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/NumberTheory/PellMatiyasevic.lean | Pell.eq_of_xn_modEq' | [
{
"state_after": "a : ℕ\na1 : 1 < a\ni j n : ℕ\nipos : 0 < i\nhin : i ≤ n\nj4n : j ≤ 4 * n\nh : xn a1 j ≡ xn a1 i [MOD xn a1 n]\n⊢ n ≤ 2 * n",
"state_before": "a : ℕ\na1 : 1 < a\ni j n : ℕ\nipos : 0 < i\nhin : i ≤ n\nj4n : j ≤ 4 * n\nh : xn a1 j ≡ xn a1 i [MOD xn a1 n]\n⊢ i ≤ 2 * n",
"tactic": "apply le... | [
800,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
779,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Reflexive.lean | CategoryTheory.section_comp_left | [] | [
83,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
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Std/Data/Array/Init/Lemmas.lean | Array.getElem_eq_data_get | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ni : Nat\na : Array α\nh : i < size a\n⊢ a[i] = List.get a.data { val := i, isLt := h }",
"tactic": "by_cases i < a.size <;> simp [*] <;> rfl"
}
] | [
29,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.ord_isLimit | [
{
"state_after": "case refine'_1\nc : Cardinal\nco : ℵ₀ ≤ c\nh : ord c = 0\n⊢ ℵ₀ = 0\n\ncase refine'_2\nc : Cardinal\nco : ℵ₀ ≤ c\na : Ordinal\nh : ord c ≤ succ a\n⊢ ord c ≤ a",
"state_before": "c : Cardinal\nco : ℵ₀ ≤ c\n⊢ Ordinal.IsLimit (ord c)",
"tactic": "refine' ⟨fun h => aleph0_ne_zero _, fun a =... | [
72,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
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Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | UniformOnFun.gen_mono | [] | [
588,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
587,
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Mathlib/Algebra/Order/Floor.lean | Nat.lt_of_floor_lt | [] | [
150,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.not_one_mem_div_iff | [] | [
1169,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1168,
1
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Mathlib/Algebra/GroupWithZero/Units/Lemmas.lean | eq_div_of_mul_eq | [] | [
112,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.card_eq_zero | [] | [
73,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.cof_eq | [] | [
179,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
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Mathlib/Data/Set/Finite.lean | Set.Finite.toFinset_empty | [
{
"state_after": "case a\nα : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ns t : Set α\na : α\nhs : Set.Finite s\nht : Set.Finite t\nh : Set.Finite ∅\na✝ : α\n⊢ a✝ ∈ Finite.toFinset h ↔ a✝ ∈ ∅",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ns t : Set α\na : α\nhs : Set.Finite s\nht : Set.F... | [
272,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
11
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.eq_iff_modEq_nat | [
{
"state_after": "case zero\na b : ℕ\n⊢ ↑a = ↑b ↔ a ≡ b [MOD Nat.zero]\n\ncase succ\na b n✝ : ℕ\n⊢ ↑a = ↑b ↔ a ≡ b [MOD Nat.succ n✝]",
"state_before": "n a b : ℕ\n⊢ ↑a = ↑b ↔ a ≡ b [MOD n]",
"tactic": "cases n"
},
{
"state_after": "no goals",
"state_before": "case zero\na b : ℕ\n⊢ ↑a = ↑b ↔ ... | [
674,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
670,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tsum_const_eq_top_of_ne_zero | [
{
"state_after": "α✝ : Type ?u.246869\nβ : Type ?u.246872\nγ : Type ?u.246875\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∞\nα : Type u_1\ninst✝ : Infinite α\nc : ℝ≥0∞\nhc : c ≠ 0\nA : Tendsto (fun n => ↑n * c) atTop (𝓝 (⊤ * c))\n⊢ (∑' (x : α), c) = ⊤",
"state_before": ... | [
893,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
885,
1
] |
Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.mem_closure | [] | [
396,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.one_opow | [
{
"state_after": "case H₁\na : Ordinal\n⊢ 1 ^ 0 = 1\n\ncase H₂\na : Ordinal\n⊢ ∀ (o : Ordinal), 1 ^ o = 1 → 1 ^ succ o = 1\n\ncase H₃\na : Ordinal\n⊢ ∀ (o : Ordinal), IsLimit o → (∀ (o' : Ordinal), o' < o → 1 ^ o' = 1) → 1 ^ o = 1",
"state_before": "a : Ordinal\n⊢ 1 ^ a = 1",
"tactic": "apply limitRecOn... | [
92,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Analysis/Convex/Basic.lean | Convex.starConvex | [] | [
61,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_norm_mulLeftRight_apply_apply_le | [] | [
1142,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1137,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.totalDegree_X | [
{
"state_after": "R✝ : Type u\nS : Type v\nσ : Type u_2\nτ : Type ?u.396116\nr : R✝\ne : ℕ\nn m : σ\ns✝ : σ →₀ ℕ\ninst✝² : CommSemiring R✝\np q : MvPolynomial σ R✝\nR : Type u_1\ninst✝¹ : CommSemiring R\ninst✝ : Nontrivial R\ns : σ\n⊢ (Finset.sup {Finsupp.single s 1} fun s => sum s fun x e => e) = 1",
"stat... | [
640,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
637,
1
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Mathlib/Data/Finset/Slice.lean | Finset.Set.Sized.card_le | [
{
"state_after": "α : Type u_1\nι : Sort ?u.4153\nκ : ι → Sort ?u.4158\ninst✝ : Fintype α\n𝒜 : Finset (Finset α)\ns : Finset α\nr : ℕ\nh𝒜 : Set.Sized r ↑𝒜\n⊢ card 𝒜 ≤ card (powersetLen r univ)",
"state_before": "α : Type u_1\nι : Sort ?u.4153\nκ : ι → Sort ?u.4158\ninst✝ : Fintype α\n𝒜 : Finset (Finset... | [
119,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Analysis/InnerProductSpace/Calculus.lean | ContDiffWithinAt.dist | [
{
"state_after": "𝕜 : Type ?u.282045\nE : Type u_2\nF : Type ?u.282051\ninst✝⁷ : IsROrC 𝕜\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : InnerProductSpace 𝕜 E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace ℝ F\ninst✝² : NormedSpace ℝ E\nG : Type u_1\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace ℝ... | [
198,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/GroupTheory/Submonoid/Inverses.lean | Submonoid.mul_fromLeftInv | [] | [
108,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/RingTheory/AlgebraicIndependent.lean | algebraicIndependent_of_finite | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.745808\nι' : Type ?u.745811\nR : Type u_2\nK : Type ?u.745817\nA : Type u_1\nA' : Type ?u.745823\nA'' : Type ?u.745826\nV : Type u\nV' : Type ?u.745831\nx : ι → A\ninst✝⁶ : CommRing R\ninst✝⁵ : CommRing A\ninst✝⁴ : CommRing A'\ninst✝³ : CommRing A''\... | [
311,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.sigmaUncurry_zero | [] | [
1558,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1555,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iic_inter_Ioi | [] | [
647,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
646,
1
] |
Mathlib/CategoryTheory/Limits/ConeCategory.lean | CategoryTheory.Limits.hasLimit_iff_hasTerminal_cone | [] | [
92,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.eq_top_of_neBot | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.91776\nι : Sort x\nf g : Filter α\ns✝ t : Set α\ninst✝¹ : Subsingleton α\nl : Filter α\ninst✝ : NeBot l\ns : Set α\nhs : s ∈ l\n⊢ s ∈ ⊤",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.91776\nι : Sort x\nf g : Filter α\ns t ... | [
763,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
760,
1
] |
Mathlib/CategoryTheory/Sites/CoverLifting.lean | CategoryTheory.ran_isSheaf_of_coverLifting | [
{
"state_after": "C D : Type u\ninst✝³ : Category C\ninst✝² : Category D\nA : Type w\ninst✝¹ : Category A\ninst✝ : HasLimits A\nJ : GrothendieckTopology C\nK : GrothendieckTopology D\nG : C ⥤ D\nhG : CoverLifting J K G\nℱ : Sheaf J A\nX : A\nU : D\nS : Sieve U\nhS : S ∈ GrothendieckTopology.sieves K U\nx : Fami... | [
300,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Infinite.diff | [] | [
1312,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1311,
1
] |
Mathlib/ModelTheory/Definability.lean | FirstOrder.Language.DefinableSet.mem_sup | [] | [
324,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/Algebra/Lie/IdealOperations.lean | LieIdeal.map_bracket_le | [
{
"state_after": "R : Type u\nL : Type v\nL' : Type w₂\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\ninst✝¹ : LieRing L'\ninst✝ : LieAlgebra R L'\nf : L →ₗ⁅R⁆ L'\nI : LieIdeal R L\nJ : LieIdeal R L'\nI₁ I₂ : LieIdeal R L\n⊢ ⁅I₁, I₂⁆ ≤ comap f ⁅map f I₁, map f I₂⁆",
"state_before": "R : ... | [
277,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/LinearAlgebra/TensorAlgebra/Basic.lean | TensorAlgebra.algebraMap_leftInverse | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝² : CommSemiring R\nM : Type u_2\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nx : R\n⊢ ↑algebraMapInv (↑(algebraMap R (TensorAlgebra R M)) x) = x",
"tactic": "simp [algebraMapInv]"
}
] | [
202,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/NumberTheory/Padics/PadicNorm.lean | padicNorm.add_eq_max_of_ne | [
{
"state_after": "case inr\np : ℕ\nhp : Fact (Nat.Prime p)\nq r : ℚ\nhne : padicNorm p q ≠ padicNorm p r\nthis :\n ∀ {p : ℕ} [hp : Fact (Nat.Prime p)] {q r : ℚ},\n padicNorm p q ≠ padicNorm p r →\n padicNorm p r < padicNorm p q → padicNorm p (q + r) = max (padicNorm p q) (padicNorm p r)\nhlt : ¬padicNo... | [
250,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Algebra/Order/Kleene.lean | kstar_le_of_mul_le_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.34264\nι : Type ?u.34267\nπ : ι → Type ?u.34272\ninst✝ : KleeneAlgebra α\na b c : α\nhb : 1 ≤ b\n⊢ b * a ≤ b → a∗ ≤ b",
"tactic": "simpa using mul_kstar_le hb"
}
] | [
231,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/MeasureTheory/Measure/Portmanteau.lean | MeasureTheory.limsup_measure_compl_le_of_le_liminf_measure | [
{
"state_after": "case pos\nΩ : Type u_2\ninst✝² : MeasurableSpace Ω\nι : Type u_1\nL : Filter ι\nμ : Measure Ω\nμs : ι → Measure Ω\ninst✝¹ : IsProbabilityMeasure μ\ninst✝ : ∀ (i : ι), IsProbabilityMeasure (μs i)\nE : Set Ω\nE_mble : MeasurableSet E\nh : ↑↑μ E ≤ liminf (fun i => ↑↑(μs i) E) L\nL_bot : L = ⊥\n⊢ ... | [
158,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.le_one_iff_subsingleton | [] | [
415,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Data/Polynomial/UnitTrinomial.lean | Polynomial.trinomial_mirror | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nk m n : ℕ\nu v w : R\nhkm : k < m\nhmn : m < n\nhu : u ≠ 0\nhw : w ≠ 0\n⊢ mirror (trinomial k m n u v w) = trinomial k (n - m + k) n w v u",
"tactic": "rw [mirror, trinomial_natTrailingDegree hkm hmn hu, reverse, trinomial_n... | [
120,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Data/Finsupp/Multiset.lean | Multiset.toFinsupp_toMultiset | [] | [
177,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Topology/Algebra/ValuedField.lean | Valuation.inversion_estimate | [
{
"state_after": "K : Type u_2\ninst✝¹ : DivisionRing K\nΓ₀ : Type u_1\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nv : Valuation K Γ₀\nx y : K\nγ : Γ₀ˣ\ny_ne : y ≠ 0\nh : ↑v (x - y) < min (↑γ * (↑v y * ↑v y)) (↑v y)\nhyp1 : ↑v (x - y) < ↑γ * (↑v y * ↑v y)\n⊢ ↑v (x⁻¹ - y⁻¹) < ↑γ",
"state_before": "K : Type u... | [
75,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.abs_le_sqrt_two_mul_max | [
{
"state_after": "case mk\nx y : ℝ\n⊢ ↑abs { re := x, im := y } ≤ Real.sqrt 2 * max (Abs.abs { re := x, im := y }.re) (Abs.abs { re := x, im := y }.im)",
"state_before": "z : ℂ\n⊢ ↑abs z ≤ Real.sqrt 2 * max (Abs.abs z.re) (Abs.abs z.im)",
"tactic": "cases' z with x y"
},
{
"state_after": "case m... | [
1091,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1076,
1
] |
Mathlib/Data/Fintype/Prod.lean | Fintype.card_prod | [] | [
59,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.add_zero | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\ninst✝ : NeZero n\nk : Fin n\n⊢ k + 0 = k",
"tactic": "simp [eq_iff_veq, add_def, mod_eq_of_lt (is_lt k)]"
}
] | [
664,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
663,
11
] |
Mathlib/Computability/Halting.lean | ComputablePred.of_eq | [] | [
162,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/RingTheory/LaurentSeries.lean | PowerSeries.coe_X | [] | [
237,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/StrongEpi.lean | CategoryTheory.StrongMono.mk' | [] | [
82,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Logic/Basic.lean | imp_iff_not_or | [] | [
372,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.sum_apply | [] | [
464,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/Logic/Equiv/Nat.lean | Equiv.natSumNatEquivNat_apply | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.747\n⊢ ↑natSumNatEquivNat = Sum.elim bit0 bit1",
"tactic": "ext (x | x) <;> rfl"
}
] | [
52,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.set_induction_bounded | [] | [
368,
46
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366,
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Mathlib/Algebra/Hom/Ring.lean | RingHom.comp_apply | [] | [
709,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
707,
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Mathlib/Algebra/Lie/SkewAdjoint.lean | BilinForm.isSkewAdjoint_bracket | [
{
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56,
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Std/Data/Int/Lemmas.lean | Int.add_lt_add_of_le_of_lt | [] | [
806,
76
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805,
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Mathlib/Analysis/Normed/Group/Seminorm.lean | GroupNorm.coe_lt_coe | [] | [
802,
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801,
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Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.KernelFork.condition | [
{
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] | [
91,
51
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90,
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.sum_measure | [
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Mathlib/Logic/Basic.lean | exists_iff_of_forall | [] | [
879,
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878,
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Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.ContinuousHom.ωSup_bind | [
{
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Mathlib/Algebra/GCDMonoid/Basic.lean | isUnit_gcd_of_eq_mul_gcd | [
{
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685,
27
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679,
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Mathlib/Algebra/Homology/HomologicalComplex.lean | ChainComplex.mkHom_f_0 | [] | [
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Mathlib/Order/Chain.lean | IsChain.succ | [
{
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176,
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Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.IsFundamentalDomain.integral_eq_tsum_of_ac | [
{
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410,
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.sub | [
{
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689,
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Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.mem_centralizer_iff | [] | [
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1402,
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Mathlib/GroupTheory/GroupAction/ConjAct.lean | MulAut.conjNormal_inv_apply | [] | [
353,
35
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351,
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Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.unique' | [
{
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Mathlib/Data/Nat/EvenOddRec.lean | Nat.evenOddRec_even | [
{
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.norm_precompL_le | [
{
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1010,
34
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1008,
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Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.zero_apply | [] | [
216,
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215,
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Mathlib/LinearAlgebra/Basic.lean | LinearMap.comap_injective | [] | [
1434,
96
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1433,
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Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.coeff_comp_monomial | [] | [
178,
41
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177,
1
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Mathlib/Data/List/Basic.lean | List.zipRight_nil_cons | [] | [
4229,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4227,
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Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.lift_unique | [
{
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Mathlib/Analysis/Convex/Strict.lean | strictConvex_uIoc | [] | [
209,
23
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208,
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Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.log_of_left_le_one | [] | [
275,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
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Mathlib/RingTheory/Multiplicity.lean | multiplicity.Int.coe_nat_multiplicity | [
{
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Mathlib/Data/Nat/Parity.lean | neg_one_pow_eq_one_iff_even | [] | [
341,
22
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339,
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Mathlib/RingTheory/Finiteness.lean | RingHom.Finite.comp | [
{
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698,
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691,
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Mathlib/Topology/Separation.lean | normal_exists_closure_subset | [
{
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1721,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1714,
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Mathlib/MeasureTheory/Integral/IntegrableOn.lean | StronglyMeasurableAtFilter.eventually | [] | [
52,
72
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Mathlib/Order/CompleteLattice.lean | sSup_inter_le | [] | [
476,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.sum_fintype | [
{
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60
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2077,
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Mathlib/Topology/ContinuousOn.lean | Embedding.continuousOn_iff | [] | [
1082,
33
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1080,
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Mathlib/Data/Finset/Powerset.lean | Finset.powersetLen_succ_insert | [
{
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252,
52
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241,
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Mathlib/Data/Rat/NNRat.lean | Rat.toNNRat_eq_zero | [
{
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"tactic": "simpa [-toNNRat_pos] using (@toNNRat_pos q).not"
}
] | [
353,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
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Std/Data/Int/DivMod.lean | Int.emod_emod_of_dvd | [
{
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"state_before": "n m k : Int\nh : m ∣ k\n⊢ n % k % m = n % m",
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{
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492,
62
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488,
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Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.nodup_Ioc | [] | [
40,
17
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39,
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Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.span_le_adjoin | [] | [
197,
28
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196,
1
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Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.add_eq_coe | [
{
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{
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171,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
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Mathlib/FieldTheory/Adjoin.lean | IntermediateField.adjoin_algebraic_toSubalgebra | [
{
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521,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
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Mathlib/Data/Vector/Basic.lean | Vector.length_val | [] | [
90,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
9
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Mathlib/Data/Set/Basic.lean | Set.union_eq_compl_compl_inter_compl | [] | [
1709,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1708,
1
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Mathlib/FieldTheory/Minpoly/Field.lean | minpoly.add_algebraMap | [
{
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158,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
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Mathlib/Data/Polynomial/UnitTrinomial.lean | Polynomial.IsUnitTrinomial.coeff_isUnit | [
{
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167,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/RingTheory/Coprime/Lemmas.lean | IsCoprime.prod_right_iff | [
{
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"tactic": "simpa only [isCoprime_comm] using IsCoprime.prod_left_iff (R := R)"
}
] | [
70,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
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Mathlib/Topology/Algebra/InfiniteSum/Ring.lean | HasSum.mul_left | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nκ : Type ?u.64\nR : Type ?u.67\nα : Type u_1\ninst✝² : NonUnitalNonAssocSemiring α\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSemiring α\nf g : ι → α\na a₁ a₂✝ a₂ : α\nh : HasSum f a₁\n⊢ HasSum (fun i => a₂ * f i) (a₂ * a₁)",
"tactic": "s... | [
38,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.tmul_pow | [
{
"state_after": "case zero\nR : Type u\ninst✝⁴ : CommSemiring R\nA : Type v₁\ninst✝³ : Semiring A\ninst✝² : Algebra R A\nB : Type v₂\ninst✝¹ : Semiring B\ninst✝ : Algebra R B\na : A\nb : B\n⊢ a ⊗ₜ[R] b ^ Nat.zero = (a ^ Nat.zero) ⊗ₜ[R] (b ^ Nat.zero)\n\ncase succ\nR : Type u\ninst✝⁴ : CommSemiring R\nA : Type ... | [
476,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
1
] |
Mathlib/Topology/UniformSpace/Completion.lean | UniformSpace.Completion.denseEmbedding_coe | [] | [
480,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | tendsto_of_uniformContinuous_subtype | [
{
"state_after": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.149761\ninst✝¹ : UniformSpace α\ninst✝ : UniformSpace β\nf : α → β\ns : Set α\na : α\nhf : UniformContinuous fun x => f ↑x\nha : s ∈ 𝓝 a\n⊢ Tendsto f (map Subtype.val (𝓝 { val := a, property := (_ : a ∈ s) })) (𝓝 (f a))",
"... | [
1511,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1507,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_ite_eq | [] | [
1085,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1083,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | isIntegral_mul | [] | [
529,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_le_ofReal | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.805537\nβ : Type ?u.805540\na b c d : ℝ≥0∞\nr p✝ q✝ : ℝ≥0\np q : ℝ\nh : p ≤ q\n⊢ ENNReal.ofReal p ≤ ENNReal.ofReal q",
"tactic": "simp [ENNReal.ofReal, Real.toNNReal_le_toNNReal h]"
}
] | [
2084,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2083,
1
] |
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