/Topology/UniformSpace/Basic.lean | uniformContinuous_ofMul | [] | [
1448,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1447,
1
] |
Mathlib/Algebra/GroupWithZero/Basic.lean | ne_zero_and_ne_zero_of_mul | [] | [
64,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
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] |
Mathlib/Algebra/Order/Floor.lean | Int.ceil_int | [] | [
619,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.multiset_prod_mem | [] | [
217,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
11
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | gcd_mul_right' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : GCDMonoid α\na b c : α\n⊢ Associated (gcd (b * a) (c * a)) (gcd b c * a)",
"tactic": "simp only [mul_comm, gcd_mul_left']"
}
] | [
470,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
469,
1
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Mathlib/FieldTheory/Adjoin.lean | IntermediateField.exists_finset_of_mem_supr'' | [
{
"state_after": "F : Type u_2\ninst✝² : Field F\nE : Type u_3\ninst✝¹ : Field E\ninst✝ : Algebra F E\nS : Set E\nα : E\nι : Type u_1\nf : ι → IntermediateField F E\nh : ∀ (i : ι), Algebra.IsAlgebraic F { x // x ∈ f i }\nx : E\nhx : x ∈ ⨆ (i : ι), f i\ni : ι\n⊢ f i ≤ ⨆ (i : (i : ι) × { x // x ∈ f i }), adjoin F... | [
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654,
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Mathlib/Data/Set/Intervals/WithBotTop.lean | WithBot.preimage_coe_Iio | [] | [
159,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
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Mathlib/Probability/ProbabilityMassFunction/Basic.lean | Pmf.toMeasure_apply_eq_one_iff | [] | [
274,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
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Mathlib/Order/Filter/Extr.lean | IsMinOn.comp_mapsTo | [] | [
431,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.iSup_add_iSup_of_monotone | [] | [
627,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
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Std/Logic.lean | true_iff_false | [] | [
94,
85
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.functor_galoisConnection | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nF : C ⥤ D\nX✝ Y Z : C\nf : Y ⟶ X✝\nS✝ R✝ : Sieve X✝\nE : Type u₃\ninst✝ : Category E\nG : D ⥤ E\nX : C\nR : Sieve X\nS : Sieve (F.obj X)\n⊢ functorPushforward F R ≤ S ↔ R ≤ functorPullback F S",
"state_before": "C : Type u... | [
666,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
1
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Mathlib/Order/InitialSeg.lean | PrincipalSeg.ofElement_apply | [] | [
387,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
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Mathlib/Order/Heyting/Basic.lean | compl_unique | [] | [
868,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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] |
Mathlib/Data/Finset/Sups.lean | Finset.singleton_sups_singleton | [] | [
160,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Order/BooleanAlgebra.lean | sdiff_sdiff_right | [
{
"state_after": "α : Type u\nβ : Type ?u.23496\nw x y z : α\ninst✝ : GeneralizedBooleanAlgebra α\n⊢ x \\ (y \\ z) = z ⊓ x ⊔ x \\ y",
"state_before": "α : Type u\nβ : Type ?u.23496\nw x y z : α\ninst✝ : GeneralizedBooleanAlgebra α\n⊢ x \\ (y \\ z) = x \\ y ⊔ x ⊓ y ⊓ z",
"tactic": "rw [sup_comm, inf_comm... | [
365,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
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Mathlib/Data/Matrix/Block.lean | Matrix.fromBlocks_inj | [] | [
144,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Topology/Sheaves/SheafCondition/PairwiseIntersections.lean | TopCat.Sheaf.objSupIsoProdEqLocus_hom_fst | [] | [
475,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.pred_le_pred_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝² : Preorder α\ninst✝¹ : PredOrder α\na b : α\ninst✝ : NoMinOrder α\n⊢ pred a ≤ pred b ↔ a ≤ b",
"tactic": "simp"
}
] | [
709,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
1
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Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.appr_lt | [
{
"state_after": "case zero\np : ℕ\nhp_prime : Fact (Nat.Prime p)\nr : ℚ\nx✝¹ x✝ x : ℤ_[p]\n⊢ appr x zero < p ^ zero\n\ncase succ\np : ℕ\nhp_prime : Fact (Nat.Prime p)\nr : ℚ\nx✝¹ x✝ : ℤ_[p]\nn : ℕ\nih : ∀ (x : ℤ_[p]), appr x n < p ^ n\nx : ℤ_[p]\n⊢ appr x (succ n) < p ^ succ n",
"state_before": "p : ℕ\nhp_... | [
328,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/CategoryTheory/Sites/Subsheaf.lean | CategoryTheory.GrothendieckTopology.Subpresheaf.le_sheafify | [
{
"state_after": "C : Type u\ninst✝ : Category C\nJ : GrothendieckTopology C\nF F' F'' : Cᵒᵖ ⥤ Type w\nG G' : Subpresheaf F\nU : Cᵒᵖ\ns : F.obj U\nhs : s ∈ obj G U\n⊢ s ∈ obj (sheafify J G) U",
"state_before": "C : Type u\ninst✝ : Category C\nJ : GrothendieckTopology C\nF F' F'' : Cᵒᵖ ⥤ Type w\nG G' : Subpr... | [
201,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
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Mathlib/Order/Filter/Pi.lean | Filter.mem_pi | [
{
"state_after": "case mp\nι : Type u_1\nα : ι → Type u_2\nf f₁ f₂ : (i : ι) → Filter (α i)\ns✝ : (i : ι) → Set (α i)\ns : Set ((i : ι) → α i)\n⊢ s ∈ pi f → ∃ I, Set.Finite I ∧ ∃ t, (∀ (i : ι), t i ∈ f i) ∧ Set.pi I t ⊆ s\n\ncase mpr\nι : Type u_1\nα : ι → Type u_2\nf f₁ f₂ : (i : ι) → Filter (α i)\ns✝ : (i : ι... | [
84,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
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Mathlib/Topology/Instances/Int.lean | Int.closedEmbedding_coe_real | [] | [
51,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
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Mathlib/Analysis/SpecialFunctions/Complex/LogDeriv.lean | HasDerivWithinAt.clog | [
{
"state_after": "α : Type ?u.48747\ninst✝² : TopologicalSpace α\nE : Type ?u.48753\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf : ℂ → ℂ\nf' x : ℂ\ns : Set ℂ\nh₁ : HasDerivWithinAt f f' s x\nh₂ : 0 < (f x).re ∨ (f x).im ≠ 0\n⊢ HasDerivWithinAt (fun t => log (f t)) ((f x)⁻¹ * f') s x",
"state_b... | [
127,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.lastCases_castSucc | [] | [
1835,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1832,
1
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | tendsto_pow_atTop_atTop_of_one_lt | [] | [
94,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Differentiable.csinh | [] | [
540,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
] |
Mathlib/CategoryTheory/Filtered.lean | CategoryTheory.IsFiltered.coeq_condition | [] | [
194,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Order/Lattice.lean | SemilatticeSup.ext | [
{
"state_after": "α✝ : Type u\nβ : Type v\ninst✝ : SemilatticeSup α✝\na b c d : α✝\nα : Type u_1\nA B : SemilatticeSup α\nH : ∀ (x y : α), x ≤ y ↔ x ≤ y\nss : toSup = toSup\n⊢ A = B",
"state_before": "α✝ : Type u\nβ : Type v\ninst✝ : SemilatticeSup α✝\na b c d : α✝\nα : Type u_1\nA B : SemilatticeSup α\nH :... | [
336,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/Algebra/IsPrimePow.lean | IsPrimePow.two_le | [] | [
120,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.isTopologicalBasis_basic_opens | [
{
"state_after": "case h_open\nR : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\n⊢ ∀ (u : Set (PrimeSpectrum R)), (u ∈ Set.range fun r => ↑(basicOpen r)) → IsOpen u\n\ncase h_nhds\nR : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\n⊢ ∀ (a : PrimeSpectrum R) (u : Set (PrimeSpectrum R... | [
832,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
821,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.natTrailingDegree_monomial | [
{
"state_after": "R : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nha : a ≠ 0\n⊢ Option.getD (↑n) 0 = n",
"state_before": "R : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nha : a ≠ 0\n⊢ natTrailingDegree (↑(monomial n) a) = n",
"tactic": "rw [natTrai... | [
209,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesOnBall.uniform_geometric_approx | [
{
"state_after": "case intro.intro.intro.intro\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.690610\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpa... | [
694,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
683,
1
] |
Mathlib/CategoryTheory/Limits/Opposites.lean | CategoryTheory.Limits.hasFiniteProducts_of_opposite | [] | [
391,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.cons_add | [
{
"state_after": "no goals",
"state_before": "R : Type u\nι : Type u'\nn : ℕ\nM : Fin (Nat.succ n) → Type v\nM₁ : ι → Type v₁\nM₂ : Type v₂\nM₃ : Type v₃\nM' : Type v'\ninst✝¹⁰ : Semiring R\ninst✝⁹ : (i : Fin (Nat.succ n)) → AddCommMonoid (M i)\ninst✝⁸ : (i : ι) → AddCommMonoid (M₁ i)\ninst✝⁷ : AddCommMonoi... | [
351,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/Topology/Instances/Nat.lean | Nat.preimage_ball | [] | [
52,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.contractNth_apply_of_eq | [
{
"state_after": "m n : ℕ\nα : Type u_1\nj : Fin (n + 1)\nop : α → α → α\ng : Fin (n + 1) → α\nk : Fin n\nh : ↑k = ↑j\nthis : ¬↑k < ↑j\n⊢ contractNth j op g k = op (g (↑castSucc k)) (g (succ k))",
"state_before": "m n : ℕ\nα : Type u_1\nj : Fin (n + 1)\nop : α → α → α\ng : Fin (n + 1) → α\nk : Fin n\nh : ↑k... | [
970,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
967,
1
] |
Mathlib/Order/Basic.lean | Decidable.le_iff_eq_or_lt | [] | [
370,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
11
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_eq_single | [
{
"state_after": "ι : Type ?u.372604\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ninst✝ : CommMonoid β\ns : Finset α\nf : α → β\nthis✝ : DecidableEq α\nb : α\nhb : b ∈ s\nh₀ : ∀ (b_1 : α), b_1 ∈ s → b_1 ≠ b → f b_1 = 1\nh₁ : ¬b ∈ s → f b = 1\nthis : ¬b ∈ s\n⊢ False",
"state... | [
806,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
801,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.coeff_X | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type u_1\na a' a₁ a₂ : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S₁\np q : MvPolynomial σ R\ni : σ\n⊢ coeff (Finsupp.single i 1) (X i) = 1",
"tactic": "classical rw [co... | [
689,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
688,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | lt_mul_of_lt_of_one_lt_of_pos | [] | [
813,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
811,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_eq_zero_iff | [] | [
391,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Algebra/Hom/Iterate.lean | MonoidHom.coe_pow | [] | [
88,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Iso.preconnected_iff | [] | [
1940,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1937,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_sum | [] | [
754,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
752,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.mk_div | [] | [
756,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
754,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.coeff_zero_one | [] | [
197,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Topology/Algebra/OpenSubgroup.lean | OpenSubgroup.comap_comap | [] | [
301,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/Analysis/SpecialFunctions/NonIntegrable.lean | intervalIntegrable_inv_iff | [
{
"state_after": "no goals",
"state_before": "E : Type ?u.35816\nF : Type ?u.35819\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : SecondCountableTopology E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedAddCommGroup F\na b : ℝ\n⊢ IntervalIntegrable (fun x => x⁻¹) volume a b ↔ a = b ∨ ¬0 ∈ [[a,... | [
178,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Topology/Order.lean | continuous_id_of_le | [] | [
823,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
822,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | ContDiffOn.cosh | [] | [
1112,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1110,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | le_of_mul_le_mul_right' | [] | [
80,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.disjoint_def' | [] | [
571,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
1
] |
Mathlib/Topology/Constructions.lean | ContinuousAt.prod_map' | [] | [
613,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
611,
1
] |
Mathlib/Data/Nat/Factors.lean | Nat.mem_factors_mul | [
{
"state_after": "a b : ℕ\nha : a ≠ 0\nhb : b ≠ 0\np : ℕ\n⊢ Prime p ∧ p ∣ a * b ↔ Prime p ∧ (p ∣ a ∨ p ∣ b)",
"state_before": "a b : ℕ\nha : a ≠ 0\nhb : b ≠ 0\np : ℕ\n⊢ p ∈ factors (a * b) ↔ p ∈ factors a ∨ p ∈ factors b",
"tactic": "rw [mem_factors (mul_ne_zero ha hb), mem_factors ha, mem_factors hb, ←... | [
261,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.coe_toRealHom | [] | [
241,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
9
] |
Mathlib/Topology/Algebra/Module/WeakDual.lean | WeakBilin.eval_continuous | [] | [
125,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.norm_integral_le_integral_norm | [
{
"state_after": "α : Type u_2\nE : Type u_1\nF : Type ?u.1238187\n𝕜 : Type ?u.1238190\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace ℝ E\ninst✝⁸ : CompleteSpace E\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : SMulCommClass ℝ 𝕜 E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : Norm... | [
1338,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1328,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_from_quotient | [] | [
490,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
1
] |
Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.Completion.ofRat_one | [] | [
73,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.ofFractionRing_comp_algebraMap | [] | [
913,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
1
] |
Mathlib/Data/FunLike/Fintype.lean | FunLike.finite | [] | [
70,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsField.localization_map_bijective | [
{
"state_after": "R✝ : Type ?u.3191178\ninst✝⁷ : CommRing R✝\nM✝ : Submonoid R✝\nS : Type ?u.3191370\ninst✝⁶ : CommRing S\ninst✝⁵ : Algebra R✝ S\nP : Type ?u.3191607\ninst✝⁴ : CommRing P\nR : Type u_1\nRₘ : Type u_2\ninst✝³ : CommRing R\ninst✝² : CommRing Rₘ\nM : Submonoid R\nhM : ¬0 ∈ M\nhR : IsField R\ninst✝¹... | [
1279,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1271,
1
] |
Mathlib/Logic/Encodable/Basic.lean | Encodable.encode_sigma_val | [] | [
374,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/FieldTheory/Minpoly/Field.lean | minpoly.root | [
{
"state_after": "A : Type u_1\nB : Type u_2\ninst✝³ : Field A\ninst✝² : Ring B\ninst✝¹ : IsDomain B\ninst✝ : Algebra A B\nx✝ x : B\nhx : IsIntegral A x\ny : A\nh : IsRoot (minpoly A x) y\nkey : minpoly A x = X - ↑C y\n⊢ ↑(algebraMap A B) y = x",
"state_before": "A : Type u_1\nB : Type u_2\ninst✝³ : Field A... | [
260,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.le_iff_bounds | [] | [
174,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Topology/Bases.lean | TopologicalSpace.empty_nmem_countableBasis | [] | [
634,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
633,
1
] |
Mathlib/Order/PFilter.lean | Order.PFilter.inf_mem | [] | [
163,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Algebra/Group/Basic.lean | one_div_one | [] | [
347,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
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