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/CategoryTheory/Whiskering.lean | CategoryTheory.whiskerRight_twice | [] | [
217,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | mul_sub_mul_div_mul_neg_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.192047\nα : Type u_1\nβ : Type ?u.192053\ninst✝ : LinearOrderedField α\na b c d : α\nn : ℤ\nhc : c ≠ 0\nhd : d ≠ 0\n⊢ (a * d - b * c) / (c * d) < 0 ↔ a / c < b / d",
"tactic": "rw [mul_comm b c, ← div_sub_div _ _ hc hd, sub_lt_zero]"
}
] | [
957,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
955,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.nat_cast_re | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ (↑n).re = ↑n",
"tactic": "rw [← ofReal_nat_cast, ofReal_re]"
}
] | [
839,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
839,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | Basis.mk_range_eq_rank | [] | [
799,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
798,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | HomologicalComplex.Hom.sqTo_right | [] | [
596,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
1
] |
Mathlib/Control/Traversable/Instances.lean | Option.naturality | [
{
"state_after": "no goals",
"state_before": "F G : Type u → Type u\ninst✝³ : Applicative F\ninst✝² : Applicative G\ninst✝¹ : LawfulApplicative F\ninst✝ : LawfulApplicative G\nη : ApplicativeTransformation F G\nα : Type u_1\nβ : Type u\nf : α → F β\nx : Option α\n⊢ (fun {α} => ApplicativeTransformation.app ... | [
56,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Std/Data/List/Lemmas.lean | List.foldr_hom | [
{
"state_after": "no goals",
"state_before": "β₁ : Type u_1\nβ₂ : Type u_2\nα : Type u_3\nf : β₁ → β₂\ng₁ : α → β₁ → β₁\ng₂ : α → β₂ → β₂\nl : List α\ninit : β₁\nH : ∀ (x : α) (y : β₁), g₂ x (f y) = f (g₁ x y)\n⊢ foldr g₂ (f init) l = f (foldr g₁ init l)",
"tactic": "induction l <;> simp [*, H]"
}
] | [
1423,
30
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1421,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mem_closure_singleton | [
{
"state_after": "case refine'_1\nG : Type u_1\nG' : Type ?u.216540\ninst✝² : Group G\ninst✝¹ : Group G'\nA : Type ?u.216549\ninst✝ : AddGroup A\nH K : Subgroup G\nk : Set G\nx y : G\nhy : y ∈ closure {x}\n⊢ ∀ (x_1 : G), x_1 ∈ {x} → ∃ n, x ^ n = x_1\n\ncase refine'_2\nG : Type u_1\nG' : Type ?u.216540\ninst✝² :... | [
1293,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1282,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.mem_darts_reverse | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V\nd : Dart G\np : Walk G u v\n⊢ d ∈ darts (reverse p) ↔ Dart.symm d ∈ darts p",
"tactic": "simp"
}
] | [
719,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
718,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.get_one_right | [
{
"state_after": "α : Type u_1\ninst✝¹ : Monoid α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\na : α\nha : Finite a 1\n⊢ 1 ∣ 1 ∧ ¬a ^ (0 + 1) ∣ 1",
"state_before": "α : Type u_1\ninst✝¹ : Monoid α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\na : α\nha : Finite a 1\n⊢ Part.get (multiplicity a 1) ha = 0",
"... | [
196,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.target_inter_inv_preimage_preimage | [] | [
526,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
524,
1
] |
Mathlib/Data/Sum/Order.lean | OrderIso.sumAssoc_symm_apply_inr_inl | [] | [
594,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/Computability/Partrec.lean | Nat.Partrec.none | [
{
"state_after": "no goals",
"state_before": "n a : ℕ\nx✝ : a ∈ Nat.rfind fun n_1 => (fun m => decide (m = 0)) <$> (↑fun x => 1) (Nat.pair n n_1)\nh : (Nat.rfind fun n_1 => (fun m => decide (m = 0)) <$> (↑fun x => 1) (Nat.pair n n_1)).Dom\nh✝ : Part.get (Nat.rfind fun n_1 => (fun m => decide (m = 0)) <$> (↑... | [
208,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Data/List/Lattice.lean | List.bagInter_sublist_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl l₁ l₂✝ : List α\np : α → Prop\na : α\ninst✝ : DecidableEq α\nl₂ : List α\n⊢ List.bagInter [] l₂ <+ []",
"tactic": "simp"
},
{
"state_after": "case pos\nα : Type u_1\nl l₁✝ l₂✝ : List α\np : α → Prop\na : α\ninst✝ : DecidableEq α\nb : ... | [
273,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.neg_eq_self_iff | [
{
"state_after": "no goals",
"state_before": "θ : Angle\n⊢ -θ = θ ↔ θ = 0 ∨ θ = ↑π",
"tactic": "rw [eq_comm, eq_neg_self_iff]"
}
] | [
222,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Topology/ContinuousOn.lean | continuousOn_of_locally_continuousOn | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.347413\nδ : Type ?u.347416\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α → β\ns : Set α\nh : ∀ (x : α), x ∈ s → ∃ t, IsOpen t ∧ x ∈ t ∧ ContinuousOn f (s ∩ t)\nx : α\nxs : x ∈ s\... | [
1039,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1034,
1
] |
Mathlib/Algebra/Group/UniqueProds.lean | eq_and_eq_of_le_of_le_of_mul_le | [
{
"state_after": "A : Type u_1\ninst✝⁴ : Mul A\ninst✝³ : LinearOrder A\ninst✝² : CovariantClass A A (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\ninst✝¹ : CovariantClass A A (Function.swap fun x x_1 => x * x_1) fun x x_1 => x < x_1\ninst✝ : ContravariantClass A A (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b ... | [
218,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.principal_coprod_principal | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.62155\nδ : Type ?u.62158\nι : Sort ?u.62161\nf : Filter α\ng : Filter β\ns : Set α\nt : Set β\n⊢ Filter.coprod (𝓟 s) (𝓟 t) = 𝓟 ((sᶜ ×ˢ tᶜ)ᶜ)",
"tactic": "rw [Filter.coprod, comap_principal, comap_principal, sup_prin... | [
520,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | Embedding.aestronglyMeasurable_comp_iff | [
{
"state_after": "α : Type u_3\nβ : Type u_1\nγ : Type u_2\nι : Type ?u.351271\ninst✝⁴ : Countable ι\nm : MeasurableSpace α\nμ : Measure α\ninst✝³ : TopologicalSpace β\ninst✝² : TopologicalSpace γ\nf✝ g✝ : α → β\ninst✝¹ : PseudoMetrizableSpace β\ninst✝ : PseudoMetrizableSpace γ\ng : β → γ\nf : α → β\nhg : _root... | [
1619,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1600,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | LinearMap.zero_apply | [] | [
856,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
855,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.filter_and | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.394516\nγ : Type ?u.394519\np q : α → Prop\ninst✝² : DecidablePred p\ninst✝¹ : DecidablePred q\ninst✝ : DecidableEq α\ns : Finset α\nx✝ : α\n⊢ x✝ ∈ filter (fun a => p a ∧ q a) s ↔ x✝ ∈ filter p s ∩ filter q s",
"tactic": "simp [mem_... | [
2855,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2854,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.ext | [] | [
120,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
8
] |
Mathlib/Deprecated/Subgroup.lean | IsSubgroup.eq_trivial_iff | [
{
"state_after": "G : Type u_1\nH : Type ?u.34551\nA : Type ?u.34554\na a₁ a₂ b c : G\ninst✝ : Group G\ns : Set G\nhs : IsSubgroup s\n⊢ (∀ (x : G), x ∈ s ↔ x = 1) ↔ ∀ (x : G), x ∈ s → x = 1",
"state_before": "G : Type u_1\nH : Type ?u.34551\nA : Type ?u.34554\na a₁ a₂ b c : G\ninst✝ : Group G\ns : Set G\nhs... | [
255,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/LinearAlgebra/SModEq.lean | SModEq.eval | [
{
"state_after": "R✝ : Type ?u.82108\ninst✝⁵ : Ring R✝\nM : Type ?u.82114\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R✝ M\nU U₁ U₂ : Submodule R✝ M\nx✝ x₁ x₂ y✝ y₁ y₂ z z₁ z₂ : M\nN : Type ?u.83145\ninst✝² : AddCommGroup N\ninst✝¹ : Module R✝ N\nV V₁ V₂ : Submodule R✝ N\nR : Type u_1\ninst✝ : CommRing R\nI : Ide... | [
115,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.flip_flip | [
{
"state_after": "case h.H\nR : Type u_2\nM : Type u_3\ninst✝¹⁵ : Semiring R\ninst✝¹⁴ : AddCommMonoid M\ninst✝¹³ : Module R M\nR₁ : Type ?u.234780\nM₁ : Type ?u.234783\ninst✝¹² : Ring R₁\ninst✝¹¹ : AddCommGroup M₁\ninst✝¹⁰ : Module R₁ M₁\nR₂ : Type u_1\nM₂ : Type ?u.235395\ninst✝⁹ : CommSemiring R₂\ninst✝⁸ : Ad... | [
342,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Data/Set/Intervals/Monotone.lean | strictAntiOn_Ici_of_lt_pred | [] | [
271,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/RingTheory/WittVector/Defs.lean | WittVector.wittAdd_vars | [] | [
400,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/Topology/Semicontinuous.lean | LowerSemicontinuous.lowerSemicontinuousWithinAt | [] | [
169,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.num_mul_dvd | [
{
"state_after": "case pos\nK : Type u\ninst✝ : Field K\nx y : RatFunc K\nhx : x = 0\n⊢ num (x * y) ∣ num x * num y\n\ncase neg\nK : Type u\ninst✝ : Field K\nx y : RatFunc K\nhx : ¬x = 0\n⊢ num (x * y) ∣ num x * num y",
"state_before": "K : Type u\ninst✝ : Field K\nx y : RatFunc K\n⊢ num (x * y) ∣ num x * n... | [
1322,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1315,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.ae_ball_iff | [] | [
419,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | Finset.stronglyMeasurable_prod' | [] | [
585,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | aemeasurable_iSup | [] | [
1265,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1263,
1
] |
Mathlib/RingTheory/PrincipalIdealDomain.lean | Submodule.IsPrincipal.eq_bot_iff_generator_eq_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u\nM : Type v\ninst✝³ : AddCommGroup M\ninst✝² : Ring R\ninst✝¹ : Module R M\nS : Submodule R M\ninst✝ : IsPrincipal S\n⊢ S = ⊥ ↔ generator S = 0",
"tactic": "rw [← @span_singleton_eq_bot R M, span_singleton_generator]"
}
] | [
126,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.preimage_symm | [] | [
283,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | reflection_apply | [] | [
652,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
651,
1
] |
Mathlib/Topology/MetricSpace/IsometricSMul.lean | EMetric.smul_closedBall | [] | [
289,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.content_X | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\n⊢ content X = 1",
"tactic": "rw [← mul_one X, content_X_mul, content_one]"
}
] | [
146,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Data/Part.lean | Part.not_none_dom | [] | [
190,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_mem_smul_set_iff | [] | [
880,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
879,
1
] |
Mathlib/CategoryTheory/Monoidal/OfChosenFiniteProducts/Basic.lean | CategoryTheory.Limits.BinaryFan.assoc_snd | [] | [
113,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Order/Heyting/Basic.lean | Pi.hnot_def | [] | [
166,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Analysis/Convex/Basic.lean | MonotoneOn.convex_ge | [] | [
352,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.Memℒp.mono' | [] | [
545,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
] |
Mathlib/Logic/Hydra.lean | Relation.cutExpand_singleton | [] | [
81,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.div_mem_div | [] | [
610,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
1
] |
Mathlib/Analysis/Calculus/Inverse.lean | HasStrictFDerivAt.approximates_deriv_on_open_nhds | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁹ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace 𝕜 F\nG : Type ?u.526060\ninst✝⁴ : NormedAddCommGroup G\ninst✝³ : NormedSpace 𝕜 G\nG' : Type ?u.526163\... | [
575,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.nfp_le_iff | [
{
"state_after": "f : Ordinal → Ordinal\na b : Ordinal\n⊢ (fun a => sup fun n => (f^[n]) a) a ≤ b ↔ ∀ (n : ℕ), (f^[n]) a ≤ b",
"state_before": "f : Ordinal → Ordinal\na b : Ordinal\n⊢ nfp f a ≤ b ↔ ∀ (n : ℕ), (f^[n]) a ≤ b",
"tactic": "rw [← sup_iterate_eq_nfp]"
},
{
"state_after": "no goals",
... | [
454,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/Algebra/Order/Ring/WithTop.lean | WithBot.bot_mul | [] | [
245,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.productive_iff | [] | [
216,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.neg_lt_of_neg_lt | [] | [
828,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
828,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.integrable_average | [
{
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593,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
589,
1
] |
Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.outerMeasure_eq_iInf | [] | [
281,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Data/Finset/Basic.lean | coe_notMemRangeEquiv | [] | [
3101,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3099,
1
] |
Mathlib/Algebra/Module/LocalizedModule.lean | IsLocalizedModule.mk'_cancel | [
{
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952,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
949,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.bijective_eq_sup | [] | [
636,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
634,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Complex.differentiable_sin | [] | [
57,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Data/List/Basic.lean | Function.Involutive.exists_mem_and_apply_eq_iff | [
{
"state_after": "case intro.intro\nι : Type ?u.2112\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf : α → α\nhf : Involutive f\nl : List α\ny : α\nh : y ∈ l\n⊢ f (f y) ∈ l",
"state_before": "ι : Type ?u.2112\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf : α → α\nhf :... | [
137,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Algebra/Order/Module.lean | smul_lowerBounds_subset_upperBounds_smul | [] | [
205,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.sub_const_eq_X_mul_shift | [] | [
1945,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1943,
1
] |
Mathlib/Topology/Sets/Compacts.lean | exists_positiveCompacts_subset | [] | [
421,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/Order/RelClasses.lean | Subrelation.isWellFounded | [] | [
521,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/Algebra/Algebra/Spectrum.lean | spectrum.scalar_eq | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\nA : Type v\ninst✝³ : Field 𝕜\ninst✝² : Ring A\ninst✝¹ : Algebra 𝕜 A\ninst✝ : Nontrivial A\nk : 𝕜\n⊢ σ (↑↑ₐ k) = {k}",
"tactic": "rw [← add_zero (↑ₐ k), ← singleton_add_eq, zero_eq, Set.singleton_add_singleton, add_zero]"
}
] | [
347,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.div_eq_of_eq_mul_left | [
{
"state_after": "no goals",
"state_before": "n m k : Nat\nH1 : 0 < n\nH2 : m = k * n\n⊢ m / n = k",
"tactic": "rw [H2, Nat.mul_div_cancel _ H1]"
}
] | [
596,
36
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
595,
11
] |
Mathlib/Data/Rat/Defs.lean | Rat.divInt_eq_zero | [
{
"state_after": "no goals",
"state_before": "a b : ℤ\nb0 : b ≠ 0\n⊢ a /. b = 0 ↔ a = 0",
"tactic": "rw [←zero_divInt b, divInt_eq_iff b0 b0, zero_mul, mul_eq_zero, or_iff_left b0]"
}
] | [
88,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Log.lean | Complex.log_exp | [
{
"state_after": "no goals",
"state_before": "x : ℂ\nhx₁ : -π < x.im\nhx₂ : x.im ≤ π\n⊢ log (exp x) = x",
"tactic": "rw [log, abs_exp, Real.log_exp, exp_eq_exp_re_mul_sin_add_cos, ← ofReal_exp,\n arg_mul_cos_add_sin_mul_I (Real.exp_pos _) ⟨hx₁, hx₂⟩, re_add_im]"
}
] | [
65,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.sum_elim_dotProduct_sum_elim | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.141692\nm : Type u_2\nn : Type u_1\no : Type ?u.141701\nm' : o → Type ?u.141706\nn' : o → Type ?u.141711\nR : Type ?u.141714\nS : Type ?u.141717\nα : Type v\nβ : Type w\nγ : Type ?u.141724\ninst✝² : Fintype m\ninst✝¹ : Fintype n\ninst✝ : NonUnitalNon... | [
778,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
777,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | extChartAt_source | [] | [
1042,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1041,
1
] |
Mathlib/Data/List/Basic.lean | List.getD_replicate_default_eq | [
{
"state_after": "case zero\nι : Type ?u.502826\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l : List α\nx : α\nxs : List α\nd : α\nn✝¹ n✝ n : ℕ\n⊢ getD (replicate zero d) n d = d\n\ncase succ\nι : Type ?u.502826\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l : List α\nx : α\nxs : List α\nd ... | [
4424,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4421,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.moveLeft_neg_symm' | [
{
"state_after": "no goals",
"state_before": "x : PGame\ni : LeftMoves x\n⊢ moveLeft x i = -moveRight (-x) (↑toRightMovesNeg i)",
"tactic": "simp"
}
] | [
1293,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1292,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.mem_prod | [] | [
1103,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1102,
1
] |
Mathlib/Algebra/EuclideanDomain/Defs.lean | EuclideanDomain.gcdA_zero_left | [
{
"state_after": "R : Type u\ninst✝¹ : EuclideanDomain R\ninst✝ : DecidableEq R\ns : R\n⊢ (xgcd 0 s).fst = 0",
"state_before": "R : Type u\ninst✝¹ : EuclideanDomain R\ninst✝ : DecidableEq R\ns : R\n⊢ gcdA 0 s = 0",
"tactic": "unfold gcdA"
},
{
"state_after": "no goals",
"state_before": "R : ... | [
269,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Topology/Constructions.lean | continuous_ofDual | [] | [
163,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Std/Data/String/Lemmas.lean | String.utf8ByteSize.go_eq | [] | [
43,
70
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
43,
9
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | aestronglyMeasurable_id | [] | [
1447,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1444,
1
] |
Mathlib/RingTheory/IntegrallyClosed.lean | IsIntegrallyClosed.integralClosure_eq_bot_iff | [
{
"state_after": "R : Type u_2\ninst✝² : CommRing R\nid : IsDomain R\niic : IsIntegrallyClosed R\nK : Type u_1\ninst✝¹ : Field K\ninst✝ : Algebra R K\nifr : IsFractionRing R K\n⊢ integralClosure R K ≤ ⊥ ↔ IsIntegrallyClosed R",
"state_before": "R : Type u_2\ninst✝² : CommRing R\nid : IsDomain R\niic : IsInt... | [
117,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | le_mul_iff_one_le_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na b c d : α\ninst✝⁴ : MulOneClass α\ninst✝³ : Zero α\ninst✝² : Preorder α\ninst✝¹ : MulPosMono α\ninst✝ : MulPosMonoRev α\na0 : 0 < a\n⊢ a ≤ b * a ↔ 1 * a ≤ b * a",
"tactic": "rw [one_mul]"
}
] | [
643,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
642,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.star_eq_self | [] | [
1158,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1157,
1
] |
Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isNat_mul | [] | [
353,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/Logic/Encodable/Basic.lean | Directed.sequence_mono_nat | [
{
"state_after": "α : Type u_2\nβ : Type u_1\ninst✝¹ : Encodable α\ninst✝ : Inhabited α\nr : β → β → Prop\nf : α → β\nhf : Directed r f\nn : ℕ\n⊢ r (f (Directed.sequence f hf n))\n (f\n (match decode (n + 0) with\n | none =>\n Classical.choose\n (_ : ∃ z, r (f (Directed.sequence f h... | [
652,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
646,
1
] |
Mathlib/RingTheory/EuclideanDomain.lean | EuclideanDomain.span_gcd | [] | [
84,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | completeSpace_iff_isComplete_univ | [] | [
405,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_pi_over_two_pow | [
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ cos (π / 2 ^ (0 + 1)) = sqrtTwoAddSeries 0 0 / 2",
"tactic": "simp"
},
{
"state_after": "x : ℝ\nn : ℕ\nthis : 2 ≠ 0\n⊢ cos (π / 2 ^ (n + 1 + 1)) = sqrtTwoAddSeries 0 (n + 1) / 2",
"state_before": "x : ℝ\nn : ℕ\n⊢ cos (π / 2 ^ (n + 1 + 1)... | [
747,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
726,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.lintegral_lintegral_swap | [] | [
799,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | DoubleQuot.coe_quotQuotEquivQuotOfLEₐ_symm | [] | [
847,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
845,
1
] |
Mathlib/Algebra/Ring/Defs.lean | mul_add_one | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : Type x\ninst✝² : Add α\ninst✝¹ : MulOneClass α\ninst✝ : LeftDistribClass α\na b : α\n⊢ a * (b + 1) = a * b + a",
"tactic": "rw [mul_add, mul_one]"
}
] | [
162,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Lemmas.lean | map_ne_zero | [] | [
214,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIocDiv_sub_zsmul' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\nm : ℤ\n⊢ toIocDiv hp (a - m • p) b = toIocDiv hp a b + m",
"tactic": "rw [sub_eq_add_neg, ← neg_smul, toIocDiv_add_zsmul', sub_neg_eq_add]"... | [
295,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Data/Int/Bitwise.lean | Int.bit1_ne_zero | [
{
"state_after": "no goals",
"state_before": "m : ℤ\n⊢ bit1 m ≠ 0",
"tactic": "simpa only [bit0_zero] using bit1_ne_bit0 m 0"
}
] | [
193,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | edist_le_Ico_sum_of_edist_le | [] | [
153,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/LinearAlgebra/TensorAlgebra/Grading.lean | TensorAlgebra.GradedAlgebra.ι_apply | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.13352\nM : Type ?u.13355\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nm : M\n⊢ ↑(TensorAlgebra.ι R) m ∈ LinearMap.range (TensorAlgebra.ι R) ^ 1",
"tactic": "simpa only [pow_one] using LinearMap.mem_range_self _ m"
}
] | [
41,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.AEEqFun.Integrable.sub | [] | [
1250,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1248,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.preimage_open_of_open_symm | [] | [
645,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.HasFiniteIntegral.norm | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.729415\nδ : Type ?u.729418\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\nf : α → β\nhfi : HasFiniteIntegral f\neq : (fun a => ↑‖‖f a‖‖₊) = fun a => ↑‖f a‖₊\n⊢ HasFiniteIn... | [
252,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Combinatorics/Quiver/Cast.lean | Quiver.Hom.eq_cast_iff_heq | [
{
"state_after": "U : Type u_1\ninst✝ : Quiver U\nu v u' v' : U\nhu : u = u'\nhv : v = v'\ne : u ⟶ v\ne' : u' ⟶ v'\n⊢ HEq e e' ↔ HEq e' e",
"state_before": "U : Type u_1\ninst✝ : Quiver U\nu v u' v' : U\nhu : u = u'\nhv : v = v'\ne : u ⟶ v\ne' : u' ⟶ v'\n⊢ e' = cast hu hv e ↔ HEq e' e",
"tactic": "rw [e... | [
75,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_bot | [] | [
621,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
620,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.eq_iff_exists | [] | [
589,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
Mathlib/Order/Directed.lean | Directed.mono_comp | [] | [
107,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.innerContent_iUnion_nat | [
{
"state_after": "G : Type w\ninst✝¹ : TopologicalSpace G\nμ : Content G\ninst✝ : T2Space G\nU : ℕ → Set G\nhU : ∀ (i : ℕ), IsOpen (U i)\nthis :\n innerContent μ (⨆ (i : ℕ), { carrier := U i, is_open' := (_ : IsOpen (U i)) }) ≤\n ∑' (i : ℕ), innerContent μ { carrier := U i, is_open' := (_ : IsOpen (U i)) }\... | [
205,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Analysis/Convex/Between.lean | left_mem_affineSegment | [] | [
65,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.LiftRelO.imp_right | [] | [
468,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
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