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/Order/SuccPred/Basic.lean | exists_succ_iterate_iff_le | [
{
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"tactic... | [
1382,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1379,
1
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Mathlib/Algebra/GroupPower/Lemmas.lean | isUnit_pow_succ_iff | [] | [
84,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coeIdeal_ne_zero | [] | [
1016,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1015,
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Mathlib/Algebra/Ring/Commute.lean | mul_self_sub_mul_self | [] | [
152,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
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Mathlib/Data/Set/Lattice.lean | Set.biInter_insert | [
{
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60
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Mathlib/Algebra/Jordan/Basic.lean | aux3 | [
{
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246,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
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Mathlib/LinearAlgebra/Pi.lean | Submodule.mem_pi | [] | [
278,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
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Mathlib/GroupTheory/SpecificGroups/Quaternion.lean | QuaternionGroup.quaternionGroup_one_isCyclic | [
{
"state_after": "case hx\nn : ℕ\n⊢ orderOf ?x = Fintype.card (QuaternionGroup 1)\n\ncase x\nn : ℕ\n⊢ QuaternionGroup 1",
"state_before": "n : ℕ\n⊢ IsCyclic (QuaternionGroup 1)",
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},
{
"state_after": "case hx\nn : ℕ\n⊢ orderOf ?x = 4\n\ncase x\nn : ℕ\... | [
233,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
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Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.modPart_nonneg | [
{
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"tactic": "exact_mod_cast hp_prime.1.ne_zero"
}
] | [
81,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
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Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.aecover_Ico_of_Ico | [] | [
244,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
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Mathlib/Logic/Basic.lean | Ne.ite_eq_right_iff | [] | [
1189,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1188,
11
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Mathlib/Topology/PartitionOfUnity.lean | BumpCovering.exists_finset_toPartitionOfUnity_eventuallyEq | [] | [
469,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
1
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Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.mem_coe | [] | [
148,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
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Mathlib/Topology/Algebra/Order/Field.lean | tendsto_pow_neg_atTop | [
{
"state_after": "no goals",
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"tactic": "simpa only [zpow_neg, zpow_ofNat... | [
161,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
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Mathlib/Data/Set/Basic.lean | Set.union_insert | [] | [
1196,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1195,
1
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Mathlib/Algebra/Module/Projective.lean | Module.Projective.of_lifting_property'' | [] | [
129,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.count_eq_zero_iff' | [] | [
2291,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2290,
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Mathlib/Data/Set/Intervals/Basic.lean | Set.nonempty_Ico | [] | [
276,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
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Mathlib/Algebra/Homology/Single.lean | ChainComplex.single₀_map_f_succ | [] | [
189,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Data/Set/Countable.lean | Set.countable_iUnion | [
{
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"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\nt : ι → Set α\ninst✝ : Countable ... | [
189,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
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Mathlib/Algebra/Order/Monoid/ToMulBot.lean | WithZero.toMulBot_coe_ofAdd | [] | [
54,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
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Mathlib/Analysis/SpecificLimits/Basic.lean | summable_geometric_two | [] | [
205,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.range_eq_empty_of_isEmpty | [
{
"state_after": "α : Type u_2\nβ✝ : Type ?u.125758\nγ : Type ?u.125761\nδ : Type ?u.125764\ninst✝ : MeasurableSpace α\nβ : Type u_1\nhα : IsEmpty α\nf : α →ₛ β\n⊢ ¬Finset.Nonempty (SimpleFunc.range f)",
"state_before": "α : Type u_2\nβ✝ : Type ?u.125758\nγ : Type ?u.125761\nδ : Type ?u.125764\ninst✝ : Meas... | [
556,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
1
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Mathlib/Data/Set/Basic.lean | Set.nonempty_of_nonempty_subtype | [] | [
551,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
550,
1
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Mathlib/Data/Set/Lattice.lean | Set.iUnion_congr_Prop | [] | [
220,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
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Mathlib/Algebra/Periodic.lean | Int.fract_periodic | [
{
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"tactic": "exact_mod_cast Int.fract_add_int a 1"
}
] | [
548,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
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Mathlib/Analysis/Calculus/LocalExtr.lean | IsLocalMin.deriv_eq_zero | [] | [
237,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.natSize_to_nat | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.444246\nn : Num\n⊢ natSize n = Nat.size ↑n",
"tactic": "rw [← size_eq_natSize, size_to_nat]"
}
] | [
762,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
762,
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] |
Mathlib/Algebra/Polynomial/GroupRingAction.lean | prodXSubSmul.eval | [
{
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"tactic": "simp"
}
] | [
112,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
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Mathlib/LinearAlgebra/AffineSpace/Slope.lean | lineMap_slope_lineMap_slope_lineMap | [
{
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135,
20
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129,
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Mathlib/Deprecated/Subgroup.lean | IsGroupHom.inv_iff_ker' | [
{
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398,
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397,
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Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.comap_apply | [] | [
1142,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1136,
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Mathlib/GroupTheory/Complement.lean | Subgroup.MemRightTransversals.toFun_mul_inv_mem | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝ : Group G\nH K : Subgroup G\nS T : Set G\nhS : S ∈ rightTransversals ↑H\ng : G\n⊢ (g * (↑(toFun hS g))⁻¹)⁻¹ = ↑(toFun hS g) * g⁻¹",
"tactic": "rw [mul_inv_rev, inv_inv]"
}
] | [
433,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
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Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.coe_toSubalgebra | [] | [
97,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
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Mathlib/Data/Set/Function.lean | Set.piecewise_eq_of_mem | [] | [
1385,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1384,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | mul_le_of_le_of_le_one | [] | [
551,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_union_Icc_eq_Icc | [] | [
1540,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1537,
1
] |
Mathlib/Data/Int/Cast/Lemmas.lean | Int.cast_min | [] | [
165,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.reflection_vadd_smul_vsub_orthogonalProjection | [] | [
659,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
654,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.CokernelCofork.π_eq_zero | [
{
"state_after": "no goals",
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"tactic": "simp [Cofork.app_zero_eq_comp_π_right]"
}
] | [
555,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
] |
Mathlib/Topology/LocallyFinite.lean | LocallyFinite.nhdsWithin_iUnion | [
{
"state_after": "case intro.intro\nι : Type u_1\nι' : Type ?u.3024\nα : Type ?u.3027\nX : Type u_2\nY : Type ?u.3033\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nf g : ι → Set X\nhf : LocallyFinite f\na : X\nU : Set X\nhaU : U ∈ 𝓝 a\nhfin : Set.Finite {i | Set.Nonempty (f i ∩ U)}\n⊢ 𝓝[⋃ (i : ι),... | [
91,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
11
] |
Mathlib/Topology/Sheaves/SheafCondition/UniqueGluing.lean | TopCat.Presheaf.isSheafUniqueGluing_of_isSheaf_types | [
{
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"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : ConcreteCategory C\nX : To... | [
194,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
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Mathlib/Data/Finset/Basic.lean | Finset.filter_subset_filter | [] | [
2729,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2728,
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Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.im_imK | [] | [
130,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.RespectsIso.cancel_left_isIso | [
{
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"tactic": "simpa using hP.1 (asIso f).symm (f ≫ g) h"
}
] | [
156,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
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Mathlib/Topology/Instances/EReal.lean | continuous_coe_real_ereal | [] | [
72,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.seq_add | [] | [
309,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Init/Data/Nat/Bitwise.lean | Nat.bodd_zero | [] | [
57,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | FractionalIdeal.coe_ideal_mul_inv | [
{
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"state_before": "R : Type ?u.444206\n... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
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Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.coe_const | [] | [
178,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | AddSubgroup.pointwise_smul_le_pointwise_smul_iff₀ | [] | [
547,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
1
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Mathlib/Topology/Instances/Matrix.lean | summable_matrix_blockDiagonal' | [] | [
433,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.add_lt_of_lt | [
{
"state_after": "a b c : Cardinal\nhc : ℵ₀ ≤ c\nh1 : a < c\nh2 : b < c\nh : ℵ₀ ≤ max a b\n⊢ max a b < c",
"state_before": "a b c : Cardinal\nhc : ℵ₀ ≤ c\nh1 : a < c\nh2 : b < c\nh : ℵ₀ ≤ max a b\n⊢ max a b + max a b < c",
"tactic": "rw [add_eq_self h]"
},
{
"state_after": "no goals",
"state... | [
766,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
763,
1
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Mathlib/Data/List/Perm.lean | List.nthLe_permutations'Aux | [
{
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1362,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1354,
1
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Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.toLinAlgEquiv'_apply | [] | [
482,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
480,
1
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Mathlib/Analysis/Calculus/MeanValue.lean | concaveOn_of_deriv2_nonpos | [
{
"state_after": "no goals",
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1183,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1178,
1
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Mathlib/CategoryTheory/Limits/Preserves/Shapes/Zero.lean | CategoryTheory.Functor.preservesZeroMorphisms_of_map_zero_object | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝⁵ : Category C\nD : Type u₂\ninst✝⁴ : Category D\ninst✝³ : HasZeroObject C\ninst✝² : HasZeroObject D\ninst✝¹ : HasZeroMorphisms C\ninst✝ : HasZeroMorphisms D\nF : C ⥤ D\ni : F.obj 0 ≅ 0\nX Y : C\n⊢ F.map 0 = F.map 0 ≫ F.map 0",
"tactic": "r... | [
133,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
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Mathlib/Topology/VectorBundle/Basic.lean | Trivialization.linearMapAt_def_of_not_mem | [] | [
259,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.add_apply | [] | [
710,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Iso.inv_comp_eq | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX Y Z : C\nα : X ≅ Y\nf : X ⟶ Z\ng : Y ⟶ Z\nH : α.inv ≫ f = g\n⊢ f = α.hom ≫ g",
"tactic": "simp [H.symm]"
},
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX Y Z : C\nα : X ≅ Y\nf : ... | [
222,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/GroupTheory/Subsemigroup/Centralizer.lean | Set.centralizer_univ | [] | [
144,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | bit0_mono | [] | [
1685,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1683,
1
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Mathlib/Data/Rat/NNRat.lean | NNRat.coe_indicator | [] | [
246,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Std/Data/Int/DivMod.lean | Int.mul_fdiv_cancel | [
{
"state_after": "no goals",
"state_before": "a b : Int\nH : b ≠ 0\nb0 : 0 ≤ b\n⊢ fdiv (a * b) b = a",
"tactic": "rw [fdiv_eq_ediv _ b0, mul_ediv_cancel _ H]"
},
{
"state_after": "no goals",
"state_before": "a b x✝¹ : Int\nx✝ : x✝¹ < 0\nH : x✝¹ ≠ 0\nb0 : ¬0 ≤ x✝¹\n⊢ fdiv (0 * x✝¹) x✝¹ = 0",
... | [
198,
23
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
189,
9
] |
Mathlib/Data/Set/Function.lean | Set.mapsTo_range | [] | [
509,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | LocalRing.comap_closedPoint | [] | [
996,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
994,
1
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.multichoose_one_right | [
{
"state_after": "case zero\n\n⊢ multichoose zero 1 = zero\n\ncase succ\nn : ℕ\nIH : multichoose n 1 = n\n⊢ multichoose (succ n) 1 = succ n",
"state_before": "n : ℕ\n⊢ multichoose n 1 = n",
"tactic": "induction' n with n IH"
},
{
"state_after": "no goals",
"state_before": "case succ\nn : ℕ\n... | [
392,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/Algebra/GroupWithZero/Divisibility.lean | ne_zero_of_dvd_ne_zero | [
{
"state_after": "case intro\nα : Type u_1\ninst✝ : MonoidWithZero α\np u : α\nh₁ : p * u ≠ 0\n⊢ p ≠ 0",
"state_before": "α : Type u_1\ninst✝ : MonoidWithZero α\np q : α\nh₁ : q ≠ 0\nh₂ : p ∣ q\n⊢ p ≠ 0",
"tactic": "rcases h₂ with ⟨u, rfl⟩"
},
{
"state_after": "no goals",
"state_before": "ca... | [
107,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Order/Chain.lean | ChainClosure.succ_fixpoint_iff | [] | [
261,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.isConnected_setOf_sSameSide | [
{
"state_after": "case intro\nR : Type ?u.472035\nV : Type u_1\nV' : Type ?u.472041\nP : Type u_2\nP' : Type ?u.472047\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : NormedSpace ℝ V\ninst✝¹ : PseudoMetricSpace P\ninst✝ : NormedAddTorsor V P\ns : AffineSubspace ℝ P\nx : P\nhx : ¬x ∈ s\np : P\nhp : p ∈ ↑s\n⊢ IsConn... | [
891,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
884,
1
] |
Mathlib/Data/Set/Pairwise/Basic.lean | Set.PairwiseDisjoint.image_of_le | [
{
"state_after": "case intro.intro.intro.intro\nα : Type u_1\nβ : Type ?u.36078\nγ : Type ?u.36081\nι : Type u_2\nι' : Type ?u.36087\nr p q : α → α → Prop\ninst✝¹ : PartialOrder α\ninst✝ : OrderBot α\ns t : Set ι\nf g✝ : ι → α\nhs : PairwiseDisjoint s f\ng : ι → ι\nhg : f ∘ g ≤ f\na : ι\nha : a ∈ s\nb : ι\nhb :... | [
295,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.coe_int_val | [
{
"state_after": "no goals",
"state_before": "d n : ℤ\n⊢ ↑n = { re := n, im := 0 }",
"tactic": "simp [ext]"
}
] | [
306,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.basis_repr_tmul | [] | [
1059,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1057,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Basic.lean | Units.exists0' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.14573\nM₀ : Type ?u.14576\nG₀ : Type u_1\nM₀' : Type ?u.14582\nG₀' : Type ?u.14585\nF : Type ?u.14588\nF' : Type ?u.14591\ninst✝¹ : MonoidWithZero M₀\ninst✝ : GroupWithZero G₀\na b : G₀\np : (g : G₀) → g ≠ 0 → Prop\n⊢ (∃ g hg, p g hg) ↔ ∃ g hg, p ↑(m... | [
230,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Data/Int/Cast/Lemmas.lean | ofLex_intCast | [] | [
414,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.cast_one | [] | [
285,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/LinearAlgebra/ProjectiveSpace/Subspace.lean | Projectivization.Subspace.span_le_subspace_iff | [] | [
166,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Complex.lean | Complex.cpow_conj | [
{
"state_after": "no goals",
"state_before": "x n : ℂ\nhx : arg x ≠ π\n⊢ x ^ ↑(starRingEnd ℂ) n = ↑(starRingEnd ((fun x => ℂ) x)) (↑(starRingEnd ℂ) x ^ n)",
"tactic": "rw [conj_cpow _ _ hx, conj_conj]"
}
] | [
214,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Tactic/PushNeg.lean | Mathlib.Tactic.PushNeg.not_not_eq | [] | [
19,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
19,
1
] |
Mathlib/Order/LocallyFinite.lean | Prod.card_Icc | [] | [
989,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
986,
1
] |
Mathlib/Data/Set/Basic.lean | Set.subset_eq_empty | [] | [
630,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
629,
1
] |
Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.toEnd_zsmul | [] | [
469,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.norm_add_eq_add_norm_iff_angle_eq_zero | [
{
"state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y✝ x y : V\nhx : x ≠ 0\nhy : y ≠ 0\nh : ‖x + y‖ = ‖x‖ + ‖y‖\n⊢ angle x y = 0",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y✝ x y : V\nhx : x ≠ 0\nhy : y ≠ 0\n... | [
318,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Data/List/OfFn.lean | List.ofFn_inj' | [] | [
280,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.homothety_mul_apply | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.809738\nk : Type u_3\nV1 : Type u_2\nP1 : Type u_1\nV2 : Type ?u.809750\ninst✝⁵ : CommRing k\ninst✝⁴ : AddCommGroup V1\ninst✝³ : AffineSpace V1 P1\ninst✝² : AddCommGroup V2\ninst✝¹ : Module k V1\ninst✝ : Module k V2\nc : P1\nr₁ r₂ : k\np : P1\n⊢ ↑(ho... | [
817,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
815,
1
] |
Mathlib/Data/Countable/Basic.lean | countable_iff_nonempty_embedding | [] | [
38,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/Analysis/NormedSpace/FiniteDimension.lean | exists_seq_norm_le_one_le_norm_sub' | [
{
"state_after": "𝕜 : Type u\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type v\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\nF : Type w\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace 𝕜 F\nF' : Type x\ninst✝⁵ : AddCommGroup F'\ninst✝⁴ : Module 𝕜 F'\ninst✝³ : TopologicalSpace F'\ninst✝² : To... | [
434,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.lt_iff_exists_nnreal_btwn | [] | [
827,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
826,
1
] |
Mathlib/MeasureTheory/Function/LpOrder.lean | MeasureTheory.Lp.coeFn_sup | [] | [
97,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Data/Set/Function.lean | Set.exists_injOn_iff_injective | [
{
"state_after": "case intro\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.34812\nι : Sort ?u.34815\nπ : α → Type ?u.34820\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\np : Set γ\nf✝ f₁ f₂ f₃ : α → β\ng g₁ g₂ : β → γ\nf' f₁' f₂' : β → α\ng' : γ → β\na : α\nb : β\ninst✝ : Nonempty β\nx✝ : ∃ f, Injective f\nf : α → β\nhf : Injec... | [
699,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
694,
1
] |
Mathlib/CategoryTheory/Closed/Monoidal.lean | CategoryTheory.MonoidalClosed.ofEquiv_curry_def | [] | [
328,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/Data/List/Infix.lean | List.tails_eq_inits | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.46111\nl l₁ l₂ l₃ : List α\na b : α\nm n : ℕ\n⊢ tails [] = reverse (map reverse (inits (reverse [])))",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.46111\nl✝ l₁ l₂ l₃ : Lis... | [
402,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | mul_lt_one_of_nonneg_of_lt_one_left | [] | [
329,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | cauchySeq_finset_iff_vanishing | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.669264\nδ : Type ?u.669267\ninst✝² : AddCommGroup α\ninst✝¹ : UniformSpace α\ninst✝ : UniformAddGroup α\nf g : β → α\na a₁ a₂ : α\n⊢ (∀ (s : Set α), s ∈ 𝓝 0 → ∃ a, ∀ (b : Finset β × Finset β), b ≥ a → ∑ b in b.snd, f b - ∑ b in b.fst, f b ∈ s) ↔\n ∀ ... | [
1119,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1098,
1
] |
Mathlib/Analysis/Convex/Basic.lean | convex_halfspace_gt | [] | [
311,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.singleton_injective | [] | [
705,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
704,
1
] |
Mathlib/Order/Filter/NAry.lean | Filter.map₂_map₂_right | [
{
"state_after": "case a\nα : Type u_2\nα' : Type ?u.35089\nβ : Type u_4\nβ' : Type ?u.35095\nγ : Type u_5\nγ' : Type ?u.35101\nδ : Type u_3\nδ' : Type ?u.35107\nε : Type u_1\nε' : Type ?u.35113\nm✝ : α → β → γ\nf f₁ f₂ : Filter α\ng g₁ g₂ : Filter β\nh h₁ h₂ : Filter γ\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\nu : Se... | [
261,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Algebra/Order/Interval.lean | Interval.bot_mul | [] | [
213,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mk'_self | [] | [
845,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
845,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | TopologicalSpace.IsSeparable.separableSpace | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.278821\ninst✝ : PseudoEMetricSpace α\nx y z : α\nε ε₁ ε₂ : ℝ≥0∞\ns✝ t s : Set α\nhs : IsSeparable s\nthis : ∀ (ε : ℝ≥0∞), ε > 0 → ∃ t, Set.Countable t ∧ s ⊆ ⋃ (x : α) (_ : x ∈ t), closedBall x ε\n⊢ SeparableSpace ↑s",
"state_before": "α : Type u\nβ : Typ... | [
823,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
813,
1
] |
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