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/Order/ConditionallyCompleteLattice/Basic.lean | ciSup_mem_Inter_Icc_of_antitone_Icc | [] | [
904,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
899,
1
] |
Mathlib/Data/Num/Lemmas.lean | PosNum.cmp_eq | [
{
"state_after": "α : Type ?u.392175\nm n : PosNum\nthis : Ordering.casesOn (cmp m n) (↑m < ↑n) (m = n) (↑n < ↑m)\n⊢ cmp m n = Ordering.eq ↔ m = n",
"state_before": "α : Type ?u.392175\nm n : PosNum\n⊢ cmp m n = Ordering.eq ↔ m = n",
"tactic": "have := cmp_to_nat m n"
},
{
"state_after": "α : Ty... | [
697,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
693,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.def | [] | [
167,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.sum_repr_mul_repr | [
{
"state_after": "ι : Type u_4\nι'✝ : Type ?u.761324\nR : Type u_2\nR₂ : Type ?u.761330\nK : Type ?u.761333\nM : Type u_3\nM' : Type ?u.761339\nM'' : Type ?u.761342\nV : Type u\nV' : Type ?u.761347\ninst✝⁵ : CommSemiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\ninst✝² : AddCommMonoid M'\ninst✝¹ : Modul... | [
1067,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1062,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.natAbs_valMinAbs_add_le | [
{
"state_after": "case zero\nn a✝ : ℕ\na b : ZMod Nat.zero\n⊢ Int.natAbs (valMinAbs (a + b)) ≤ Int.natAbs (valMinAbs a + valMinAbs b)\n\ncase succ\nn✝ a✝ n : ℕ\na b : ZMod (Nat.succ n)\n⊢ Int.natAbs (valMinAbs (a + b)) ≤ Int.natAbs (valMinAbs a + valMinAbs b)",
"state_before": "n✝ a✝ n : ℕ\na b : ZMod n\n⊢ ... | [
1112,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1106,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_list_count_of_subset | [
{
"state_after": "ι : Type ?u.498342\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf g : α → β\ninst✝² : CommMonoid β\ninst✝¹ : DecidableEq α\ninst✝ : CommMonoid α\nm : List α\ns : Finset α\nhs : toFinset m ⊆ s\n⊢ ∏ m_1 in toFinset m, m_1 ^ count m_1 m = ∏ i in s, i ^ count i m",
"state_b... | [
1306,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1301,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.snd_diag | [
{
"state_after": "case h\nn : ℕ\nα : TypeVec n\ni : Fin2 n\n⊢ (prod.snd ⊚ prod.diag) i = id i",
"state_before": "n : ℕ\nα : TypeVec n\n⊢ prod.snd ⊚ prod.diag = id",
"tactic": "funext i"
},
{
"state_after": "case h.fz\nn n✝ : ℕ\nα : TypeVec (succ n✝)\n⊢ (prod.snd ⊚ prod.diag) Fin2.fz = id Fin2.fz... | [
593,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
590,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.IntegrableOn.add_measure | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1518598\nE : Type u_2\nF : Type ?u.1518604\ninst✝¹ : MeasurableSpace α\ninst✝ : NormedAddCommGroup E\nf g : α → E\ns t : Set α\nμ ν : Measure α\nhμ : IntegrableOn f s\nhν : IntegrableOn f s\n⊢ Integrable f",
"state_before": "α : Type u_1\nβ : Type ?u.1518598\nE : ... | [
226,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Analysis/Calculus/TangentCone.lean | uniqueDiffOn_Icc_zero_one | [] | [
453,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.coe_injective | [] | [
569,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.sups_inter_subset_left | [] | [
172,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.refl_prod_refl | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.63296\nδ : Type ?u.63299\ne : LocalEquiv α β\ne' : LocalEquiv β γ\n⊢ prod (LocalEquiv.refl α) (LocalEquiv.refl β) = LocalEquiv.refl (α × β)",
"tactic": "ext ⟨x, y⟩ <;> simp"
}
] | [
971,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
968,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.iff_def | [] | [
340,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.mabs_sup_div_sup_le_mabs | [
{
"state_after": "case h\nα : 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 b c : α\n⊢ abs ((a ⊔ c) / (b ⊔ c)) * ?b ≤ abs (a / b)\n\ncase hle\nα : Type u\ninst✝² : Lattice α\ninst✝¹ : CommGroup α\ninst✝ : CovariantClass α α (fun x x_1... | [
538,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/RingTheory/EuclideanDomain.lean | EuclideanDomain.dvd_or_coprime | [] | [
103,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Analysis/Convex/Combination.lean | convexHull_eq_union_convexHull_finite_subsets | [
{
"state_after": "case refine'_1\nR : Type u_2\nE : Type u_1\nF : Type ?u.239379\nι : Type ?u.239382\nι' : Type ?u.239385\nα : Type ?u.239388\ninst✝⁷ : LinearOrderedField R\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : LinearOrderedAddCommGroup α\ninst✝³ : Module R E\ninst✝² : Module R F\ninst✝¹ :... | [
374,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.sum_integral_adjacent_intervals | [
{
"state_after": "ι : Type ?u.15613852\n𝕜 : Type ?u.15613855\nE : Type u_1\nF : Type ?u.15613861\nA : Type ?u.15613864\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na✝ b c d : ℝ\nf g : ℝ → E\nμ : MeasureTheory.Measure ℝ\na : ℕ → ℝ\nn : ℕ\nhint : ∀ (k : ℕ), k < n → IntervalI... | [
928,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
924,
1
] |
Mathlib/Order/Hom/Lattice.lean | SupHom.bot_apply | [] | [
505,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | exp_neg_of_mem_ball | [] | [
362,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Order/SymmDiff.lean | disjoint_symmDiff_inf | [
{
"state_after": "ι : Type ?u.59758\nα : Type u_1\nβ : Type ?u.59764\nπ : ι → Type ?u.59769\ninst✝ : GeneralizedBooleanAlgebra α\na b c d : α\n⊢ Disjoint ((a ⊔ b) \\ (a ⊓ b)) (a ⊓ b)",
"state_before": "ι : Type ?u.59758\nα : Type u_1\nβ : Type ?u.59764\nπ : ι → Type ?u.59769\ninst✝ : GeneralizedBooleanAlgeb... | [
403,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.valMinAbs_natAbs_eq_min | [
{
"state_after": "n✝ a✝ n : ℕ\nhpos : NeZero n\na : ZMod n\n⊢ Int.natAbs (if val a ≤ n / 2 then ↑(val a) else ↑(val a) - ↑n) = min (val a) (n - val a)",
"state_before": "n✝ a✝ n : ℕ\nhpos : NeZero n\na : ZMod n\n⊢ Int.natAbs (valMinAbs a) = min (val a) (n - val a)",
"tactic": "rw [valMinAbs_def_pos]"
... | [
1065,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1049,
1
] |
Mathlib/Data/Fintype/Basic.lean | Finset.codisjoint_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.4270\nγ : Type ?u.4273\ninst✝ : Fintype α\ns t : Finset α\n⊢ Codisjoint s t ↔ ∀ ⦃a : α⦄, ¬a ∈ s → a ∈ t",
"tactic": "classical simp [codisjoint_iff, eq_univ_iff_forall, or_iff_not_imp_left]"
},
{
"state_after": "no goals",
... | [
146,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.continuous_eval_const | [] | [
326,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/Data/Set/Image.lean | Set.exists_image_iff | [] | [
582,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.map_comp_proj | [] | [
320,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Analysis/Convex/Between.lean | wbtw_self_iff | [
{
"state_after": "case refine'_1\nR : Type u_1\nV : Type u_2\nV' : Type ?u.153895\nP : Type u_3\nP' : Type ?u.153901\ninst✝⁶ : OrderedRing R\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddTorsor V P\ninst✝² : AddCommGroup V'\ninst✝¹ : Module R V'\ninst✝ : AddTorsor V' P'\nx y : P\nh : Wbtw R x y x\n... | [
307,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Algebra/Order/Sub/Canonical.lean | tsub_lt_self_iff | [] | [
482,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/LinearAlgebra/Orientation.lean | Orientation.map_refl | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁴ : StrictOrderedCommSemiring R\nM : Type u_2\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\nN : Type ?u.10058\ninst✝¹ : AddCommMonoid N\ninst✝ : Module R N\nι : Type u_3\n⊢ map ι (LinearEquiv.refl R M) = Equiv.refl (Orientation R M ι)",
... | [
83,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Algebra/Category/ModuleCat/Monoidal/Basic.lean | ModuleCat.MonoidalCategory.associator_naturality | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : CommRing R\nX₁ : ModuleCat R\nX₂ : ModuleCat R\nX₃ : ModuleCat R\nY₁ : ModuleCat R\nY₂ : ModuleCat R\nY₃ : ModuleCat R\nf₁ : X₁ ⟶ Y₁\nf₂ : X₂ ⟶ Y₂\nf₃ : X₃ ⟶ Y₃\n⊢ tensorHom (tensorHom f₁ f₂) f₃ ≫ (associator Y₁ Y₂ Y₃).hom =\n (associator ... | [
127,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.head_cons | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\na : α\ns : Seq α\n⊢ head (cons a s) = some a",
"tactic": "rw [head_eq_destruct, destruct_cons, Option.map_eq_map, Option.map_some']"
}
] | [
262,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.toAddSubmonoid_eq | [] | [
135,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Data/Quot.lean | Quotient.ind' | [] | [
653,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
651,
11
] |
Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.adjoin_iUnion | [] | [
75,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/FieldTheory/Minpoly/Field.lean | minpoly.eq_X_sub_C | [] | [
212,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.coe_natCast | [] | [
1290,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1290,
1
] |
Mathlib/CategoryTheory/IsConnected.lean | CategoryTheory.zigzag_equivalence | [] | [
274,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Data/List/Intervals.lean | List.Ico.chain'_succ | [
{
"state_after": "case pos\nn m : ℕ\nh : n < m\n⊢ Chain' (fun a b => b = succ a) (Ico n m)\n\ncase neg\nn m : ℕ\nh : ¬n < m\n⊢ Chain' (fun a b => b = succ a) (Ico n m)",
"state_before": "n m : ℕ\n⊢ Chain' (fun a b => b = succ a) (Ico n m)",
"tactic": "by_cases n < m"
},
{
"state_after": "case po... | [
150,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_eq_mul_iff_eq_and_eq_of_pos | [
{
"state_after": "case inl\nα : Type u_1\na c d : α\ninst✝⁵ : MulZeroClass α\ninst✝⁴ : PartialOrder α\ninst✝³ : PosMulStrictMono α\ninst✝² : MulPosStrictMono α\ninst✝¹ : PosMulMonoRev α\ninst✝ : MulPosMonoRev α\nhbd : c ≤ d\na0 : 0 < a\nd0 : 0 < d\nhac : a ≤ a\nh : a * c = a * d\n⊢ a = a ∧ c = d\n\ncase inr\nα ... | [
539,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | AddValuation.map_lt_add | [] | [
696,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
695,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.continuousAt_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.100766\nι : Type ?u.100769\ninst✝¹ : PseudoMetricSpace α\nx y z : α\nδ ε ε₁ ε₂ : ℝ\ns : Set α\ninst✝ : PseudoMetricSpace β\nf : α → β\na : α\n⊢ ContinuousAt f a ↔ ∀ (ε : ℝ), ε > 0 → ∃ δ, δ > 0 ∧ ∀ {x : α}, dist x a < δ → dist ... | [
1054,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1052,
1
] |
Mathlib/Data/Nat/Log.lean | Nat.log_eq_one_iff' | [
{
"state_after": "no goals",
"state_before": "b n : ℕ\n⊢ log b n = 1 ↔ b ≤ n ∧ n < b * b",
"tactic": "rw [log_eq_iff (Or.inl one_ne_zero), pow_add, pow_one]"
}
] | [
165,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Order/Basic.lean | strongLT_of_strongLT_of_le | [] | [
838,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
837,
1
] |
Mathlib/Data/Set/Basic.lean | Set.Nontrivial.ne_empty | [] | [
2528,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2527,
11
] |
Mathlib/LinearAlgebra/Basis.lean | atom_iff_nonzero_span | [
{
"state_after": "case refine'_1\nι : Type ?u.1173697\nι' : Type ?u.1173700\nR : Type ?u.1173703\nR₂ : Type ?u.1173706\nK : Type u_1\nM : Type ?u.1173712\nM' : Type ?u.1173715\nM'' : Type ?u.1173718\nV : Type u\nV' : Type ?u.1173723\ninst✝⁴ : DivisionRing K\ninst✝³ : AddCommGroup V\ninst✝² : AddCommGroup V'\nin... | [
1550,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1539,
1
] |
Mathlib/Tactic/CancelDenoms.lean | CancelDenoms.sub_subst | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Ring α\nn e1 e2 t1 t2 : α\nh1 : n * e1 = t1\nh2 : n * e2 = t2\n⊢ n * (e1 - e2) = t1 - t2",
"tactic": "simp [left_distrib, *, sub_eq_add_neg]"
}
] | [
58,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Analysis/NormedSpace/Basic.lean | rescale_to_shell | [] | [
416,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.eval_assoc | [
{
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1171,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1167,
1
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Mathlib/MeasureTheory/Measure/GiryMonad.lean | MeasureTheory.Measure.lintegral_bind | [] | [
188,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
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Mathlib/Logic/Basic.lean | pi_congr | [] | [
621,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
620,
1
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Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.norm_eq_ciSup | [
{
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401,
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399,
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Mathlib/Data/Real/ENNReal.lean | ENNReal.le_of_top_imp_top_of_toNNReal_le | [
{
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926,
23
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920,
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Mathlib/Algebra/Hom/Units.lean | IsUnit.div_div_cancel | [
{
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"tactic": "rw [div_div_eq_mul_div, h.mul_div_cancel_left]"
}
] | [
505,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
11
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Mathlib/Analysis/Convex/Function.lean | ConvexOn.dual | [] | [
82,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
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Mathlib/Logic/Nontrivial.lean | nontrivial_of_lt | [] | [
67,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
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Mathlib/Data/List/Basic.lean | List.nthLe_set_eq | [] | [
1572,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1571,
1
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Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.lintegral_fn_integral_sub | [
{
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386,
30
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380,
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEFinStronglyMeasurable.ae_eq_zero_compl | [] | [
1947,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1945,
1
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Mathlib/Algebra/Lie/Matrix.lean | Matrix.lieConj_symm_apply | [
{
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"tactic": "simp [LinearEquiv.symm_conj_apply, Matrix.lieConj, LinearMap.toMatrix'... | [
83,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
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Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.surj | [] | [
129,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
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Mathlib/Data/Set/Function.lean | StrictMonoOn.comp_strictAntiOn | [] | [
1561,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1558,
1
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Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.extend_empty | [] | [
1378,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1377,
1
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Mathlib/Analysis/Calculus/MeanValue.lean | exists_ratio_hasDerivAt_eq_ratio_slope' | [
{
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749,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
728,
1
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Mathlib/Order/SuccPred/Basic.lean | Order.Ioc_pred_left | [] | [
741,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
1
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Std/Data/Int/DivMod.lean | Int.div_sign | [
{
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"tactic": "simp [sign, Int.mul_one]"
},
{
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"state_before": "x✝ : Int\n⊢ div x✝ (sign 0) = x✝ * sign 0",
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... | [
827,
58
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
824,
1
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Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.mul_mem | [] | [
177,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
11
] |
Mathlib/Data/Real/Basic.lean | Real.ofCauchy_zero | [] | [
116,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.Nonempty.to_type | [] | [
523,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
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Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.coeFn_abs | [
{
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881,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
877,
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Mathlib/Data/List/Basic.lean | List.getLast_concat' | [] | [
721,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
720,
1
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Mathlib/Data/Set/Image.lean | Set.mem_range | [] | [
651,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
650,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.finset_card_lt_aleph0 | [] | [
2063,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2062,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.HasFiniteIntegral.add_measure | [
{
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198,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
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Mathlib/Data/PNat/Prime.lean | Nat.Primes.coe_pnat_inj | [] | [
44,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Std/Logic.lean | Decidable.not_iff_not | [
{
"state_after": "a b : Prop\ninst✝¹ : Decidable a\ninst✝ : Decidable b\n⊢ (¬a → ¬b) ∧ (¬b → ¬a) ↔ (b → a) ∧ (a → b)",
"state_before": "a b : Prop\ninst✝¹ : Decidable a\ninst✝ : Decidable b\n⊢ (¬a ↔ ¬b) ↔ (a ↔ b)",
"tactic": "rw [@iff_def (¬a), @iff_def' a]"
},
{
"state_after": "no goals",
"... | [
577,
75
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
576,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_neg_uIcc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\na b c d : α\n⊢ -[[a, b]] = [[-a, -b]]",
"tactic": "simp only [← Icc_min_max, preimage_neg_Icc, min_neg_neg, max_neg_neg]"
}
] | [
441,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/Order/BoundedOrder.lean | max_bot_left | [] | [
847,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
846,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.idZeroEquivIsoZero_apply_inv | [] | [
431,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/Data/Set/Image.lean | Function.Surjective.preimage_injective | [] | [
1283,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1282,
1
] |
Mathlib/Order/WithBot.lean | WithBot.none_eq_bot | [] | [
79,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_update_of_not_mem | [
{
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1615,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1608,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.inter_div_union_subset_union | [] | [
686,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_add_aux | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.853934\nγ : Type ?u.853937\nδ : Type ?u.853940\nm : MeasurableSpace α\nμ ν : Measure α\nf g : α → ℝ≥0∞\nhf : Measurable f\nhg : Measurable g\n⊢ (∫⁻ (a : α), f a + g a ∂μ) = ∫⁻ (a : α), (⨆ (n : ℕ), ↑(eapprox f n) a) + ⨆ (n : ℕ), ↑(eappro... | [
563,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
536,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Lemmas.lean | mul_mul_div | [] | [
128,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.upperClosure | [] | [
1317,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1316,
11
] |
Mathlib/Data/Finset/Basic.lean | Finset.induction_on' | [] | [
1235,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1229,
1
] |
Mathlib/LinearAlgebra/Matrix/ZPow.lean | Matrix.zpow_sub | [
{
"state_after": "no goals",
"state_before": "n' : Type u_1\ninst✝² : DecidableEq n'\ninst✝¹ : Fintype n'\nR : Type u_2\ninst✝ : CommRing R\nA : M\nha : IsUnit (det A)\nz1 z2 : ℤ\n⊢ A ^ (z1 - z2) = A ^ z1 / A ^ z2",
"tactic": "rw [sub_eq_add_neg, zpow_add ha, zpow_neg ha, div_eq_mul_inv]"
}
] | [
307,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisInsertion.l_sSup_u_image | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\nκ : ι → Sort ?u.39544\na a₁ a₂ : α\nb b₁ b₂ : β\nl : α → β\nu : β → α\ninst✝¹ : CompleteLattice α\ninst✝ : CompleteLattice β\ngi : GaloisInsertion l u\ns : Set β\n⊢ l (sSup (u '' s)) = sSup s",
"tactic": "rw [s... | [
553,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
1
] |
Mathlib/Data/TwoPointing.lean | TwoPointing.bool_snd | [] | [
153,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.invRev_injective | [] | [
584,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
] |
Mathlib/RingTheory/Ideal/IdempotentFG.lean | Ideal.isIdempotentElem_iff_eq_bot_or_top | [
{
"state_after": "case mp\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nI : Ideal R\nh : FG I\n⊢ IsIdempotentElem I → I = ⊥ ∨ I = ⊤\n\ncase mpr\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nI : Ideal R\nh : FG I\n⊢ I = ⊥ ∨ I = ⊤ → IsIdempotentElem I",
"state_before": "R : Type u_1\ninst✝... | [
49,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.max_eq_zero | [] | [
1014,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1013,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.mem_ball | [] | [
531,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
9
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.isCompact_image | [] | [
262,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/LinearAlgebra/Ray.lean | Module.Ray.ind | [] | [
263,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | VectorBundleCore.localTriv_coordChange_eq | [
{
"state_after": "case a\nR : Type u_2\nB : Type u_1\nF : Type u_3\nE : B → Type ?u.414625\ninst✝⁸ : NontriviallyNormedField R\ninst✝⁷ : (x : B) → AddCommMonoid (E x)\ninst✝⁶ : (x : B) → Module R (E x)\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace R F\ninst✝³ : TopologicalSpace B\ninst✝² : TopologicalSpa... | [
732,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
729,
1
] |
Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.sup_factors_of_factors_right | [] | [
535,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
1
] |
Mathlib/Topology/Order/Basic.lean | pi_Ioi_mem_nhds | [] | [
1496,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1495,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.top_prod_top | [] | [
680,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
679,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | IsAbsoluteValue.abv_sum | [] | [
749,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
747,
1
] |
Mathlib/Topology/Separation.lean | IsCompact.isClosed | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝³ : TopologicalSpace α\nγ : Type ?u.129636\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : T2Space α\ns : Set α\nhs : IsCompact s\nx : α\nhx : x ∈ sᶜ\nu v : Set α\nleft✝ : IsOpen u\nvo : IsOpen v\nsu : s ⊆ u\nxv : ... | [
1266,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1262,
1
] |
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