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/Data/IsROrC/Basic.lean | IsROrC.normSq_one | [] | [
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17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/LinearAlgebra/Dual.lean | Subspace.quotAnnihilatorEquiv_apply | [
{
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Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.natDegree_coe_units | [] | [
850,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/UnitaryGroup.lean | Matrix.det_of_mem_unitary | [
{
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Mathlib/Algebra/Module/LocalizedModule.lean | IsLocalizedModule.mk_eq_mk' | [
{
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measureUnivNNReal_eq_zero | [
{
"state_after": "α : Type u_1\nβ : Type ?u.617950\nγ : Type ?u.617953\nδ : Type ?u.617956\nι : Type ?u.617959\nR : Type ?u.617962\nR' : Type ?u.617965\nm0 : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set α\ninst✝ : IsFiniteMeasure μ\n⊢... | [
3139,
12
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3137,
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Mathlib/ModelTheory/Definability.lean | Set.definable_finset_inf | [
{
"state_after": "no goals",
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"tactic": "class... | [
117,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
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Mathlib/Data/Setoid/Basic.lean | Setoid.ker_apply_mk_out' | [] | [
114,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
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Mathlib/Algebra/Order/Ring/Lemmas.lean | Left.mul_le_one_of_le_of_le | [] | [
725,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
723,
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Mathlib/Topology/Bornology/Hom.lean | LocallyBoundedMap.coe_comp | [] | [
169,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
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Mathlib/Data/List/Func.lean | List.Func.eq_of_equiv | [
{
"state_after": "no goals",
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"tactic": "cases h1"
... | [
252,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
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Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.CompactOpens.coe_top | [] | [
554,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
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Mathlib/Data/Complex/Basic.lean | Complex.nat_cast_im | [
{
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"tactic": "rw [← ofReal_nat_cast, ofReal_im]"
}
] | [
843,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
843,
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Mathlib/Data/Bundle.lean | Bundle.coe_snd_map_smul | [] | [
181,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
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Mathlib/Analysis/Calculus/FDeriv/Mul.lean | DifferentiableWithinAt.const_mul | [] | [
480,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
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Mathlib/GroupTheory/GroupAction/Defs.lean | SMulCommClass.symm | [] | [
224,
42
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222,
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Mathlib/Algebra/Category/GroupCat/EpiMono.lean | GroupCat.SurjectiveOfEpiAuxs.g_apply_infinity | [] | [
257,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.generate_of_contains_isSplitEpi | [
{
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"state_before": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category ... | [
439,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
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Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.le_of_opNorm_le | [
{
"state_after": "no goals",
"state_before": "V : Type ?u.229529\nV₁ : Type u_1\nV₂ : Type u_2\nV₃ : Type ?u.229538\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : SeminormedAddCommGroup V₁\ninst✝¹ : SeminormedAddCommGroup V₂\ninst✝ : SeminormedAddCommGroup V₃\nf g : NormedAddGroupHom V₁ V₂\nc : ℝ\nh : ‖f‖ ≤ c... | [
258,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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src/lean/Init/Prelude.lean | Nat.lt_irrefl | [] | [
1660,
25
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1659,
11
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Mathlib/Order/Height.lean | Set.singleton_mem_subchain_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1018\ninst✝¹ : LT α\ninst✝ : LT β\ns t : Set α\nl : List α\na : α\n⊢ [a] ∈ subchain s ↔ a ∈ s",
"tactic": "simp [cons_mem_subchain_iff]"
}
] | [
80,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.iUnion_closedBall_nat | [] | [
653,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
652,
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] |
Mathlib/Algebra/Order/Ring/Abs.lean | abs_le_one_iff_mul_self_le_one | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedRing α\na b c : α\n⊢ abs a ≤ 1 ↔ a * a ≤ 1",
"tactic": "simpa only [abs_one, one_mul] using @abs_le_iff_mul_self_le α _ a 1"
}
] | [
102,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/RingTheory/Localization/AtPrime.lean | IsLocalization.AtPrime.isUnit_to_map_iff | [] | [
143,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
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Mathlib/Data/List/Cycle.lean | List.prev_next | [
{
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"state_before": "α : Type u_1\ninst✝ : DecidableEq α\... | [
385,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | Left.one_le_pow_of_le | [
{
"state_after": "β : Type ?u.46829\nA : Type ?u.46832\nG : Type ?u.46835\nM : Type u_1\nR : Type ?u.46841\ninst✝² : Monoid M\ninst✝¹ : Preorder M\ninst✝ : CovariantClass M M (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\nx : M\nhx : 1 ≤ x\nn : ℕ\n⊢ 1 ≤ x * x ^ n",
"state_before": "β : Type ?u.46829\nA : Type... | [
119,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
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Mathlib/LinearAlgebra/Dual.lean | Submodule.dualRestrict_def | [] | [
787,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
786,
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.diam_empty | [] | [
2592,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2591,
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Mathlib/Data/Finset/Powerset.lean | Finset.powerset_mono | [] | [
67,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.not_nondegenerate_zero | [] | [
1285,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1283,
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Mathlib/Algebra/Group/Pi.lean | Pi.single_mul | [] | [
513,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
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] |
Mathlib/Topology/Algebra/ContinuousAffineMap.lean | ContinuousAffineMap.sub_apply | [] | [
236,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
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Mathlib/Order/Lattice.lean | ofDual_sup | [] | [
958,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
957,
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Mathlib/Order/UpperLower/Basic.lean | UpperSet.mem_iInf_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.59735\nγ : Type ?u.59738\nι : Sort u_2\nκ : ι → Sort ?u.59746\ninst✝ : LE α\nS : Set (UpperSet α)\ns t : UpperSet α\na : α\nf : ι → UpperSet α\n⊢ (a ∈ ⋃ (i : ι), ↑(f i)) ↔ ∃ i, a ∈ f i",
"state_before": "α : Type u_1\nβ : Type ?u.59735\nγ : Type ?u.59738\nι : Sort... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.span_union | [] | [
728,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
727,
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Mathlib/Data/Fintype/Fin.lean | Fin.Ioi_succ | [
{
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"state_before": "α : Type ?u.7053\nβ : Type ?u.7056\nn : ℕ\ni : Fin n\n⊢ Ioi (succ i) = map (succEmbedding n).toEmbedding (Ioi i)",
... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
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Mathlib/Algebra/Hom/GroupAction.lean | MulSemiringActionHom.map_add | [] | [
517,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
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] |
Mathlib/Data/Real/Basic.lean | Real.mk_le_of_forall_le | [
{
"state_after": "case intro\nx✝ y : ℝ\nf : CauSeq ℚ abs\nx : ℝ\ni : ℕ\nH : ∀ (j : ℕ), j ≥ i → ↑(↑f j) ≤ x\n⊢ mk f ≤ x",
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"tactic": "cases' h with i H"
},
{
"state_after": "case intro\nx✝ y :... | [
633,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
629,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.Nonempty.zero_mul | [
{
"state_after": "no goals",
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"tactic": "simpa [mem_mul] using hs"
}
] | [
1102,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1101,
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Mathlib/Data/Set/Lattice.lean | Set.union_iUnion_nat_succ | [] | [
2224,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2223,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.map_mono | [
{
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1258,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1257,
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Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.antitone_lower | [] | [
232,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
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Mathlib/Algebra/GCDMonoid/Basic.lean | Associated.gcd_eq_right | [] | [
508,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
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Mathlib/Data/List/Nodup.lean | List.Nodup.pairwise_of_set_pairwise | [] | [
437,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
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Std/Data/Int/Lemmas.lean | Int.sub_lt_of_sub_lt | [] | [
1117,
59
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1116,
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Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.le_logb_iff_rpow_le_of_base_lt_one | [
{
"state_after": "no goals",
"state_before": "b x y : ℝ\nb_pos : 0 < b\nb_lt_one : b < 1\nhy : 0 < y\n⊢ x ≤ logb b y ↔ y ≤ b ^ x",
"tactic": "rw [← rpow_le_rpow_left_iff_of_base_lt_one b_pos b_lt_one, rpow_logb b_pos (b_ne_one b_lt_one) hy]"
}
] | [
281,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
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Mathlib/AlgebraicTopology/DoldKan/PInfty.lean | AlgebraicTopology.DoldKan.QInfty_f_comp_PInfty_f | [
{
"state_after": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\nn : ℕ\n⊢ HomologicalComplex.Hom.f (𝟙 K[X] - PInfty) n ≫ HomologicalComplex.Hom.f PInfty n = 0",
"state_before": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\nn : ℕ\n⊢ Hom... | [
150,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
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] |
Std/Data/Int/Lemmas.lean | Int.negSucc_coe | [] | [
43,
58
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
43,
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Mathlib/Data/List/Basic.lean | List.modifyHead_modifyHead | [
{
"state_after": "no goals",
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"tactic": "cases l <;> simp"
}
] | [
983,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
982,
1
] |
Mathlib/Topology/Algebra/Order/Compact.lean | IsCompact.lt_sInf_iff_of_continuous | [] | [
345,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.coeff_X_pow_mul' | [
{
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1634,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1625,
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.mem_closure_iff_infEdist_zero | [
{
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78
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153,
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Mathlib/Topology/UniformSpace/Cauchy.lean | totallyBounded_subset | [] | [
501,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
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Mathlib/Topology/Sheaves/SheafCondition/Sites.lean | TopCat.Opens.coverDense_iff_isBasis | [
{
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146,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
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Mathlib/Order/CompleteLattice.lean | Monotone.map_sInf_le | [] | [
1032,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1030,
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Mathlib/Analysis/Calculus/UniformLimitsDeriv.lean | hasDerivAt_of_tendstoLocallyUniformlyOn | [
{
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541,
92
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533,
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Std/Data/String/Lemmas.lean | String.extract.go₁_add_right_cancel | [
{
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415,
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404,
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Mathlib/Data/Finset/Pointwise.lean | Finset.div_mem_div | [] | [
565,
20
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Mathlib/Data/Matrix/Basic.lean | Matrix.mul_sub | [
{
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70
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Mathlib/Topology/Order/Lattice.lean | continuous_sup | [] | [
100,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Nat/Squarefree.lean | Nat.squarefree_iff_minSqFac | [
{
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},
{
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247,
20
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240,
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Mathlib/Order/Hom/Lattice.lean | SupHom.ext | [] | [
358,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
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Mathlib/Analysis/InnerProductSpace/PiL2.lean | exists_orthonormalBasis | [] | [
811,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
808,
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Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.distortion_filter_le | [] | [
463,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
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Mathlib/Order/SymmDiff.lean | top_symmDiff | [] | [
733,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
732,
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Mathlib/Data/Fin/Tuple/Basic.lean | Fin.comp_tail | [
{
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250,
14
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247,
1
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Mathlib/Topology/Separation.lean | Inducing.regularSpace | [
{
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55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1594,
11
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_union_Icc_eq_Icc | [] | [
1654,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1651,
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Mathlib/Data/Set/Lattice.lean | Set.biInter_empty | [] | [
917,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
916,
1
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Mathlib/Data/List/NodupEquivFin.lean | List.Sorted.get_mono | [] | [
85,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Algebra/Category/GroupCat/Basic.lean | GroupCat.coe_of | [] | [
101,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Data/Real/ConjugateExponents.lean | Real.IsConjugateExponent.nonneg | [] | [
53,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | MvPolynomial.IsWeightedHomogeneous.sum | [] | [
275,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
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Mathlib/Topology/Algebra/Module/Basic.lean | Submodule.range_subtypeL | [] | [
1053,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1052,
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Mathlib/Topology/Connected.lean | isPreconnected_connectedComponentIn | [
{
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627,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_union_toMeasurable | [] | [
384,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
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Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.basis_repr_symm_apply | [
{
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1065,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1062,
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Mathlib/GroupTheory/GroupAction/ConjAct.lean | ConjAct.ofConjAct_zero | [] | [
221,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
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Mathlib/Control/Traversable/Basic.lean | ApplicativeTransformation.preserves_pure | [] | [
144,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
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Mathlib/Algebra/Category/Ring/Basic.lean | CommRingCat.coe_of | [] | [
403,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
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] |
Mathlib/Data/Fintype/Quotient.lean | Quotient.finChoiceAux_eq | [
{
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55,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
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Mathlib/Data/Set/Basic.lean | Set.Nontrivial.choose_snd_mem | [] | [
2452,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2451,
11
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.withDensity_indicator_one | [
{
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"tactic": "rw [withDensity_indicator hs, withDensit... | [
1645,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1643,
1
] |
Mathlib/Combinatorics/SimpleGraph/StronglyRegular.lean | SimpleGraph.compl_neighborFinset_sdiff_inter_eq | [
{
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"state_before": ... | [
122,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Topology/ContinuousFunction/StoneWeierstrass.lean | ContinuousMap.subalgebra_isROrC_topologicalClosure_eq_top_of_separatesPoints | [
{
"state_after": "𝕜 : Type u_1\nX : Type u_2\ninst✝² : IsROrC 𝕜\ninst✝¹ : TopologicalSpace X\ninst✝ : CompactSpace X\nA : Subalgebra 𝕜 C(X, 𝕜)\nhA : Subalgebra.SeparatesPoints A\nhA' : ConjInvariantSubalgebra (Subalgebra.restrictScalars ℝ A)\n⊢ ∀ (x : C(X, 𝕜)), x ∈ Subalgebra.topologicalClosure A",
"st... | [
448,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.mul_swap_mul_self | [
{
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"tactic": "rw [mul_assoc, swap_mul_self, mul_one]"
}
] | [
552,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_unique_nonempty | [
{
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"tactic... | [
1941,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1939,
1
] |
Mathlib/RingTheory/Localization/NumDen.lean | IsFractionRing.isUnit_den_of_num_eq_zero | [] | [
114,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.mem_ae_dirac_iff | [
{
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3006,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3005,
1
] |
Mathlib/Topology/Sheaves/Presheaf.lean | TopCat.Presheaf.toPushforwardOfIso_app | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX Y : TopCat\nH₁ : X ≅ Y\nℱ : Presheaf C X\n𝒢 : Presheaf C Y\nH₂ : H₁.hom _* ℱ ⟶ 𝒢\nU : (Opens ↑X)ᵒᵖ\n⊢ U = (Functor.op (Opens.map H₁.hom)).obj ((Opens.map H₁.inv).obj U.unop).op",
"tactic": "simp [Opens.map, Set.preimage_pr... | [
430,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.localizationToStalk_stalkToFiberRingHom | [] | [
616,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
614,
1
] |
Mathlib/Topology/Order/Basic.lean | Filter.tendsto_nhds_max_left | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : TopologicalSpace α\ninst✝¹ : LinearOrder α\ninst✝ : OrderClosedTopology α\nf g : β → α\nl : Filter β\na : α\nh : Tendsto f l (𝓝[Ioi a] a)\n⊢ Tendsto (fun i => max a (f i)) l (𝓝[Ioi a] a)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ni... | [
732,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
729,
1
] |
Mathlib/Data/Finsupp/Multiset.lean | Finsupp.coe_orderIsoMultiset_symm | [] | [
216,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Independent.lean | affineIndependent_equiv | [
{
"state_after": "k : Type u_3\nV : Type u_4\nP : Type u_5\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type u_2\nι' : Type u_1\ne : ι ≃ ι'\np : ι' → P\n⊢ AffineIndependent k (p ∘ ↑e) → AffineIndependent k p",
"state_before": "k : Type u_3\nV : Type u_4\nP : T... | [
339,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.pred_lt_pred_iff | [
{
"state_after": "no goals",
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"tactic": "simp"
}
] | [
712,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
712,
1
] |
Mathlib/Data/Dfinsupp/Order.lean | Dfinsupp.add_eq_zero_iff | [
{
"state_after": "no goals",
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"tactic": "simp [FunLike.ext_iff, forall_and]"
}
] | [
158,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/MeasureTheory/Integral/CircleTransform.lean | Complex.continuousOn_abs_circleTransformBoundingFunction | [
{
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128,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_lt_of_lt_of_le_one_of_nonneg | [] | [
719,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
717,
1
] |
Mathlib/Analysis/PSeries.lean | Real.tendsto_sum_range_one_div_nat_succ_atTop | [
{
"state_after": "⊢ ¬Summable fun i => 1 / (↑i + 1)\n\n\n⊢ ∀ (n : ℕ), 0 ≤ 1 / (↑n + 1)",
"state_before": "⊢ Tendsto (fun n => ∑ i in Finset.range n, 1 / (↑i + 1)) atTop atTop",
"tactic": "rw [← not_summable_iff_tendsto_nat_atTop_of_nonneg]"
},
{
"state_after": "no goals",
"state_before": "⊢ ... | [
265,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.support_swap_iff | [
{
"state_after": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nx y : α\nh : support (swap x y) = {x, y}\n⊢ x ≠ y",
"state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nx y : α\n⊢ support (swap x y) = {x, y} ↔ x ≠ y",
"tactic": "refine' ⟨fun h ... | [
451,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
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