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/Topology/Basic.lean | IsOpen.inter_closure | [
{
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"tactic": "simpa only [← interior_compl, compl_inter] using IsClosed.interior_u... | [
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99
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Mathlib/Data/Real/ConjugateExponents.lean | Real.IsConjugateExponent.conjugate_eq | [] | [
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Mathlib/Analysis/Seminorm.lean | balanced_ball_zero | [
{
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Mathlib/GroupTheory/Commutator.lean | Subgroup.commutator_mem_commutator | [] | [
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Mathlib/RingTheory/MvPolynomial/Homogeneous.lean | MvPolynomial.homogeneousComponent_eq_zero' | [
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Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_sSup | [] | [
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Mathlib/Order/UpperLower/Basic.lean | UpperSet.coe_iSup₂ | [
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562,
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.measure_ge_lt_top | [
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Mathlib/SetTheory/Game/PGame.lean | PGame.mk_add_moveLeft_inr | [] | [
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Mathlib/MeasureTheory/Measure/Lebesgue/Integral.lean | Real.integrable_of_summable_norm_Icc | [
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Mathlib/Algebra/Ring/Regular.lean | isRightRegular_of_non_zero_divisor | [
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Mathlib/Algebra/BigOperators/Finsupp.lean | map_finsupp_prod | [] | [
223,
17
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221,
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Mathlib/Data/Set/Prod.lean | Set.prod_range_univ_eq | [
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}
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Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.cof_succ | [
{
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"tactic": "apply le_antisymm"
},
{
... | [
513,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.deleteEdges_le | [
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Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | mem_skewAdjointMatricesSubmodule | [
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Mathlib/Data/Matrix/Basic.lean | Matrix.dotProduct_mulVec | [
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.comp_sub_right | [
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Mathlib/Algebra/Order/Pointwise.lean | csSup_mul | [] | [
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72
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Mathlib/Combinatorics/SimpleGraph/StronglyRegular.lean | SimpleGraph.IsSRGWith.top | [
{
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.PullbackCone.equalizer_ext | [
{
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Mathlib/Algebra/Group/Defs.lean | mul_inv_self | [] | [
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Mathlib/RingTheory/DedekindDomain/Dvr.lean | IsLocalization.isDedekindDomain | [
{
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Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.mem_prod | [] | [
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Mathlib/CategoryTheory/Preadditive/AdditiveFunctor.lean | CategoryTheory.Functor.map_sum | [] | [
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Mathlib/Data/Set/Prod.lean | Set.inter_prod | [
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161,
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Mathlib/Topology/Semicontinuous.lean | LowerSemicontinuousAt.lowerSemicontinuousWithinAt | [] | [
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60
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144,
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Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.StableUnderComposition.universally | [
{
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Mathlib/Algebra/ContinuedFractions/Computation/Translations.lean | GeneralizedContinuedFraction.IntFractPair.stream_zero | [] | [
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Std/Data/List/Lemmas.lean | List.filterMap_cons_none | [
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Mathlib/Data/Finset/Lattice.lean | Finset.sup_inf_sup | [
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Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_eq_fract_mul | [
{
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurable_coe_ennreal_ereal | [] | [
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Mathlib/Analysis/InnerProductSpace/Projection.lean | reflection_mem_subspace_orthogonal_precomplement_eq_neg | [] | [
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86
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Mathlib/Analysis/Normed/Ring/Seminorm.lean | RingSeminorm.ext | [] | [
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18
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Mathlib/Data/Complex/Exponential.lean | Complex.sin_ofReal_re | [] | [
947,
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Mathlib/RingTheory/Localization/AtPrime.lean | IsLocalization.AtPrime.comap_maximalIdeal | [
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Mathlib/LinearAlgebra/FiniteDimensional.lean | Subalgebra.eq_bot_of_rank_le_one | [
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Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.CompactOpens.coe_sdiff | [] | [
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Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isInt_pow | [
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}
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Mathlib/Data/Polynomial/Mirror.lean | Polynomial.mirror_C | [] | [
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22
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Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.mul_bind | [] | [
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Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsColimit.existsUnique | [] | [
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Mathlib/Analysis/Calculus/ContDiffDef.lean | HasCompactSupport.iteratedFDeriv | [
{
"state_after": "case zero\n𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nX : Type uX\ninst✝¹ ... | [
1564,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1556,
1
] |
Mathlib/CategoryTheory/Opposites.lean | CategoryTheory.NatTrans.removeOp_id | [] | [
356,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.eq_zero_or_pos | [] | [
290,
31
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
288,
1
] |
Mathlib/Order/UpperLower/Basic.lean | lowerClosure_min | [] | [
1304,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1303,
1
] |
Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isInt_lt_true | [] | [
700,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
698,
1
] |
Mathlib/RingTheory/TensorProduct.lean | TensorProduct.AlgebraTensorModule.smul_eq_lsmul_rTensor | [] | [
82,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Analysis/NormedSpace/Banach.lean | ContinuousLinearMap.NonlinearRightInverse.right_inv | [] | [
49,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.not_wOppSide_bot | [] | [
234,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.comap_id | [] | [
1639,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1638,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidWithZeroHom.comp_id | [] | [
708,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
708,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsLeast.isGreatest_image2_of_isGreatest | [] | [
1542,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1539,
1
] |
Mathlib/RingTheory/Subsemiring/Pointwise.lean | Subsemiring.pointwise_smul_le_iff₀ | [] | [
169,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Std/Logic.lean | exists_false | [] | [
430,
69
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
430,
9
] |
Mathlib/Data/Nat/Prime.lean | Nat.Prime.eq_two_or_odd | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : Prime p\nh : p % 2 = 0\n⊢ ¬2 = 1",
"tactic": "decide"
}
] | [
497,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
495,
1
] |
Mathlib/LinearAlgebra/Dual.lean | LinearMap.dualMap_apply' | [] | [
206,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisConnection.isGLB_u_image | [] | [
139,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_lt_of_le_one_of_lt_of_nonneg | [] | [
831,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
829,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | ContDiffWithinAt.cosh | [] | [
1117,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1115,
1
] |
Mathlib/RingTheory/WittVector/StructurePolynomial.lean | wittStructureInt_vars | [
{
"state_after": "p : ℕ\nR : Type ?u.2119290\nidx : Type u_1\ninst✝¹ : CommRing R\nhp : Fact (Nat.Prime p)\ninst✝ : Fintype idx\nΦ : MvPolynomial idx ℤ\nn : ℕ\nthis : Function.Injective ↑(Int.castRingHom ℚ)\n⊢ vars (wittStructureInt p Φ n) ⊆ Finset.univ ×ˢ Finset.range (n + 1)",
"state_before": "p : ℕ\nR : ... | [
414,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.le_inter_iff | [] | [
1819,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1818,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.lt_or_equiv_or_gf | [
{
"state_after": "x y : PGame\n⊢ x < y ∨ (x ≈ y) ∨ y < x ∨ x ‖ y",
"state_before": "x y : PGame\n⊢ x < y ∨ (x ≈ y) ∨ y ⧏ x",
"tactic": "rw [lf_iff_lt_or_fuzzy, Fuzzy.swap_iff]"
},
{
"state_after": "no goals",
"state_before": "x y : PGame\n⊢ x < y ∨ (x ≈ y) ∨ y < x ∨ x ‖ y",
"tactic": "ex... | [
1004,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1002,
1
] |
Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.mod_one | [] | [
75,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.toEquiv_inj | [] | [
316,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
9
] |
Mathlib/Analysis/Calculus/FDeriv/Linear.lean | IsBoundedLinearMap.differentiable | [] | [
146,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.factors_lemma | [
{
"state_after": "case h\nk : ℕ\n⊢ 1 < k + 2",
"state_before": "k : ℕ\n⊢ k + 2 ≠ 1",
"tactic": "apply Nat.ne_of_gt"
},
{
"state_after": "case h.a\nk : ℕ\n⊢ 0 < k + 1",
"state_before": "case h\nk : ℕ\n⊢ 1 < k + 2",
"tactic": "apply Nat.succ_lt_succ"
},
{
"state_after": "no goals",... | [
541,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
536,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffAt.snd'' | [] | [
840,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
838,
1
] |
Mathlib/Data/TwoPointing.lean | TwoPointing.sum_snd | [] | [
140,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Order/Circular.lean | btw_refl_left_right | [] | [
295,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.NullMeasurableSet.mono | [] | [
2669,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2668,
1
] |
Mathlib/Algebra/Parity.lean | isSquare_one | [] | [
73,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Algebra/Homology/Homotopy.lean | Homotopy.mkInductiveAux₃ | [
{
"state_after": "ι : Type ?u.344609\nV : Type u\ninst✝¹ : Category V\ninst✝ : Preadditive V\nc : ComplexShape ι\nC D E : HomologicalComplex V c\nf g : C ⟶ D\nh k : D ⟶ E\ni✝ : ι\nP Q : ChainComplex V ℕ\ne : P ⟶ Q\nzero : X P 0 ⟶ X Q 1\ncomm_zero : Hom.f e 0 = zero ≫ d Q 1 0\none : X P 1 ⟶ X Q 2\ncomm_one : Hom... | [
535,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/CategoryTheory/EqToHom.lean | CategoryTheory.Functor.congr_hom | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF : C ⥤ D\nX Y : C\nf : X ⟶ Y\n⊢ F.map f = eqToHom (_ : F.obj X = F.obj X) ≫ F.map f ≫ eqToHom (_ : F.obj Y = F.obj Y)",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF G : C ⥤ D\nh : F... | [
211,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.coe_finset_inf | [] | [
217,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Data/Set/NAry.lean | Set.mem_image2 | [] | [
44,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.ConnectedComponent.connectedComponentMk_eq_of_adj | [] | [
2016,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2014,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.sign_neg | [
{
"state_after": "no goals",
"state_before": "θ : Angle\n⊢ sign (-θ) = -sign θ",
"tactic": "simp_rw [sign, sin_neg, Left.sign_neg]"
}
] | [
867,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
866,
1
] |
Mathlib/Data/Multiset/Fold.lean | Multiset.fold_cons_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.4822\nop : α → α → α\nhc : IsCommutative α op\nha : IsAssociative α op\nb a : α\ns : Multiset α\n⊢ fold op b (a ::ₘ s) = op (fold op b s) a",
"tactic": "simp [hc.comm]"
}
] | [
68,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | lipschitzWith_iff_dist_le_mul | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\nK : ℝ≥0\nf : α → β\n⊢ (∀ (x y : α), ↑(nndist (f x) (f y)) ≤ ↑K * ↑(nndist x y)) ↔ ∀ (x y : α), ↑(nndist (f x) (f y)) ≤ ↑K * ↑(nndist x y)",
"state_before": "α : Type u\nβ : Type v\nγ ... | [
62,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Order/Atoms.lean | isCoatom_dual_iff_isAtom | [] | [
125,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Computability/Encoding.lean | Computability.inclusionBoolΓ'_injective | [] | [
95,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Submodule.annihilator_mono | [] | [
96,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arccos_of_le_neg_one | [
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx : x ≤ -1\n⊢ arccos x = π",
"tactic": "rw [arccos, arcsin_of_le_neg_one hx, sub_neg_eq_add, add_halves']"
}
] | [
416,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Std/Data/Int/Lemmas.lean | Int.sub_le_sub | [] | [
1037,
42
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1036,
11
] |
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | Matrix.toBilin_toMatrix | [] | [
349,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | MonoidHomClass.antilipschitz_of_bound | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type u_1\n𝕜 : Type ?u.369462\nα : Type ?u.369465\nι : Type ?u.369468\nκ : Type ?u.369471\nE : Type u_2\nF : Type u_3\nG : Type ?u.369480\ninst✝³ : SeminormedGroup E\ninst✝² : SeminormedGroup F\ninst✝¹ : SeminormedGroup G\ns : Set E\na a₁ a₂ b b₁ b₂ : E\nr ... | [
1010,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1007,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.deleteEdges_verts | [] | [
1038,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1037,
1
] |
Mathlib/Logic/Equiv/Fin.lean | finCongr_symm | [] | [
118,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
9
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_pos_of_mem_Ioo | [] | [
414,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Data/Set/Prod.lean | Set.range_pair_subset | [
{
"state_after": "α : Type u_3\nβ : Type u_2\nγ : Type u_1\nδ : Type ?u.78105\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\na : α\nb : β\nf : α → β\ng : α → γ\nthis : (fun x => (f x, g x)) = Prod.map f g ∘ fun x => (x, x)\n⊢ (range fun x => (f x, g x)) ⊆ range f ×ˢ range g",
"state_before": "α : Type u_3\nβ : Type u_2... | [
307,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/Algebra/Order/Ring/Abs.lean | abs_cases | [
{
"state_after": "case pos\nα : Type u_1\ninst✝ : LinearOrderedRing α\na✝ b c a : α\nh : 0 ≤ a\n⊢ abs a = a ∧ 0 ≤ a ∨ abs a = -a ∧ a < 0\n\ncase neg\nα : Type u_1\ninst✝ : LinearOrderedRing α\na✝ b c a : α\nh : ¬0 ≤ a\n⊢ abs a = a ∧ 0 ≤ a ∨ abs a = -a ∧ a < 0",
"state_before": "α : Type u_1\ninst✝ : LinearO... | [
77,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | div_nonpos_of_nonpos_of_nonneg | [
{
"state_after": "ι : Type ?u.10909\nα : Type u_1\nβ : Type ?u.10915\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nha : a ≤ 0\nhb : 0 ≤ b\n⊢ a * b⁻¹ ≤ 0",
"state_before": "ι : Type ?u.10909\nα : Type u_1\nβ : Type ?u.10915\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nha : a ≤ 0\nh... | [
103,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.surjective | [] | [
203,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
11
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.tail_sum | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.161222\nα : Type ?u.161225\nM : Type ?u.161228\nN : Type ?u.161231\nP : Type ?u.161234\nM₀ : Type ?u.161237\nG : Type ?u.161240\nR : Type ?u.161243\nL : List ℕ\n⊢ sum (tail L) = sum L - headI L",
"tactic": "rw [← headI_add_tail_sum L, add_comm, @... | [
613,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
612,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.ofReal_finsupp_sum | [] | [
243,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.isFiniteMeasure_withDensity | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1762622\nγ : Type ?u.1762625\nδ : Type ?u.1762628\nm : MeasurableSpace α\nμ ν : Measure α\nf : α → ℝ≥0∞\nhf : (∫⁻ (a : α), f a ∂μ) ≠ ⊤\n⊢ ↑↑(withDensity μ f) univ < ⊤",
"tactic": "rwa [withDensity_apply _ MeasurableSet.univ, Measure... | [
1605,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1602,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.ofSet_trans | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.72442\nδ : Type ?u.72445\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ne : LocalHomeomorph α β\ne' : LocalHomeomorph β γ\ns : Set α\nhs : IsOpen s\n⊢ (L... | [
878,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
877,
1
] |
Mathlib/MeasureTheory/Function/L2Space.lean | MeasureTheory.L2.snorm_rpow_two_norm_lt_top | [
{
"state_after": "α : Type u_1\nE : Type ?u.42419\nF : Type u_2\n𝕜 : Type ?u.42425\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : MeasurableSpace α\nμ : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : NormedAddCommGroup F\nf : { x // x ∈ Lp F 2 }\nh_two : ENNReal.ofReal 2 = 2\n⊢ snorm (fun x ... | [
128,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
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