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/Matrix/Block.lean | Matrix.blockDiagonal'_injective | [] | [
859,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
857,
1
] |
Mathlib/Data/List/Rotate.lean | List.rotate'_mod | [
{
"state_after": "no goals",
"state_before": "α : Type u\nl : List α\nn : ℕ\n⊢ rotate' l (n % length l) = rotate' (rotate' l (n % length l)) (length (rotate' l (n % length l)) * (n / length l))",
"tactic": "rw [rotate'_length_mul]"
},
{
"state_after": "no goals",
"state_before": "α : Type u\... | [
108,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Algebra/Star/Pointwise.lean | Set.star_inv | [
{
"state_after": "case h\nα : Type u_1\ns✝ t : Set α\na : α\ninst✝¹ : Group α\ninst✝ : StarSemigroup α\ns : Set α\nx✝ : α\n⊢ x✝ ∈ s⁻¹⋆ ↔ x✝ ∈ s⋆⁻¹",
"state_before": "α : Type u_1\ns✝ t : Set α\na : α\ninst✝¹ : Group α\ninst✝ : StarSemigroup α\ns : Set α\n⊢ s⁻¹⋆ = s⋆⁻¹",
"tactic": "ext"
},
{
"sta... | [
142,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
11
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.Integrable.simpleFunc_mul' | [
{
"state_after": "α : Type ?u.5138263\nβ : Type u_1\nE : Type ?u.5138269\nF : Type ?u.5138272\ninst✝¹ : MeasurableSpace α\nι : Type ?u.5138278\ninst✝ : NormedAddCommGroup E\nf : β → ℝ\nm m0 : MeasurableSpace β\nμ : Measure β\nhm : m ≤ m0\ng : SimpleFunc β ℝ\nhf : Integrable f\n⊢ Integrable (↑(SimpleFunc.toLarge... | [
1344,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1342,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.continuous_conj | [] | [
979,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
978,
1
] |
Mathlib/Data/Real/GoldenRatio.lean | inv_goldConj | [
{
"state_after": "⊢ -ψ = φ⁻¹",
"state_before": "⊢ ψ⁻¹ = -φ",
"tactic": "rw [inv_eq_iff_eq_inv, ← neg_inv, ← neg_eq_iff_eq_neg]"
},
{
"state_after": "no goals",
"state_before": "⊢ -ψ = φ⁻¹",
"tactic": "exact inv_gold.symm"
}
] | [
59,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.const_mul | [] | [
1304,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1302,
11
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.frontier_closedBall_subset_sphere | [] | [
1890,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1889,
1
] |
Mathlib/Algebra/Order/Ring/Canonical.lean | CanonicallyOrderedCommSemiring.mul_pos | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.21641\ninst✝ : CanonicallyOrderedCommSemiring α\na b : α\n⊢ 0 < a * b ↔ 0 < a ∧ 0 < b",
"tactic": "simp only [pos_iff_ne_zero, ne_eq, mul_eq_zero, not_or]"
}
] | [
120,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | mul_lt_mul_iff_left | [] | [
110,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/CategoryTheory/EqToHom.lean | CategoryTheory.Functor.congr_inv_of_congr_hom | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF G : C ⥤ D\nX Y : C\ne : X ≅ Y\nhX : F.obj X = G.obj X\nhY : F.obj Y = G.obj Y\n⊢ F.obj X = G.obj X",
"tactic": "rw [hX]"
},
{
"state_after": "no goals",
"state_before": "C : Typ... | [
219,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Data/Multiset/Fintype.lean | Multiset.prod_toEnumFinset | [
{
"state_after": "α : Type u_2\ninst✝¹ : DecidableEq α\nm✝ : Multiset α\nβ : Type u_1\ninst✝ : CommMonoid β\nm : Multiset α\nf : α → ℕ → β\n⊢ ∏ x in toEnumFinset m, f x.fst x.snd = ∏ x : { x // x ∈ toEnumFinset m }, f (↑x).fst (↑x).snd\n\nα : Type u_2\ninst✝¹ : DecidableEq α\nm✝ : Multiset α\nβ : Type u_1\ninst... | [
284,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image_uncurry_product | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nα' : Type ?u.67520\nβ : Type u_2\nβ' : Type ?u.67526\nγ : Type u_3\nγ' : Type ?u.67532\nδ : Type ?u.67535\nδ' : Type ?u.67538\nε : Type ?u.67541\nε' : Type ?u.67544\nζ : Type ?u.67547\nζ' : Type ?u.67550\nν : Type ?u.67553\ninst✝⁷ : DecidableEq α'\... | [
347,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/Analysis/Calculus/FDerivAnalytic.lean | AnalyticOn.iteratedFDeriv | [
{
"state_after": "case zero\n𝕜 : Type u_2\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nF : Type u_1\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\nr : ℝ≥0∞\nf : E → F\nx : E\ns : Set E\ninst✝ : Comp... | [
143,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_of_subsingleton | [] | [
251,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.coe_trans_symm | [] | [
809,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
808,
1
] |
Mathlib/LinearAlgebra/Finrank.lean | FiniteDimensional.nontrivial_of_finrank_pos | [] | [
103,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atBot_of_add_const_right | [] | [
710,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
708,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.mem_zeroLocus | [] | [
142,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_X_sub_C | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na✝ b c d : R\nn m : ℕ\ninst✝¹ : Ring R\ninst✝ : Nontrivial R\na : R\n⊢ degree (X - ↑C a) = 1",
"tactic": "rw [sub_eq_add_neg, ← map_neg C a, degree_X_add_C]"
}
] | [
1468,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1467,
1
] |
Mathlib/Data/QPF/Univariate/Basic.lean | Qpf.Cofix.bisim_aux | [
{
"state_after": "F : Type u → Type u\ninst✝ : Functor F\nq : Qpf F\nr : Cofix F → Cofix F → Prop\nh' : ∀ (x : Cofix F), r x x\nh : ∀ (x y : Cofix F), r x y → Quot.mk r <$> dest x = Quot.mk r <$> dest y\nx : Cofix F\n⊢ ∀ (y : Cofix F), r x y → x = y",
"state_before": "F : Type u → Type u\ninst✝ : Functor F\... | [
469,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
9
] |
Mathlib/Data/Real/ConjugateExponents.lean | Real.IsConjugateExponent.ne_zero | [] | [
56,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPushout.of_hasBinaryCoproduct' | [] | [
401,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/Data/Nat/Bitwise.lean | Nat.testBit_two_pow_self | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ testBit (2 ^ n) n = true",
"tactic": "rw [testBit, shiftr_eq_div_pow, Nat.div_self (pow_pos (α := ℕ) zero_lt_two n), bodd_one]"
}
] | [
143,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Analysis/Convex/Exposed.lean | exposedPoints_empty | [] | [
218,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Data/Nat/Count.lean | Nat.count_le_card | [
{
"state_after": "p : ℕ → Prop\ninst✝ : DecidablePred p\nhp : Set.Finite (setOf p)\nn : ℕ\n⊢ card (filter p (range n)) ≤ card (Set.Finite.toFinset hp)",
"state_before": "p : ℕ → Prop\ninst✝ : DecidablePred p\nhp : Set.Finite (setOf p)\nn : ℕ\n⊢ count p n ≤ card (Set.Finite.toFinset hp)",
"tactic": "rw [... | [
145,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Topology/Instances/EReal.lean | EReal.tendsto_coe | [] | [
68,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.add_eq_max' | [
{
"state_after": "no goals",
"state_before": "a b : Cardinal\nha : ℵ₀ ≤ b\n⊢ a + b = max a b",
"tactic": "rw [add_comm, max_comm, add_eq_max ha]"
}
] | [
736,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
1
] |
Mathlib/Combinatorics/SimpleGraph/Regularity/Uniform.lean | Finpartition.IsUniform.mono | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\n𝕜 : Type u_2\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : DecidableEq α\nA : Finset α\nP : Finpartition A\nG : SimpleGraph α\ninst✝ : DecidableRel G.Adj\nε✝ ε ε' : 𝕜\nhP : IsUniform P G ε\nh : ε ≤ ε'\n⊢ ↑(card P.parts * (card P.parts - 1)) * ε ≤ ↑(c... | [
252,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | InnerProductSpace.Core.inner_neg_left | [
{
"state_after": "𝕜 : Type u_1\nE : Type ?u.582097\nF : Type u_2\ninst✝² : IsROrC 𝕜\ninst✝¹ : AddCommGroup F\ninst✝ : Module 𝕜 F\nc : Core 𝕜 F\nx y : F\n⊢ ↑(starRingEnd 𝕜) (-1) * inner x y = -inner x y",
"state_before": "𝕜 : Type u_1\nE : Type ?u.582097\nF : Type u_2\ninst✝² : IsROrC 𝕜\ninst✝¹ : AddC... | [
285,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/GroupTheory/GroupAction/SubMulAction.lean | SubMulAction.val_smul | [] | [
185,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Topology/ContinuousOn.lean | ContinuousOn.mono_rng | [] | [
642,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
639,
1
] |
Mathlib/Data/Nat/ModEq.lean | Nat.odd_mul_odd | [
{
"state_after": "no goals",
"state_before": "m✝ n✝ a b c d n m : ℕ\n⊢ n % 2 = 1 → m % 2 = 1 → n * m % 2 = 1",
"tactic": "simpa [Nat.ModEq] using @ModEq.mul 2 n 1 m 1"
}
] | [
497,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
] |
Mathlib/Data/Set/Basic.lean | Set.empty_inter | [] | [
922,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
921,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | toTopologicalSpace_mono | [] | [
1333,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1331,
1
] |
Mathlib/Data/List/Basic.lean | List.splitOnP_eq_single | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.302293\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\np : α → Bool\nxs ys : List α\nls : List (List α)\nf : List α → List α\nh : ∀ (x : α), x ∈ xs → ¬p x = true\n⊢ splitOnP p xs = [xs]",
"tactic": "induction xs with\n| nil => rf... | [
2972,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2966,
1
] |
Mathlib/RingTheory/Noetherian.lean | set_has_maximal_iff_noetherian | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nM : Type u_1\nP : Type ?u.118511\nN : Type w\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\ninst✝³ : AddCommMonoid N\ninst✝² : Module R N\ninst✝¹ : AddCommMonoid P\ninst✝ : Module R P\n⊢ (∀ (a : Set (Submodule R M)), Set.Nonem... | [
349,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.IntegrableOn.indicator | [] | [
278,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Algebra/Associated.lean | Associates.mk_le_mk_iff_dvd_iff | [] | [
944,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
943,
1
] |
Mathlib/RingTheory/Polynomial/Bernstein.lean | bernsteinPolynomial.variance | [
{
"state_after": "R : Type u_1\ninst✝ : CommRing R\nn : ℕ\np :\n ∑ ν in Finset.range (n + 1), (ν * (ν - 1)) • bernsteinPolynomial R n ν +\n (↑1 - (2 * n) • X) * ∑ ν in Finset.range (n + 1), ν • bernsteinPolynomial R n ν +\n n ^ 2 • X ^ 2 * ∑ ν in Finset.range (n + 1), bernsteinPolynomial R n ν =\n ... | [
417,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
] |
Mathlib/LinearAlgebra/Matrix/MvPolynomial.lean | Matrix.mvPolynomialX_map_eval₂ | [] | [
56,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Topology/PathConnected.lean | Path.extend_one | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\nY : Type ?u.157058\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx y z : X\nι : Type ?u.157073\nγ : Path x y\n⊢ extend γ 1 = y",
"tactic": "simp"
}
] | [
274,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | integrableOn_Icc_iff_integrableOn_Ico | [
{
"state_after": "α : Type u_1\nβ : Type ?u.4109768\nE : Type u_2\nF : Type ?u.4109774\ninst✝⁴ : MeasurableSpace α\ninst✝³ : NormedAddCommGroup E\ninst✝² : PartialOrder α\ninst✝¹ : MeasurableSingletonClass α\nf : α → E\nμ : MeasureTheory.Measure α\na b : α\ninst✝ : NoAtoms μ\n⊢ 0 ≠ ⊤",
"state_before": "α : ... | [
684,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | Int.ofAdd_mul | [] | [
1228,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1227,
1
] |
Mathlib/Topology/Filter.lean | Filter.nhds_eq' | [] | [
84,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.coe_sort_coe | [] | [
289,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIocDiv_zsmul_sub_toIocMod | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\n⊢ toIocDiv hp a b • p + toIocMod hp a b = b",
"tactic": "rw [add_comm, toIocMod_add_toIocDiv_zsmul]"
}
] | [
171,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | pow_sub | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.95648\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝³ : Group G\ninst✝² : Group H\ninst✝¹ : AddGroup A\ninst✝ : AddGroup B\na : G\nm n : ℕ\nh : n ≤ m\n⊢ a ^ (m - n) * a ^ n = a ^ m",
"tact... | [
425,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.cancel_left | [
{
"state_after": "no goals",
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_le_mk_mul_of_mk_preimage_le | [
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915,
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Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | MvPolynomial.isWeightedHomogeneous_C | [] | [
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Mathlib/Analysis/Complex/CauchyIntegral.lean | Complex.integral_boundary_rect_of_hasFDerivAt_real_off_countable | [
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Mathlib/Order/CompleteLattice.lean | Function.Surjective.iSup_comp | [
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Mathlib/RingTheory/GradedAlgebra/Radical.lean | Ideal.IsHomogeneous.radical_eq | [
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Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.zero_re | [] | [
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Bounded.dual_iff | [
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.IsNormal.refl | [] | [
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Mathlib/LinearAlgebra/Matrix/ToLin.lean | LinearMap.toMatrixAlgEquiv_toLinAlgEquiv | [
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Mathlib/Algebra/Lie/IdealOperations.lean | LieSubmodule.mono_lie_right | [] | [
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Mathlib/Topology/DenseEmbedding.lean | DenseInducing.continuous | [] | [
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Mathlib/Algebra/Hom/Iterate.lean | AddMonoidHom.iterate_map_smul | [] | [
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Mathlib/Order/MinMax.lean | max_left_commutative | [] | [
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Mathlib/Analysis/Convex/Join.lean | subset_convexJoin_left | [] | [
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Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.sub_mem | [] | [
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Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.IsPrenex.relabel | [
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Mathlib/Data/List/Basic.lean | List.reverse_surjective | [] | [
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Mathlib/RingTheory/Valuation/ValuationRing.lean | ValuationRing.le_total | [
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.three_le | [
{
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.single_of_embDomain_single | [
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Mathlib/Data/Set/Image.lean | Set.image_perm | [
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Mathlib/Data/Finset/PImage.lean | Part.mem_toFinset | [
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Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.deterministic_apply | [] | [
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Mathlib/Data/Fin/VecNotation.lean | Matrix.add_cons | [
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Mathlib/Data/Multiset/Fold.lean | Multiset.max_le_of_forall_le | [
{
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Mathlib/LinearAlgebra/StdBasis.lean | LinearMap.stdBasis_eq_pi_diag | [
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Mathlib/Algebra/Lie/Subalgebra.lean | LieHom.mem_range | [] | [
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.tan_eq_sin_div_cos | [] | [
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Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.angle_smul_left_of_pos | [
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Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.domDomCongr_refl | [] | [
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.L1.SimpleFunc.integral_L1_eq_integral | [
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Mathlib/Data/Polynomial/Div.lean | Polynomial.degree_modByMonic_le | [
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | smul_vsub_vadd_mem_affineSpan_pair | [] | [
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Mathlib/RingTheory/AlgebraicIndependent.lean | AlgebraicIndependent.repr_ker | [] | [
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Mathlib/Analysis/InnerProductSpace/Basic.lean | real_inner_smul_self_right | [
{
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.eq_zero_of_comapDomain_eq_zero | [
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Mathlib/GroupTheory/FreeAbelianGroupFinsupp.lean | FreeAbelianGroup.support_zero | [
{
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67
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.of_pow | [
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Mathlib/Data/Sign.lean | sign_eq_zero_iff | [
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{
"state_after": "α : T... | [
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Mathlib/Data/Set/Basic.lean | Set.union_subset_union | [] | [
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Iso.connectedComponentEquiv_refl | [
{
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2110,
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Mathlib/Order/GameAdd.lean | Sym2.gameAdd_mk'_iff | [] | [
174,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.mod_eq_of_lt | [
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"state_after": "no goals",
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"tactic": "simp only [mod_def, div_eq_zero_of_lt h, mul_zero, sub_zero]"
}
] | [
1040,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1039,
1
] |
Mathlib/Topology/Order/LowerTopology.lean | LowerTopology.closure_singleton | [] | [
208,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Topology/UniformSpace/Completion.lean | CauchyFilter.uniformInducing_pureCauchy | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : UniformSpace α\nβ : Type v\nγ : Type w\ninst✝¹ : UniformSpace β\ninst✝ : UniformSpace γ\ns : Set (α × α)\nx✝ : α × α\na₁ a₂ : α\n⊢ (a₁, a₂) ∈ ((preimage fun x => (pureCauchy x.fst, pureCauchy x.snd)) ∘ gen) s ↔ (a₁, a₂) ∈ id s",
"tactic"... | [
169,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.graph_inj | [] | [
114,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tendsto_atTop_zero_of_tsum_ne_top | [
{
"state_after": "α : Type ?u.262359\nβ : Type ?u.262362\nγ : Type ?u.262365\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\nf✝ g : α → ℝ≥0∞\nf : ℕ → ℝ≥0∞\nhf : (∑' (x : ℕ), f x) ≠ ⊤\n⊢ Tendsto f cofinite (𝓝 0)",
"state_before": "α : Type ?u.262359\nβ : Type ?u.262362\nγ : Type ?u.262365\... | [
960,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
957,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.coe_neg | [] | [
382,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/Algebra/Homology/Augment.lean | ChainComplex.augmentTruncate_hom_f_zero | [] | [
171,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.weightedSMul_smul_measure | [
{
"state_after": "case h\nα : Type u_1\nE : Type ?u.30268\nF : Type u_2\n𝕜 : Type ?u.30274\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nm✝ : MeasurableSpace α\nμ✝ : Measure α\nm : MeasurableSpace α\nμ : Measure α\nc : ℝ≥0∞\ns : Set α\nx : F\n⊢ ↑(weightedSMul (c • μ) s) x = ↑(ENNReal.toReal c • weig... | [
203,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Topology/Bornology/Basic.lean | Bornology.isBounded_union | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.4828\nα : Type u_1\nβ : Type ?u.4834\ninst✝ : Bornology α\ns t : Set α\nx : α\n⊢ IsBounded (s ∪ t) ↔ IsBounded s ∧ IsBounded t",
"tactic": "simp only [← isCobounded_compl_iff, compl_union, isCobounded_inter]"
}
] | [
201,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
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