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/Nat/Hyperoperation.lean | hyperoperation_zero | [
{
"state_after": "no goals",
"state_before": "m k : ℕ\n⊢ hyperoperation 0 m k = Nat.succ k",
"tactic": "rw [hyperoperation, Nat.succ_eq_add_one]"
}
] | [
51,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
src/lean/Init/Core.lean | type_eq_of_heq | [] | [
640,
20
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
639,
1
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | continuous_circleMap | [] | [
189,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.power_bit0 | [] | [
548,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
1
] |
Mathlib/Order/Basic.lean | LE.le.ge_iff_eq | [] | [
280,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Order/Monotone/Monovary.lean | MonovaryOn.comp_right | [] | [
156,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/AlgebraicGeometry/PresheafedSpace/HasColimits.lean | AlgebraicGeometry.PresheafedSpace.colimit_carrier | [] | [
194,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_le_rpow_of_exponent_ge | [
{
"state_after": "x y z : ℝ\nhx0 : 0 < x\nhx1 : x ≤ 1\nhyz : z ≤ y\n⊢ exp (log x * y) ≤ exp (log x * z)",
"state_before": "x y z : ℝ\nhx0 : 0 < x\nhx1 : x ≤ 1\nhyz : z ≤ y\n⊢ x ^ y ≤ x ^ z",
"tactic": "repeat' rw [rpow_def_of_pos hx0]"
},
{
"state_after": "x y z : ℝ\nhx0 : 0 < x\nhx1 : x ≤ 1\nhy... | [
499,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | HasFDerivWithinAt.add_const | [] | [
189,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
8
] |
Mathlib/LinearAlgebra/Span.lean | LinearMap.ext_on | [] | [
965,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
964,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.FTCFilter.finite_at_inner | [] | [
221,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | strictMonoOn_pow | [] | [
492,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
] |
Mathlib/Data/Int/Log.lean | Int.clog_of_one_le_right | [] | [
193,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_zero | [] | [
1621,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1620,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.disjiUnion_val | [] | [
3444,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3442,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.uniformEmbedding_iff' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.310325\ninst✝² : PseudoEMetricSpace α\nγ : Type w\ninst✝¹ : EMetricSpace γ\ninst✝ : EMetricSpace β\nf : γ → β\n⊢ UniformEmbedding f ↔\n (∀ (ε : ℝ≥0∞), ε > 0 → ∃ δ, δ > 0 ∧ ∀ {a b : γ}, edist a b < δ → edist (f a) (f b) < ε)... | [
1040,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1036,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | NonUnitalStarAlgHom.zero_apply | [] | [
281,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_empty | [] | [
492,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
] |
Mathlib/Computability/Language.lean | Language.nil_mem_one | [] | [
109,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Data/Polynomial/Module.lean | PolynomialModule.zero_apply | [] | [
78,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Analysis/Calculus/FDerivAnalytic.lean | HasFPowerSeriesAt.fderiv_eq | [] | [
66,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzOnWith.of_le_add_mul | [
{
"state_after": "no goals",
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558,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
11
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.naturalityProperty.stableUnderInverse | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\nD : Type u_2\ninst✝ : Category D\nF₁ F₂ : C ⥤ D\napp : (X : C) → F₁.obj X ⟶ F₂.obj X\nX Y : C\ne : X ≅ Y\nhe : F₁.map e.hom ≫ app Y = app X ≫ F₂.map e.hom\n⊢ F₁.map e.inv ≫ app X = app Y ≫ F₂.map e.inv",
"state_before": "C : Type u\ninst✝¹ : Category C\nD :... | [
364,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.X.mul_snd | [] | [
244,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/LinearAlgebra/Trace.lean | LinearMap.trace_eq_matrix_trace_of_finset | [
{
"state_after": "R : Type u\ninst✝⁶ : CommSemiring R\nM : Type v\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\nι : Type w\ninst✝³ : DecidableEq ι\ninst✝² : Fintype ι\nκ : Type ?u.216025\ninst✝¹ : DecidableEq κ\ninst✝ : Fintype κ\nb✝ : Basis ι R M\nc : Basis κ R M\ns : Finset M\nb : Basis { x // x ∈ s } R M\n... | [
102,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Order/Heyting/Basic.lean | sup_sdiff_left_self | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.137716\nα : Type u_1\nβ : Type ?u.137722\ninst✝ : GeneralizedCoheytingAlgebra α\na b c d : α\n⊢ (a ⊔ b) \\ a = b \\ a",
"tactic": "rw [sup_comm, sup_sdiff_right_self]"
}
] | [
662,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
662,
1
] |
Mathlib/Analysis/NormedSpace/Basic.lean | NormedSpace.unbounded_univ | [] | [
439,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
11
] |
Mathlib/Analysis/Normed/Group/Pointwise.lean | ball_div | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\ninst✝ : SeminormedCommGroup E\nε δ : ℝ\ns t : Set E\nx y : E\n⊢ ball x δ / s = x • thickening δ s⁻¹",
"tactic": "simp [div_eq_mul_inv]"
}
] | [
248,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.natDegree_of_c_ne_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.591482\nF : Type ?u.591485\nK : Type ?u.591488\nP Q : Cubic R\na b c d a' b' c' d' : R\ninst✝ : Semiring R\nha : P.a = 0\nhb : P.b = 0\nhc : P.c ≠ 0\n⊢ natDegree (toPoly P) = 1",
"tactic": "rw [of_b_eq_zero ha hb, natDegree_linear h... | [
423,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | EuclideanGeometry.sin_angle_of_angle_eq_pi_div_two | [
{
"state_after": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np₁ p₂ p₃ : P\nh : inner (p₂ -ᵥ p₃) (p₁ -ᵥ p₂) = 0\nh0 : p₁ ≠ p₂ ∨ p₃ ≠ p₂\n⊢ Real.sin (∠ p₂ p₃ p₁) = dist p₁ p₂ / dist p₁ p₃",
"state_before": "V ... | [
449,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_union_add_inter' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.6873\nγ : Type ?u.6876\nδ : Type ?u.6879\nι : Type ?u.6882\nR : Type ?u.6885\nR' : Type ?u.6888\nm : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns s₁ s₂ t✝ : Set α\nhs : MeasurableSet s\nt : Set α\n⊢ ↑↑μ (s ∪ t) + ↑↑μ (s ∩ t) = ↑↑μ s + ↑↑μ ... | [
153,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Cardinal.lt_univ' | [
{
"state_after": "α : Type ?u.235536\nβ : Type ?u.235539\nγ : Type ?u.235542\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nc : Cardinal\nh : c < univ\na : Cardinal\ne : lift a = c\nh' : a < (#Ordinal)\n⊢ ∃ c', c = lift c'",
"state_before": "α : Type ?u.235536\nβ : Type ?u.235539\nγ : Type ?u.235542... | [
1537,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1532,
1
] |
Mathlib/Combinatorics/Composition.lean | Composition.length_pos_of_pos | [
{
"state_after": "case h\nn : ℕ\nc : Composition n\nh : 0 < n\n⊢ 0 < sum c.blocks",
"state_before": "n : ℕ\nc : Composition n\nh : 0 < n\n⊢ 0 < length c",
"tactic": "apply length_pos_of_sum_pos"
},
{
"state_after": "case h.e'_4\nn : ℕ\nc : Composition n\nh : 0 < n\n⊢ sum c.blocks = n",
"stat... | [
209,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.hom.injective | [] | [
743,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
742,
1
] |
Mathlib/Data/Set/Function.lean | Set.piecewise_empty | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.71934\nγ : Type ?u.71937\nι : Sort ?u.71940\nπ : α → Type ?u.71945\nδ : α → Sort u_2\ns : Set α\nf g : (i : α) → δ i\ninst✝ : (i : α) → Decidable (i ∈ ∅)\ni : α\n⊢ piecewise ∅ f g i = g i",
"state_before": "α : Type u_1\nβ : Type ?u.71934\nγ : Type ?u.7193... | [
1352,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1350,
1
] |
Mathlib/Computability/PartrecCode.lean | Nat.Partrec.Code.eval_const | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\n⊢ eval (Code.const (n + 1)) m = Part.some (n + 1)",
"tactic": "simp! [eval_const n m]"
}
] | [
662,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
] |
Mathlib/Logic/Relation.lean | Relation.reflexive_join | [] | [
629,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
629,
1
] |
Std/Data/Int/DivMod.lean | Int.mul_div_cancel | [
{
"state_after": "no goals",
"state_before": "a b : Int\nH✝ : b ≠ 0\na✝ b✝ : Nat\nH : ↑b✝ ≠ 0\n⊢ div (↑a✝ * ↑b✝) ↑b✝ = ↑a✝",
"tactic": "rw [← ofNat_mul, ← ofNat_div,\n Nat.mul_div_cancel _ <| Nat.pos_of_ne_zero <| Int.ofNat_ne_zero.1 H]"
},
{
"state_after": "no goals",
"state_before": "a✝ b... | [
211,
66
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
200,
19
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.coe_comap | [] | [
1317,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1317,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiffOn_clm_apply | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹² : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝¹¹ : NormedAddCommGroup D\ninst✝¹⁰ : NormedSpace 𝕜 D\nE : Type uE\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace 𝕜 F\nG : Type uG\ninst✝⁵ : Norm... | [
1888,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1880,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_image | [] | [
367,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | pi_norm_const_le' | [] | [
2523,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2522,
1
] |
Mathlib/Algebra/Ring/Prod.lean | NonUnitalRingHom.coe_fst | [] | [
119,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Data/Set/Intervals/ProjIcc.lean | Set.IccExtend_of_le_left | [] | [
115,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | isCoprime_zero_left | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : CommSemiring R\nx y z : R\nx✝ : IsCoprime 0 x\na b : R\nH : a * 0 + b * x = 1\n⊢ x * b = 1",
"tactic": "rwa [mul_zero, zero_add, mul_comm] at H"
},
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : CommSemiring... | [
65,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Data/Dfinsupp/NeLocus.lean | Dfinsupp.not_mem_neLocus | [] | [
50,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.or_inl | [
{
"state_after": "no goals",
"state_before": "a b : Bool\nH : a = true\n⊢ (a || b) = true",
"tactic": "simp [H]"
}
] | [
159,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Std/Data/List/Lemmas.lean | List.tailD_eq_tail? | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl l' : List α\n⊢ tailD l l' = Option.getD (tail? l) l'",
"tactic": "cases l <;> rfl"
}
] | [
448,
18
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
447,
9
] |
Mathlib/Logic/Basic.lean | ExistsUnique.elim₂ | [
{
"state_after": "ι : Sort ?u.24682\nα✝ : Sort ?u.24687\nκ : ι → Sort ?u.24684\np✝ q✝ : α✝ → Prop\nα : Sort u_1\np : α → Sort u_2\ninst✝ : ∀ (x : α), Subsingleton (p x)\nq : (x : α) → p x → Prop\nb : Prop\nh₁ : ∀ (x : α) (h : p x), q x h → (∀ (y : α) (hy : p y), q y hy → y = x) → b\nh₂ : ∃! x, ∃ h, q x h\n⊢ b",... | [
935,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
930,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.isBridge_iff_mem_and_forall_cycle_not_mem | [] | [
2536,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2534,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.eq_top_iff | [
{
"state_after": "α : Type u_1\ninst✝¹ : Monoid α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\na b : α\n⊢ (∀ (n : ℕ), a ^ (n + 1) ∣ b) ↔ ∀ (n : ℕ), a ^ n ∣ b",
"state_before": "α : Type u_1\ninst✝¹ : Monoid α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\na b : α\n⊢ (∀ (n : ℕ), ¬¬a ^ (n + 1) ∣ b) ↔ ∀ (n : ℕ), a... | [
180,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.join_principal_eq_sSup | [] | [
665,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
665,
9
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.ppow_apply | [
{
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"state_before": "R : Type u_1\ninst✝ : Semiring R\nf : ArithmeticFunction R\nk x : ℕ\nkpos : 0 < k\n⊢ ↑(ppow f k... | [
557,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.constr_def | [] | [
626,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
624,
1
] |
Mathlib/Data/Set/Intervals/Instances.lean | Set.Icc.coe_one | [] | [
66,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.SimpleFunc.norm_approxOn_zero_le | [
{
"state_after": "α : Type ?u.14817\nβ : Type u_2\nι : Type ?u.14823\nE : Type u_1\nF : Type ?u.14829\n𝕜 : Type ?u.14832\ninst✝⁵ : MeasurableSpace β\ninst✝⁴ : MeasurableSpace E\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\nq : ℝ\np : ℝ≥0∞\ninst✝¹ : OpensMeasurableSpace E\nf : β → E\nhf : Measu... | [
95,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSpace.generateFrom_singleton_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.20176\nγ : Type ?u.20179\nδ : Type ?u.20182\nδ' : Type ?u.20185\nι : Sort ?u.20188\ns t u : Set α\n⊢ ∀ (t : Set α), t ∈ {∅} → MeasurableSet t",
"tactic": "simp [@MeasurableSet.empty α ⊥]"
}
] | [
443,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/ModelTheory/LanguageMap.lean | FirstOrder.Language.withConstants_funMap_sum_inr | [
{
"state_after": "L : Language\nL' : Language\nM : Type w\ninst✝¹ : Structure L M\nα : Type u_1\ninst✝ : Structure (constantsOn α) M\na : α\nx : Fin 0 → M\n⊢ funMap (Sum.inr a) default = ↑(Language.con L a)",
"state_before": "L : Language\nL' : Language\nM : Type w\ninst✝¹ : Structure L M\nα : Type u_1\nins... | [
576,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.erase_add_right_neg | [] | [
1061,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1059,
1
] |
Std/Data/List/Lemmas.lean | List.disjoint_iff_ne | [] | [
1359,
83
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1358,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.map_mono | [] | [
471,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/Computability/Primrec.lean | Nat.Primrec.of_eq | [] | [
94,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | indicator_meas_zero | [] | [
4695,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4694,
1
] |
Mathlib/Data/Set/Intervals/Monotone.lean | AntitoneOn.Ici | [] | [
53,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
11
] |
Mathlib/Data/Finset/NoncommProd.lean | Finset.noncommProd_congr | [
{
"state_after": "F : Type ?u.139635\nι : Type ?u.139638\nα : Type ?u.139641\nβ : Type ?u.139644\nγ : Type ?u.139647\nf✝ : α → β → β\nop : α → α → α\ninst✝¹ : Monoid β\ninst✝ : Monoid γ\ns₁ s₂ : Finset α\nf g : α → β\nh₁ : s₁ = s₂\nh₂ : ∀ (x : α), x ∈ s₂ → f x = g x\ncomm : Set.Pairwise ↑s₁ fun a b => Commute (... | [
260,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Std/Data/List/Lemmas.lean | List.mem_eraseP_of_neg | [
{
"state_after": "α : Type u_1\np : α → Bool\na : α\nl : List α\npa : ¬p a = true\nal : a ∈ l\n⊢ a ∈ eraseP p l",
"state_before": "α : Type u_1\np : α → Bool\na : α\nl : List α\npa : ¬p a = true\n⊢ a ∈ eraseP p l ↔ a ∈ l",
"tactic": "refine ⟨mem_of_mem_eraseP, fun al => ?_⟩"
},
{
"state_after": ... | [
1007,
33
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1000,
9
] |
Mathlib/CategoryTheory/Action.lean | CategoryTheory.ActionCategory.id_val | [] | [
138,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
11
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.smul | [] | [
244,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.Cofork.IsColimit.existsUnique | [] | [
487,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Std/Data/List/Lemmas.lean | List.leftpad_prefix | [
{
"state_after": "α : Type u_1\nn : Nat\na : α\nl : List α\n⊢ ∃ t, replicate (n - length l) a ++ t = replicate (n - length l) a ++ l",
"state_before": "α : Type u_1\nn : Nat\na : α\nl : List α\n⊢ replicate (n - length l) a <+: leftpad n a l",
"tactic": "simp only [isPrefix, leftpad]"
},
{
"state... | [
1466,
27
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1463,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Set.infinite_iff_exists_lt | [] | [
857,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
856,
1
] |
Mathlib/Data/Finset/Prod.lean | Finset.offDiag_card | [
{
"state_after": "α : Type u_1\nβ : Type ?u.112877\nγ : Type ?u.112880\ninst✝ : DecidableEq α\ns t : Finset α\nx : α × α\nthis : card (diag s) + card (offDiag s) = card s * card s\n⊢ card (offDiag s) = card (diag s) * card (diag s) - card (diag s)",
"state_before": "α : Type u_1\nβ : Type ?u.112877\nγ : Typ... | [
340,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_insert | [
{
"state_after": "α✝ β α : Type u\ns : Set α\na : α\nh : ¬a ∈ s\n⊢ Disjoint s {a}",
"state_before": "α✝ β α : Type u\ns : Set α\na : α\nh : ¬a ∈ s\n⊢ (#↑(insert a s)) = (#↑s) + 1",
"tactic": "rw [← union_singleton, mk_union_of_disjoint, mk_singleton]"
},
{
"state_after": "no goals",
"state_b... | [
2109,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2106,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.mul_add_div | [
{
"state_after": "case a\nα : Type ?u.240963\nβ : Type ?u.240966\nγ : Type ?u.240969\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na b : Ordinal\nb0 : b ≠ 0\nc : Ordinal\n⊢ (b * a + c) / b ≤ a + c / b\n\ncase a\nα : Type ?u.240963\nβ : Type ?u.240966\nγ : Type ?u.240969\nr : α → α → Prop\ns : β → β → P... | [
947,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
941,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.cast_nat_cast' | [] | [
399,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.aecover_Ioc_of_Ioo | [] | [
234,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | LinearMap.toMatrix_toLin | [
{
"state_after": "no goals",
"state_before": "R : Type u_3\ninst✝⁷ : CommSemiring R\nl : Type ?u.1454587\nm : Type u_1\nn : Type u_2\ninst✝⁶ : Fintype n\ninst✝⁵ : Fintype m\ninst✝⁴ : DecidableEq n\nM₁ : Type u_4\nM₂ : Type u_5\ninst✝³ : AddCommMonoid M₁\ninst✝² : AddCommMonoid M₂\ninst✝¹ : Module R M₁\ninst... | [
572,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
570,
1
] |
Std/Data/Range/Lemmas.lean | Std.Range.numElems_stop_le_start | [
{
"state_after": "start stop step : Nat\nh : { start := start, stop := stop, step := step }.stop ≤ { start := start, stop := stop, step := step }.start\n⊢ (if step = 0 then if stop ≤ start then 0 else stop else (stop - start + step - 1) / step) = 0",
"state_before": "start stop step : Nat\nh : { start := st... | [
18,
26
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
14,
1
] |
Std/Logic.lean | Decidable.or_iff_not_imp_right | [] | [
547,
34
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
546,
1
] |
Mathlib/Data/Set/Intervals/OrdConnected.lean | Set.ordConnected_Icc | [] | [
156,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.finiteIndex_of_le | [] | [
584,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.fp_family_unbounded | [
{
"state_after": "ι : Type u\nf : ι → Ordinal → Ordinal\nH : ∀ (i : ι), IsNormal (f i)\na : Ordinal\ns : Set Ordinal\nx✝ : s ∈ Set.range fun i => fixedPoints (f i)\ni : ι\nhi : (fun i => fixedPoints (f i)) i = s\n⊢ f i (nfpFamily f a) = nfpFamily f a",
"state_before": "ι : Type u\nf : ι → Ordinal → Ordinal\... | [
152,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | StrictMonoOn.exists_deriv_lt_slope | [
{
"state_after": "case pos\nE : Type ?u.439267\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type ?u.439363\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nx y : ℝ\nf : ℝ → ℝ\nhf : ContinuousOn f (Icc x y)\nhxy : x < y\nhf'_mono : StrictMonoOn (deriv f) (Ioo x y)\nh : ∀ (w : ℝ), w ∈ Ioo... | [
1097,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1067,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_mul_symm_re_eq_norm | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1772395\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx y : E\n⊢ ↑re (inner y x * ↑(starRingEnd 𝕜) (inner y x)) = ‖inner y x * ↑... | [
661,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
659,
1
] |
Mathlib/Data/Multiset/Fintype.lean | Multiset.card_coe | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\nm✝ m : Multiset α\n⊢ Fintype.card { x // x ∈ toEnumFinset m } = ↑card m",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\nm✝ m : Multiset α\n⊢ Fintype.card (ToType m) = ↑card m",
"tactic": "rw [Fintype.card_congr m.coeEquiv]"
},
{
"sta... | [
259,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.bound_of_isBigO_cofinite | [
{
"state_after": "case intro.intro\nα : Type u_1\nβ : Type ?u.669259\nE : Type u_2\nF : Type ?u.669265\nG : Type ?u.669268\nE' : Type ?u.669271\nF' : Type ?u.669274\nG' : Type ?u.669277\nE'' : Type ?u.669280\nF'' : Type u_3\nG'' : Type ?u.669286\nR : Type ?u.669289\nR' : Type ?u.669292\n𝕜 : Type ?u.669295\n𝕜'... | [
2107,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2099,
1
] |
Mathlib/Data/Matrix/Notation.lean | Matrix.mulVec_cons | [
{
"state_after": "case h\nα✝ : Type u\no n m : ℕ\nm' : Type uₘ\nn' : Type uₙ\no' : Type uₒ\na b : ℕ\ninst✝¹ : Semiring α✝\nα : Type u_1\ninst✝ : CommSemiring α\nA : m' → Fin (Nat.succ n) → α\nx : α\nv : Fin n → α\ni : m'\n⊢ mulVec (↑of A) (vecCons x v) i = (x • vecHead ∘ A + mulVec (↑of (vecTail ∘ A)) v) i",
... | [
321,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/Topology/UniformSpace/AbstractCompletion.lean | AbstractCompletion.uniformContinuous_map | [] | [
194,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Data/List/Chain.lean | List.chain_of_chain_pmap | [
{
"state_after": "case nil\nα : Type u\nβ : Type v\nR r : α → α → Prop\nl✝ l₁ l₂ : List α\na✝¹ b : α\nS : β → β → Prop\np : α → Prop\nf : (a : α) → p a → β\nl : List α\nhl₁✝ : ∀ (a : α), a ∈ l → p a\na✝ : α\nha✝ : p a✝\nhl₂✝ : Chain S (f a✝ ha✝) (pmap f l hl₁✝)\nH : ∀ (a b : α) (ha : p a) (hb : p b), S (f a ha)... | [
113,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalRingHom.map_sclosure | [] | [
933,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
929,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.mem_inv_smul_set_iff₀ | [] | [
1022,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1021,
1
] |
Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingIso.toRingEquiv_eq_coe | [] | [
410,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.L1.SimpleFunc.coe_posPart | [] | [
497,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Submodule.annihilator_bot | [] | [
85,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/LinearAlgebra/Ray.lean | Module.Ray.someVector_ne_zero | [] | [
377,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/CategoryTheory/Sites/DenseSubsite.lean | CategoryTheory.CoverDense.sheafHom_eq | [
{
"state_after": "case w.h\nC : Type u_5\ninst✝⁴ : Category C\nD : Type u_1\ninst✝³ : Category D\nE : Type ?u.131136\ninst✝² : Category E\nJ : GrothendieckTopology C\nK : GrothendieckTopology D\nL : GrothendieckTopology E\nA : Type u_4\ninst✝¹ : Category A\nG : C ⥤ D\nH : CoverDense K G\ninst✝ : Full G\nℱ : Dᵒᵖ... | [
448,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/Data/Finset/Basic.lean | List.disjoint_toFinset_iff_disjoint | [] | [
3804,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3803,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.edist_map | [] | [
635,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
634,
1
] |
Mathlib/Algebra/Order/Field/Power.lean | zpow_le_one_of_nonpos | [] | [
43,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | PSet.Mem.congr_left | [] | [
311,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
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