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/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.mem_verts_if_mem_edge | [
{
"state_after": "ι : Sort ?u.10234\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : Subgraph G\na b : V\nG' : Subgraph G\ne : Sym2 V\nv : V\nhe : e ∈ edgeSet G'\n⊢ v ∈ e → v ∈ G'.verts",
"state_before": "ι : Sort ?u.10234\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : Subgraph G\na b : V\nG' : Subg... | [
253,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.mul_assoc | [
{
"state_after": "no goals",
"state_before": "a b c : ℚ\nn₁ : ℤ\nd₁ : ℕ\nh₁ : d₁ ≠ 0\nn₂ : ℤ\nd₂ : ℕ\nh₂ : d₂ ≠ 0\nn₃ : ℤ\nd₃ : ℕ\nh₃ : d₃ ≠ 0\n⊢ n₁ /. ↑d₁ * (n₂ /. ↑d₂) * (n₃ /. ↑d₃) = n₁ /. ↑d₁ * (n₂ /. ↑d₂ * (n₃ /. ↑d₃))",
"tactic": "simp [h₁, h₂, h₃, mul_ne_zero, mul_comm, mul_assoc, mul_left_comm]"... | [
269,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
11
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Mathlib/Analysis/Convex/Side.lean | AffineSubspace.WOppSide.trans_sSameSide | [] | [
584,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
582,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.subset_vanishingIdeal_zeroLocus | [] | [
162,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.encdec | [] | [
241,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.bounded_range_of_tendsto_cofinite | [] | [
2445,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2442,
1
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Std/Data/List/Lemmas.lean | List.forM_append | [
{
"state_after": "no goals",
"state_before": "m : Type u_1 → Type u_2\nα : Type u_3\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nl₁ l₂ : List α\nf : α → m PUnit\n⊢ List.forM (l₁ ++ l₂) f = do\n List.forM l₁ f\n List.forM l₂ f",
"tactic": "induction l₁ <;> simp [*]"
}
] | [
1484,
82
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1483,
9
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Mathlib/Topology/UniformSpace/Basic.lean | lift_nhds_left | [
{
"state_after": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.77543\ninst✝ : UniformSpace α\nx : α\ng : Set α → Filter β\nhg : Monotone g\n⊢ Filter.lift (𝓤 α) (g ∘ preimage (Prod.mk x)) = Filter.lift (𝓤 α) fun s => g (ball x s)",
"state_before": "α : Type ua\nβ : Type ub\nγ : Type uc\n... | [
870,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
867,
1
] |
Mathlib/Analysis/InnerProductSpace/Positive.lean | ContinuousLinearMap.IsPositive.orthogonalProjection_comp | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.275809\ninst✝⁷ : IsROrC 𝕜\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : InnerProductSpace 𝕜 E\ninst✝³ : InnerProductSpace 𝕜 F\ninst✝² : CompleteSpace E\ninst✝¹ : CompleteSpace F\nT : E →L[𝕜] E\nhT : IsPositive T\nU : Submod... | [
118,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Analysis/Calculus/FDerivMeasurable.lean | measurableSet_of_differentiableAt_of_isComplete | [
{
"state_after": "𝕜 : Type u_3\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_1\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nf : E → F\nK✝ : Set (E →L[𝕜] F)\ninst✝¹ : MeasurableSpace E\ninst✝ : OpensMeasurableSpace E\nK : ... | [
396,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
1
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Mathlib/Data/Vector.lean | Vector.toList_nil | [] | [
222,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidHom.comp_apply | [] | [
423,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.exists_eq_succ_of_ne_zero | [] | [
308,
50
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
307,
1
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Mathlib/RingTheory/Localization/Away/Basic.lean | IsLocalization.away_of_isUnit_of_bijective | [
{
"state_after": "case mk.intro\nR✝ : Type ?u.305976\ninst✝⁷ : CommSemiring R✝\nM : Submonoid R✝\nS✝ : Type ?u.306165\ninst✝⁶ : CommSemiring S✝\ninst✝⁵ : Algebra R✝ S✝\nP : Type ?u.306345\ninst✝⁴ : CommSemiring P\ninst✝³ : IsLocalization M S✝\nR : Type u_1\nS : Type u_2\ninst✝² : CommRing R\ninst✝¹ : CommRing S... | [
168,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Std/Data/Option/Lemmas.lean | Option.liftOrGet_eq_or_eq | [
{
"state_after": "α : Type u_1\nf : α → α → α\nh : ∀ (a b : α), f a b = a ∨ f a b = b\na b : α\nthis : f a b = a ∨ f a b = b\n⊢ liftOrGet f (some a) (some b) = some a ∨ liftOrGet f (some a) (some b) = some b",
"state_before": "α : Type u_1\nf : α → α → α\nh : ∀ (a b : α), f a b = a ∨ f a b = b\na b : α\n⊢ l... | [
182,
79
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
177,
1
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Mathlib/Order/SuccPred/Basic.lean | Order.pred_eq_iff_isMin | [] | [
769,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
768,
1
] |
Mathlib/Algebra/Order/Rearrangement.lean | Monovary.sum_comp_perm_mul_le_sum_mul | [] | [
480,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/MeasureTheory/Measure/Sub.lean | MeasureTheory.Measure.zero_sub | [] | [
64,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.IntegrableOn.restrict_toMeasurable | [
{
"state_after": "case intro.intro.intro\nα : Type u_1\nβ : Type ?u.1644972\nE : Type u_2\nF : Type ?u.1644978\ninst✝¹ : MeasurableSpace α\ninst✝ : NormedAddCommGroup E\nf g : α → E\ns t : Set α\nμ ν : Measure α\nhf : IntegrableOn f s\nh's : ∀ (x : α), x ∈ s → f x ≠ 0\nu : ℕ → ℝ\nleft✝ : StrictAnti u\nu_pos : ∀... | [
308,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.iUnion_div | [] | [
756,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
755,
1
] |
Mathlib/Algebra/Order/Group/Abs.lean | le_abs' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\na b c d : α\n⊢ a ≤ abs b ↔ b ≤ -a ∨ a ≤ b",
"tactic": "rw [le_abs, or_comm, @le_neg α]"
}
] | [
240,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Analysis/InnerProductSpace/Adjoint.lean | LinearMap.im_inner_adjoint_mul_self_eq_zero | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.2366720\nG : Type ?u.2366723\ninst✝⁹ : IsROrC 𝕜\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedAddCommGroup G\ninst✝⁵ : InnerProductSpace 𝕜 E\ninst✝⁴ : InnerProductSpace 𝕜 F\ninst✝³ : InnerProductSpace 𝕜 G\ninst✝² : Fi... | [
523,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
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Mathlib/Data/Nat/Factorization/Basic.lean | Nat.factorization_mul_of_coprime | [
{
"state_after": "case h\na b : ℕ\nhab : coprime a b\nq : ℕ\n⊢ ↑(factorization (a * b)) q = ↑(factorization a + factorization b) q",
"state_before": "a b : ℕ\nhab : coprime a b\n⊢ factorization (a * b) = factorization a + factorization b",
"tactic": "ext q"
},
{
"state_after": "no goals",
"s... | [
761,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
758,
1
] |
Mathlib/Data/Set/Basic.lean | Set.exists_eq_singleton_iff_nonempty_subsingleton | [
{
"state_after": "case refine'_1\nα : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns s₁ s₂ t t₁ t₂ u : Set α\n⊢ (∃ a, s = {a}) → Set.Nonempty s ∧ Set.Subsingleton s\n\ncase refine'_2\nα : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns s₁ s₂ t t₁ t₂ u : Set α\nh : Set.Nonempty s ∧ Set.Subsingleto... | [
2405,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2400,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.liftRel_join.lem | [
{
"state_after": "case intro\nα : Type u\nβ : Type v\nγ : Type w\nR : α → β → Prop\nS : WSeq (WSeq α)\nT : WSeq (WSeq β)\nU : WSeq α → WSeq β → Prop\nST : LiftRel (LiftRel R) S T\nHU :\n ∀ (s1 : WSeq α) (s2 : WSeq β),\n (∃ s t S T, s1 = append s (join S) ∧ s2 = append t (join T) ∧ LiftRel R s t ∧ LiftRel (L... | [
1638,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1589,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.not_mem_of_coe_lt_min | [] | [
1289,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1288,
1
] |
Mathlib/RingTheory/WittVector/Basic.lean | WittVector.ghostFun_one | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nR : Type u_1\nS : Type ?u.650613\nT : Type ?u.650616\nhp : Fact (Nat.Prime p)\ninst✝² : CommRing R\ninst✝¹ : CommRing S\ninst✝ : CommRing T\nα : Type ?u.650631\nβ : Type ?u.650634\nx y : 𝕎 R\n⊢ WittVector.ghostFun 1 = 1",
"tactic": "ghost_fun_tac 1, ... | [
193,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
9
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.mul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.27631\nf g : α → β\nc c₁ c₂ x : α\ninst✝¹ : Add α\ninst✝ : Mul β\nhf : Periodic f c\nhg : Periodic g c\n⊢ Periodic (f * g) c",
"tactic": "simp_all"
}
] | [
71,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
11
] |
Mathlib/Algebra/Associated.lean | Associates.mul_eq_one_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.285626\nγ : Type ?u.285629\nδ : Type ?u.285632\ninst✝ : CommMonoid α\nx y : Associates α\na b : α\nh : Quotient.mk (Associated.setoid α) a * Quotient.mk (Associated.setoid α) b = 1\nthis : a * b ~ᵤ 1\n⊢ b * ?m.287732 a b h this ~ᵤ 1",
... | [
870,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
864,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.angle_neg_self_of_nonzero | [
{
"state_after": "no goals",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y x : V\nhx : x ≠ 0\n⊢ angle (-x) x = π",
"tactic": "rw [angle_comm, angle_self_neg_of_nonzero hx]"
}
] | [
150,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/NumberTheory/RamificationInertia.lean | Ideal.le_comap_of_ramificationIdx_ne_zero | [] | [
142,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.le_rootMultiplicity_iff | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\na✝ b : R\nn✝ : ℕ\ninst✝ : CommRing R\np : R[X]\np0 : p ≠ 0\na : R\nn : ℕ\n⊢ (∀ (m : ℕ), m < n → ¬¬(X - ↑C a) ^ (m + 1) ∣ p) ↔ (X - ↑C a) ^ n ∣ p",
"state_before": "R : Type u\nS : Type v\nT : Type w\na✝ b : R\nn✝ : ℕ\ninst✝ : CommRing R\np : R[X]\np0 : p... | [
377,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.iUnion_def | [] | [
69,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/LinearAlgebra/Ray.lean | Module.Ray.units_smul_of_pos | [
{
"state_after": "case h\nR : Type u_1\ninst✝⁵ : StrictOrderedCommSemiring R\nM : Type u_2\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nN : Type ?u.131381\ninst✝² : AddCommMonoid N\ninst✝¹ : Module R N\nι : Type ?u.131463\ninst✝ : DecidableEq ι\nu : Rˣ\nhu : 0 < ↑u\nv✝ : M\nhv✝ : v✝ ≠ 0\n⊢ u • rayOfNeZero R ... | [
355,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_mono_nnreal | [] | [
139,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Algebra/Lie/Solvable.lean | LieAlgebra.derivedSeriesOfIdeal_succ | [] | [
71,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/SetTheory/Cardinal/Finite.lean | Nat.finite_of_card_ne_zero | [] | [
53,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/CategoryTheory/Functor/Functorial.lean | CategoryTheory.Functorial.map_id | [] | [
54,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Order/FixedPoints.lean | OrderHom.le_map_sup_fixedPoints | [] | [
247,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_non_aestronglyMeasurable | [] | [
840,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
839,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.eq_span_singleton_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u\nι : Type ?u.243853\ninst✝ : CommSemiring R\nI✝ J✝ K L : Ideal R\nx : R\nI J : Ideal R\n⊢ I = span {x} * J ↔ (∀ (zI : R), zI ∈ I → ∃ zJ, zJ ∈ J ∧ x * zJ = zI) ∧ ∀ (z : R), z ∈ J → x * z ∈ I",
"tactic": "simp only [le_antisymm_iff, le_span_singleto... | [
601,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
599,
1
] |
Mathlib/Topology/Maps.lean | IsOpenMap.comp | [
{
"state_after": "α : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.139304\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\nf✝ : α → β\ng : β → γ\nf : α → β\nhg : IsOpenMap g\nhf : IsOpenMap f\ns : Set α\nhs : IsOpen s\n⊢ IsOpen (g '' (f '' s))",
"state_before": "α ... | [
350,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
11
] |
Mathlib/Algebra/BigOperators/Order.lean | Finset.prod_le_prod_of_ne_one' | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : Type ?u.118811\nβ : Type ?u.118814\nM : Type u_2\nN : Type ?u.118820\nG : Type ?u.118823\nk : Type ?u.118826\nR : Type ?u.118829\ninst✝ : CanonicallyOrderedMonoid M\nf : ι → M\ns t : Finset ι\nh : ∀ (x : ι), x ∈ s → f x ≠ 1 → x ∈ t\n⊢ ∏ x in s,... | [
429,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Mathlib/Analysis/Calculus/Deriv/Polynomial.lean | Polynomial.differentiableAt_aeval | [] | [
108,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
11
] |
Mathlib/Topology/ContinuousOn.lean | ContinuousWithinAt.preimage_mem_nhdsWithin | [] | [
929,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
927,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | comap_swap_uniformity | [] | [
532,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
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Mathlib/CategoryTheory/Shift/Basic.lean | CategoryTheory.shift_shift' | [
{
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394,
28
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391,
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Mathlib/Algebra/Star/StarAlgHom.lean | NonUnitalStarAlgHom.coe_zero | [] | [
277,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
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Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.testAgainstNN_one | [
{
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361,
6
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359,
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Mathlib/LinearAlgebra/Basis.lean | Basis.exists_basis | [] | [
1497,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1496,
1
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Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.lim_neg | [
{
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397,
39
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393,
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Mathlib/Order/PartialSups.lean | partialSups_disjoint_of_disjoint | [
{
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148,
49
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143,
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Mathlib/Order/Bounded.lean | Set.bounded_le_iff_bounded_lt | [
{
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"state_before": "α : Type u_1\nr : α → α → Prop\ns t : Set α\ninst✝¹ : Preorder α\ninst✝ : NoMaxOrder α\n⊢ Bounded (fun x x_1 =... | [
115,
53
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110,
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Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.seq_apply | [
{
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129,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
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Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.prod.lift_snd | [] | [
635,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
633,
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.prod_subtypeDomain_index | [
{
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1064,
101
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1061,
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Mathlib/Data/Nat/Prime.lean | Int.prime_three | [] | [
813,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
812,
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycle.eq_swap_of_apply_apply_eq_self | [
{
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515,
16
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498,
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Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.IsThreeCycle.cycleType | [] | [
568,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
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Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.SimpleFunc.memℒp_of_isFiniteMeasure | [] | [
393,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
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Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.IsOrthoᵢ.separatingLeft_of_not_isOrtho_basis_self | [
{
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814,
40
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797,
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Mathlib/Algebra/GeomSum.lean | Nat.geom_sum_le | [
{
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430,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
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Mathlib/Algebra/DirectSum/Internal.lean | DirectSum.coe_mul_apply_eq_dfinsupp_sum | [
{
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179,
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167,
1
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Mathlib/GroupTheory/Coset.lean | QuotientGroup.mk_surjective | [] | [
473,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
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Mathlib/Deprecated/Subring.lean | RingHom.isSubring_set_range | [] | [
72,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
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Mathlib/Order/Bounds/Basic.lean | Monotone.map_bddBelow | [] | [
1290,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1289,
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Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.X.mul_fst | [] | [
238,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
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Mathlib/RingTheory/Ideal/AssociatedPrime.lean | associatedPrimes.subset_of_injective | [] | [
113,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
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Mathlib/Data/List/Sort.lean | List.perm_merge | [
{
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"state_before": "α : Type uu\nr : α → α → Prop\ninst✝ : DecidableRel r\n⊢ merge r [] [] ~ [] ++ []",
"tactic": "simp [merge]"
},
{
"state_after": "no goals",
"state_before": "α : Type uu\nr : α → α → Prop\ninst✝ : DecidableRel r\nb : α\nl' : List α\n⊢ merge r [] ... | [
386,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
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Mathlib/Data/Set/Intervals/Instances.lean | Set.Icc.coe_zero | [] | [
61,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
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Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.coe_trans | [] | [
313,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
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Mathlib/Analysis/Convex/Integral.lean | ConcaveOn.le_map_set_average | [] | [
204,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
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Mathlib/Data/Fin/Tuple/Basic.lean | Fin.append_left_eq_cons | [
{
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362,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
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Mathlib/Data/Set/Basic.lean | Set.univ_unique | [] | [
719,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
718,
1
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Mathlib/Data/Set/Image.lean | Set.exists_range_iff' | [
{
"state_after": "no goals",
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"tactic": "simpa only [exists_prop] using exists_range_iff"
}
] | [
674,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
673,
1
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Mathlib/Algebra/Order/Floor.lean | Nat.le_ceil | [] | [
303,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/Topology/Homotopy/HSpaces.lean | Path.continuous_delayReflLeft | [] | [
278,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/Data/List/Basic.lean | List.pmap_eq_map | [
{
"state_after": "no goals",
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"tactic": "induction l <;> [rfl; simp only [*, pmap, map]]"
}
] | [
3090,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3088,
1
] |
Mathlib/GroupTheory/Complement.lean | Subgroup.isComplement_singleton_right | [
{
"state_after": "G : Type u_1\ninst✝ : Group G\nH K : Subgroup G\nS T : Set G\ng : G\nh : IsComplement S {g}\nx : G\nx✝ : x ∈ ⊤\n⊢ x ∈ S",
"state_before": "G : Type u_1\ninst✝ : Group G\nH K : Subgroup G\nS T : Set G\ng : G\n⊢ IsComplement S {g} ↔ S = ⊤",
"tactic": "refine'\n ⟨fun h => top_le_iff.mp f... | [
142,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Algebra/Algebra/Spectrum.lean | spectrum.ne_zero_of_mem_of_unit | [] | [
201,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Data/Finite/Defs.lean | Finite.false | [] | [
133,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
11
] |
Mathlib/Algebra/GroupPower/Basic.lean | zpow_neg | [
{
"state_after": "α : Type u_1\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : DivisionMonoid α\na✝ b a : α\n⊢ a ^ 0 = (a ^ 0)⁻¹",
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340,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.map_bot | [] | [
1564,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1563,
1
] |
Mathlib/MeasureTheory/Covering/VitaliFamily.lean | VitaliFamily.FineSubfamilyOn.covering_disjoint | [] | [
139,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Analysis/Complex/Basic.lean | IsROrC.conj_tsum | [] | [
501,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
500,
1
] |
Mathlib/Data/Finite/Defs.lean | Equiv.finite_iff | [] | [
79,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/CategoryTheory/Monoidal/OfChosenFiniteProducts/Basic.lean | CategoryTheory.Limits.BinaryFan.swap_fst | [] | [
55,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/RingTheory/Algebraic.lean | inv_eq_of_aeval_divX_ne_zero | [
{
"state_after": "R : Type ?u.584800\nS : Type ?u.584803\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDomain R\ninst✝³ : CommRing S\nK : Type u_1\nL : Type u_2\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Algebra K L\nA : Subalgebra K L\nx : L\np : K[X]\naeval_ne : ↑(aeval x) (divX p) ≠ 0\n⊢ ↑(aeval x) p = ↑(aeval x) (divX... | [
347,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean | ContDiffAt.arctan | [] | [
214,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | isNoetherian_adjoin_finset | [] | [
249,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/RingTheory/Bezout.lean | IsBezout.gcd_dvd_right | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹ : CommRing R\ninst✝ : IsBezout R\nx y : R\n⊢ y ∈ {x, y}",
"tactic": "simp"
}
] | [
76,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.cosh_sub | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ cosh (x - y) = cosh x * cosh y - sinh x * sinh y",
"tactic": "simp [sub_eq_add_neg, cosh_add, sinh_neg, cosh_neg]"
}
] | [
641,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
640,
1
] |
Mathlib/Algebra/Support.lean | Function.support_mul_subset_right | [
{
"state_after": "no goals",
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366,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
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] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.prod.pentagon | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\nX✝ Y✝ : C\ninst✝ : HasBinaryProducts C\nW X Y Z : C\n⊢ map (associator W X Y).hom (𝟙 Z) ≫ (associator W (X ⨯ Y) Z).hom ≫ map (𝟙 W) (associator X Y Z).hom =\n (associator (W ⨯ X) Y Z).hom ≫ (associator W X (Y ⨯ Z)).hom",
... | [
1037,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1033,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | Measurable.sumElim | [] | [
1012,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1010,
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] |
Mathlib/Data/Real/Pi/Wallis.lean | Real.Wallis.W_succ | [] | [
57,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Data/Part.lean | Part.map_some | [] | [
460,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/MeasureTheory/Covering/Differentiation.lean | VitaliFamily.measure_le_mul_of_subset_limRatioMeas_lt | [
{
"state_after": "α : Type u_1\ninst✝⁵ : MetricSpace α\nm0 : MeasurableSpace α\nμ : MeasureTheory.Measure α\nv : VitaliFamily μ\nE : Type ?u.3718349\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : SecondCountableTopology α\ninst✝² : BorelSpace α\ninst✝¹ : IsLocallyFiniteMeasure μ\nρ : MeasureTheory.Measure α\ninst✝ : ... | [
466,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/Topology/Order.lean | nhds_false | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.47259\ninst✝ : TopologicalSpace α\n⊢ (⨅ (s : Set Prop) (_ : s ∈ {s | False ∈ s ∧ s ∈ {{True}}}), 𝓟 s) = ⊤",
"tactic": "simp [@and_comm (_ ∈ _)]"
}
] | [
912,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
1
] |
Mathlib/Order/Bounds/Basic.lean | mem_upperBounds | [] | [
87,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
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