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/LinearAlgebra/AdicCompletion.lean | IsAdicComplete.subsingleton | [] | [
280,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
11
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Mathlib/MeasureTheory/Integral/IntegrableOn.lean | integrableOn_Iic_iff_integrableOn_Iio' | [
{
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672,
80
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669,
1
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Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.map_sub_int | [] | [
373,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
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Mathlib/Data/Sum/Basic.lean | Sum.inl_injective | [] | [
65,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
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Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.one_rpow | [] | [
77,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | differentiableWithinAt_univ | [
{
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Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.norm_nat_cast | [] | [
543,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
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Mathlib/Order/BooleanAlgebra.lean | inf_sdiff | [
{
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"tactic": "rw [sup_inf_left]"
},
{
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435,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
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Mathlib/Data/Nat/Interval.lean | Finset.range_eq_Ico | [] | [
93,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
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Mathlib/Topology/ContinuousFunction/Basic.lean | ContinuousMap.comp_id | [] | [
262,
19
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Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.prod_coe_symm | [] | [
958,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
956,
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Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.curry_apply | [] | [
586,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
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Mathlib/Data/Complex/Basic.lean | Complex.ofReal_re | [] | [
95,
6
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94,
1
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Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | IsBoundedBilinearMap.isBoundedLinearMap_right | [] | [
438,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
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Mathlib/CategoryTheory/Bicategory/Basic.lean | CategoryTheory.Bicategory.leftUnitor_whiskerRight | [
{
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"tactic": "rw [← whiskerLeft_iff, whiskerLeft_comp, ← cancel_epi (α_ _ _ _).hom, ←\n cancel_epi ((α_ _ _ _).hom ▷ _), pentag... | [
431,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
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Mathlib/Algebra/Order/SMul.lean | le_inv_smul_iff | [
{
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256,
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255,
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Mathlib/Data/Matrix/Basic.lean | Matrix.smul_eq_mul_diagonal | [
{
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1284,
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Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atBot_add_nonpos_right | [] | [
646,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
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Mathlib/Analysis/Convex/Function.lean | ConcaveOn.comp_convexOn | [] | [
151,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
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Mathlib/Data/List/Zip.lean | List.zip_of_prod | [
{
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"tactic": "rw [← hl, ← hr, ← zip_unzip lp, ← unzip_left, ← u... | [
253,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
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Mathlib/Data/Nat/PartENat.lean | PartENat.ne_top_iff | [
{
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}
] | [
366,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
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Mathlib/Analysis/Calculus/FDeriv/Mul.lean | DifferentiableWithinAt.mul_const | [] | [
425,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
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Mathlib/Algebra/Ring/Commute.lean | Commute.neg_left_iff | [] | [
109,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
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Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | Ideal.homogeneousHull.gc | [] | [
615,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
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Mathlib/Data/List/Rotate.lean | List.rotate_perm | [
{
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{
"state_after": "case zero\nα : Type u\nl✝ l : List α\n⊢ rotate' l zero ~ l\n\ncase succ\nα : Type u\nl✝ : List α\nn : ℕ\... | [
193,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
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Mathlib/Data/Set/Semiring.lean | SetSemiring.down_one | [] | [
198,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
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Mathlib/Order/Lattice.lean | inf_right_comm | [] | [
528,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
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Mathlib/GroupTheory/Coset.lean | normal_of_eq_cosets | [
{
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"tactic": "rw ... | [
261,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
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Mathlib/GroupTheory/SpecificGroups/Alternating.lean | alternatingGroup.nontrivial_of_three_le_card | [
{
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"tacti... | [
224,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/FieldTheory/RatFunc.lean | RatFunc.mul_inv_cancel | [
{
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421,
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Mathlib/RingTheory/Polynomial/ScaleRoots.lean | Polynomial.scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero | [] | [
140,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
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Mathlib/Data/Num/Lemmas.lean | ZNum.cast_to_int | [
{
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},
{
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1113,
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Mathlib/CategoryTheory/Elements.lean | CategoryTheory.CategoryOfElements.fromStructuredArrow_obj | [] | [
164,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
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Mathlib/Order/Filter/Prod.lean | Filter.mem_coprod_iff | [
{
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... | [
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474,
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Mathlib/Data/List/Nodup.lean | List.Nodup.product | [
{
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"state_before": "α : Type ... | [
353,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
11
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Mathlib/Data/Set/Basic.lean | Set.empty_diff | [] | [
1898,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1897,
1
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Mathlib/Data/Finset/Lattice.lean | Finset.coe_sup_of_nonempty | [
{
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"tactic": "si... | [
1002,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1001,
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Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.zero_rpow_eq_iff | [
{
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"tactic": "constructor"
},
{
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121,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.span_nat_eq_addSubmonoid_closure | [
{
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189,
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183,
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.isCycle_def | [] | [
907,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
905,
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Mathlib/Analysis/InnerProductSpace/Orientation.lean | OrthonormalBasis.same_orientation_iff_det_eq_det | [
{
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87,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.degrees_rename | [
{
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"tactic": "classical\nintro i\nrw... | [
251,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.eventually_nhds' | [
{
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405,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
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Mathlib/Algebra/Order/Group/Defs.lean | StrictMonoOn.inv | [] | [
1330,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1329,
1
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Mathlib/Algebra/Group/Basic.lean | mul_right_eq_self | [
{
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"tactic": "rw [mul_one]"
}
] | [
184,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.uniformContinuousOn_iff_le | [] | [
833,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
830,
1
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Mathlib/MeasureTheory/MeasurableSpaceDef.lean | Set.Countable.measurableSet | [
{
"state_after": "α : Type u_1\nβ : Type ?u.13908\nγ : Type ?u.13911\nδ : Type ?u.13914\nδ' : Type ?u.13917\nι : Sort ?u.13920\ns✝ t u : Set α\ninst✝¹ : MeasurableSpace α\ninst✝ : MeasurableSingletonClass α\ns : Set α\nhs : Set.Countable s\n⊢ MeasurableSet (⋃ (x : α) (_ : x ∈ s), {x})",
"state_before": "α :... | [
320,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/RingTheory/Localization/NumDen.lean | IsFractionRing.eq_zero_of_num_eq_zero | [
{
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99,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
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src/lean/Init/Data/List/Basic.lean | List.append_cons | [
{
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"state_before": "α : Type u\nβ : Type v\nγ : Type w\nas : List α\nb : α\nbs : List α\n⊢ as ++ b :: bs = as ++ b :: nil ++ bs",
"tactic": "induction as with\n| nil => simp\n| cons a as ih => simp [ih]"
},
{
"state_after": "no goals",
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111,
30
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
108,
1
] |
Mathlib/Topology/Semicontinuous.lean | UpperSemicontinuous.add' | [] | [
928,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
925,
1
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Mathlib/Data/Set/Lattice.lean | Set.mapsTo_iUnion₂ | [] | [
1434,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1432,
1
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Mathlib/Order/Hom/CompleteLattice.lean | sInfHom.comp_assoc | [] | [
474,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.bound_of_isBigO_nat_atTop | [
{
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2120,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2118,
1
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Mathlib/Topology/UniformSpace/UniformConvergence.lean | uniformCauchySeqOn_iff_uniformCauchySeqOnFilter | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝ : UniformSpace β\nF : ι → α → β\nf : α → β\ns s' : Set α\nx : α\np : Filter ι\np' : Filter α\ng : ι → α\n⊢ (∀ (u : Set (β × β)), u ∈ 𝓤 β → ∀ᶠ (m : ι × ι) in p ×ˢ p, ∀ (x : α), x ∈ s → (F m.fst x, F m.snd x) ∈ u) ↔\n ∀ (u : Set (β × β)),... | [
414,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
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src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.ExprCnstr.denote_toPoly | [
{
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"state_before": "ctx : Context\nc : ExprCnstr\n⊢ PolyCnstr.denote ctx (toPoly c) = denote ctx c",
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564,
39
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
559,
1
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Mathlib/Topology/Order/Basic.lean | nhdsWithin_Iic_neBot | [] | [
259,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_preimage_of_subset_range_lift | [
{
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"state_before": "α✝ β✝ α : Type u\nβ : Type v\nf : α → β\ns : Set β\nh : s ⊆ range f\n⊢ lift (#↑s) ≤ lift (#↑(f ⁻¹' s))",
"tactic": "rw [lift_mk_le.{v, u, 0}]"
},
{
"state_after"... | [
2182,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2172,
1
] |
Mathlib/RingTheory/Artinian.lean | IsArtinian.exists_endomorphism_iterate_ker_sup_range_eq_top | [
{
"state_after": "case intro\nR : Type u_1\nM : Type u_2\ninst✝³ : Ring R\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\ninst✝ : IsArtinian R M\nf : M →ₗ[R] M\nn : ℕ\nw :\n ∀ (m : ℕ),\n n ≤ m →\n ↑(OrderHom.comp (LinearMap.iterateRange f)\n { toFun := fun n => n + 1,\n monot... | [
239,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
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Mathlib/CategoryTheory/Sums/Basic.lean | CategoryTheory.Sum.swap_obj_inl | [] | [
122,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.compl_sSup | [
{
"state_after": "no goals",
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"tactic": "simp only [coe_compl, coe... | [
909,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
908,
11
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Mathlib/Analysis/Convex/Caratheodory.lean | Caratheodory.minCardFinsetOfMemConvexHull_nonempty | [
{
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"state_before": "𝕜 : Type u_1\nE : Type u\ni... | [
126,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
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Mathlib/Data/Polynomial/Mirror.lean | Polynomial.mirror_X | [] | [
65,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
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src/lean/Init/Classical.lean | Classical.em | [
{
"state_after": "no goals",
"state_before": "p : Prop\nU : Prop → Prop := fun x => x = True ∨ p\nV : Prop → Prop := fun x => x = False ∨ p\nexU : ∃ x, U x\nexV : ∃ x, V x\nu : Prop := choose exU\nv : Prop := choose exV\nu_def : U u\nv_def : V v\nhut : u = True\nhvf : v = False\n⊢ u ≠ v",
"tactic": "sim... | [
57,
27
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
26,
1
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Mathlib/Algebra/Hom/Ring.lean | RingHom.copy_eq | [] | [
514,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | WithTop.coe_sSup | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.95088\nγ : Type ?u.95091\nι : Sort ?u.95094\ninst✝ : ConditionallyCompleteLinearOrderBot α\ns : Set α\nhb : BddAbove s\n⊢ ↑(sSup s) = ⨆ (a : α) (_ : a ∈ s), ↑a",
"tactic": "rw [coe_sSup' hb, sSup_image]"
}
] | [
1226,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1225,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.max_eq_left | [
{
"state_after": "a b : Nat\nh : b ≤ a\n⊢ max b a = a",
"state_before": "a b : Nat\nh : b ≤ a\n⊢ max a b = a",
"tactic": "rw [← Nat.max_comm b a]"
},
{
"state_after": "no goals",
"state_before": "a b : Nat\nh : b ≤ a\n⊢ max b a = a",
"tactic": "exact Nat.max_eq_right h"
}
] | [
214,
52
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
213,
11
] |
Mathlib/Topology/Algebra/Module/FiniteDimension.lean | LinearMap.det_toContinuousLinearMap | [] | [
318,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/Data/Set/Prod.lean | Set.mk_preimage_prod_left_eq_empty | [
{
"state_after": "case h\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.26517\nδ : Type ?u.26520\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\na✝ : α\nb : β\nhb : ¬b ∈ t\na : α\n⊢ a ∈ (fun a => (a, b)) ⁻¹' s ×ˢ t ↔ a ∈ ∅",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.26517\nδ : Type ?u.26520\ns s₁ s₂ : Set α\nt ... | [
239,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.floor_eq_iff | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.139599\nα : Type u_1\nβ : Type ?u.139605\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na : α\n⊢ ⌊a⌋ = z ↔ ↑z ≤ a ∧ a < ↑z + 1",
"tactic": "rw [le_antisymm_iff, le_floor, ← Int.lt_add_one_iff, floor_lt, Int.cast_add, Int.cast_one,\n ... | [
781,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
779,
1
] |
Mathlib/Topology/Order/Basic.lean | IsLUB.mem_lowerBounds_of_tendsto | [] | [
2065,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2062,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalMax.on | [] | [
98,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Topology/UniformSpace/Equiv.lean | UniformEquiv.image_preimage | [] | [
233,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.Quotient.mk_smul | [] | [
144,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Std/Data/List/Lemmas.lean | List.singleton_sublist | [
{
"state_after": "α : Type u_1\na : α\nl : List α\nh : a ∈ l\n⊢ [a] <+ l",
"state_before": "α : Type u_1\na : α\nl : List α\n⊢ [a] <+ l ↔ a ∈ l",
"tactic": "refine ⟨fun h => h.subset (mem_singleton_self _), fun h => ?_⟩"
},
{
"state_after": "case intro.intro\nα : Type u_1\na : α\nw✝¹ w✝ : List α... | [
426,
66
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
423,
9
] |
Mathlib/Algebra/Category/GroupCat/Colimits.lean | AddCommGroupCat.Colimits.cocone_naturality | [
{
"state_after": "case w\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ AddCommGroupCat\nj j' : J\nf : j ⟶ j'\nx✝ : ↑(F.obj j)\n⊢ ↑(F.map f ≫ coconeMorphism F j') x✝ = ↑(coconeMorphism F j) x✝",
"state_before": "J : Type v\ninst✝ : SmallCategory J\nF : J ⥤ AddCommGroupCat\nj j' : J\nf : j ⟶ j'\n⊢ F.map f ≫ c... | [
219,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/CategoryTheory/Opposites.lean | Quiver.Hom.unop_op | [] | [
55,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Data/Sum/Order.lean | WithBot.orderIsoPUnitSumLex_symm_inr | [] | [
766,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
765,
1
] |
Std/Data/String/Lemmas.lean | String.join_eq | [
{
"state_after": "no goals",
"state_before": "ss : List String\nx✝ : List Char\n⊢ List.foldl (fun x x_1 => x ++ x_1) { data := x✝ } [] = { data := x✝ ++ List.join (List.map data []) }",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "ss✝ : List String\ns : List Char\nss : L... | [
478,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
475,
1
] |
Mathlib/Control/Basic.lean | CommApplicative.commutative_map | [
{
"state_after": "no goals",
"state_before": "α✝ β✝ γ✝ : Type u\nm✝ : ?m.20189\nm : Type u → Type v\nh : Applicative m\ninst✝ : CommApplicative m\nα β γ : Type u\na : m α\nb : m β\nf : α → β → γ\n⊢ (Seq.seq (f <$> a) fun x => b) = (fun p => f p.fst p.snd) <$> Seq.seq (Prod.mk <$> a) fun x => b",
"tactic... | [
275,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.Ioo_succ_right_eq_insert | [] | [
512,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.le_iff_val_le_val | [] | [
290,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Data/Polynomial/EraseLead.lean | Polynomial.lt_natDegree_of_mem_eraseLead_support | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\nf : R[X]\na : ℕ\nh : a ≠ natDegree f ∧ a ∈ support f\n⊢ a < natDegree f",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nf : R[X]\na : ℕ\nh : a ∈ support (eraseLead f)\n⊢ a < natDegree f",
"tactic": "rw [eraseLead_support, mem_erase] at h"
},
{... | [
100,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Order/Disjoint.lean | Disjoint.mono_left | [] | [
73,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Data/Finite/Basic.lean | Finite.prod_left | [] | [
77,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/RingTheory/MvPolynomial/Ideal.lean | MvPolynomial.mem_ideal_span_monomial_image | [
{
"state_after": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\nx : MvPolynomial σ R\ns : Set (σ →₀ ℕ)\n⊢ (∀ (m : σ →₀ ℕ), m ∈ x.support → ∃ m', m' ∈ s ∧ ∃ d, m = d + m') ↔\n ∀ (xi : σ →₀ ℕ), xi ∈ support x → ∃ si, si ∈ s ∧ si ≤ xi",
"state_before": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring... | [
39,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/Data/Polynomial/Lifts.lean | Polynomial.X_pow_mem_lifts | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹ : Semiring R\nS : Type v\ninst✝ : Semiring S\nf✝ f : R →+* S\nn : ℕ\n⊢ ↑(mapRingHom f) (X ^ n) = X ^ n",
"tactic": "simp only [coe_mapRingHom, map_pow, Set.mem_univ, Subsemiring.coe_top, eq_self_iff_true,\n map_X, and_self_iff]"
}
] | [
110,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.cardDistinctFactors_apply | [] | [
918,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
917,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | WithBot.ciSup_empty | [] | [
136,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/CategoryTheory/Types.lean | CategoryTheory.types_id_apply | [] | [
75,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_eq_restrict_biUnion_finset_iff | [] | [
2782,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2780,
1
] |
Mathlib/Analysis/Convex/Normed.lean | isConnected_setOf_sameRay | [
{
"state_after": "case pos\nι : Type ?u.49013\nE : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\ns t : Set E\nx : E\nhx : x = 0\n⊢ IsConnected {y | SameRay ℝ x y}\n\ncase neg\nι : Type ?u.49013\nE : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\ns t : Set E\nx : E\... | [
145,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Combinatorics/Composition.lean | Composition.index_embedding | [
{
"state_after": "n : ℕ\nc : Composition n\ni : Fin (length c)\nj : Fin (blocksFun c i)\n⊢ i = index c (↑(embedding c i) j)",
"state_before": "n : ℕ\nc : Composition n\ni : Fin (length c)\nj : Fin (blocksFun c i)\n⊢ index c (↑(embedding c i) j) = i",
"tactic": "symm"
},
{
"state_after": "n : ℕ\n... | [
438,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/Order/Hom/Set.lean | OrderIso.range_eq | [] | [
31,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.SummableFamily.coe_ofFinsupp | [] | [
1680,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1679,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.degree_of_b_eq_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.580862\nF : Type ?u.580865\nK : Type ?u.580868\nP Q : Cubic R\na b c d a' b' c' d' : R\ninst✝ : Semiring R\nha : P.a = 0\nhb : P.b = 0\n⊢ degree (toPoly P) ≤ 1",
"tactic": "simpa only [of_b_eq_zero ha hb] using degree_linear_le"
}... | [
332,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/Topology/Instances/TrivSqZeroExt.lean | TrivSqZeroExt.nhds_inl | [] | [
54,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Topology/Hom/Open.lean | ContinuousOpenMap.copy_eq | [] | [
101,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Data/Real/Basic.lean | Real.sSup_nonpos | [] | [
890,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
889,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderIso.injective | [] | [
818,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
817,
11
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.injective_pointReflection_left_of_module | [
{
"state_after": "no goals",
"state_before": "k : Type u_1\nP₁ : Type u_2\nP₂ : Type ?u.663302\nP₃ : Type ?u.663305\nP₄ : Type ?u.663308\nV₁ : Type u_3\nV₂ : Type ?u.663314\nV₃ : Type ?u.663317\nV₄ : Type ?u.663320\ninst✝¹³ : Ring k\ninst✝¹² : AddCommGroup V₁\ninst✝¹¹ : Module k V₁\ninst✝¹⁰ : AffineSpace V₁... | [
603,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
599,
1
] |
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