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/Analysis/InnerProductSpace/Basic.lean | Orthonormal.inner_right_sum | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1919924\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\nι : Type u_3\ndec_ι : DecidableEq ι\nv : ι → E\nhv : Orthonormal 𝕜 v\nl : ... | [
802,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
799,
1
] |
Std/Data/Nat/Gcd.lean | Nat.gcd_mul_lcm | [
{
"state_after": "no goals",
"state_before": "m n : Nat\n⊢ gcd m n * lcm m n = m * n",
"tactic": "rw [lcm, Nat.mul_div_cancel' (Nat.dvd_trans (gcd_dvd_left m n) (Nat.dvd_mul_right m n))]"
}
] | [
204,
91
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
203,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | mk_eq_mk_of_basis' | [] | [
572,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.exists_maximal_wrt | [
{
"state_after": "case refine'_1\nα : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ninst✝ : PartialOrder β\nf : α → β\ns : Set α\nh : Set.Finite s\n⊢ Set.Nonempty ∅ → ∃ a, a ∈ ∅ ∧ ∀ (a' : α), a' ∈ ∅ → f a ≤ f a' → f a = f a'\n\ncase refine'_2\nα : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ninst✝ : PartialOrder β... | [
1587,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1570,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasFDerivAt.hasFDerivAtFilter | [] | [
369,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | Submodule.subtypeₗᵢ_toContinuousLinearMap | [] | [
476,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.exists_isOpen_bounded_image_of_isCompact_of_forall_continuousAt | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.524771\nι : Type ?u.524774\ninst✝¹ : PseudoMetricSpace α\nx : α\ns t : Set α\nr : ℝ\ninst✝ : TopologicalSpace β\nk : Set β\nf : β → α\nhk : IsCompact k\nhf : ∀ (x : β), x ∈ k → ContinuousWithinAt f univ x\n⊢ ∃ t, k ⊆ t ∧ IsOpen t ∧ Bounded (f '' t)",
"st... | [
2490,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2485,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Additive.lean | BoxIntegral.BoxAdditiveMap.sum_boxes_congr | [
{
"state_after": "case intro\nι : Type u_1\nM : Type u_2\nn : ℕ\nN : Type ?u.77819\ninst✝² : AddCommMonoid M\ninst✝¹ : AddCommMonoid N\nI₀ : WithTop (Box ι)\nI J : Box ι\ni : ι\ninst✝ : Finite ι\nf : ι →ᵇᵃ[I₀] M\nhI : ↑I ≤ I₀\nπ₁ π₂ : Prepartition I\nh : Prepartition.iUnion π₁ = Prepartition.iUnion π₂\ns : Fins... | [
172,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Tactic/Sat/FromLRAT.lean | Sat.Fmla.refute | [] | [
175,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.map_const' | [] | [
1299,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1298,
9
] |
Mathlib/Computability/Primrec.lean | Nat.Primrec.pred | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ Nat.casesOn n 0 id = Nat.pred n",
"tactic": "cases n <;> simp [*]"
}
] | [
130,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Data/List/Basic.lean | List.reduceOption_append | [] | [
3445,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3443,
1
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Mathlib/Probability/Independence/ZeroOne.lean | ProbabilityTheory.indep_biSup_limsup | [
{
"state_after": "Ω : Type u_1\nι : Type u_2\nm m0 : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\ninst✝ : IsProbabilityMeasure μ\ns : ι → MeasurableSpace Ω\nα : Type ?u.378750\np : Set ι → Prop\nf : Filter ι\nns : α → Set ι\nh_le : ∀ (n : ι), s n ≤ m0\nh_indep : iIndep s\nhf : ∀ (t : Set ι), p t → tᶜ ∈ f\nt ... | [
82,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.not_mem_of_not_mem_closure | [] | [
408,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean | MeasureTheory.ProbabilityMeasure.nonempty | [
{
"state_after": "Ω : Type u_1\ninst✝ : MeasurableSpace Ω\nμ : ProbabilityMeasure Ω\nmaybe_empty : ¬Nonempty Ω\n⊢ False",
"state_before": "Ω : Type u_1\ninst✝ : MeasurableSpace Ω\nμ : ProbabilityMeasure Ω\n⊢ Nonempty Ω",
"tactic": "by_contra maybe_empty"
},
{
"state_after": "Ω : Type u_1\ninst✝ ... | [
185,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Algebra/Hom/GroupAction.lean | MulActionHom.comp_apply | [] | [
161,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/NumberTheory/PythagoreanTriples.lean | sq_ne_two_fin_zmod_four | [
{
"state_after": "z : Fin 4\n⊢ z * z ≠ 2",
"state_before": "z : ZMod 4\n⊢ z * z ≠ 2",
"tactic": "change Fin 4 at z"
},
{
"state_after": "no goals",
"state_before": "z : Fin 4\n⊢ z * z ≠ 2",
"tactic": "fin_cases z <;> norm_num [Fin.ext_iff, Fin.val_bit0, Fin.val_bit1]"
}
] | [
35,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.pi_div_two_le_two | [
{
"state_after": "⊢ choose exists_cos_eq_zero ≤ 2",
"state_before": "⊢ π / 2 ≤ 2",
"tactic": "rw [Real.pi, mul_div_cancel_left _ (two_ne_zero' ℝ)]"
},
{
"state_after": "no goals",
"state_before": "⊢ choose exists_cos_eq_zero ≤ 2",
"tactic": "exact (Classical.choose_spec exists_cos_eq_zer... | [
150,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/CategoryTheory/Limits/Constructions/ZeroObjects.lean | CategoryTheory.Limits.pullbackZeroZeroIso_inv_fst | [
{
"state_after": "C : Type u_2\ninst✝³ : Category C\ninst✝² : HasZeroObject C\ninst✝¹ : HasZeroMorphisms C\nX Y : C\ninst✝ : HasBinaryProduct X Y\n⊢ (limit.isoLimitCone\n { cone := PullbackCone.mk prod.fst prod.snd (_ : prod.fst ≫ 0 = prod.snd ≫ 0),\n isLimit :=\n isPullbackOfIs... | [
176,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.of_one_div | [
{
"state_after": "no goals",
"state_before": "q : ℚ\nx y : ℝ\nh : Irrational (1 / x)\n⊢ Irrational (↑1 / x)",
"tactic": "rwa [cast_one]"
}
] | [
462,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
] |
Mathlib/Algebra/Order/Rearrangement.lean | MonovaryOn.sum_comp_perm_mul_lt_sum_mul_iff | [] | [
398,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.get_eq_get | [] | [
119,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.affineSpan_coe | [
{
"state_after": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nS : AffineSpace V P\np₁ p₂ : P\ns : AffineSubspace k P\n⊢ affineSpan k ↑s ≤ s",
"state_before": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝... | [
1010,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1007,
1
] |
Mathlib/CategoryTheory/Filtered.lean | CategoryTheory.IsCofiltered.eq_condition | [] | [
593,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.IsIso.eq_comp_inv | [] | [
439,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.Iic_add_bij | [] | [
415,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/Topology/Semicontinuous.lean | LowerSemicontinuous.lowerSemicontinuousOn | [] | [
173,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalMaxOn.neg | [] | [
413,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
8
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPullback.of_map | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nF : C ⥤ D\nW X Y Z : C\nf : W ⟶ X\ng : W ⟶ Y\nh : X ⟶ Z\ni : Y ⟶ Z\ninst✝ : ReflectsLimit (cospan h i) F\ne : f ≫ h = g ≫ i\nH : IsPullback (F.map f) (F.map g) (F.map h) (F.map i)\n⊢ IsLimit (F.mapCone (PullbackCone.mk f g (_ ... | [
1035,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1028,
1
] |
Mathlib/Data/Set/Intervals/Pi.lean | Set.pi_univ_Ioc_update_union | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nα : ι → Type u_1\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → LinearOrder (α i)\nx y : (i : ι) → α i\ni₀ : ι\nm : α i₀\nhm : m ∈ Icc (x i₀) (y i₀)\n⊢ ((pi univ fun i => Ioc (x i) (update y i₀ m i)) ∪ pi univ fun i => Ioc (update x i₀ m i) (y i)) =\n ... | [
343,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_union_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.47327\ninst✝ : PartialOrder α\na b c : α\nhab : a ≤ b\n⊢ Ioc a b ∪ {a} = Icc a b",
"tactic": "rw [← Icc_diff_left, diff_union_self,\n union_eq_self_of_subset_right (singleton_subset_iff.2 <| left_mem_Icc.2 hab)]"
}
] | [
868,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
866,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.closure_induction_right | [] | [
87,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | Dense.eq_of_inner_right | [] | [
965,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
963,
1
] |
Mathlib/Data/Finset/NatAntidiagonal.lean | Finset.Nat.antidiagonal.snd_le | [
{
"state_after": "n : ℕ\nkl : ℕ × ℕ\nhlk : kl ∈ antidiagonal n\n⊢ ∃ c, n = kl.snd + c",
"state_before": "n : ℕ\nkl : ℕ × ℕ\nhlk : kl ∈ antidiagonal n\n⊢ kl.snd ≤ n",
"tactic": "rw [le_iff_exists_add]"
},
{
"state_after": "n : ℕ\nkl : ℕ × ℕ\nhlk : kl ∈ antidiagonal n\n⊢ n = kl.snd + kl.fst",
... | [
110,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelEmbedding.isTotal | [] | [
363,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
11
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | ciInf_eq_of_forall_ge_of_forall_gt_exists_lt | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.60897\nγ : Type ?u.60900\nι : Sort u_1\ninst✝¹ : ConditionallyCompleteLattice α\ns t : Set α\na b : α\ninst✝ : Nonempty ι\nf : ι → α\nh₁ : ∀ (i : ι), b ≤ f i\nh₂ : ∀ (w : α), b < w → ∃ i, f i < w\n⊢ (⨅ (i : ι), f i) = b",
"tactic": ... | [
884,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
882,
1
] |
Mathlib/Data/List/Zip.lean | List.get_zip | [] | [
421,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/GroupTheory/GroupAction/Basic.lean | MulAction.mem_fixedPoints_iff_card_orbit_eq_one | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : Monoid α\ninst✝¹ : MulAction α β\na : β\ninst✝ : Fintype ↑(orbit α a)\n⊢ (∀ (x : α), x • a = a) ↔ ∃ x, ∀ (y : ↑(orbit α a)), y = x",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : Monoid α\ninst✝¹ : MulAction α β\na : β\ninst✝ : F... | [
192,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/GroupTheory/Perm/Subgroup.lean | Equiv.Perm.subtypeCongrHom.card_range | [] | [
68,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Algebra/Module/Opposites.lean | MulOpposite.coe_opLinearEquiv | [] | [
41,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.m_pos_abs | [
{
"state_after": "α : Type u\ninst✝² : Lattice α\ninst✝¹ : CommGroup α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na : α\n⊢ abs a⁺ = abs a⁺ / abs a⁻",
"state_before": "α : Type u\ninst✝² : Lattice α\ninst✝¹ : CommGroup α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x... | [
365,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/CategoryTheory/Preadditive/FunctorCategory.lean | CategoryTheory.NatTrans.app_sum | [
{
"state_after": "no goals",
"state_before": "C : Type u_2\nD : Type u_4\ninst✝² : Category C\ninst✝¹ : Category D\ninst✝ : Preadditive D\nF G : C ⥤ D\nι : Type u_1\ns : Finset ι\nX : C\nα : ι → (F ⟶ G)\n⊢ (∑ i in s, α i).app X = ∑ i in s, (α i).app X",
"tactic": "simp only [← appHom_apply, map_sum]"
... | [
118,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Algebra/Lie/Solvable.lean | LieAlgebra.le_solvable_ideal_solvable | [] | [
260,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Order/Closure.lean | ClosureOperator.closed_eq_range_close | [
{
"state_after": "case intro\nα : Type u_1\nι : Sort ?u.5391\nκ : ι → Sort ?u.5396\ninst✝¹ inst✝ : PartialOrder α\nc : ClosureOperator α\ny : α\n⊢ ↑c.toOrderHom y ∈ closed c",
"state_before": "α : Type u_1\nι : Sort ?u.5391\nκ : ι → Sort ?u.5396\ninst✝¹ inst✝ : PartialOrder α\nc : ClosureOperator α\nx : α\n... | [
195,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Data/Finset/Sym.lean | Finset.eq_empty_of_sym_eq_empty | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\na b : α\nn : ℕ\nm : Sym α n\nh : ¬Finset.Nonempty (Finset.sym s n)\n⊢ ¬Finset.Nonempty s",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\na b : α\nn : ℕ\nm : Sym α n\nh : Finset.sym s n = ∅\n⊢ s = ∅",
"tactic":... | [
188,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | Algebra.smul_leftMulMatrix_algebraMap_eq | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type u_5\nT : Type u_2\ninst✝¹⁰ : CommRing R\ninst✝⁹ : CommRing S\ninst✝⁸ : Ring T\ninst✝⁷ : Algebra R S\ninst✝⁶ : Algebra S T\ninst✝⁵ : Algebra R T\ninst✝⁴ : IsScalarTower R S T\nm : Type u_3\nn : Type u_4\ninst✝³ : Fintype m\ninst✝² : Fintype... | [
944,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
942,
1
] |
Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.fundamentalInterior_smul | [
{
"state_after": "no goals",
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625,
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623,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.cos_two_pi_sub | [] | [
1228,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1227,
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Mathlib/LinearAlgebra/Alternating.lean | MultilinearMap.alternatization_def | [] | [
881,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
879,
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Mathlib/Data/Sigma/Interval.lean | Sigma.card_Ioo | [] | [
76,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
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Mathlib/Order/PrimeIdeal.lean | Order.Ideal.PrimePair.compl_F_eq_I | [] | [
66,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
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Mathlib/Algebra/IndicatorFunction.lean | Set.indicator_one_preimage | [] | [
327,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
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Mathlib/Combinatorics/Additive/Etransform.lean | Finset.mulDysonEtransform_idem | [
{
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Mathlib/GroupTheory/Perm/Cycle/Concrete.lean | Cycle.formPerm_coe | [] | [
150,
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149,
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Mathlib/Algebra/Hom/Group.lean | MulHom.congr_arg | [] | [
704,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
1
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Mathlib/Algebra/Group/Conj.lean | ConjClasses.mk_surjective | [] | [
193,
36
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192,
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Mathlib/Topology/Connected.lean | isConnected_connectedComponent | [] | [
631,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
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Mathlib/RingTheory/RootsOfUnity/Basic.lean | map_rootsOfUnity_eq_pow_self | [
{
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262,
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256,
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Mathlib/Logic/Function/Basic.lean | Function.Injective2.right' | [] | [
953,
38
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950,
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Mathlib/GroupTheory/Sylow.lean | not_dvd_card_sylow | [] | [
349,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
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Mathlib/AlgebraicGeometry/PrimeSpectrum/Noetherian.lean | PrimeSpectrum.exists_primeSpectrum_prod_le | [
{
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58,
78
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31,
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Mathlib/Data/Bool/Basic.lean | Bool.and_elim_right | [
{
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] | [
179,
65
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179,
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Mathlib/Data/Polynomial/Laurent.lean | LaurentPolynomial.invOf_T | [] | [
267,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
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Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_const_mul_Ioo_of_neg | [
{
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}
] | [
667,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
665,
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Mathlib/Order/Monotone/Basic.lean | Antitone.reflect_lt | [] | [
760,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
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Std/Data/Option/Lemmas.lean | Option.some_ne_none | [] | [
15,
53
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
15,
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Mathlib/Data/Int/Order/Basic.lean | Int.emod_abs | [] | [
231,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
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Mathlib/MeasureTheory/Lattice.lean | Measurable.const_inf | [] | [
182,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
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Mathlib/Topology/UniformSpace/Equicontinuity.lean | Set.Equicontinuous.continuous_of_mem | [] | [
173,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
11
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Mathlib/LinearAlgebra/Ray.lean | Module.Ray.someRayVector_ray | [] | [
366,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
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Std/Data/Rat/Lemmas.lean | Rat.divInt_eq_iff | [
{
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136,
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Mathlib/CategoryTheory/Sums/Basic.lean | CategoryTheory.Functor.sum_obj_inl | [] | [
197,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
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Mathlib/Algebra/GroupWithZero/Units/Basic.lean | Ring.inverse_mul_cancel_right | [
{
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"tactic": "rw [mul_assoc, inverse_mul_cancel x h, mu... | [
121,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
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Mathlib/Data/Subtype.lean | exists_eq_subtype_mk_iff | [] | [
142,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
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Mathlib/Topology/Order/Basic.lean | pi_Ico_mem_nhds | [
{
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1514,
35
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.ext | [] | [
138,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
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Mathlib/Data/MvPolynomial/Supported.lean | MvPolynomial.supportedEquivMvPolynomial_symm_C | [
{
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65,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.nat_add_aleph0 | [
{
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] | [
1663,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1663,
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Mathlib/Analysis/Convex/Function.lean | LinearOrder.convexOn_of_lt | [
{
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423,
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411,
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Mathlib/CategoryTheory/Localization/Construction.lean | CategoryTheory.MorphismProperty.Q_inverts | [] | [
147,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
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Mathlib/Topology/Algebra/Module/FiniteDimension.lean | LinearMap.continuous_of_nonzero_on_open | [
{
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195,
34
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188,
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Mathlib/GroupTheory/Submonoid/Pointwise.lean | Submonoid.sup_eq_closure | [
{
"state_after": "no goals",
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}
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97,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
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Mathlib/RingTheory/Nilpotent.lean | nilradical_eq_zero | [] | [
215,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
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Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.degree_gcd_le_left | [
{
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"state_before": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMon... | [
509,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
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Mathlib/RingTheory/Valuation/Integers.lean | Valuation.Integers.le_of_dvd | [
{
"state_after": "R : Type u\nΓ₀ : Type v\ninst✝⁵ : CommRing R\ninst✝⁴ : LinearOrderedCommGroupWithZero Γ₀\nv : Valuation R Γ₀\nO : Type w\ninst✝³ : CommRing O\ninst✝² : Algebra O R\ninst✝¹ : CommRing O\ninst✝ : Algebra O R\nhv : Integers v O\nx y : O\nh : x ∣ y\nz : O\nhz : y = x * z\n⊢ ↑v (↑(algebraMap O R) y... | [
99,
36
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Mathlib/Order/UpperLower/Basic.lean | upperClosure_min | [] | [
1300,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1299,
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.coeff_mul_X_sub_C | [
{
"state_after": "no goals",
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}
] | [
533,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
1
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Mathlib/Logic/Embedding/Basic.lean | Function.Embedding.coeFn_mk | [] | [
117,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Geometry/Euclidean/Sphere/Basic.lean | EuclideanGeometry.cospherical_def | [] | [
157,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
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Mathlib/CategoryTheory/Types.lean | CategoryTheory.Iso.toEquiv_symm_fun | [] | [
361,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/WidePullbacks.lean | CategoryTheory.Limits.WidePullback.hom_eq_lift | [
{
"state_after": "no goals",
"state_before": "J : Type w\nC : Type u\ninst✝² : Category C\nD : Type ?u.242573\ninst✝¹ : Category D\nB : D\nobjs : J → D\narrows : (j : J) → objs j ⟶ B\ninst✝ : HasWidePullback B objs arrows\nX : D\nf : X ⟶ B\nfs : (j : J) → X ⟶ objs j\nw : ∀ (j : J), fs j ≫ arrows j = f\ng : ... | [
368,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
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Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.isUnit_iff | [
{
"state_after": "case intro\np : ℕ\nhp : Fact (Nat.Prime p)\nz : ℤ_[p]\nh : IsUnit z\nw : ℤ_[p]\neq : 1 = z * w\n⊢ ‖z‖ = 1",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nz : ℤ_[p]\nh : IsUnit z\n⊢ ‖z‖ = 1",
"tactic": "rcases isUnit_iff_dvd_one.1 h with ⟨w, eq⟩"
},
{
"state_after": "case int... | [
452,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Mathlib/Data/Set/Basic.lean | Set.inter_diff_self | [] | [
1861,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1860,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.lift_unique' | [] | [
2000,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1998,
1
] |
Mathlib/RingTheory/Polynomial/Eisenstein/Basic.lean | Polynomial.IsEisensteinAt.Polynomial.Monic.leadingCoeff_not_mem | [] | [
202,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.measure_image_eq_zero_of_comap_eq_zero | [] | [
1344,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1340,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.disjoint_iff_not_le | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.6498\nf✝ g✝ : Ultrafilter α\ns t : Set α\np q : α → Prop\nf : Ultrafilter α\ng : Filter α\n⊢ Disjoint (↑f) g ↔ ¬↑f ≤ g",
"tactic": "rw [← inf_neBot_iff, neBot_iff, Ne.def, not_not, disjoint_iff]"
}
] | [
118,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
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Mathlib/Analysis/Complex/Basic.lean | Complex.conj_tsum | [] | [
588,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
587,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.closure_induction_left | [
{
"state_after": "M : Type u_1\nA : Type ?u.83795\nB : Type ?u.83798\ninst✝ : Monoid M\ns : Set M\np : M → Prop\nx : M\nh : x ∈ mrange (↑FreeMonoid.lift Subtype.val)\nH1 : p 1\nHmul : ∀ (x : M), x ∈ s → ∀ (y : M), p y → p (x * y)\n⊢ p x",
"state_before": "M : Type u_1\nA : Type ?u.83795\nB : Type ?u.83798\n... | [
392,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Topology/Basic.lean | Continuous.congr | [
{
"state_after": "case h.e'_5\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.162528\nδ : Type ?u.162531\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\nf g : α → β\nh : Continuous f\nh' : ∀ (x : α), f x = g x\n⊢ g = f",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?... | [
1578,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1575,
1
] |
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