file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/Set/Lattice.lean | Set.sUnion_image | [] | [
1168,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1167,
1
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.self_le_factorial | [] | [
147,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.forM_eq_forM_toList | [
{
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"state_before": "m : Type u_1 → Type u_2\nα : Type u_3\nf : α → m PUnit\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nt : RBNode α\n⊢ forM f t = List.forM (toList t) f",
"tactic": "induction t <;> simp [*]"
}
] | [
350,
71
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
349,
1
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Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsColimit.OfNatIso.coconeOfHom_homOfCocone | [
{
"state_after": "J : Type u₁\ninst✝² : Category J\nK : Type u₂\ninst✝¹ : Category K\nC : Type u₃\ninst✝ : Category C\nF : J ⥤ C\nt : Cocone F\nX : C\nh : coyoneda.obj X.op ⋙ uliftFunctor ≅ Functor.cocones F\ns : Cocone F\n⊢ { pt := s.pt, ι := h.hom.app s.pt { down := (h.inv.app s.pt s.ι).down } } = s",
"st... | [
1009,
84
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1005,
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Mathlib/Order/Monotone/Basic.lean | StrictAntiOn.lt_iff_lt | [] | [
803,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
801,
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Std/Data/Rat/Lemmas.lean | Rat.mk_eq_divInt | [
{
"state_after": "no goals",
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}
] | [
120,
21
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
119,
1
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Std/Data/RBMap/WF.lean | Std.RBNode.Ordered.append | [
{
"state_after": "α : Type u_1\ncmp : α → α → Ordering\nl : RBNode α\nv : α\nr : RBNode α\nlv : All (fun x => cmpLT cmp x v) l\nvr : All (fun x => cmpLT cmp v x) r\nhl : Ordered cmp l\nhr : Ordered cmp r\n⊢ Ordered cmp\n (match l, r with\n | nil, x => x\n | x, nil => x\n | node red a x b, node red c... | [
344,
36
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinitePos_neg | [] | [
473,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
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Mathlib/Analysis/Convex/Integral.lean | Convex.average_mem_interior_of_set | [
{
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269,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
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Mathlib/Algebra/Homology/HomologicalComplex.lean | HomologicalComplex.Hom.sqTo_left | [] | [
591,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
590,
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Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_sum | [] | [
1006,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1002,
1
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Mathlib/Data/Set/Intervals/Monotone.lean | Monotone.Ioi | [] | [
73,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
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Mathlib/Data/Dfinsupp/Interval.lean | Dfinsupp.card_pi | [
{
"state_after": "ι : Type u_1\nα : ι → Type u_2\ninst✝² : (i : ι) → Zero (α i)\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → DecidableEq (α i)\nf : Π₀ (i : ι), Finset (α i)\n⊢ ∏ i in support f, card (↑f i) = prod f fun i => ↑(card (↑f i))",
"state_before": "ι : Type u_1\nα : ι → Type u_2\ninst✝² : (i : ι) → Z... | [
157,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
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Mathlib/Topology/Inseparable.lean | not_specializes_iff_exists_open | [
{
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223,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
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Mathlib/Topology/Connected.lean | locallyConnectedSpace_iff_connected_basis | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.116595\nπ : ι → Type ?u.116600\ninst✝ : TopologicalSpace α\ns t u v : Set α\n⊢ (∀ (x : α) (U : Set α), U ∈ 𝓝 x → ∃ V, V ∈ 𝓝 x ∧ IsPreconnected V ∧ V ⊆ U) ↔\n ∀ (x : α), Filter.HasBasis (𝓝 x) (fun s => s ∈ 𝓝 x ∧ IsPreconnected s) id",
"state_before... | [
1201,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1197,
1
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Mathlib/Data/Num/Lemmas.lean | PosNum.lt_to_nat | [
{
"state_after": "α : Type ?u.160166\nm n : PosNum\nh : ↑m < ↑n\n⊢ ↑m < ↑n ↔ Ordering.lt = Ordering.lt",
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"tactic": "simp at h"
},
{
"state_afte... | [
194,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.isMultiplicative_one | [
{
"state_after": "no goals",
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},
{
"state_after": "R : Type u_1\ninst✝ : MonoidWithZero R\nm n : ℕ\nhm : m ≠ 0\n_hn : n ≠ 0\nhmn : coprime m n\n⊢ ↑1 (m * n) = ↑1 m * ↑1 n",
"state_before": "R : Type u_1\nin... | [
816,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
808,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.disc_eq_prod_three_roots | [
{
"state_after": "R : Type ?u.1160753\nS : Type ?u.1160756\nF : Type u_1\nK : Type u_2\nP : Cubic F\ninst✝¹ : Field F\ninst✝ : Field K\nφ : F →+* K\nx y z : K\nha : P.a ≠ 0\nh3 : roots (map φ P) = {x, y, z}\n⊢ ↑φ P.b ^ 2 * ↑φ P.c ^ 2 - ↑φ 4 * ↑φ P.a * ↑φ P.c ^ 3 - ↑φ 4 * ↑φ P.b ^ 3 * ↑φ P.d - ↑φ 27 * ↑φ P.a ^ 2... | [
578,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
570,
1
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Mathlib/Topology/MetricSpace/Contracting.lean | ContractingWith.tendsto_iterate_fixedPoint | [
{
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"state_before": "α : Type u_1\ninst✝² : MetricSpace α\nK : ℝ≥0\nf : ... | [
344,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
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Mathlib/Order/Filter/Basic.lean | Filter.tendsto_inf_left | [] | [
2991,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2989,
1
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Mathlib/Data/List/Basic.lean | List.eq_of_mem_map_const | [
{
"state_after": "ι : Type ?u.144145\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nb₁ b₂ : β\nl : List α\nh : b₁ ∈ replicate (length l) b₂\n⊢ b₁ = b₂",
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1892,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1891,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.meas_ge_le_mul_pow_snorm | [
{
"state_after": "case pos\nα : Type u_1\nE : Type u_2\nF : Type ?u.4798273\nG : Type ?u.4798276\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf : α → E\nhp_ne_zero : p ≠ 0\nhp_ne_top : p ≠ ⊤\nhf : AEStron... | [
1171,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1162,
1
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Mathlib/Analysis/Convex/Extreme.lean | IsExtreme.trans | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1093\nι : Type ?u.1096\nπ : ι → Type ?u.1101\ninst✝² : OrderedSemiring 𝕜\ninst✝¹ : AddCommMonoid E\ninst✝ : SMul 𝕜 E\nA B C : Set E\nx✝ : E\nhAB : IsExtreme 𝕜 A B\nhBC : IsExtreme 𝕜 B C\nx₁ : E\nhx₁A : x₁ ∈ A\nx₂ : E\nhx₂A : x₂ ∈ A\nx : E\nhxC : x ∈... | [
87,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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] |
Mathlib/Algebra/Parity.lean | Odd.pow_neg_iff | [] | [
499,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
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] |
Mathlib/Data/Finset/Lattice.lean | iSup_eq_iSup_finset | [
{
"state_after": "no goals",
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"tactic": "classical\n re... | [
1819,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1815,
1
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Mathlib/Order/Monotone/Monovary.lean | antivaryOn_id_iff | [] | [
310,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
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Mathlib/RingTheory/Ideal/Over.lean | Ideal.exists_ideal_over_maximal_of_isIntegral | [
{
"state_after": "case intro.intro\nR : Type u_2\ninst✝³ : CommRing R\nS : Type u_1\ninst✝² : CommRing S\nf : R →+* S\nI J : Ideal S\ninst✝¹ : Algebra R S\ninst✝ : IsDomain S\nH : Algebra.IsIntegral R S\nP : Ideal R\nP_max : IsMaximal P\nhP : RingHom.ker (algebraMap R S) ≤ P\nQ : Ideal S\nQ_prime : IsPrime Q\nh... | [
423,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.nhds_basis_ball_inv_nat_pos | [] | [
991,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
989,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.two_nsmul_ne_zero_iff | [
{
"state_after": "no goals",
"state_before": "θ : Angle\n⊢ 2 • θ ≠ 0 ↔ θ ≠ 0 ∧ θ ≠ ↑π",
"tactic": "rw [← not_or, ← two_nsmul_eq_zero_iff]"
}
] | [
203,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/LinearAlgebra/BilinearMap.lean | LinearMap.congr_fun₂ | [] | [
123,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.translationNumber_eq_of_semiconjBy | [] | [
719,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
716,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzOnWith.of_le_add_mul' | [] | [
551,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
11
] |
Mathlib/Data/Finset/Basic.lean | Finset.not_mem_erase | [] | [
1864,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1863,
1
] |
Mathlib/Data/Set/Intervals/OrdConnected.lean | Set.OrdConnected.inter | [] | [
86,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.natTrailingDegree_mul | [] | [
428,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.lift_uzero | [] | [
719,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
718,
1
] |
Mathlib/Data/Complex/ExponentialBounds.lean | Real.exp_one_gt_d9 | [
{
"state_after": "no goals",
"state_before": "⊢ 2.7182818283 < 2244083 / 825552 - 1 / 10 ^ 10",
"tactic": "norm_num"
}
] | [
40,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.map_inl | [] | [
911,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
908,
1
] |
Mathlib/Data/Finset/Sum.lean | Finset.disjSum_ssubset_disjSum_of_subset_of_ssubset | [] | [
104,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.le_inf | [
{
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522,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
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] |
Mathlib/RingTheory/Ideal/Over.lean | Ideal.exists_ideal_over_prime_of_isIntegral | [
{
"state_after": "case intro.intro\nR : Type u_1\ninst✝⁴ : CommRing R\nS : Type u_2\ninst✝³ : CommRing S\nf : R →+* S\nI✝ J : Ideal S\ninst✝² : Algebra R S\nH : Algebra.IsIntegral R S\nP : Ideal R\ninst✝¹ : IsPrime P\nI : Ideal S\ninst✝ : IsPrime I\nhIP : comap (algebraMap R S) I ≤ P\nQ' : Ideal (S ⧸ I)\nQ'_pri... | [
413,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
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Mathlib/SetTheory/ZFC/Basic.lean | PSet.Equiv.euc | [] | [
188,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
11
] |
Mathlib/MeasureTheory/Measure/Portmanteau.lean | MeasureTheory.measure_of_cont_bdd_of_tendsto_filter_indicator | [
{
"state_after": "case h.e'_5.h.e'_3\nΩ : Type u_2\ninst✝⁴ : MeasurableSpace Ω\nι : Type u_1\nL : Filter ι\ninst✝³ : IsCountablyGenerated L\ninst✝² : TopologicalSpace Ω\ninst✝¹ : OpensMeasurableSpace Ω\nμ : Measure Ω\ninst✝ : IsFiniteMeasure μ\nc : ℝ≥0\nE : Set Ω\nE_mble : MeasurableSet E\nfs : ι → Ω →ᵇ ℝ≥0\nfs... | [
297,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Topology/Algebra/GroupWithZero.lean | Filter.Tendsto.div_const | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.448\nG₀ : Type u_2\ninst✝² : DivInvMonoid G₀\ninst✝¹ : TopologicalSpace G₀\ninst✝ : ContinuousMul G₀\nf : α → G₀\ns : Set α\nl : Filter α\nx : G₀\nhf : Tendsto f l (𝓝 x)\ny : G₀\n⊢ Tendsto (fun a => f a / y) l (𝓝 (x / y))",
"tacti... | [
57,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Topology/ContinuousOn.lean | continuousOn_snd | [] | [
1283,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1282,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.coe_center | [] | [
2069,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2068,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.bddAbove_range_norm_comp | [] | [
922,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
921,
1
] |
Mathlib/InformationTheory/Hamming.lean | Hamming.toHamming_add | [] | [
371,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.ext | [] | [
200,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Topology/Inseparable.lean | specializes_prod | [
{
"state_after": "no goals",
"state_before": "X : Type u_2\nY : Type u_1\nZ : Type ?u.15556\nα : Type ?u.15559\nι : Type ?u.15562\nπ : ι → Type ?u.15567\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace Y\ninst✝¹ : TopologicalSpace Z\ninst✝ : (i : ι) → TopologicalSpace (π i)\nx y z : X\ns : Set X\nf :... | [
207,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.adjugate_mul_distrib_aux | [
{
"state_after": "m : Type u\nn : Type v\nα : Type w\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\ninst✝ : CommRing α\nA B : Matrix n n α\nhA : IsLeftRegular (det A)\nhB : IsLeftRegular (det B)\nhAB : IsLeftRegular (det (A ⬝ B))\n⊢ adjugate (A ⬝ B) = adjugate B ⬝ adjug... | [
481,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | nullMeasurableSet_lt | [] | [
550,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
] |
Mathlib/AlgebraicGeometry/PresheafedSpace.lean | AlgebraicGeometry.PresheafedSpace.comp_c_app | [] | [
246,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.map_closure | [] | [
2937,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2935,
1
] |
Mathlib/Data/Rel.lean | Rel.core_id | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.25523\nγ : Type ?u.25526\nr : Rel α β\ns : Set α\n⊢ core Eq s = s",
"tactic": "simp [core]"
}
] | [
239,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.map_think | [] | [
1410,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1409,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.SummableFamily.hsum_ofFinsupp | [
{
"state_after": "case coeff.h\nΓ : Type u_3\nR : Type u_2\ninst✝¹ : PartialOrder Γ\ninst✝ : AddCommMonoid R\nα : Type u_1\nf : α →₀ HahnSeries Γ R\ng : Γ\n⊢ coeff (hsum (ofFinsupp f)) g = coeff (Finsupp.sum f fun x => id) g",
"state_before": "Γ : Type u_3\nR : Type u_2\ninst✝¹ : PartialOrder Γ\ninst✝ : Add... | [
1692,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1684,
1
] |
Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | isBounded_le_nhds | [] | [
40,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | Real.diam_eq | [
{
"state_after": "α : Type ?u.495306\nβ : Type ?u.495309\nγ : Type ?u.495312\ninst✝ : PseudoEMetricSpace α\ns : Set ℝ\nh : Metric.Bounded s\n⊢ 0 ≤ sSup s - sInf s",
"state_before": "α : Type ?u.495306\nβ : Type ?u.495309\nγ : Type ?u.495312\ninst✝ : PseudoEMetricSpace α\ns : Set ℝ\nh : Metric.Bounded s\n⊢ M... | [
1526,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1523,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Theory.completeTheory.subset | [] | [
868,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
867,
1
] |
Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Equivalence.cancel_counitInv_right_assoc | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nE : Type u₃\ninst✝ : Category E\ne : C ≌ D\nW X X' Y : D\nf : W ⟶ X\ng : X ⟶ Y\nf' : W ⟶ X'\ng' : X' ⟶ Y\n⊢ f ≫ g ≫ (counitInv e).app Y = f' ≫ g' ≫ (counitInv e).app Y ↔ f ≫ g = f' ≫ g'",
"t... | [
414,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/Algebra/CharP/Two.lean | CharTwo.multiset_sum_sq | [] | [
108,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Order/Compare.lean | Ordering.Compares.inj | [] | [
127,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.piCongrRight_trans | [] | [
675,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
673,
1
] |
Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.productMap_left_apply | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nA : Type u_3\nB : Type u_4\nS : Type u_1\ninst✝⁶ : CommSemiring R\ninst✝⁵ : Semiring A\ninst✝⁴ : Semiring B\ninst✝³ : CommSemiring S\ninst✝² : Algebra R A\ninst✝¹ : Algebra R B\ninst✝ : Algebra R S\nf : A →ₐ[R] S\ng : B →ₐ[R] S\na : A\n⊢ ↑(productM... | [
970,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
969,
1
] |
Mathlib/Order/MinMax.lean | lt_min_iff | [] | [
57,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_const_smul_right | [
{
"state_after": "α : Type u_2\nβ : Type ?u.557160\nE : Type u_3\nF : Type ?u.557166\nG : Type ?u.557169\nE' : Type u_4\nF' : Type ?u.557175\nG' : Type ?u.557178\nE'' : Type ?u.557181\nF'' : Type ?u.557184\nG'' : Type ?u.557187\nR : Type ?u.557190\nR' : Type ?u.557193\n𝕜 : Type u_1\n𝕜' : Type ?u.557199\ninst✝... | [
1741,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1736,
1
] |
Std/Data/Int/Lemmas.lean | Int.sub_left_le_of_le_add | [
{
"state_after": "a b c : Int\nh✝ : a ≤ b + c\nh : a + -b ≤ b + c + -b\n⊢ a - b ≤ c",
"state_before": "a b c : Int\nh : a ≤ b + c\n⊢ a - b ≤ c",
"tactic": "have h := Int.add_le_add_right h (-b)"
},
{
"state_after": "no goals",
"state_before": "a b c : Int\nh✝ : a ≤ b + c\nh : a + -b ≤ b + c ... | [
988,
56
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
986,
11
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.IsPath.takeUntil | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\ninst✝ : DecidableEq V\nu v w : V\np : Walk G v w\nhc : IsPath p\nh : u ∈ support p\n⊢ IsPath (append (takeUntil p u h) (?m.255816 hc h))",
"tactic": "rwa [←... | [
1193,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1191,
11
] |
Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.IsRefl.domRestrict | [
{
"state_after": "R : Type u_1\nR₁ : Type u_2\nR₂ : Type ?u.107426\nR₃ : Type ?u.107429\nM : Type ?u.107432\nM₁ : Type u_3\nM₂ : Type ?u.107438\nMₗ₁ : Type ?u.107441\nMₗ₁' : Type ?u.107444\nMₗ₂ : Type ?u.107447\nMₗ₂' : Type ?u.107450\nK : Type ?u.107453\nK₁ : Type ?u.107456\nK₂ : Type ?u.107459\nV : Type ?u.107... | [
188,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Order/CompactlyGenerated.lean | DirectedOn.disjoint_sSup_left | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.99428\nα : Type u_1\ninst✝² : CompleteLattice α\nf : ι → α\ninst✝¹ : CompleteLattice α\ninst✝ : IsCompactlyGenerated α\na b : α\ns : Set α\nh : DirectedOn (fun x x_1 => x ≤ x_1) s\n⊢ Disjoint (sSup s) a ↔ ∀ ⦃b : α⦄, b ∈ s → Disjoint b a",
"tactic... | [
399,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
11
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | edist_pi_def | [] | [
479,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.log_nonpos_iff' | [
{
"state_after": "case inl\ny : ℝ\nhx : 0 ≤ 0\n⊢ log 0 ≤ 0 ↔ 0 ≤ 1\n\ncase inr\nx y : ℝ\nhx✝ : 0 ≤ x\nhx : 0 < x\n⊢ log x ≤ 0 ↔ x ≤ 1",
"state_before": "x y : ℝ\nhx : 0 ≤ x\n⊢ log x ≤ 0 ↔ x ≤ 1",
"tactic": "rcases hx.eq_or_lt with (rfl | hx)"
},
{
"state_after": "no goals",
"state_before": "... | [
201,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_coprod | [] | [
1143,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1141,
1
] |
Mathlib/Topology/Bornology/Basic.lean | Bornology.isCobounded_iInter | [] | [
276,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/RingTheory/FreeCommRing.lean | FreeRing.coe_eq | [
{
"state_after": "case h\nα : Type u\nx : FreeRing α\n⊢ ↑x = (fun l => ↑l) <$> x",
"state_before": "α : Type u\n⊢ castFreeCommRing = Functor.map fun l => ↑l",
"tactic": "funext x"
},
{
"state_after": "case h\nα : Type u\nx : FreeRing α\n⊢ ↑(↑FreeAbelianGroup.lift ↑(↑FreeMonoid.lift FreeCommRing.... | [
392,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | le_of_pow_le_pow | [] | [
611,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
610,
1
] |
Mathlib/RingTheory/Nilpotent.lean | IsNilpotent.mk | [] | [
43,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.hasFiniteIntegral_iff_ofReal | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.701577\nγ : Type ?u.701580\nδ : Type ?u.701583\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\nf : α → ℝ\nh : 0 ≤ᵐ[μ] f\n⊢ HasFiniteIntegral f ↔ (∫⁻ (a : ... | [
132,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | inv_pos_le_iff_one_le_mul' | [
{
"state_after": "ι : Type ?u.39811\nα : Type u_1\nβ : Type ?u.39817\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nha : 0 < a\n⊢ 1 / a ≤ b ↔ 1 ≤ a * b",
"state_before": "ι : Type ?u.39811\nα : Type u_1\nβ : Type ?u.39817\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nha : 0 < a\n⊢ a... | [
217,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.transpose_mul | [
{
"state_after": "case a.h\nl : Type u_3\nm : Type u_2\nn : Type u_1\no : Type ?u.927478\nm' : o → Type ?u.927483\nn' : o → Type ?u.927488\nR : Type ?u.927491\nS : Type ?u.927494\nα : Type v\nβ : Type w\nγ : Type ?u.927501\ninst✝² : AddCommMonoid α\ninst✝¹ : CommSemigroup α\ninst✝ : Fintype n\nM : Matrix m n α\... | [
2003,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2000,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.sign_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "θ : Angle\n⊢ sign θ = 0 ↔ θ = 0 ∨ θ = ↑π",
"tactic": "rw [sign, _root_.sign_eq_zero_iff, sin_eq_zero_iff]"
}
] | [
894,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
893,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.of_nat_div | [] | [
446,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
Mathlib/MeasureTheory/Function/AEMeasurableSequence.lean | aeSeq.measurable | [] | [
100,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/CategoryTheory/Types.lean | CategoryTheory.ofTypeFunctor_map | [] | [
299,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/Topology/Bornology/Constructions.lean | Bornology.isBounded_prod | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type u_2\nι : Type ?u.2500\nπ : ι → Type ?u.2505\ninst✝³ : Fintype ι\ninst✝² : Bornology α\ninst✝¹ : Bornology β\ninst✝ : (i : ι) → Bornology (π i)\nt : Set β\nS : (i : ι) → Set (π i)\n⊢ IsBounded (∅ ×ˢ t) ↔ ∅ = ∅ ∨ t = ∅ ∨ IsBounded ∅ ∧ IsBounded t\n\ncase inr\nα :... | [
90,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/CategoryTheory/Simple.lean | CategoryTheory.id_nonzero | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\ninst✝¹ : HasZeroMorphisms C\nX : C\ninst✝ : Simple X\n⊢ IsIso (𝟙 X)",
"tactic": "infer_instance"
}
] | [
115,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.tan_periodic | [
{
"state_after": "no goals",
"state_before": "⊢ Function.Periodic tan π",
"tactic": "simpa only [Function.Periodic, tan_eq_sin_div_cos] using sin_antiperiodic.div cos_antiperiodic"
}
] | [
1003,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1002,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.coeFn_mk | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.309815\nδ : Type ?u.309818\ninst✝³ : MeasurableSpace α\nμ ν : Measure α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α → β\nhf : AEStronglyMeasurable f μ\n⊢ ↑(Quotient.out' (mk f hf)) =ᵐ[μ] f",
"state_bef... | [
185,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.delta_lt_false | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.268\na b : ℕ\nh₁ : delta * a < b\nh₂ : delta * b < a\n⊢ 0 < delta",
"tactic": "decide"
},
{
"state_after": "no goals",
"state_before": "α : Type ?u.268\na b : ℕ\nh₁ : delta * a < b\nh₂ : delta * b < a\n⊢ a ≤ delta * (delta * a)",
... | [
87,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.card_incidenceSet_eq_degree | [
{
"state_after": "ι : Sort ?u.274831\n𝕜 : Type ?u.274834\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v w : V\ne : Sym2 V\ninst✝¹ : Fintype ↑(neighborSet G v)\ninst✝ : DecidableEq V\n⊢ Fintype.card ↑(neighborSet G v) = degree G v",
"state_before": "ι : Sort ?u.274831\... | [
1410,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1407,
1
] |
Mathlib/Data/ZMod/Parity.lean | ZMod.eq_one_iff_odd | [
{
"state_after": "n : ℕ\n⊢ n % 2 = 1 % 2 ↔ n % 2 = 1",
"state_before": "n : ℕ\n⊢ ↑n = 1 ↔ Odd n",
"tactic": "rw [← @Nat.cast_one (ZMod 2), ZMod.eq_iff_modEq_nat, Nat.odd_iff, Nat.ModEq]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ n % 2 = 1 % 2 ↔ n % 2 = 1",
"tactic": "norm... | [
33,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
31,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycle.support_pow_of_pos_of_lt_orderOf | [] | [
643,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
1
] |
Mathlib/LinearAlgebra/TensorPower.lean | TensorPower.mul_algebraMap₀ | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nM : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nn : ℕ\nr : R\na : (⨂[R]^n) M\n⊢ ↑(cast R M (_ : n + 0 = n)) (GradedMonoid.GMul.mul a (↑algebraMap₀ r)) = r • a",
"tactic": "rw [gMul_eq_coe_linearMap, algebraM... | [
253,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Std/Data/Int/DivMod.lean | Int.ediv_neg | [
{
"state_after": "m : Nat\n⊢ ofNat 0 = -↑0",
"state_before": "m : Nat\n⊢ ofNat (m / 0) = -↑(m / 0)",
"tactic": "rw [Nat.div_zero]"
},
{
"state_after": "no goals",
"state_before": "m : Nat\n⊢ ofNat 0 = -↑0",
"tactic": "rfl"
}
] | [
74,
73
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
71,
19
] |
Mathlib/Order/SuccPred/Basic.lean | Order.pred_succ_of_not_isMax | [] | [
948,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
947,
1
] |
Mathlib/Data/Nat/Periodic.lean | Nat.periodic_mod | [
{
"state_after": "no goals",
"state_before": "a : ℕ\n⊢ Periodic (fun n => n % a) a",
"tactic": "simp only [forall_const, eq_self_iff_true, add_mod_right, Periodic]"
}
] | [
36,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.le_add_mul | [] | [
343,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
11
] |
Mathlib/Topology/UrysohnsLemma.lean | Urysohns.CU.left_U_subset | [] | [
127,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Analysis/Calculus/Deriv/Slope.lean | HasDerivWithinAt.liminf_right_slope_norm_le | [
{
"state_after": "E : Type u\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : ℝ → E\nf' : E\ns : Set ℝ\nx r : ℝ\nhf : HasDerivWithinAt f f' (Ici x) x\nhr : ‖f'‖ < r\nthis : ∃ᶠ (x_1 : ℝ) in 𝓝[Ioi x] x, ‖x_1 - x‖⁻¹ * (‖f x_1‖ - ‖f x‖) < r\n⊢ ∃ᶠ (z : ℝ) in 𝓝[Ioi x] x, (z - x)⁻¹ * (‖f z‖ - ‖f x‖) < r"... | [
181,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
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