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/Algebra/DirectSum/Ring.lean | DirectSum.mul_comm | [
{
"state_after": "ι : Type u_1\ninst✝³ : DecidableEq ι\nA : ι → Type u_2\ninst✝² : (i : ι) → AddCommMonoid (A i)\ninst✝¹ : AddCommMonoid ι\ninst✝ : GCommSemiring A\na b : ⨁ (i : ι), A i\n⊢ mulHom A = AddMonoidHom.flip (mulHom A)",
"state_before": "ι : Type u_1\ninst✝³ : DecidableEq ι\nA : ι → Type u_2\ninst... | [
348,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
9
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.angle_self_neg_of_nonzero | [
{
"state_after": "no goals",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y x : V\nhx : x ≠ 0\n⊢ angle x (-x) = π",
"tactic": "rw [angle_neg_right, angle_self hx, sub_zero]"
}
] | [
143,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/SetTheory/Ordinal/Topology.lean | Ordinal.enumOrd_isNormal_iff_isClosed | [
{
"state_after": "s : Set Ordinal\na : Ordinal\nhs : Set.Unbounded (fun x x_1 => x < x_1) s\nHs : StrictMono (enumOrd s)\n⊢ IsNormal (enumOrd s) ↔ IsClosed s",
"state_before": "s : Set Ordinal\na : Ordinal\nhs : Set.Unbounded (fun x x_1 => x < x_1) s\n⊢ IsNormal (enumOrd s) ↔ IsClosed s",
"tactic": "hav... | [
238,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.boundedBy_union_of_top_of_nonempty_inter | [] | [
927,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
923,
1
] |
Mathlib/Order/CompleteBooleanAlgebra.lean | compl_iInf | [] | [
300,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.extend_comp | [] | [
471,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
8
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.pos_of_mem_ball | [] | [
557,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image₂_singleton_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nα' : Type ?u.26477\nβ : Type u_3\nβ' : Type ?u.26483\nγ : Type u_1\nγ' : Type ?u.26489\nδ : Type ?u.26492\nδ' : Type ?u.26495\nε : Type ?u.26498\nε' : Type ?u.26501\nζ : Type ?u.26504\nζ' : Type ?u.26507\nν : Type ?u.26510\ninst✝⁷ : DecidableEq α'\... | [
155,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Dynamics/OmegaLimit.lean | mem_omegaLimit_iff_frequently₂ | [
{
"state_after": "no goals",
"state_before": "τ : Type u_2\nα : Type u_3\nβ : Type u_1\nι : Type ?u.30321\ninst✝ : TopologicalSpace β\nf : Filter τ\nϕ : τ → α → β\ns s₁ s₂ : Set α\ny : β\n⊢ y ∈ ω f ϕ s ↔ ∀ (n : Set β), n ∈ 𝓝 y → ∃ᶠ (t : τ) in f, Set.Nonempty (ϕ t '' s ∩ n)",
"tactic": "simp_rw [mem_ome... | [
152,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_pos_iff | [
{
"state_after": "b x y : ℝ\nhb : 1 < b\nhx : 0 < x\n⊢ logb b 1 < logb b x ↔ 1 < x",
"state_before": "b x y : ℝ\nhb : 1 < b\nhx : 0 < x\n⊢ 0 < logb b x ↔ 1 < x",
"tactic": "rw [← @logb_one b]"
},
{
"state_after": "no goals",
"state_before": "b x y : ℝ\nhb : 1 < b\nhx : 0 < x\n⊢ logb b 1 < lo... | [
181,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Continuous.nndist | [] | [
1850,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1848,
11
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean | Real.differentiableAt_tan | [] | [
60,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.concat_ne_nil | [
{
"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\np : Walk G u v\nh : Adj G v u\n⊢ concat p h ≠ nil",
"tactic": "cases p <;> simp [concat]"
}
] | [
484,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/Topology/Order/Basic.lean | isClosed_Icc | [] | [
154,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.succ_ne_zero | [] | [
813,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
812,
1
] |
Mathlib/GroupTheory/GroupAction/ConjAct.lean | ConjAct.toConjAct_zero | [] | [
226,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Logic/Basic.lean | funext₃ | [] | [
606,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
605,
1
] |
Mathlib/LinearAlgebra/FreeModule/Finite/Rank.lean | Submodule.finrank_quotient_le | [
{
"state_after": "no goals",
"state_before": "R : Type u\nM : Type v\nN : Type w\ninst✝⁶ : Ring R\ninst✝⁵ : StrongRankCondition R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\ninst✝² : AddCommGroup N\ninst✝¹ : Module R N\ninst✝ : Module.Finite R M\ns : Submodule R M\n⊢ finrank R (M ⧸ s) ≤ finrank R M",
... | [
214,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/RingTheory/Int/Basic.lean | Int.sq_of_coprime | [] | [
244,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | mem_rootsOfUnity' | [
{
"state_after": "M : Type u_1\nN : Type ?u.155571\nG : Type ?u.155574\nR : Type ?u.155577\nS : Type ?u.155580\nF : Type ?u.155583\ninst✝² : CommMonoid M\ninst✝¹ : CommMonoid N\ninst✝ : DivisionCommMonoid G\nk✝ l k : ℕ+\nζ : Mˣ\n⊢ ζ ^ ↑k = 1 ↔ ↑ζ ^ ↑k = 1",
"state_before": "M : Type u_1\nN : Type ?u.155571\... | [
100,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Algebra/Category/GroupCat/Basic.lean | CommGroupCat.coe_of | [] | [
257,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Order/Basic.lean | eq_of_le_of_forall_ge_of_dense | [] | [
1327,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1325,
1
] |
Mathlib/Combinatorics/SimpleGraph/Acyclic.lean | SimpleGraph.isAcyclic_iff_path_unique | [] | [
129,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Data/Finite/Defs.lean | Finite.ofBijective | [] | [
87,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Algebra/Associated.lean | Associates.dvdNotUnit_iff_lt | [] | [
1145,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1144,
1
] |
Mathlib/Algebra/Group/Commute.lean | Commute.inv_inv_iff | [] | [
312,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | HomogeneousIdeal.mem_irrelevant_iff | [] | [
667,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
665,
1
] |
Mathlib/Order/Interval.lean | Interval.coe_iInf₂ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.68647\nγ : Type ?u.68650\nδ : Type ?u.68653\nι : Sort u_2\nκ : ι → Sort u_3\ninst✝¹ : CompleteLattice α\ninst✝ : DecidableRel fun x x_1 => x ≤ x_1\nf : (i : ι) → κ i → Interval α\n⊢ ↑(⨅ (i : ι) (j : κ i), f i j) = ⋂ (i : ι) (j : κ i), ↑... | [
786,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
785,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.top_div_coe | [] | [
1548,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1548,
9
] |
Mathlib/MeasureTheory/PiSystem.lean | isPiSystem_Icc_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nι : Sort ?u.19636\nι' : Sort ?u.19639\ninst✝ : LinearOrder α\ns t : Set α\n⊢ ∀ {a₁ b₁ a₂ b₂ : α}, Icc a₁ b₁ ∩ Icc a₂ b₂ = Icc (max a₁ a₂) (min b₁ b₂)",
"tactic": "exact Icc_inter_Icc"
}
] | [
212,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Combinatorics/Composition.lean | List.sum_take_map_length_splitWrtComposition | [
{
"state_after": "case e_a.e_a\nn : ℕ\nα : Type u_1\nl : List α\nc : Composition (length l)\ni : ℕ\n⊢ map length (splitWrtComposition l c) = c.blocks",
"state_before": "n : ℕ\nα : Type u_1\nl : List α\nc : Composition (length l)\ni : ℕ\n⊢ sum (take i (map length (splitWrtComposition l c))) = Composition.siz... | [
722,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
719,
1
] |
Mathlib/Data/Polynomial/Lifts.lean | Polynomial.C_mem_lifts | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹ : Semiring R\nS : Type v\ninst✝ : Semiring S\nf✝ f : R →+* S\nr : R\n⊢ ↑(mapRingHom f) (↑C r) = ↑C (↑f r)",
"tactic": "simp only [coe_mapRingHom, map_C, Set.mem_univ, Subsemiring.coe_top, eq_self_iff_true,\n and_self_iff]"
}
] | [
85,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Any.imp | [] | [
461,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/Topology/Sheaves/Stalks.lean | TopCat.Presheaf.section_ext | [
{
"state_after": "C : Type u\ninst✝⁶ : Category C\ninst✝⁵ : HasColimits C\nX Y Z : TopCat\ninst✝⁴ : ConcreteCategory C\ninst✝³ : PreservesFilteredColimits (forget C)\ninst✝² : HasLimits C\ninst✝¹ : PreservesLimits (forget C)\ninst✝ : ReflectsIsomorphisms (forget C)\nF : Sheaf C X\nU : Opens ↑X\ns t : (forget C)... | [
468,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
456,
1
] |
Mathlib/Order/Hom/Lattice.lean | LatticeHom.dual_id | [] | [
1528,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1528,
9
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.closure_le | [] | [
1123,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1122,
1
] |
Mathlib/Analysis/InnerProductSpace/EuclideanDist.lean | Euclidean.nhds_basis_closedBall | [
{
"state_after": "E : Type u_1\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : TopologicalAddGroup E\ninst✝³ : T2Space E\ninst✝² : Module ℝ E\ninst✝¹ : ContinuousSMul ℝ E\ninst✝ : FiniteDimensional ℝ E\nx : E\n⊢ Filter.HasBasis\n (Filter.comap (↑(ContinuousLinearEquiv.toHomeomorph toEuclidean... | [
113,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.toReal_pi | [
{
"state_after": "⊢ -π < π ∧ π ≤ π",
"state_before": "⊢ toReal ↑π = π",
"tactic": "rw [toReal_coe_eq_self_iff]"
},
{
"state_after": "no goals",
"state_before": "⊢ -π < π ∧ π ≤ π",
"tactic": "exact ⟨Left.neg_lt_self Real.pi_pos, le_refl _⟩"
}
] | [
600,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
1
] |
Mathlib/Analysis/Calculus/FDerivMeasurable.lean | FDerivMeasurableAux.differentiable_set_eq_d | [] | [
371,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/RingTheory/PrincipalIdealDomain.lean | IsField.isPrincipalIdealRing | [] | [
236,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Data/FunLike/Equiv.lean | EquivLike.bijective_comp | [] | [
193,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Order/Directed.lean | directedOn_iff_directed | [
{
"state_after": "α : Type u\nβ : Type v\nι : Sort w\nr r' s✝ : α → α → Prop\ns : Set α\n⊢ (∀ (x : α), x ∈ s → ∀ (y : α), y ∈ s → ∃ z, z ∈ s ∧ r x z ∧ r y z) ↔\n ∀ (a : α), a ∈ s → ∀ (a_1 : α), a_1 ∈ s → ∃ a_2, r a a_2 ∧ a_2 ∈ s ∧ r a_1 a_2",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nr r' s✝ :... | [
60,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_coe_sort_eq_attach | [] | [
903,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
902,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.reverseAux_append | [
{
"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 w x : V\np : Walk G u v\nq : Walk G u w\nr : Walk G w x\n⊢ append (Walk.reverseAux p q) r = Walk.reverseAux p (append q r)",
"tactic": "induction p with... | [
348,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
11
] |
Mathlib/Data/Complex/Exponential.lean | Real.cosh_eq | [
{
"state_after": "no goals",
"state_before": "x✝ y x : ℝ\n⊢ cosh x * 2 = exp x + exp (-x)",
"tactic": "rw [cosh, exp, exp, Complex.ofReal_neg, Complex.cosh, mul_two, ← Complex.add_re, ← mul_two,\n div_mul_cancel _ (two_ne_zero' ℂ), Complex.add_re]"
}
] | [
1361,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1358,
1
] |
Mathlib/Data/List/Chain.lean | List.chain'_append | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nR r : α → α → Prop\nl✝ l₁ l₂ : List α\na b : α\nl : List α\n⊢ Chain' R ([] ++ l) ↔ Chain' R [] ∧ Chain' R l ∧ ∀ (x : α), x ∈ getLast? [] → ∀ (y : α), y ∈ head? l → R x y",
"tactic": "simp"
},
{
"state_after": "no goals",
"... | [
293,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.HasFiniteIntegral.const_mul | [] | [
419,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.norm_id | [
{
"state_after": "𝕜 : Type u_2\n𝕜₂ : Type ?u.2599087\n𝕜₃ : Type ?u.2599090\nE : Type u_1\nEₗ : Type ?u.2599096\nF : Type ?u.2599099\nFₗ : Type ?u.2599102\nG : Type ?u.2599105\nGₗ : Type ?u.2599108\n𝓕 : Type ?u.2599111\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NormedAddCommGro... | [
1480,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1477,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | AddValuation.map_le_sub | [] | [
803,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
802,
1
] |
Mathlib/Data/Set/Function.lean | Set.surjOn_iff_surjective | [] | [
861,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
855,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | LinearMap.smul_def | [] | [
1134,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1133,
11
] |
Mathlib/Algebra/DirectSum/Decomposition.lean | DirectSum.decompose_of_mem | [] | [
118,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.ae_eq_set_compl_compl | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.111469\nγ : Type ?u.111472\nδ : Type ?u.111475\nι : Type ?u.111478\ninst✝ : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns✝ s₁ s₂ t✝ s t : Set α\n⊢ sᶜ =ᵐ[μ] tᶜ ↔ s =ᵐ[μ] t",
"tactic": "simp only [← measure_symmDiff_eq_zero_iff, compl_sym... | [
494,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
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Mathlib/Algebra/Order/Floor.lean | Int.lt_ceil | [] | [
1108,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1107,
1
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Mathlib/Topology/SubsetProperties.lean | IrreducibleSpace.isIrreducible_univ | [] | [
1835,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1833,
1
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Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.kernelSubobjectIsoComp_hom_arrow | [
{
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217,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
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Mathlib/GroupTheory/GroupAction/SubMulAction.lean | SetLike.val_smul | [] | [
85,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
11
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Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | orthogonalFamily_iff_pairwise | [] | [
423,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/Topology/SubsetProperties.lean | IsClosed.sigmaCompactSpace | [] | [
1367,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1366,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Finset.lean | Finset.Nonempty.sup'_id_eq_cSup | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.5868\nγ : Type ?u.5871\ninst✝ : ConditionallyCompleteLattice α\ns✝ t : Set α\na b : α\ns : Finset α\nhs : Finset.Nonempty s\n⊢ sup' s hs id = sSup ↑s",
"tactic": "rw [hs.sup'_eq_cSup_image, Set.image_id]"
}
] | [
35,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.exists_mem_Ico_zpow | [] | [
737,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
8
] |
Mathlib/Data/Part.lean | Part.bind_some | [
{
"state_after": "no goals",
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"tactic": "simp"
}
] | [
521,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
] |
Mathlib/Topology/Support.lean | exists_compact_iff_hasCompactMulSupport | [
{
"state_after": "no goals",
"state_before": "X : Type ?u.9177\nα : Type u_1\nα' : Type ?u.9183\nβ : Type u_2\nγ : Type ?u.9189\nδ : Type ?u.9192\nM : Type ?u.9195\nE : Type ?u.9198\nR : Type ?u.9201\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : TopologicalSpace α'\ninst✝³ : One β\ninst✝² : One γ\ninst✝¹ : One δ\n... | [
151,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
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Mathlib/Data/Nat/Prime.lean | Nat.prime_iff | [] | [
574,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
1
] |
Mathlib/Tactic/Abel.lean | Mathlib.Tactic.Abel.unfold_smulg | [] | [
258,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Std/Data/PairingHeap.lean | Std.PairingHeapImp.Heap.size_deleteMin_lt | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nle : α → α → Bool\na : α\ns' s : Heap α\neq : deleteMin le s = some (a, s')\n⊢ size s' < size s",
"tactic": "cases s with cases eq | node a c => simp_arith [size_combine, size]"
},
{
"state_after": "no goals",
"state_before": "case ... | [
157,
70
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
155,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.inverse_equiv | [
{
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2501,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2497,
1
] |
Mathlib/Data/Part.lean | Part.some_inter_some | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.88117\nγ : Type ?u.88120\ninst✝ : Inter α\na b : α\n⊢ some a ∩ some b = some (a ∩ b)",
"tactic": "simp [inter_def]"
}
] | [
840,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
839,
1
] |
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | ContinuousOn.clm_comp | [] | [
540,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.stalkToFiberRingHom_germ | [
{
"state_after": "case mk\nR : Type u\ninst✝ : CommRing R\nU : Opens ↑(PrimeSpectrum.Top R)\ns : ↑((structureSheaf R).val.obj U.op)\nval✝ : ↑(PrimeSpectrum.Top R)\nproperty✝ : val✝ ∈ U\n⊢ ↑(stalkToFiberRingHom R ↑{ val := val✝, property := property✝ })\n (↑(germ (Sheaf.presheaf (structureSheaf R)) { val :=... | [
555,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Deriv.lean | ContDiff.log | [] | [
181,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | LocalHomeomorph.extend_coord_change_source_mem_nhdsWithin' | [
{
"state_after": "case hx\n𝕜 : Type u_4\nE : Type u_3\nM : Type u_1\nH : Type u_2\nE' : Type ?u.173038\nM' : Type ?u.173041\nH' : Type ?u.173044\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : TopologicalSpace H\ninst✝⁴ : TopologicalSpace M\nf f' : Local... | [
989,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
984,
1
] |
Mathlib/Analysis/Calculus/Conformal/NormedSpace.lean | ConformalAt.congr | [] | [
101,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.two_mul_ne_two_mul_add_one | [
{
"state_after": "no goals",
"state_before": "m✝ n✝ k n m : ℕ\n⊢ ¬2 * n % 2 = (2 * m + 1) % 2",
"tactic": "rw [add_comm, add_mul_mod_self_left, mul_mod_right, mod_eq_of_lt] <;> simp"
}
] | [
342,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.sInter_eq_univ | [] | [
1105,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1104,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.secondCountable_of_sigmaCompact | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.281110\ninst✝¹ : PseudoEMetricSpace α\nx y z : α\nε ε₁ ε₂ : ℝ≥0∞\ns t : Set α\ninst✝ : SigmaCompactSpace α\n⊢ SeparableSpace α",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.281110\ninst✝¹ : PseudoEMetricSpace α\nx y z : α\nε ε₁ ε₂ : ℝ≥0∞\ns t : ... | [
852,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
846,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.PosDef.smul | [] | [
928,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
927,
1
] |
Mathlib/AlgebraicTopology/FundamentalGroupoid/Basic.lean | Path.Homotopy.continuous_transReflReparamAux | [
{
"state_after": "case refine'_5\nX : Type u\nY : Type v\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx₀ x₁ : X\n⊢ ∀ (x : ↑I), ↑x = 1 / 2 → 2 * ↑x = 1",
"state_before": "X : Type u\nY : Type v\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx₀ x₁ : X\n⊢ Continuous transReflReparamAux"... | [
143,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | ContDiffBump.one_of_mem_closedBall | [
{
"state_after": "case a\nE : Type u_1\nX : Type ?u.80093\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedAddCommGroup X\ninst✝¹ : NormedSpace ℝ X\ninst✝ : HasContDiffBump E\nc : E\nf : ContDiffBump c\nx : E\nn : ℕ∞\nhx : x ∈ closedBall c f.rIn\n⊢ ‖(fun x => f.rIn⁻¹ • (x - c)) x‖ ≤ 1",
... | [
388,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/Data/Int/Cast/Basic.lean | Nat.cast_sub | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : AddGroupWithOne R\nm n : ℕ\nh : m ≤ n\n⊢ ↑(n - m) + ↑m = ↑n",
"tactic": "rw [← cast_add, Nat.sub_add_cancel h]"
}
] | [
36,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Std/Data/Int/DivMod.lean | Int.mod_def' | [] | [
233,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
233,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.tail_drop' | [
{
"state_after": "case a\nα : Type u\nβ : Type v\nδ : Type w\ni : ℕ\ns : Stream' α\nn✝ : ℕ\n⊢ nth (tail (drop i s)) n✝ = nth (drop (i + 1) s) n✝",
"state_before": "α : Type u\nβ : Type v\nδ : Type w\ni : ℕ\ns : Stream' α\n⊢ tail (drop i s) = drop (i + 1) s",
"tactic": "ext"
},
{
"state_after": "... | [
74,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
9
] |
Mathlib/MeasureTheory/Covering/Differentiation.lean | VitaliFamily.ae_tendsto_div | [
{
"state_after": "case intro.intro.intro.intro\nα : Type u_1\ninst✝⁵ : MetricSpace α\nm0 : MeasurableSpace α\nμ : MeasureTheory.Measure α\nv : VitaliFamily μ\nE : Type ?u.2032110\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : SecondCountableTopology α\ninst✝² : BorelSpace α\ninst✝¹ : IsLocallyFiniteMeasure μ\nρ : Mea... | [
267,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.toFinset_insert' | [] | [
1066,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1064,
1
] |
Mathlib/Data/Fintype/Option.lean | Fintype.induction_empty_option | [
{
"state_after": "case mk\nα✝ : Type ?u.7602\nβ : Type ?u.7605\nγ : Type ?u.7608\nP : (α : Type u) → [inst : Fintype α] → Prop\nof_equiv : ∀ (α β : Type u) [inst : Fintype β] (e : α ≃ β), P α → P β\nh_empty : P PEmpty\nh_option : ∀ (α : Type u) [inst : Fintype α], P α → P (Option α)\nα : Type u\nh_fintype : Fin... | [
107,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Algebra/LinearRecurrence.lean | LinearRecurrence.geom_sol_iff_root_charPoly | [
{
"state_after": "α : Type u_1\ninst✝ : CommRing α\nE : LinearRecurrence α\nq : α\n⊢ (IsSolution E fun n => q ^ n) ↔\n eval₂ (RingHom.id α) q (↑(monomial E.order) 1 - ∑ i : Fin E.order, ↑(monomial ↑i) (coeffs E i)) = 0",
"state_before": "α : Type u_1\ninst✝ : CommRing α\nE : LinearRecurrence α\nq : α\n⊢ ... | [
230,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Analysis/Convex/Hull.lean | convexHull_univ | [] | [
94,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.radical_idem | [] | [
890,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
889,
1
] |
Mathlib/CategoryTheory/Bicategory/Basic.lean | CategoryTheory.Bicategory.leftUnitor_inv_naturality | [
{
"state_after": "no goals",
"state_before": "B : Type u\ninst✝ : Bicategory B\na b c d e : B\nf g : a ⟶ b\nη : f ⟶ g\n⊢ η ≫ (λ_ g).inv = (λ_ f).inv ≫ 𝟙 a ◁ η",
"tactic": "simp"
}
] | [
396,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | gcd_one_right | [] | [
417,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.restrictScalars_toSubalgebra | [] | [
641,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
639,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.monic_of_c_eq_one' | [] | [
268,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Analysis/Normed/Group/HomCompletion.lean | NormedAddGroupHom.completion_neg | [] | [
121,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Order/Lattice.lean | le_sup_right' | [] | [
149,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.diam_le | [] | [
899,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
898,
1
] |
Mathlib/Combinatorics/SetFamily/Compression/UV.lean | UV.mem_compression | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝² : GeneralizedBooleanAlgebra α\ninst✝¹ : DecidableRel Disjoint\ninst✝ : DecidableRel fun x x_1 => x ≤ x_1\ns : Finset α\nu v a b : α\n⊢ a ∈ 𝓒 u v s ↔ a ∈ s ∧ compress u v a ∈ s ∨ ¬a ∈ s ∧ ∃ b, b ∈ s ∧ compress u v b = a",
"tactic": "simp... | [
122,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Order/CompleteBooleanAlgebra.lean | iSup₂_disjoint_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nκ : ι → Sort u_1\ninst✝ : Frame α\ns t : Set α\na b : α\nf : (i : ι) → κ i → α\n⊢ Disjoint (⨆ (i : ι) (j : κ i), f i j) a ↔ ∀ (i : ι) (j : κ i), Disjoint (f i j) a",
"tactic": "simp_rw [iSup_disjoint_iff]"
}
] | [
142,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/NumberTheory/BernoulliPolynomials.lean | Polynomial.bernoulli_def | [
{
"state_after": "n : ℕ\n⊢ ∑ i in range (n + 1), ↑(monomial (n - i)) (_root_.bernoulli i * ↑(Nat.choose n i)) =\n ∑ j in range (n + 1), ↑(monomial (n - j)) (_root_.bernoulli (n - (n - j)) * ↑(Nat.choose n (n - j)))",
"state_before": "n : ℕ\n⊢ bernoulli n = ∑ i in range (n + 1), ↑(monomial i) (_root_.bern... | [
67,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Std/Data/List/Lemmas.lean | List.range_add | [
{
"state_after": "a b : Nat\n⊢ range (a + b) = range a ++ range' a b",
"state_before": "a b : Nat\n⊢ range (a + b) = range a ++ map (fun x => a + x) (range b)",
"tactic": "rw [← range'_eq_map_range]"
},
{
"state_after": "no goals",
"state_before": "a b : Nat\n⊢ range (a + b) = range a ++ ran... | [
1930,
75
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1928,
1
] |
Mathlib/Data/Set/Basic.lean | Set.not_not_mem | [] | [
431,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
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