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/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.lt_map_of_int_lt_translationNumber | [] | [
883,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
882,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.order_X_pow | [
{
"state_after": "case h\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : Nontrivial R\nn : ℕ\n⊢ 1 ≠ 0",
"state_before": "R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : Nontrivial R\nn : ℕ\n⊢ order (X ^ n) = ↑n",
"tactic": "rw [X_pow_eq, order_monomial_of_ne_zero]"
},
{
"state_after": "no goals",
"st... | [
2500,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2498,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | lipschitzOnWith_empty | [] | [
78,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.isPrincipal_iff | [] | [
1339,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1336,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.one_add_nat_cast | [
{
"state_after": "m : ℕ\n⊢ ↑(m + 1) = ↑(succ m)",
"state_before": "m : ℕ\n⊢ 1 + ↑m = ↑(succ m)",
"tactic": "rw [← Nat.cast_one, ← Nat.cast_add, add_comm]"
},
{
"state_after": "no goals",
"state_before": "m : ℕ\n⊢ ↑(m + 1) = ↑(succ m)",
"tactic": "rfl"
}
] | [
2295,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2293,
1
] |
Mathlib/MeasureTheory/Function/SpecialFunctions/IsROrC.lean | IsROrC.measurable_ofReal | [] | [
72,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
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Mathlib/RingTheory/AlgebraicIndependent.lean | AlgebraicIndependent.to_subtype_range | [
{
"state_after": "ι✝ : Type ?u.537278\nι' : Type ?u.537281\nR : Type u_2\nK : Type ?u.537287\nA : Type u_3\nA' : Type ?u.537293\nA'' : Type ?u.537296\nV : Type u\nV' : Type ?u.537301\nx : ι✝ → A\ninst✝⁶ : CommRing R\ninst✝⁵ : CommRing A\ninst✝⁴ : CommRing A'\ninst✝³ : CommRing A''\ninst✝² : Algebra R A\ninst✝¹ ... | [
283,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equivalence.lean | CategoryTheory.Equivalence.hasTerminal_iff | [] | [
45,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
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Mathlib/RingTheory/TensorProduct.lean | LinearMap.baseChange_add | [
{
"state_after": "case a.h.h\nR : Type u_4\nA : Type u_1\nB : Type ?u.408400\nM : Type u_2\nN : Type u_3\ninst✝⁸ : CommSemiring R\ninst✝⁷ : Semiring A\ninst✝⁶ : Algebra R A\ninst✝⁵ : Semiring B\ninst✝⁴ : Algebra R B\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\ninst✝¹ : AddCommMonoid N\ninst✝ : Module R N\nr ... | [
278,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.multiplicity_add_of_gt | [
{
"state_after": "case a\nα : Type u_1\ninst✝¹ : Ring α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\np a b : α\nh : multiplicity p b < multiplicity p a\n⊢ multiplicity p (a + b) ≤ multiplicity p b\n\ncase a\nα : Type u_1\ninst✝¹ : Ring α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\np a b : α\nh : multiplicity p b... | [
452,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Mathlib/Algebra/Hom/Units.lean | IsUnit.eq_div_of_mul_eq | [] | [
430,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
11
] |
Mathlib/Algebra/Hom/GroupInstances.lean | AddMonoidHom.map_mul_iff | [] | [
333,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_mul_const_atTop_of_neg | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.229995\nι' : Type ?u.229998\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.230007\ninst✝ : LinearOrderedField α\nl : Filter β\nf : β → α\nr : α\nhr : r < 0\n⊢ Tendsto (fun x => f x * r) l atTop ↔ Tendsto f l atBot",
"tactic": "simpa only [mul_comm] usi... | [
1100,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1098,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurable_coe_nnreal_real_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.2693810\nγ : Type ?u.2693813\nγ₂ : Type ?u.2693816\nδ : Type ?u.2693819\nι : Sort y\ns t u : Set α\ninst✝ : MeasurableSpace α\nf : α → ℝ≥0\nh : Measurable fun x => ↑(f x)\n⊢ Measurable f",
"tactic": "simpa only [Real.toNNReal_coe] u... | [
1805,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1803,
1
] |
Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.Measure.map_mul_right_inv_eq_self | [] | [
482,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
480,
1
] |
Mathlib/Init/Data/Nat/Bitwise.lean | Nat.testBit_zero | [] | [
348,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Mathlib/Data/PFunctor/Multivariate/W.lean | MvPFunctor.w_ind | [
{
"state_after": "n : ℕ\nP : MvPFunctor (n + 1)\nα : TypeVec n\nC : W P α → Prop\nih :\n ∀ (a : P.A) (f' : B (drop P) a ⟹ α) (f : PFunctor.B (last P) a → W P α),\n (∀ (i : PFunctor.B (last P) a), C (f i)) → C (wMk P a f' f)\nx : W P α\n⊢ C x",
"state_before": "n : ℕ\nP : MvPFunctor (n + 1)\nα : TypeVec ... | [
231,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.coe_eq_one | [] | [
54,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Computability/Primrec.lean | Nat.Primrec'.prim_iff₁ | [
{
"state_after": "no goals",
"state_before": "f : ℕ → ℕ\nh : Primrec fun v => f (Vector.head v)\nv : ℕ\n⊢ f (Vector.head (ofFn fun i => id v)) = f v",
"tactic": "simp"
}
] | [
1552,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1549,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.integrableOn_congr_fun_ae | [] | [
153,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Analysis/Normed/Group/Quotient.lean | norm_mk_lt' | [
{
"state_after": "case intro.intro\nM : Type u_1\nN : Type ?u.220188\ninst✝¹ : SeminormedAddCommGroup M\ninst✝ : SeminormedAddCommGroup N\nS : AddSubgroup M\nm : M\nε : ℝ\nhε : 0 < ε\nn : M\nhn : ↑(mk' S) n = ↑(mk' S) m\nhn' : ‖n‖ < ‖↑(mk' S) m‖ + ε\n⊢ ∃ s, s ∈ S ∧ ‖m + s‖ < ‖↑(mk' S) m‖ + ε",
"state_before... | [
208,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Algebra/Category/Ring/Colimits.lean | CommRingCat.Colimits.quot_add | [] | [
231,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Data/Vector/Mem.lean | Vector.get_mem | [
{
"state_after": "α : Type u_1\nβ : Type ?u.17\nn : ℕ\na a' : α\ni : Fin n\nv : Vector α n\n⊢ List.get (toList v) (↑(Fin.cast (_ : n = List.length (toList v))) i) ∈ toList v",
"state_before": "α : Type u_1\nβ : Type ?u.17\nn : ℕ\na a' : α\ni : Fin n\nv : Vector α n\n⊢ get v i ∈ toList v",
"tactic": "rw ... | [
31,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
29,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.of_mem_filter | [] | [
1983,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1982,
1
] |
Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.eq_of_dist_eq_of_dist_eq_of_finrank_eq_two | [
{
"state_after": "V : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\ninst✝ : FiniteDimensional ℝ V\nhd : finrank ℝ V = 2\nc₁ c₂ p₁ p₂ p : P\nr₁ r₂ : ℝ\nhc : c₁ ≠ c₂\nhp : p₁ ≠ p₂\nhp₁c₁ : dist p₁ c₁ = r₁\nhp₂c₁ : dist ... | [
227,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Std/Data/Nat/Gcd.lean | Nat.eq_zero_of_gcd_eq_zero_right | [
{
"state_after": "m n : Nat\nH : gcd n m = 0\n⊢ n = 0",
"state_before": "m n : Nat\nH : gcd m n = 0\n⊢ n = 0",
"tactic": "rw [gcd_comm] at H"
},
{
"state_after": "no goals",
"state_before": "m n : Nat\nH : gcd n m = 0\n⊢ n = 0",
"tactic": "exact eq_zero_of_gcd_eq_zero_left H"
}
] | [
110,
38
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
108,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | sq_lt_sq' | [] | [
697,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Submodule.dualCoannihilator_iSup_eq | [] | [
918,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
916,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_lt_pi_iff | [
{
"state_after": "no goals",
"state_before": "z : ℂ\n⊢ arg z < π ↔ 0 ≤ z.re ∨ z.im ≠ 0",
"tactic": "rw [(arg_le_pi z).lt_iff_ne, not_iff_comm, not_or, not_le, Classical.not_not, arg_eq_pi_iff]"
}
] | [
246,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | hasSum_unop | [] | [
1362,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1360,
1
] |
Mathlib/Algebra/Homology/ShortExact/Preadditive.lean | CategoryTheory.Splitting.exact | [
{
"state_after": "𝒜 : Type u_2\ninst✝⁶ : Category 𝒜\nA B C A' B' C' : 𝒜\nf : A ⟶ B\ng : B ⟶ C\nf' : A' ⟶ B'\ng' : B' ⟶ C'\ninst✝⁵ : Preadditive 𝒜\ninst✝⁴ : HasBinaryBiproducts 𝒜\nh : Splitting f g\ninst✝³ : HasKernels 𝒜\ninst✝² : HasImages 𝒜\ninst✝¹ : HasZeroObject 𝒜\ninst✝ : HasCokernels 𝒜\n⊢ Exact bi... | [
322,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
11
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycle.zpowersEquivSupport_apply | [] | [
429,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Analysis/NormedSpace/FiniteDimension.lean | LinearIsometry.coe_toLinearIsometryEquiv | [] | [
80,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Topology/MetricSpace/Gluing.lean | Metric.glueDist_self | [] | [
79,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
9
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.toLinearEquiv_ofLinearEquiv | [
{
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632,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/LinearAlgebra/Matrix/Transvection.lean | Matrix.diagonal_transvection_induction | [
{
"state_after": "case intro.intro.intro\nn : Type u_1\np : Type ?u.330443\nR : Type u₂\n𝕜 : Type u_2\ninst✝⁴ : Field 𝕜\ninst✝³ : DecidableEq n\ninst✝² : DecidableEq p\ninst✝¹ : CommRing R\ninst✝ : Fintype n\nP : Matrix n n 𝕜 → Prop\nM : Matrix n n 𝕜\nhdiag : ∀ (D : n → 𝕜), det (diagonal D) = det M → P (di... | [
729,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
708,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.nat_cast_comp | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q r : R[X]\nn : ℕ\n⊢ comp (↑n) p = ↑n",
"tactic": "rw [← C_eq_nat_cast, C_comp]"
}
] | [
555,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/Data/Rat/Lemmas.lean | Rat.mul_den | [
{
"state_after": "no goals",
"state_before": "q₁ q₂ : ℚ\n⊢ (q₁ * q₂).den = q₁.den * q₂.den / Nat.gcd (Int.natAbs (q₁.num * q₂.num)) (q₁.den * q₂.den)",
"tactic": "rw [mul_def, normalize_eq]"
}
] | [
97,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_emb_domain | [] | [
1304,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1302,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | Measurable.smul_const | [] | [
635,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
634,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | pi_norm_le_iff_of_nonempty' | [
{
"state_after": "case pos\n𝓕 : Type ?u.1269284\n𝕜 : Type ?u.1269287\nα : Type ?u.1269290\nι : Type u_1\nκ : Type ?u.1269296\nE : Type ?u.1269299\nF : Type ?u.1269302\nG : Type ?u.1269305\nπ : ι → Type u_2\ninst✝³ : Fintype ι\ninst✝² : (i : ι) → SeminormedGroup (π i)\ninst✝¹ : SeminormedGroup E\nf x : (i : ι)... | [
2490,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2484,
1
] |
Mathlib/NumberTheory/Padics/PadicVal.lean | pow_padicValNat_dvd | [
{
"state_after": "case inl\np : ℕ\n⊢ p ^ padicValNat p 0 ∣ 0\n\ncase inr\np n : ℕ\nhn : n > 0\n⊢ p ^ padicValNat p n ∣ n",
"state_before": "p n : ℕ\n⊢ p ^ padicValNat p n ∣ n",
"tactic": "rcases n.eq_zero_or_pos with (rfl | hn)"
},
{
"state_after": "case inr.inl\nn : ℕ\nhn : n > 0\n⊢ 1 ^ padicVa... | [
460,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.span_inl_union_inr | [
{
"state_after": "no goals",
"state_before": "R : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nM₅ : Type ?u.223392\nM₆ : Type ?u.223395\ninst✝⁸ : Semiring R\ninst✝⁷ : AddCommMonoid M\ninst✝⁶ : AddCommMonoid M₂\ninst✝⁵ : AddCommM... | [
495,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/Data/Tree.lean | Tree.numLeaves_pos | [
{
"state_after": "α : Type u\nx : Tree α\n⊢ 0 < numNodes x + 1",
"state_before": "α : Type u\nx : Tree α\n⊢ 0 < numLeaves x",
"tactic": "rw [numLeaves_eq_numNodes_succ]"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nx : Tree α\n⊢ 0 < numNodes x + 1",
"tactic": "exact x.num... | [
126,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Topology/Instances/Real.lean | Function.Periodic.bounded_of_continuous | [] | [
219,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/ModelTheory/LanguageMap.lean | FirstOrder.Language.LHom.sumInl_injective | [] | [
311,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.Word.rcons_inj | [
{
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Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.eq_interpolate | [] | [
377,
66
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374,
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Mathlib/GroupTheory/OrderOfElement.lean | orderOf_map_dvd | [
{
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280,
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Mathlib/Data/Real/EReal.lean | EReal.mul_top_of_neg | [] | [
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32
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Mathlib/Analysis/Calculus/FormalMultilinearSeries.lean | FormalMultilinearSeries.coeff_fslope | [
{
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315,
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312,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.sum_apply_eq_zero' | [
{
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49
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Mathlib/FieldTheory/Finite/Basic.lean | FiniteField.X_pow_card_sub_X_ne_zero | [] | [
252,
58
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248,
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Mathlib/LinearAlgebra/Basis.lean | Basis.subset_extend | [] | [
1458,
21
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1456,
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Mathlib/Analysis/Calculus/ContDiff.lean | ContDiff.comp_continuousLinearMap | [] | [
399,
84
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397,
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Mathlib/Data/Set/Basic.lean | Set.univ_union | [] | [
883,
13
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882,
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Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.IsFundamentalDomain.set_lintegral_eq_tsum' | [
{
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Mathlib/MeasureTheory/Measure/Doubling.lean | IsUnifLocDoublingMeasure.exists_measure_closedBall_le_mul' | [] | [
72,
62
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Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiffAt_zero | [
{
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1447,
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src/lean/Init/Prelude.lean | Nat.le_step | [] | [
1590,
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1589,
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Mathlib/Order/CompleteLattice.lean | Antitone.le_map_sInf | [] | [
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27
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960,
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Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.refl | [] | [
94,
41
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Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.sInf_toSubsemigroup | [] | [
443,
25
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441,
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Mathlib/MeasureTheory/Integral/SetIntegral.lean | set_integral_re_add_im | [] | [
1189,
24
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1186,
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Mathlib/Data/Finset/NoncommProd.lean | Finset.noncommProd_map | [
{
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Mathlib/LinearAlgebra/Dimension.lean | nonempty_linearEquiv_of_rank_eq | [] | [
951,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
949,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.sum_measure_preimage_singleton | [
{
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220,
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217,
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Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.comap_sup_map_of_injective | [] | [
589,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
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Mathlib/Logic/Relation.lean | Relation.ReflTransGen.total_of_right_unique | [
{
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344,
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Mathlib/Topology/List.lean | nhds_list | [
{
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65,
82
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29,
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Mathlib/Algebra/GCDMonoid/Basic.lean | gcd_mul_right | [
{
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] | [
465,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
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Mathlib/Data/Matrix/Rank.lean | Matrix.rank_zero | [
{
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61,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
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Mathlib/RingTheory/Nilpotent.lean | mem_nilradical | [] | [
196,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
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Mathlib/Topology/Algebra/FilterBasis.lean | GroupFilterBasis.prod_subset_self | [] | [
147,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
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Mathlib/ModelTheory/Satisfiability.lean | Cardinal.empty_theory_categorical | [
{
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}
] | [
678,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
677,
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] |
Mathlib/Topology/Instances/Rat.lean | Rat.uniformEmbedding_coe_real | [] | [
44,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/Data/Set/Basic.lean | Set.diff_diff_comm | [] | [
1921,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1920,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ico_subset_Ico_union_Ico | [
{
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769,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
767,
1
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Mathlib/Data/Int/Order/Units.lean | Int.units_mul_self | [
{
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}
] | [
38,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
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Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.liftPropWithinAt_indep_chart_source | [
{
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326,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurable_real_toNNReal | [] | [
1747,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1746,
1
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Mathlib/Data/List/AList.lean | AList.insert_of_neg | [] | [
280,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.case_strong_induction_on | [] | [
668,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
664,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | List.aemeasurable_prod' | [
{
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876,
28
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871,
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Mathlib/Data/Set/Finite.lean | Set.finite_preimage_inl_and_inr | [] | [
987,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
984,
1
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snormEssSup_le_nnreal_smul_snormEssSup_of_ae_le_mul | [
{
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1274,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1268,
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Mathlib/Algebra/Field/Basic.lean | Commute.div_add_div | [
{
"state_after": "no goals",
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"tactic": "rw [add_div, mul_div_mul_right _ b... | [
76,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
11
] |
Mathlib/SetTheory/Ordinal/CantorNormalForm.lean | Ordinal.CNFRec_pos | [
{
"state_after": "no goals",
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"tactic": "rw [CNFRec, dif_neg ho]"
}
] | [
67,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
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Mathlib/Algebra/Order/Rearrangement.lean | AntivaryOn.sum_smul_eq_sum_smul_comp_perm_iff | [] | [
204,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.prod_eq | [] | [
584,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
] |
Mathlib/Order/Antichain.lean | Set.Subsingleton.isStrongAntichain | [] | [
343,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.setToL1_simpleFunc_indicatorConst | [
{
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1146,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1142,
1
] |
Mathlib/Analysis/Convex/Cone/Dual.lean | innerDualCone_insert | [
{
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"tac... | [
103,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.rpow_nat_inv_pow_nat | [
{
"state_after": "x : ℝ≥0\nn : ℕ\nhn : n ≠ 0\n⊢ (↑x ^ (↑n)⁻¹) ^ n = ↑x",
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"tactic": "rw [← NNReal.coe_eq, NNReal.coe_pow, coe_rpow]"
},
{
"state_after": "no goals",
"state_before": "x : ℝ≥0\nn : ℕ\nhn : n ≠ 0\n⊢ (↑x ^ (↑n)⁻... | [
273,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
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Mathlib/Algebra/Algebra/Operations.lean | Submodule.mul_bot | [] | [
211,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Data/Matrix/Rank.lean | Matrix.rank_self_mul_conjTranspose | [
{
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226,
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224,
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Mathlib/Order/Filter/Basic.lean | Filter.EventuallyEq.smul | [] | [
1547,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1545,
1
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Mathlib/Algebra/Lie/Normalizer.lean | LieSubalgebra.mem_normalizer_iff | [
{
"state_after": "R : Type u_2\nL : Type u_1\nM : Type ?u.39536\nM' : Type ?u.39539\ninst✝¹⁰ : CommRing R\ninst✝⁹ : LieRing L\ninst✝⁸ : LieAlgebra R L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCommGroup M'\ninst✝² : Module R M'\ninst✝¹ : Lie... | [
127,
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124,
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Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.toWord_inj | [] | [
1302,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1301,
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Mathlib/Data/Sum/Interval.lean | Finset.sumLift₂_nonempty | [
{
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100,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
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