file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/Order/Filter/Pointwise.lean | Filter.mem_mul | [] | [
300,
10
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299,
1
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Mathlib/Analysis/Calculus/FDerivMeasurable.lean | RightDerivMeasurableAux.b_mem_nhdsWithin_Ioi | [
{
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26
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500,
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Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | LocalHomeomorph.extend_source | [
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Mathlib/RingTheory/IsTensorProduct.lean | IsBaseChange.of_lift_unique | [
{
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Mathlib/Data/Nat/Multiplicity.lean | Nat.multiplicity_eq_card_pow_dvd | [
{
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{
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Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_from_top | [] | [
233,
100
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Mathlib/Data/Set/Function.lean | Set.mapsTo_image | [
{
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501,
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Mathlib/Analysis/Convex/SpecificFunctions/Deriv.lean | deriv_sqrt_mul_log' | [] | [
138,
28
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136,
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Std/Data/Int/Lemmas.lean | Int.lt_of_add_one_le | [] | [
1250,
66
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1250,
1
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.essSup_trim | [
{
"state_after": "α : Type u_1\nE : Type ?u.3171975\nF : Type ?u.3171978\nG : Type ?u.3171981\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nhm : m ≤ m0\nf : α → ℝ≥0∞\nhf : Measurable f\n⊢ limsup f (Measure... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/ModEq.lean | AddCommGroup.nsmul_add_modEq | [
{
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"tactic": "simp [← sub_sub]"
}
] | [
130,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
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Mathlib/Data/Matrix/Basic.lean | Matrix.col_mulVec | [
{
"state_after": "case a.h\nl : Type ?u.1216213\nm : Type u_2\nn : Type u_1\no : Type ?u.1216222\nm' : o → Type ?u.1216227\nn' : o → Type ?u.1216232\nR : Type ?u.1216235\nS : Type ?u.1216238\nα : Type v\nβ : Type w\nγ : Type ?u.1216245\ninst✝¹ : Fintype n\ninst✝ : NonUnitalNonAssocSemiring α\nM : Matrix m n α\n... | [
2717,
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Mathlib/CategoryTheory/SingleObj.lean | CategoryTheory.SingleObj.mapHom_id | [] | [
138,
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137,
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Mathlib/Topology/MetricSpace/Gluing.lean | Metric.Sigma.fst_eq_of_dist_lt_one | [
{
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"state_before": "ι : Type u_1\nE : ι → Type u_2\ninst✝ : (i : ι) → MetricSpace... | [
348,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Complex/Exponential.lean | Complex.tanh_zero | [
{
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}
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697,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
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Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.map_piecewise_smul | [
{
"state_after": "R : Type u\nι : Type u'\nn : ℕ\nM : Fin (Nat.succ n) → Type v\nM₁ : ι → Type v₁\nM₂ : Type v₂\nM₃ : Type v₃\nM' : Type v'\ninst✝⁷ : CommSemiring R\ninst✝⁶ : (i : ι) → AddCommMonoid (M₁ i)\ninst✝⁵ : (i : Fin (Nat.succ n)) → AddCommMonoid (M i)\ninst✝⁴ : AddCommMonoid M₂\ninst✝³ : (i : Fin (Nat.... | [
851,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
838,
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Mathlib/Analysis/Calculus/Deriv/Inv.lean | DifferentiableAt.div | [] | [
219,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ioc_subset_Icc_self | [
{
"state_after": "ι : Type ?u.24849\nα : Type u_1\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x : α\n⊢ Set.Ioc a b ⊆ Set.Icc a b",
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... | [
242,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
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Std/Data/Array/Lemmas.lean | Array.getElem_ofFn | [
{
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},
{
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"... | [
302,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
300,
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Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.mod_def | [] | [
198,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
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Mathlib/RepresentationTheory/Action.lean | Action.ofMulAction_apply | [] | [
837,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/CategoryTheory/CofilteredSystem.lean | CategoryTheory.Functor.eventually_injective | [
{
"state_after": "J : Type u\ninst✝⁵ : Category J\nF : J ⥤ Type v\ni j k : J\ns : Set (F.obj i)\ninst✝⁴ : IsCofilteredOrEmpty J\ninst✝³ : ∀ (j : J), _root_.Nonempty (F.obj j)\ninst✝² : ∀ (j : J), Finite (F.obj j)\nFsur : ∀ ⦃i j : J⦄ (f : i ⟶ j), Function.Surjective (F.map f)\ninst✝¹ : _root_.Nonempty J\ninst✝ :... | [
376,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
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Mathlib/Topology/Algebra/StarSubalgebra.lean | elementalStarAlgebra.star_self_mem | [] | [
190,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
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Mathlib/Order/Monotone/Basic.lean | StrictMono.injective | [] | [
846,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
845,
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Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean | ModularGroup.T_inv_mul_apply_one | [
{
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"state_before": "g : SL(2, ℤ)\n⊢ ↑(T⁻¹ * g) 1 = ↑g 1",
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}
] | [
390,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
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Mathlib/FieldTheory/Laurent.lean | RatFunc.laurent_laurent | [
{
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39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Intervals/Monotone.lean | antitone_Ioi | [] | [
34,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Seq/Seq.lean | Stream'.Seq.append_assoc | [
{
"state_after": "case bisim\nα : Type u\nβ : Type v\nγ : Type w\ns t u : Seq α\n⊢ IsBisimulation fun s1 s2 => ∃ s t u, s1 = append (append s t) u ∧ s2 = append s (append t u)\n\ncase r\nα : Type u\nβ : Type v\nγ : Type w\ns t u : Seq α\n⊢ ∃ s_1 t_1 u_1,\n append (append s t) u = append (append s_1 t_1) u_1 ... | [
690,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
675,
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] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_lt_top_iff_lintegral_rpow_nnnorm_lt_top | [
{
"state_after": "α : Type u_1\nE : Type ?u.831489\nF : Type u_2\nG : Type ?u.831495\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf : α → F\nhp_ne_zero : p ≠ 0\nhp_ne_top : p ≠ ⊤\nh : (∫⁻ (a : α), ↑‖f a‖₊... | [
166,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
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Mathlib/Logic/Function/Basic.lean | Function.Injective.eq_iff | [] | [
99,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Basic.lean | isOpen_sInter | [
{
"state_after": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns✝ s₁ s₂ t : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\ns : Set (Set α)\nhs : Set.Finite s\nx✝ : ∀ (t : Set α), t ∈ ∅ → IsOpen t\n⊢ IsOpen univ",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns✝ s₁ s₂ t : Set α\np p₁ p₂ :... | [
166,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
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Mathlib/Algebra/Lie/Basic.lean | zero_lie | [] | [
146,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
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Mathlib/Data/Finset/Sups.lean | Finset.coe_infs | [] | [
244,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
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Mathlib/Data/Real/EReal.lean | EReal.coe_add | [] | [
355,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
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Mathlib/RingTheory/IntegralClosure.lean | IsIntegral.tmul | [
{
"state_after": "case intro.intro\nR : Type u_1\nA : Type u_3\nB : Type u_2\nS : Type ?u.811467\ninst✝⁵ : CommRing R\ninst✝⁴ : CommRing A\ninst✝³ : CommRing B\ninst✝² : CommRing S\ninst✝¹ : Algebra R A\ninst✝ : Algebra R B\nf : R →+* S\nx : A\ny : B\np : R[X]\nhp : Monic p\nhp' : eval₂ (_root_.algebraMap R B) ... | [
697,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
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Mathlib/Topology/Order/Basic.lean | Ico_subset_closure_interior | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na✝ b✝ : α\ns : Set α\na b : α\n⊢ Ico a b ⊆ closure (interior (Ico a b))",
"tactic": "simpa only [dual_Ioc] using Ioc_... | [
2323,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2322,
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Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.isIso_limit_cocone_parallelPair_of_epi | [] | [
1067,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1065,
1
] |
Mathlib/Algebra/Module/Torsion.lean | Submodule.coe_torsion_eq_annihilator_ne_bot | [
{
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"state_before": "R : Type u_2\nM : Type u_1\ninst✝⁴ : CommSemi... | [
701,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
694,
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Mathlib/Data/Finset/Basic.lean | Finset.disjUnion_singleton | [
{
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"tactic": "rw [disjUnion_comm, singleton_disjUnion]"
}
] | [
1028,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1026,
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Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.coe_ofLinearIsometry | [] | [
1104,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1101,
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Mathlib/MeasureTheory/Group/MeasurableEquiv.lean | measurableEmbedding_mulRight | [] | [
145,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
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Mathlib/Order/Filter/Basic.lean | Filter.principal_eq_bot_iff | [] | [
982,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
981,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | le_mul_of_le_mul_left | [] | [
268,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.sub_mod_eq_zero_of_mod_eq | [
{
"state_after": "no goals",
"state_before": "m n k l : ℕ\nh : m % k = n % k\n⊢ (m - n) % k = 0",
"tactic": "rw [← Nat.mod_add_div m k, ← Nat.mod_add_div n k, ← h, tsub_add_eq_tsub_tsub,\n @add_tsub_cancel_left, ← mul_tsub k, Nat.mul_mod_right]"
}
] | [
493,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | AddValuation.map_add' | [
{
"state_after": "K : Type ?u.4087485\nF : Type ?u.4087488\nR : Type u_2\ninst✝³ : DivisionRing K\nΓ₀ : Type u_1\nΓ'₀ : Type ?u.4087500\ninst✝² : Ring R\ninst✝¹ : LinearOrderedAddCommMonoidWithTop Γ₀\ninst✝ : LinearOrderedAddCommMonoidWithTop Γ'₀\nv : AddValuation R Γ₀\nx✝ y✝ z x y : R\n⊢ ↑v x ≤ ↑v (x + y) ∨ ↑v... | [
689,
16
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686,
1
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.equivFunOnFinite_symm_single | [
{
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522,
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520,
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Mathlib/Data/Set/Function.lean | Set.piecewise_eqOn | [] | [
1403,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1402,
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Mathlib/Data/Matrix/Kronecker.lean | Matrix.kroneckerMap_reindex | [
{
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163,
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158,
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Mathlib/Order/BooleanAlgebra.lean | inf_sdiff_self_left | [
{
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}
] | [
179,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
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Mathlib/Algebra/Hom/Ring.lean | RingHom.comp_id | [] | [
714,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
713,
1
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Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Continuous.log | [] | [
389,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.blsub_const | [] | [
1907,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1905,
1
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Mathlib/Topology/Algebra/Module/Basic.lean | IsClosed.submodule_topologicalClosure_eq | [] | [
184,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigOWith_prod_left | [] | [
1003,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1001,
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Mathlib/Data/List/Pairwise.lean | List.pwFilter_eq_self | [
{
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419,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
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Mathlib/Algebra/Order/Floor.lean | Nat.pos_of_floor_pos | [
{
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"tactic": "rwa [floor_of_nonpos ha] at h"
}
] | [
219,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
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Mathlib/Data/Vector/Mem.lean | Vector.not_mem_map_zero | [
{
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"tactic": "simpa only [Vector.eq_nil v, Vector.map_nil, Vector.toList_nil] using List.not_mem_nil b"
}
] | [
85,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
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Mathlib/Algebra/GeomSum.lean | Commute.geom_sum₂ | [
{
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258,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
11
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Mathlib/Topology/Connected.lean | isTotallySeparated_singleton | [] | [
1372,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1371,
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Mathlib/Algebra/Lie/Submodule.lean | LieHom.isIdealMorphism_of_surjective | [
{
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1006,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1004,
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.comapDomain_add | [
{
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1332,
85
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1329,
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Mathlib/Topology/MetricSpace/Basic.lean | ULift.dist_up_up | [] | [
1725,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1725,
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Mathlib/GroupTheory/GroupAction/Defs.lean | smul_add | [] | [
778,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
777,
1
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Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.constantCoeff_C | [] | [
495,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
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Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.toList'_think | [
{
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1303,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1292,
1
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Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.norm_one | [] | [
1423,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1422,
1
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Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.mem_support_ofFinset_iff | [
{
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"tactic": "simp"
}
] | [
174,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
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Mathlib/Data/List/Rotate.lean | List.cyclicPermutations_eq_nil_iff | [
{
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"tactic": "refine' ⟨fun h => _, fun h => by simp [h]⟩"
},
{
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"state_before": "α : Type... | [
646,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
1
] |
Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.quotEquivQuotMap_apply_mk | [
{
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870,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
866,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.swap_mem_divisorsAntidiagonal | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nx : ℕ × ℕ\n⊢ Prod.swap x ∈ divisorsAntidiagonal n ↔ x ∈ divisorsAntidiagonal n",
"tactic": "rw [mem_divisorsAntidiagonal, mem_divisorsAntidiagonal, mul_comm, Prod.swap]"
}
] | [
221,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
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Mathlib/Analysis/Complex/Basic.lean | Complex.im_tsum | [] | [
619,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
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] |
Mathlib/Topology/Order/Basic.lean | interior_Ioi | [] | [
311,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIxxMod_antisymm | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na b c : α\nn : ℤ\nh₁₂₃ : toIcoMod hp a b ≤ toIocMod hp a c\nh₁₃₂ : toIcoMod hp a c ≤ toIocMod hp a b\nh : ¬b ≡ a [PMOD p] ∧ ¬c ≡ b [PMOD p] ∧ ¬a ≡ c [PMOD p]\n⊢ False",
"state_before": "α : Type u_1\n... | [
887,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
880,
9
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Mathlib/Topology/Filter.lean | Filter.monotone_nhds | [] | [
147,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
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Mathlib/CategoryTheory/Sites/Closed.lean | CategoryTheory.GrothendieckTopology.covers_iff_mem_of_isClosed | [] | [
88,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Order/UpperLower/Hom.lean | LowerSet.iicsInfHom_apply | [] | [
110,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Analysis/SpecificLimits/Normed.lean | hasSum_coe_mul_geometric_of_norm_lt_1 | [
{
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"state_before": "α : Type ?u.155279\nβ : Type ?u.155282\n... | [
364,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/Analysis/Calculus/FDerivAnalytic.lean | HasFPowerSeriesAt.deriv | [] | [
184,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
11
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.none_eq_top | [] | [
149,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
9
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.add_choose_mul_factorial_mul_factorial | [
{
"state_after": "no goals",
"state_before": "i j : ℕ\n⊢ choose (i + j) j * i ! * j ! = (i + j)!",
"tactic": "rw [← choose_mul_factorial_mul_factorial (Nat.le_add_left _ _), add_tsub_cancel_right,\n mul_right_comm]"
}
] | [
181,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Algebra/Associated.lean | Prime.pow_dvd_of_dvd_mul_left | [
{
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118,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.map_smul_of_tower | [
{
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241,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_eq_range_sigma | [
{
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1269,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1268,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | Measurable.const_smul | [] | [
654,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
653,
1
] |
Mathlib/Analysis/Calculus/Deriv/Comp.lean | HasFDerivWithinAt.comp_hasDerivWithinAt | [] | [
247,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.self_mem_adjoin_singleton | [] | [
452,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
Mathlib/Order/Hom/Lattice.lean | BoundedLatticeHom.toFun_eq_coe | [] | [
1240,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1239,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.dist_conj_self | [
{
"state_after": "no goals",
"state_before": "E : Type ?u.15628\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nz : ℂ\n⊢ dist (↑(starRingEnd ℂ) z) z = 2 * Abs.abs z.im",
"tactic": "rw [dist_of_re_eq (conj_re z), conj_im, dist_comm, Real.dist_eq, sub_neg_eq_add, ← two_mul,\n _root_.abs_mul, abs... | [
132,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.ofList_join | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.10895\nγ : Type ?u.10898\nM : Type ?u.10901\ninst✝¹ : Monoid M\nN : Type ?u.10907\ninst✝ : Monoid N\nxs : List (List α)\n⊢ ↑toList (↑ofList (List.join xs)) = ↑toList (List.prod (List.map (↑ofList) xs))",
"tactic": "simp"
}
] | [
124,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Std/Data/List/Lemmas.lean | List.cons_union | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\na : α\nl₁ l₂ : List α\n⊢ List.union (a :: l₁) l₂ = List.insert a (List.union l₁ l₂)",
"tactic": "simp [List.union, foldr]"
}
] | [
1434,
79
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1433,
9
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.univ_mul_of_one_mem | [] | [
942,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
941,
1
] |
Mathlib/Data/List/OfFn.lean | List.last_ofFn | [
{
"state_after": "no goals",
"state_before": "α : Type u\nn : ℕ\nf : Fin n → α\nh : ofFn f ≠ []\nhn : optParam (n - 1 < n) (_ : pred (Nat.sub n 0) < Nat.sub n 0)\n⊢ getLast (ofFn f) h = f { val := n - 1, isLt := hn }",
"tactic": "simp [getLast_eq_get]"
}
] | [
140,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.head_some_of_get?_some | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : WSeq α\na : α\nn : ℕ\nh : some a ∈ get? s n\n⊢ ∃ a', some a' ∈ head s",
"tactic": "induction n generalizing a with\n| zero => exact ⟨_, h⟩\n| succ n IH =>\n let ⟨a', h'⟩ := head_some_of_head_tail_some h\n exact I... | [
869,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
863,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.isClosed_of_pairwise_le_dist | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.554897\nι : Type ?u.554900\ninst✝¹ : PseudoMetricSpace α\nγ : Type w\ninst✝ : MetricSpace γ\nx : γ\ns✝ s : Set γ\nε : ℝ\nhε : 0 < ε\nhs : Set.Pairwise s fun x y => ε ≤ dist x y\n⊢ Set.Pairwise s fun x y => ¬(x, y) ∈ {p | dist ... | [
2946,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2944,
1
] |
Mathlib/RingTheory/MvPolynomial/Homogeneous.lean | MvPolynomial.isHomogeneous_of_totalDegree_zero | [
{
"state_after": "σ : Type u_1\nτ : Type ?u.128781\nR : Type u_2\nS : Type ?u.128787\ninst✝ : CommSemiring R\np : MvPolynomial σ R\nhp : ∀ (s : σ →₀ ℕ), s ∈ support p → (Finsupp.sum s fun x e => e) = ⊥\n⊢ IsHomogeneous p 0",
"state_before": "σ : Type u_1\nτ : Type ?u.128781\nR : Type u_2\nS : Type ?u.128787... | [
135,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Data/Polynomial/Div.lean | Polynomial.modByMonic_one | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\ninst✝ : CommRing R\np✝ q p : R[X]\n⊢ Monic 1",
"tactic": "convert monic_one (R:=R)"
}
] | [
415,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/Topology/Basic.lean | closure_diff_frontier | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns✝ s₁ s₂ t : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\ns : Set α\n⊢ closure s \\ frontier s = interior s",
"tactic": "rw [frontier, diff_diff_right_self, inter_eq_self_of_subset_right interior_subset_cl... | [
701,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.map_id | [] | [
367,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.rotateL_lemma₃ | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.311144\ninst✝ : Preorder α\na b c : ℕ\nH2 : 3 * a ≤ b + c\nh : b < 2 * c\n⊢ a + b < 3 * c",
"tactic": "linarith"
}
] | [
1228,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1227,
1
] |
Mathlib/Topology/Bases.lean | TopologicalSpace.IsTopologicalBasis.inducing | [
{
"state_after": "case refine'_1\nα : Type u\nt : TopologicalSpace α\nβ : Type u_1\ninst✝ : TopologicalSpace β\nf : α → β\nT : Set (Set β)\nhf : Inducing f\nh : IsTopologicalBasis T\n⊢ ∀ (u : Set α), u ∈ preimage f '' T → IsOpen u\n\ncase refine'_2\nα : Type u\nt : TopologicalSpace α\nβ : Type u_1\ninst✝ : Topo... | [
268,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
11
] |
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