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/Sym/Basic.lean | Sym.mem_append_iff | [] | [
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19
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519,
1
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Mathlib/Algebra/ContinuedFractions/TerminatedStable.lean | GeneralizedContinuedFraction.continuantsAux_stable_step_of_terminated | [
{
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"state_before": "K : Type u_1\ng : GeneralizedContinuedFraction K\nn m : ℕ\ninst✝ : DivisionRing K\nte... | [
37,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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src/lean/Init/SimpLemmas.lean | Bool.not_eq_false | [
{
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"state_before": "b : Bool\n⊢ (¬b = false) = (b = true)",
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137,
100
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Std/Data/List/Init/Lemmas.lean | List.tailD_cons | [] | [
33,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
33,
14
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Mathlib/Data/Finset/Basic.lean | Finset.disjoint_empty_left | [] | [
949,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
948,
1
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Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.mersenne_int_ne_zero | [] | [
104,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
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Mathlib/Algebra/Module/Equiv.lean | AddEquiv.toIntLinearEquiv_symm | [] | [
870,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
869,
1
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Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.Ioc_eq_zero_of_le | [] | [
93,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
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Mathlib/Algebra/Order/Ring/Abs.lean | max_zero_add_max_neg_zero_eq_abs_self | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedRing α\na✝ b c a : α\n⊢ abs a = max a 0 + max (-a) 0",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedRing α\na✝ b c a : α\n⊢ max a 0 + max (-a) 0 = abs a",
"tactic": "symm"
},
{
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83,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_eq_sum_range | [
{
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"tactic": "simp"
}
] | [
243,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Data/Int/DivMod.lean | Int.add_ediv_of_dvd_right | [
{
"state_after": "no goals",
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"tactic": "simp [h]"
},
{
"state_after": "a b c : Int\nH : c ∣ b\nh : ¬c = 0\nk : Int\nhk : b = c * k\n⊢ (a + b) / c = a / c + b / c",
"state_before": "a b c : Int\nH : c ∣ b\nh :... | [
180,
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176,
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Mathlib/Analysis/Calculus/Deriv/Add.lean | HasDerivAt.sum | [] | [
182,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
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Mathlib/Order/Interval.lean | NonemptyInterval.coe_subset_coe | [] | [
254,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
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Std/Data/String/Lemmas.lean | String.Pos.byteIdx_zero | [] | [
84,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
84,
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Mathlib/Algebra/Homology/Exact.lean | CategoryTheory.exact_kernelSubobject_arrow | [
{
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228,
67
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225,
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Mathlib/Algebra/Order/Ring/Lemmas.lean | mulPosReflectLT_iff_contravariant_pos | [
{
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482,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
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Std/Data/String/Lemmas.lean | String.Iterator.Valid.next | [
{
"state_after": "x✝ : Iterator\nh✝ : Valid x✝\nhn : hasNext x✝ = true\nl r : List Char\nh : ValidFor l r x✝\n⊢ Valid (Iterator.next x✝)",
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"tactic": "let ⟨l, r, h⟩ := h.validFor"
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{
"state_after"... | [
638,
23
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
634,
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Mathlib/Data/Finsupp/ToDfinsupp.lean | Dfinsupp.toFinsupp_support | [
{
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"state_before": "ι : Type u_1\nR : Type ?u.6059\nM : Type u_2\ninst✝² : DecidableEq... | [
122,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_subset_Ioo_iff | [] | [
560,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
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Mathlib/Data/Real/CauSeq.lean | rat_add_continuous_lemma | [
{
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"tactic": "sim... | [
58,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Separation.lean | Filter.HasBasis.nhds_closure | [] | [
1547,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffAt.div | [] | [
1733,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1731,
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Mathlib/Data/List/BigOperators/Basic.lean | List.prod_map_erase | [
{
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568,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Multiset/Antidiagonal.lean | Multiset.antidiagonal_eq_map_powerset | [
{
"state_after": "case empty\nα : Type u_1\nβ : Type ?u.21052\ninst✝ : DecidableEq α\n⊢ antidiagonal 0 = map (fun t => (0 - t, t)) (powerset 0)\n\ncase cons\nα : Type u_1\nβ : Type ?u.21052\ninst✝ : DecidableEq α\na : α\ns : Multiset α\nhs : antidiagonal s = map (fun t => (s - t, t)) (powerset s)\n⊢ antidiagona... | [
100,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_sub_eq_left_of_degree_lt | [
{
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"state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Ring R\np q : R[X]\nh : degree q < degree p\n⊢ degree (p - q) = degree p",
"tactic"... | [
1329,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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] |
Mathlib/Probability/Integration.lean | ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun'' | [] | [
136,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
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Mathlib/Topology/Separation.lean | T0Space.of_cover | [
{
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358,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
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] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.finiteAt_principal | [] | [
4155,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4154,
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Mathlib/Analysis/SpecialFunctions/Complex/Log.lean | Complex.log_neg_one | [
{
"state_after": "no goals",
"state_before": "⊢ log (-1) = ↑π * I",
"tactic": "simp [log]"
}
] | [
100,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/Basic.lean | Submodule.subsingleton_iff | [
{
"state_after": "R : Type u_2\nR₁ : Type ?u.396898\nR₂ : Type ?u.396901\nR₃ : Type ?u.396904\nR₄ : Type ?u.396907\nS : Type ?u.396910\nK : Type ?u.396913\nK₂ : Type ?u.396916\nM : Type u_1\nM' : Type ?u.396922\nM₁ : Type ?u.396925\nM₂ : Type ?u.396928\nM₃ : Type ?u.396931\nM₄ : Type ?u.396934\nN : Type ?u.3969... | [
650,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
647,
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Mathlib/Control/Traversable/Instances.lean | List.id_traverse | [
{
"state_after": "case cons\nF G : Type u → Type u\ninst✝³ : Applicative F\ninst✝² : Applicative G\ninst✝¹ : LawfulApplicative F\ninst✝ : LawfulApplicative G\nα : Type u_1\nhead✝ : α\ntail✝ : List α\ntail_ih✝ : List.traverse pure tail✝ = tail✝\n⊢ (Seq.seq (cons head✝) fun x => tail✝) = head✝ :: tail✝",
"sta... | [
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63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
11
] |
Mathlib/AlgebraicGeometry/RingedSpace.lean | AlgebraicGeometry.RingedSpace.isUnit_res_of_isUnit_germ | [
{
"state_after": "case intro\nX : RingedSpace\nU : Opens ↑↑X.toPresheafedSpace\nf : ↑(X.presheaf.obj U.op)\nx : { x // x ∈ U }\nh : IsUnit (↑(germ X.presheaf x) f)\ng' : ↑(stalk X.presheaf ↑x)\nheq : ↑(germ X.presheaf x) f * g' = 1\n⊢ ∃ V i x, IsUnit (↑(X.presheaf.map i.op) f)",
"state_before": "X : RingedS... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
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] |
Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.card_Ioc_eq_card_Icc_sub_one | [] | [
231,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.valuation_zero | [] | [
386,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.totalDegree_finset_prod | [
{
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... | [
747,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
743,
1
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Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.dist_triangle_nonarch | [
{
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"state_before": "E : ℕ → Type u_1\nx y z : (n : ℕ) → E n\n⊢ dist x z ≤ max (dist x y) (dist y ... | [
302,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
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Mathlib/Data/Real/Hyperreal.lean | Hyperreal.coe_ne_one | [] | [
64,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
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Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Equivalence.cancel_counit_right | [
{
"state_after": "no goals",
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"tactic": "simp only [cancel_mono]"... | [
397,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.IsImage.toLocalEquiv | [] | [
474,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
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Mathlib/Algebra/Lie/Nilpotent.lean | LieIdeal.lcs_succ | [] | [
697,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
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Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.set_integral_deterministic' | [
{
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Mathlib/Topology/Order/Basic.lean | TFAE_mem_nhdsWithin_Ioi | [
{
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Mathlib/Data/PNat/Basic.lean | PNat.natPred_monotone | [] | [
53,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
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Mathlib/Topology/Algebra/Order/IntermediateValue.lean | intermediate_value_Ioo | [] | [
588,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
581,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | Right.one_lt_mul_of_lt_of_le | [] | [
948,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.bot_degree | [
{
"state_after": "ι : Sort ?u.287178\n𝕜 : Type ?u.287181\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✝ : Fintype V\nv : V\n⊢ card ∅ = 0",
"state_before": "ι : Sort ?u.287178\n𝕜 : Type ?u.287181\nV : Type u\nW : Type v\nX : Type w\nG : Simpl... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1494,
1
] |
Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.symm_apply_mem_iff_mem_image | [
{
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700,
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696,
1
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Mathlib/Data/List/Basic.lean | List.dropLast_eq_take | [
{
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2075,
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2070,
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Mathlib/Algebra/Support.lean | Function.support_div | [
{
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390,
85
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389,
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Mathlib/Data/Set/Pointwise/Basic.lean | Set.Nonempty.div | [] | [
647,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
646,
1
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Mathlib/Topology/Order/Basic.lean | Filter.tendsto_nhds_min_right | [] | [
747,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
745,
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Mathlib/Data/Vector3.lean | Vector3.recOn_nil | [] | [
143,
6
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142,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.two_zsmul_ne_zero_iff | [
{
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"tactic": "rw [← not_or, ← two_zsmul_eq_zero_iff]"
}
] | [
211,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
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Mathlib/Topology/Algebra/Order/Field.lean | Filter.Tendsto.mul_atBot | [
{
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49
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Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.bijective | [] | [
327,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
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Mathlib/CategoryTheory/Simple.lean | CategoryTheory.zero_not_simple | [
{
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"tactic": "aesop_cat"
}
] | [
135,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
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Mathlib/Data/TypeVec.lean | TypeVec.dropFun_RelLast' | [] | [
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Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.Red.Step.diamond_aux | [
{
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215,
88
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200,
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.hasSum_iff_tendsto_nat | [
{
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929,
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924,
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Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.assoc_aux_2 | [] | [
834,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.power_nat_eq | [
{
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}
] | [
962,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
961,
1
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Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.affineCombination_map | [
{
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509,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
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Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.eq_symm_apply | [
{
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"tactic": "rw [← e.right_inv hy, h]"
},
{
"sta... | [
231,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.uIcc_of_le | [
{
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"tactic": "rw [uIcc, inf_eq_left.2 h, sup_eq_right.2 h]"
}
] | [
882,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
881,
1
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Mathlib/Algebra/Group/Prod.lean | Prod.one_eq_mk | [] | [
110,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
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Mathlib/Dynamics/Ergodic/MeasurePreserving.lean | MeasureTheory.MeasurePreserving.measure_preimage_emb | [
{
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130,
34
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128,
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Mathlib/Data/Rat/Cast.lean | Rat.preimage_cast_Ici | [
{
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"state_before": "F : Type ?u.76773\nι : Type ?u.76776\nα : Type ?u.76779\nβ : Type ?u.76782\nK : Type u_1\ninst✝ ... | [
395,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
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Mathlib/LinearAlgebra/AffineSpace/Midpoint.lean | midpoint_vsub_midpoint | [] | [
93,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
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Mathlib/Data/Polynomial/Splits.lean | Polynomial.splits_of_splits_mul | [] | [
250,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
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Mathlib/Order/Filter/Prod.lean | Filter.prod_assoc | [] | [
306,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
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Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.mul_zeta_apply | [] | [
495,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
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Mathlib/Data/Real/CauSeq.lean | CauSeq.bounded' | [] | [
201,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
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Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.zeroLocus_subset_zeroLocus_iff | [] | [
259,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
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Mathlib/Data/Finset/Pi.lean | Finset.pi_val | [] | [
48,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
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Std/Data/Option/Basic.lean | Option.isNone_iff_eq_none | [] | [
22,
52
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
21,
1
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Mathlib/Algebra/GroupPower/Basic.lean | ofAdd_zsmul | [] | [
454,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
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Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.ofLE_comp_ofLE | [
{
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"state_before": "C : Type u₁\ninst✝¹ : Category C\nX✝ Y✝ Z✝ : C\nD ... | [
392,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
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Mathlib/Data/Matrix/DMatrix.lean | DMatrix.zero_apply | [] | [
127,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
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Mathlib/GroupTheory/SpecificGroups/Cyclic.lean | IsCyclic.image_range_card | [
{
"state_after": "no goals",
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"tactic": "rw [← orderOf_eq_card_of_forall_mem_zpowers ha, IsCyclic.image_range_orderOf ... | [
305,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Std/Data/Int/DivMod.lean | Int.lt_div_add_one_mul_self | [
{
"state_after": "a b : Int\nH : 0 < b\n⊢ a < b * div a b + b",
"state_before": "a b : Int\nH : 0 < b\n⊢ a < (div a b + 1) * b",
"tactic": "rw [Int.add_mul, Int.one_mul, Int.mul_comm]"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nH : 0 < b\n⊢ a < b * div a b + b",
"tactic"... | [
549,
72
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
547,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.dvd_of_dvd_mul_left | [
{
"state_after": "R : Type u\ninst✝ : CommSemiring R\nx y z : R\nH1 : IsCoprime x y\nH2 : x ∣ y * z\na b : R\nH : a * x + b * y = 1\n⊢ x ∣ z",
"state_before": "R : Type u\ninst✝ : CommSemiring R\nx y z : R\nH1 : IsCoprime x y\nH2 : x ∣ y * z\n⊢ x ∣ z",
"tactic": "let ⟨a, b, H⟩ := H1"
},
{
"state... | [
99,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.exists_pos_lintegral_lt_of_sigmaFinite | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1816357\nγ : Type ?u.1816360\nδ : Type ?u.1816363\nm m0 : MeasurableSpace α\nμ : Measure α\ninst✝ : SigmaFinite μ\nε : ℝ≥0∞\nε0 : ε ≠ 0\ns : ℕ → Set α := disjointed (spanningSets μ)\n⊢ ∃ g, (∀ (x : α), 0 < g x) ∧ Measurable g ∧ (∫⁻ (x : α), ↑(g x) ∂μ) < ε",
"state... | [
1918,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1903,
1
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Mathlib/Algebra/Lie/Basic.lean | add_lie | [] | [
117,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSpace.comap_eq_generateFrom | [] | [
112,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/AlgebraicTopology/SplitSimplicialObject.lean | SimplicialObject.Splitting.IndexSet.fac_pull | [] | [
199,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Analysis/MeanInequalities.lean | Real.Lp_add_le_hasSum_of_nonneg | [
{
"state_after": "case intro\nι : Type u\ns : Finset ι\ng : ι → ℝ\np q : ℝ\nhp : 1 ≤ p\nhg : ∀ (i : ι), 0 ≤ g i\nA B : ℝ\nhA : 0 ≤ A\nhB : 0 ≤ B\nhgB : HasSum (fun i => g i ^ p) (B ^ p)\nf : ι → ℝ≥0\nhfA : HasSum (fun i => (fun i => ↑(f i)) i ^ p) (A ^ p)\n⊢ ∃ C, 0 ≤ C ∧ C ≤ A + B ∧ HasSum (fun i => ((fun i => ... | [
712,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/Algebra/Divisibility/Units.lean | Units.mul_right_dvd | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Monoid α\na b : α\nu : αˣ\nh : a ∣ b\n⊢ a * ↑u * ↑u⁻¹ = a",
"tactic": "rw [mul_assoc, u.mul_inv, mul_one]"
}
] | [
44,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
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Mathlib/Analysis/SpecificLimits/Normed.lean | isLittleO_pow_const_const_pow_of_one_lt | [
{
"state_after": "α : Type ?u.86654\nβ : Type ?u.86657\nι : Type ?u.86660\nR : Type u_1\ninst✝ : NormedRing R\nk : ℕ\nr : ℝ\nhr : 1 < r\nthis : Tendsto (fun x => x ^ k) (𝓝[Set.Ioi 1] 1) (𝓝 1)\n⊢ (fun n => ↑n ^ k) =o[atTop] fun n => r ^ n",
"state_before": "α : Type ?u.86654\nβ : Type ?u.86657\nι : Type ?u... | [
206,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Algebra/Order/Group/MinMax.lean | max_div_div_right' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedCommGroup α\na✝ b✝ c✝ a b c : α\n⊢ max (a / c) (b / c) = max a b / c",
"tactic": "simpa only [div_eq_mul_inv] using max_mul_mul_right a b c⁻¹"
}
] | [
62,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/RingTheory/Nilpotent.lean | IsNilpotent.zero | [] | [
47,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/CategoryTheory/Monoidal/Rigid/Basic.lean | CategoryTheory.tensorRightHomEquiv_symm_naturality | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\ninst✝¹ : MonoidalCategory C\nX X' Y Y' Z : C\ninst✝ : ExactPairing Y Y'\nf : X ⟶ X'\ng : X' ⟶ Z ⊗ Y'\n⊢ (f ≫ g ⊗ 𝟙 Y) ≫ (α_ Z Y' Y).hom ≫ (𝟙 Z ⊗ ε_ Y Y') ≫ (ρ_ Z).hom =\n (f ⊗ 𝟙 Y) ≫ (g ⊗ 𝟙 Y) ≫ (α_ Z Y' Y).hom ≫ (𝟙 Z ⊗ ε_ Y Y') ≫ (ρ_ Z).hom",
"sta... | [
405,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.cosh_two_mul | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ cosh (2 * x) = cosh x ^ 2 + sinh x ^ 2",
"tactic": "rw [two_mul, cosh_add, sq, sq]"
}
] | [
769,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
769,
1
] |
Mathlib/Data/List/Duplicate.lean | List.duplicate_iff_sublist | [
{
"state_after": "case nil\nα : Type u_1\nl : List α\nx : α\n⊢ x ∈+ [] ↔ [x, x] <+ []\n\ncase cons\nα : Type u_1\nl✝ : List α\nx y : α\nl : List α\nIH : x ∈+ l ↔ [x, x] <+ l\n⊢ x ∈+ y :: l ↔ [x, x] <+ y :: l",
"state_before": "α : Type u_1\nl : List α\nx : α\n⊢ x ∈+ l ↔ [x, x] <+ l",
"tactic": "inductio... | [
130,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidWithZeroHom.copy_eq | [] | [
894,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
892,
1
] |
Mathlib/Data/Set/Prod.lean | Set.diag_preimage_prod_self | [] | [
515,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_union_add_inter | [] | [
1714,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1712,
1
] |
Mathlib/Data/Real/GoldenRatio.lean | gold_sq | [
{
"state_after": "⊢ ((1 + sqrt 5) / 2) ^ 2 - ((1 + sqrt 5) / 2 + 1) = 0",
"state_before": "⊢ φ ^ 2 = φ + 1",
"tactic": "rw [goldenRatio, ← sub_eq_zero]"
},
{
"state_after": "⊢ sqrt 5 ^ 2 * (↑(Int.ofNat 1) / ↑4) + ↑(Int.negOfNat 5) * (↑(Int.ofNat 1) / ↑4) = 0",
"state_before": "⊢ ((1 + sqrt 5... | [
99,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.Tape.mk'_head | [] | [
559,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
] |
Mathlib/Algebra/GeomSum.lean | geom_sum₂_mul | [] | [
193,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.coe_smul | [
{
"state_after": "no goals",
"state_before": "K F : Type u\ninst✝ : Field F\np q : F[X]\nf g : RatFunc F\nr : F\n⊢ ↑(r • f) = r • ↑f",
"tactic": "rw [smul_eq_C_mul, ← C_mul_eq_smul, coe_mul, coe_C]"
}
] | [
1752,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1751,
1
] |
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