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/Set/Basic.lean | Set.mem_diff_of_mem | [] | [
1800,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1799,
1
] |
Mathlib/Combinatorics/Additive/SalemSpencer.lean | Set.Subsingleton.mulSalemSpencer | [] | [
92,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.mul_eq_inf_of_coprime | [] | [
677,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.isMultiplicative_moebius | [
{
"state_after": "R : Type ?u.592093\n⊢ ↑μ 1 = 1 ∧ ∀ {m n : ℕ}, m ≠ 0 → n ≠ 0 → coprime m n → ↑μ (m * n) = ↑μ m * ↑μ n",
"state_before": "R : Type ?u.592093\n⊢ IsMultiplicative μ",
"tactic": "rw [IsMultiplicative.iff_ne_zero]"
},
{
"state_after": "R : Type ?u.592093\nn m : ℕ\nhn : n ≠ 0\nhm : m ... | [
1018,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1003,
1
] |
Mathlib/RingTheory/Algebraic.lean | Algebra.isAlgebraic_of_finite | [] | [
260,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.all_ae_ofReal_f_le_bound | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.736386\nδ : Type ?u.736389\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\nF : ℕ → α → β\nf : α → β\nbound : α → ℝ\nh_bound : ∀ (n : ℕ), ∀ᵐ (a : α) ∂μ, ‖F n a‖ ≤ bound a\nh... | [
303,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.cauchySeq_iff | [] | [
1502,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1500,
1
] |
Mathlib/Algebra/Polynomial/BigOperators.lean | Polynomial.leadingCoeff_multiset_prod' | [
{
"state_after": "case empty\nR : Type u\nι : Type w\ns : Finset ι\ninst✝ : CommSemiring R\nf : ι → R[X]\nt : Multiset R[X]\nh✝ : prod (Multiset.map leadingCoeff t) ≠ 0\nh : prod (Multiset.map leadingCoeff 0) ≠ 0\n⊢ leadingCoeff (prod 0) = prod (Multiset.map leadingCoeff 0)\n\ncase cons\nR : Type u\nι : Type w\... | [
151,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.diam_nonneg | [] | [
2582,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2581,
1
] |
Mathlib/Combinatorics/Composition.lean | Composition.single_length | [] | [
578,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
577,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.repeatEq_iff_eq | [
{
"state_after": "case fz\nn : ℕ\nα✝ : TypeVec n\ni : Fin2 n\nx✝ y✝ : α✝ i\nn✝ : ℕ\nα : TypeVec (succ n✝)\nx y : α Fin2.fz\n⊢ ofRepeat (repeatEq α Fin2.fz (prod.mk Fin2.fz x y)) ↔ x = y\n\ncase fs\nn : ℕ\nα✝ : TypeVec n\ni : Fin2 n\nx✝ y✝ : α✝ i\nn✝ : ℕ\na✝ : Fin2 n✝\ni_ih : ∀ {α : TypeVec n✝} {x y : α a✝}, ofR... | [
600,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
596,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.sub_iSup | [] | [
682,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.zero_tmul | [] | [
137,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Filter.EventuallyEq.trans_isBigO | [] | [
373,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.inv_rpow | [
{
"state_after": "no goals",
"state_before": "x y✝ z : ℝ\nhx : 0 ≤ x\ny : ℝ\n⊢ x⁻¹ ^ y = (x ^ y)⁻¹",
"tactic": "simp only [← rpow_neg_one, ← rpow_mul hx, mul_comm]"
}
] | [
397,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
] |
Mathlib/CategoryTheory/Opposites.lean | Quiver.Hom.op_unop | [] | [
60,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.prehaar_mono | [
{
"state_after": "G : Type u_1\ninst✝² : Group G\ninst✝¹ : TopologicalSpace G\ninst✝ : TopologicalGroup G\nK₀ : PositiveCompacts G\nU : Set G\nhU : Set.Nonempty (interior U)\nK₁ K₂ : Compacts G\nh : ↑K₁ ⊆ K₂.carrier\n⊢ ↑(index (↑K₁) U) / ↑(index (↑K₀) U) ≤ ↑(index (↑K₂) U) / ↑(index (↑K₀) U)",
"state_before... | [
323,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.disjoint_coe | [] | [
381,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/LinearAlgebra/Matrix/GeneralLinearGroup.lean | Matrix.SpecialLinearGroup.toGLPos_injective | [] | [
269,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_subset_smul_left | [] | [
177,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/NumberTheory/Multiplicity.lean | dvd_geom_sum₂_self | [] | [
59,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurable_of_Ioi | [
{
"state_after": "case h.e'_4\nα : Type u_2\nβ : Type ?u.1082874\nγ : Type ?u.1082877\nγ₂ : Type ?u.1082880\nδ : Type u_1\nι : Sort y\ns t u : Set α\ninst✝¹² : TopologicalSpace α\ninst✝¹¹ : MeasurableSpace α\ninst✝¹⁰ : BorelSpace α\ninst✝⁹ : TopologicalSpace β\ninst✝⁸ : MeasurableSpace β\ninst✝⁷ : BorelSpace β\... | [
1055,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1052,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.norm_eq_one_iff' | [
{
"state_after": "no goals",
"state_before": "d✝ d : ℤ\nhd : d ≤ 0\nz : ℤ√d\n⊢ norm z = 1 ↔ IsUnit z",
"tactic": "rw [← norm_eq_one_iff, ← Int.coe_nat_inj', Int.natAbs_of_nonneg (norm_nonneg hd z), Int.ofNat_one]"
}
] | [
608,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.conjTranspose_inv_natCast_smul | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.1009478\nm : Type u_2\nn : Type u_3\no : Type ?u.1009487\nm' : o → Type ?u.1009492\nn' : o → Type ?u.1009497\nR : Type u_1\nS : Type ?u.1009503\nα : Type v\nβ : Type w\nγ : Type ?u.1009510\ninst✝³ : DivisionSemiring R\ninst✝² : AddCommMonoid α\ninst✝... | [
2218,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2216,
1
] |
Mathlib/Data/Option/Defs.lean | Option.elim'_none | [] | [
69,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | Measurable.prod_map | [] | [
683,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
681,
1
] |
Mathlib/Data/List/Basic.lean | List.get_drop' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.213709\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ L : List α\ni : ℕ\nj : Fin (length (drop i L))\n⊢ get (drop i L) j = get L { val := i + ↑j, isLt := (_ : i + ↑j < length L) }",
"tactic": "rw [get_drop]"
}
] | [
2229,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2227,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Real.dist_le_of_mem_uIcc | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.195692\nι : Type ?u.195695\ninst✝ : PseudoMetricSpace α\nx y x' y' : ℝ\nhx : x ∈ uIcc x' y'\nhy : y ∈ uIcc x' y'\n⊢ y ∈ uIcc y' x'",
"tactic": "rwa [uIcc_comm]"
},
{
"state_after": "no goals",
"state_before": "... | [
1376,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1374,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | LinearMap.linearEquivOfInjective_apply | [] | [
1075,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1072,
1
] |
Mathlib/Data/Set/Prod.lean | Set.pi_subset_pi_iff | [
{
"state_after": "ι : Type u_2\nα : ι → Type u_1\nβ : ι → Type ?u.155680\ns s₁ s₂ : Set ι\nt t₁ t₂ : (i : ι) → Set (α i)\ni : ι\nh : pi s t₁ ⊆ pi s t₂\n⊢ ¬pi s t₁ = ∅ → ∀ (i : ι), i ∈ s → t₁ i ⊆ t₂ i",
"state_before": "ι : Type u_2\nα : ι → Type u_1\nβ : ι → Type ?u.155680\ns s₁ s₂ : Set ι\nt t₁ t₂ : (i : ι... | [
829,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
823,
1
] |
Mathlib/Analysis/Subadditive.lean | Subadditive.lim_le_div | [
{
"state_after": "u : ℕ → ℝ\nh : Subadditive u\nhbdd : BddBelow (range fun n => u n / ↑n)\nn : ℕ\nhn : n ≠ 0\n⊢ sInf ((fun n => u n / ↑n) '' Ici 1) ≤ u n / ↑n",
"state_before": "u : ℕ → ℝ\nh : Subadditive u\nhbdd : BddBelow (range fun n => u n / ↑n)\nn : ℕ\nhn : n ≠ 0\n⊢ Subadditive.lim h ≤ u n / ↑n",
"... | [
51,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.add_le_add_iff_le_right | [] | [
71,
66
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
70,
11
] |
Mathlib/Probability/CondCount.lean | ProbabilityTheory.condCount_empty | [
{
"state_after": "no goals",
"state_before": "Ω : Type u_1\ninst✝ : MeasurableSpace Ω\ns : Set Ω\n⊢ ↑↑(condCount s) ∅ = 0",
"tactic": "simp"
}
] | [
64,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.ext | [] | [
243,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/LinearAlgebra/Matrix/Basis.lean | Basis.toMatrix_unitsSMul | [
{
"state_after": "case a.h\nι : Type u_1\nι' : Type ?u.170437\nκ : Type ?u.170440\nκ' : Type ?u.170443\nR : Type ?u.170446\nM : Type ?u.170449\ninst✝⁶ : CommSemiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\nR₂ : Type u_2\nM₂ : Type u_3\ninst✝³ : CommRing R₂\ninst✝² : AddCommGroup M₂\ninst✝¹ : Module R₂... | [
109,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.induction_on' | [] | [
203,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
11
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.val_int_cast | [
{
"state_after": "n : ℕ\na : ℤ\ninst✝ : NeZero n\nhle : 0 ≤ ↑(val ↑a)\n⊢ ↑(val ↑a) = a % ↑n",
"state_before": "n : ℕ\na : ℤ\ninst✝ : NeZero n\n⊢ ↑(val ↑a) = a % ↑n",
"tactic": "have hle : (0 : ℤ) ≤ ↑(a : ZMod n).val := Int.coe_nat_nonneg _"
},
{
"state_after": "n : ℕ\na : ℤ\ninst✝ : NeZero n\nhl... | [
490,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/Analysis/NormedSpace/IndicatorFunction.lean | indicator_norm_le_norm_self | [] | [
44,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.ofMulEquivOfLocalizations_comp | [
{
"state_after": "case h\nM : Type u_4\ninst✝³ : CommMonoid M\nS : Submonoid M\nN : Type u_1\ninst✝² : CommMonoid N\nP : Type u_2\ninst✝¹ : CommMonoid P\nf : LocalizationMap S N\ng : M →* P\nhg : ∀ (y : { x // x ∈ S }), IsUnit (↑g ↑y)\nT : Submonoid P\nQ : Type u_3\ninst✝ : CommMonoid Q\nk : N ≃* P\nj : P ≃* Q\... | [
1475,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1472,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.ne_bmex | [
{
"state_after": "no goals",
"state_before": "case h.e'_2.h.e'_1\nα : Type ?u.383183\nβ : Type ?u.383186\nγ : Type ?u.383189\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no : Ordinal\nf : (a : Ordinal) → a < o → Ordinal\ni : Ordinal\nhi : i < o\n⊢ i = typein (fun x x_1 => x < x_1) (enum (fun x x_1 ... | [
2087,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2082,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.uIoc_ae_eq_interval | [] | [
3368,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3367,
1
] |
Mathlib/Init/Function.lean | Function.HasRightInverse.surjective | [] | [
114,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Logic/Function/Iterate.lean | Function.iterate_add_apply | [
{
"state_after": "α : Type u\nβ : Type v\nf : α → α\nm n : ℕ\nx : α\n⊢ (f^[m] ∘ f^[n]) x = (f^[m]) ((f^[n]) x)",
"state_before": "α : Type u\nβ : Type v\nf : α → α\nm n : ℕ\nx : α\n⊢ (f^[m + n]) x = (f^[m]) ((f^[n]) x)",
"tactic": "rw [iterate_add f m n]"
},
{
"state_after": "no goals",
"sta... | [
74,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | Continuous.deriv_integral | [] | [
693,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_bot | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.56497\ninst✝¹ : Preorder α\ninst✝ : OrderBot α\na : α\n⊢ Icc ⊥ a = Iic a",
"tactic": "simp [← Ici_inter_Iic]"
}
] | [
1027,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1027,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.BoundedFormula.realize_rel₁ | [
{
"state_after": "L : Language\nL' : Language\nM : Type w\nN : Type ?u.54593\nP : Type ?u.54596\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nn l : ℕ\nφ ψ : BoundedFormula L α l\nθ : BoundedFormula L α (Nat.succ l)\nv : α → M\nxs : Fin l → M\nR : Relations L 1... | [
314,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Data/Matrix/Notation.lean | Matrix.vec3_add | [
{
"state_after": "no goals",
"state_before": "α : Type u\no n m : ℕ\nm' : Type uₘ\nn' : Type uₙ\no' : Type uₒ\na b : ℕ\ninst✝ : Add α\na₀ a₁ a₂ b₀ b₁ b₂ : α\n⊢ ![a₀, a₁, a₂] + ![b₀, b₁, b₂] = ![a₀ + b₀, a₁ + b₁, a₂ + b₂]",
"tactic": "rw [cons_add_cons, cons_add_cons, cons_add_cons, empty_add_empty]"
}... | [
476,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.setToFun_undef | [] | [
1294,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1292,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_erase_le | [
{
"state_after": "case ofFinsupp\nR : Type u\nS : Type v\na b c d : R\nn✝ m : ℕ\ninst✝ : Semiring R\np✝ q : R[X]\nι : Type ?u.559926\nn : ℕ\np : AddMonoidAlgebra R ℕ\n⊢ degree (erase n { toFinsupp := p }) ≤ degree { toFinsupp := p }",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn✝ m : ℕ\ninst✝ : S... | [
738,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
732,
1
] |
Mathlib/Data/Polynomial/Expand.lean | Polynomial.coeff_expand_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹ : CommSemiring R\nS : Type v\ninst✝ : CommSemiring S\np✝ q p : ℕ\nhp : 0 < p\nf : R[X]\nn : ℕ\n⊢ coeff (↑(expand R p) f) (n * p) = coeff f n",
"tactic": "rw [coeff_expand hp, if_pos (dvd_mul_left _ _), Nat.mul_div_cancel _ hp]"
}
] | [
124,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | ciInf_set_le | [] | [
827,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
825,
1
] |
Mathlib/Topology/Algebra/Field.lean | IsPreconnected.eq_one_or_eq_neg_one_of_sq_eq | [
{
"state_after": "K : Type ?u.15846\ninst✝⁶ : DivisionRing K\ninst✝⁵ : TopologicalSpace K\nα : Type u_2\n𝕜 : Type u_1\nf g : α → 𝕜\nS : Set α\ninst✝⁴ : TopologicalSpace α\ninst✝³ : TopologicalSpace 𝕜\ninst✝² : T1Space 𝕜\ninst✝¹ : Ring 𝕜\ninst✝ : NoZeroDivisors 𝕜\nhS : IsPreconnected S\nhf : ContinuousOn f... | [
138,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.ofReal_tsum_of_nonneg | [
{
"state_after": "no goals",
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"tactic": "simp_rw [ENNReal.ofReal, ENNReal.tsum_coe_eq (NNReal.hasSum_r... | [
1319,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1317,
1
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Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.monomial_le_degreeOf | [
{
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"state_before": "R : Type u\nS : Type ... | [
542,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Pointwise.lean | Subalgebra.smul_mem_pointwise_smul | [] | [
113,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
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Mathlib/Algebra/Order/Ring/Abs.lean | abs_eq_iff_mul_self_eq | [
{
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"state_before": "α : Type u_1\ninst✝ : LinearOrderedRing α\na b c : α\n⊢ abs a = abs b ↔ a * a = b * b",
"tactic": "rw [← abs_mul_abs_self, ← abs_mul_abs_self b]"
},
{
"state... | [
88,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/RingTheory/Finiteness.lean | Submodule.exists_mem_and_smul_eq_self_of_fg_of_le_smul | [
{
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143,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
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Mathlib/Data/Int/Parity.lean | Int.even_add' | [
{
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"tactic": "rw [even_add, even_iff_not_odd, even_iff_not_odd, not_iff_not]"
}
] | [
112,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
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Mathlib/Topology/MetricSpace/Isometry.lean | Isometry.preimage_emetric_ball | [
{
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"s... | [
152,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Computability/Partrec.lean | Partrec₂.comp₂ | [] | [
518,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.IsPwo.isWf | [
{
"state_after": "no goals",
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"tactic": "simpa only [← lt_iff_le_not_le] using h.wellFoundedOn"
}
] | [
419,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
11
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Mathlib/Data/Set/Image.lean | Set.surjective_onto_image | [] | [
596,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
1
] |
Mathlib/Tactic/NormNum/Core.lean | Mathlib.Meta.NormNum.IsRat.to_isInt | [
{
"state_after": "no goals",
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"tactic": "simp"
}
] | [
157,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Data/Set/Intervals/ProjIcc.lean | Set.projIcc_surjOn | [] | [
84,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
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Mathlib/Algebra/Order/Rearrangement.lean | MonovaryOn.sum_smul_comp_perm_le_sum_smul | [
{
"state_after": "ι : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝³ : LinearOrderedRing α\ninst✝² : LinearOrderedAddCommGroup β\ninst✝¹ : Module α β\ninst✝ : OrderedSMul α β\ns : Finset ι\nf : ι → α\ng : ι → β\n⊢ ∀ {σ : Perm ι}, MonovaryOn f g ↑s → {x | ↑σ x ≠ x} ⊆ ↑s → ∑ i in s, f i • g (↑σ i) ≤ ∑ i in s, f i •... | [
111,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Topology/Algebra/Order/MonotoneConvergence.lean | tendsto_atTop_ciInf | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.27589\nι : Type u_1\ninst✝³ : Preorder ι\ninst✝² : TopologicalSpace α\ninst✝¹ : ConditionallyCompleteLattice α\ninst✝ : InfConvergenceClass α\nf : ι → α\na : α\nh_anti : Antitone f\nhbdd : BddBelow (range f)\n⊢ Tendsto f atTop (𝓝 (⨅ (i... | [
150,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Analysis/InnerProductSpace/Calculus.lean | ContDiffWithinAt.inner | [] | [
81,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.monomial_mul_X_pow | [
{
"state_after": "case zero\nR : Type u\na b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q : R[X]\nn : ℕ\nr : R\n⊢ ↑(monomial n) r * X ^ Nat.zero = ↑(monomial (n + Nat.zero)) r\n\ncase succ\nR : Type u\na b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q : R[X]\nn : ℕ\nr : R\nk : ℕ\nih : ↑(monomial n) r * X ^ k = ↑(monomial (n... | [
632,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.add_right_neg_equiv | [] | [
1698,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1697,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.map_surjective_of_surjective | [] | [
1572,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1571,
1
] |
Mathlib/RingTheory/Algebraic.lean | isAlgebraic_of_mem_rootSet | [] | [
137,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Data/Set/Basic.lean | Set.not_nontrivial_iff | [] | [
2611,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2610,
1
] |
Mathlib/Order/Atoms.lean | IsCompl.isAtom_iff_isCoatom | [] | [
849,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
847,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.filter_ne_eq_erase | [
{
"state_after": "case h\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝ : (i : ι) → Zero (β i)\ns : Finset ι\nx : (i : ↑↑s) → β ↑i\ni✝ : ι\nf : Π₀ (i : ι), β i\ni j : ι\n⊢ ↑(filter (fun x => x ≠ i) f) j = ↑(erase i f) j",
"state_before": "ι : Type u\n... | [
783,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
781,
1
] |
Mathlib/RingTheory/Congruence.lean | RingCon.coe_neg | [] | [
256,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Algebra/Group/Units.lean | Units.mul_eq_one_iff_eq_inv | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Monoid α\na✝ b c u : αˣ\na : α\n⊢ a * ↑u = 1 ↔ a = ↑u⁻¹",
"tactic": "rw [← mul_inv_eq_one, inv_inv]"
}
] | [
390,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | AEMeasurable.div' | [] | [
346,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.functorPushforward_extend_eq | [
{
"state_after": "case h\nC : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nF : C ⥤ D\nX Y✝ Z : C\nf : Y✝ ⟶ X\nS R✝ : Sieve X\nE : Type u₃\ninst✝ : Category E\nG : D ⥤ E\nR : Presieve X\nY : D\n⊢ Presieve.functorPushforward F (generate R).arrows = Presieve.functorPushforward F R",
"state_b... | [
623,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
615,
1
] |
Mathlib/Order/Iterate.lean | Monotone.seq_lt_seq_of_lt_of_le | [
{
"state_after": "case zero\nα : Type u_1\ninst✝ : Preorder α\nf : α → α\nx y : ℕ → α\nhf : Monotone f\nh₀ : x 0 < y 0\nhx : ∀ (k : ℕ), k < Nat.zero → x (k + 1) < f (x k)\nhy : ∀ (k : ℕ), k < Nat.zero → f (y k) ≤ y (k + 1)\n⊢ x Nat.zero < y Nat.zero\n\ncase succ\nα : Type u_1\ninst✝ : Preorder α\nf : α → α\nx y... | [
73,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.indicator_le_indicator_nonneg | [
{
"state_after": "α : Type u_2\nβ✝ : Type ?u.165616\nι : Type ?u.165619\nM : Type ?u.165622\nN : Type ?u.165625\nβ : Type u_1\ninst✝¹ : LinearOrder β\ninst✝ : Zero β\ns : Set α\nf : α → β\nx : α\n⊢ indicator s f x ≤ indicator {x | 0 ≤ f x} f x",
"state_before": "α : Type u_2\nβ✝ : Type ?u.165616\nι : Type ?... | [
890,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
881,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.sub_lt_self_iff | [] | [
1181,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1180,
11
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.sSup_ord | [
{
"state_after": "α : Type ?u.298606\nβ : Type ?u.298609\nγ : Type ?u.298612\nr : α → α → Prop\ns✝ : β → β → Prop\nt : γ → γ → Prop\ns : Set Cardinal\nhs : BddAbove s\na : Ordinal\n⊢ (∀ (x : Cardinal), x ∈ s → x ≤ card a) ↔ ∀ (x : Ordinal), x ∈ ord '' s → x ≤ a",
"state_before": "α : Type ?u.298606\nβ : Typ... | [
1403,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1398,
1
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Mathlib/Topology/MetricSpace/Basic.lean | dist_triangle_right | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.9917\nι : Type ?u.9920\ninst✝ : PseudoMetricSpace α\nx y z : α\n⊢ dist x y ≤ dist x z + dist z y",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.9917\nι : Type ?u.9920\ninst✝ : PseudoMetricSpace α\nx y z : α\n⊢ dist x y ≤ dist x z + dist y z",
... | [
208,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_zero_left | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1517880\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx : E\n⊢ inner 0 x = 0",
"tactic": "rw ... | [
561,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
560,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.deleteEdges_univ_eq | [
{
"state_after": "case Adj.h.h.a\nι : Sort ?u.156524\n𝕜 : Type ?u.156527\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v w : V\ne : Sym2 V\nx✝¹ x✝ : V\n⊢ Adj (deleteEdges G Set.univ) x✝¹ x✝ ↔ Adj ⊥ x✝¹ x✝",
"state_before": "ι : Sort ?u.156524\n𝕜 : Type ?u.156527\nV : ... | [
1147,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1145,
1
] |
Mathlib/FieldTheory/Minpoly/Basic.lean | minpoly.subsingleton | [
{
"state_after": "A : Type u_2\nB : Type u_1\nB' : Type ?u.53832\ninst✝⁵ : CommRing A\ninst✝⁴ : Ring B\ninst✝³ : Ring B'\ninst✝² : Algebra A B\ninst✝¹ : Algebra A B'\nx : B\ninst✝ : Subsingleton B\n✝ : Nontrivial A\n⊢ minpoly A x = 1",
"state_before": "A : Type u_2\nB : Type u_1\nB' : Type ?u.53832\ninst✝⁵ ... | [
171,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.one_le_div_iff | [
{
"state_after": "case refine'_1\nF : Type ?u.310838\nα : Type u_1\nβ : Type ?u.310844\nγ : Type ?u.310847\nδ : Type ?u.310850\nε : Type ?u.310853\ninst✝² : Group α\ninst✝¹ : DivisionMonoid β\ninst✝ : MonoidHomClass F α β\nm : F\nf g f₁ g₁ : Filter α\nf₂ g₂ : Filter β\nh : 1 ≤ f / g\nhfg : Disjoint f g\n⊢ False... | [
860,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
855,
11
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.coeFn_congr | [] | [
91,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | sq_pos_of_pos | [
{
"state_after": "β : Type ?u.233772\nA : Type ?u.233775\nG : Type ?u.233778\nM : Type ?u.233781\nR : Type u_1\ninst✝ : StrictOrderedSemiring R\na x y : R\nn m : ℕ\nha : 0 < a\n⊢ 0 < a * a",
"state_before": "β : Type ?u.233772\nA : Type ?u.233775\nG : Type ?u.233778\nM : Type ?u.233781\nR : Type u_1\ninst✝ ... | [
534,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
1
] |
Mathlib/LinearAlgebra/CrossProduct.lean | cross_anticomm' | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : CommRing R\nv w : Fin 3 → R\n⊢ ↑(↑crossProduct v) w + ↑(↑crossProduct w) v = 0",
"tactic": "rw [add_eq_zero_iff_eq_neg, cross_anticomm]"
}
] | [
84,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/RingTheory/Algebraic.lean | IsIntegral.isAlgebraic | [] | [
100,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Algebra/BigOperators/NatAntidiagonal.lean | Finset.Nat.sum_antidiagonal_succ | [] | [
35,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
1
] |
Mathlib/Algebra/Lie/Basic.lean | lie_neg | [
{
"state_after": "R : Type u\nL : Type v\nM : Type w\nN : Type w₁\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 N\ninst✝² : Module R N\ninst✝¹ : LieRingModule L N\ninst... | [
180,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/LinearAlgebra/StdBasis.lean | Pi.basis_repr_stdBasis | [
{
"state_after": "case h.mk\nR : Type u_3\nη : Type u_1\nιs : η → Type u_2\nMs : η → Type u_4\ninst✝⁴ : Semiring R\ninst✝³ : (i : η) → AddCommMonoid (Ms i)\ninst✝² : (i : η) → Module R (Ms i)\ninst✝¹ : Fintype η\ninst✝ : DecidableEq η\ns : (j : η) → Basis (ιs j) R (Ms j)\nj : η\ni : ιs j\nj' : η\ni' : ιs j'\n⊢ ... | [
256,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Analysis/Calculus/TangentCone.lean | uniqueDiffOn_Iio | [] | [
428,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/Order/RelClasses.lean | antisymm' | [] | [
39,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Algebra/Associated.lean | Associates.le_mul_left | [
{
"state_after": "α : Type u_1\nβ : Type ?u.300647\nγ : Type ?u.300650\nδ : Type ?u.300653\ninst✝ : CommMonoid α\na b : Associates α\n⊢ a ≤ a * b",
"state_before": "α : Type u_1\nβ : Type ?u.300647\nγ : Type ?u.300650\nδ : Type ?u.300653\ninst✝ : CommMonoid α\na b : Associates α\n⊢ a ≤ b * a",
"tactic":... | [
916,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
916,
1
] |
Mathlib/Data/Set/Function.lean | Set.EqOn.piecewise_ite' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.88049\nι : Sort ?u.88052\nπ : α → Type ?u.88057\nδ : α → Sort ?u.88062\ns : Set α\nf✝ g✝ : (i : α) → δ i\ninst✝ : (j : α) → Decidable (j ∈ s)\nf f' g : α → β\nt t' : Set α\nh : EqOn f g (t ∩ s)\nh' : EqOn f' g (t' ∩ sᶜ)\n⊢... | [
1460,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1458,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | dvd_mul_gcd_of_dvd_mul | [
{
"state_after": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : GCDMonoid α\nm n k : α\nH : k ∣ n * m\n⊢ k ∣ gcd k n * m",
"state_before": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : GCDMonoid α\nm n k : α\nH : k ∣ m * n\n⊢ k ∣ m * gcd k n",
"tactic": "rw [mul_comm] at H⊢"
... | [
517,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.inter_mul_subset | [] | [
454,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
] |
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