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/Analysis/Convex/Between.lean | affineSegment_const_vsub_image | [] | [
107,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.image_trans_source | [] | [
834,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
833,
1
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Mathlib/Data/Set/Image.lean | Sum.range_eq | [] | [
1076,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1074,
1
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Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.isQF_bot | [] | [
720,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
719,
1
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Mathlib/Algebra/Order/Ring/Lemmas.lean | le_of_mul_le_mul_right | [] | [
184,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
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Mathlib/Order/WellFoundedSet.lean | Set.Subsingleton.isPwo | [] | [
456,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
456,
11
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Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.irreducible_of_normalized_factor | [] | [
591,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
589,
1
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Mathlib/Order/Hom/CompleteLattice.lean | CompleteLatticeHom.dual_comp | [] | [
889,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
886,
1
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Mathlib/LinearAlgebra/Quotient.lean | LinearMap.range_eq_top_of_cancel | [
{
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600,
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596,
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Mathlib/NumberTheory/PythagoreanTriples.lean | circleEquivGen_symm_apply | [] | [
325,
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322,
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Mathlib/Algebra/Order/Monoid/Units.lean | Units.min_val | [] | [
64,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/NumberTheory/Padics/PadicVal.lean | padicValRat.one | [
{
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}
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173,
69
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Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.bind_assoc | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ns : WSeq α\nf : α → WSeq β\ng : β → WSeq γ\n⊢ join (join (map (map g) (map f s))) ~ʷ join (map (fun x => join (map g (f x))) s)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : WSeq α\nf : α → WSeq β\ng : β → WSeq γ\n⊢ bind (bind s f) g ~ʷ bind... | [
1802,
18
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1799,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean | HasFDerivWithinAt.arctan | [] | [
179,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
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Mathlib/CategoryTheory/Abelian/Pseudoelements.lean | CategoryTheory.Abelian.Pseudoelement.pseudoApply_aux | [
{
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"tactic": "rw [reassoc_of% comm]"... | [
172,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
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Mathlib/Analysis/Convex/Quasiconvex.lean | QuasiconvexOn.convex_lt | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.20104\nβ : Type u_3\ninst✝⁴ : OrderedSemiring 𝕜\ninst✝³ : AddCommMonoid E\ninst✝² : AddCommMonoid F\ninst✝¹ : LinearOrderedAddCommMonoid β\ninst✝ : SMul 𝕜 E\ns : Set E\nf g : E → β\nhf : QuasiconvexOn 𝕜 s f\nr : β\nx : E\nhx : x ∈ {x | x ∈ s ∧ f x < ... | [
151,
48
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147,
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Mathlib/Order/Filter/Pointwise.lean | Filter.one_mem_one | [] | [
92,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
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Mathlib/RingTheory/Localization/NumDen.lean | IsFractionRing.num_mul_den_eq_num_iff_eq' | [
{
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90,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.comp_measurable | [] | [
610,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
608,
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.all_ae_tendsto_ofReal_norm | [] | [
293,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
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Mathlib/Combinatorics/Composition.lean | CompositionAsSet.mem_boundaries_iff_exists_blocks_sum_take_eq | [
{
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... | [
974,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Calculus/Deriv/Add.lean | deriv_add_const | [
{
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112,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
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Mathlib/CategoryTheory/Monoidal/End.lean | CategoryTheory.obj_μ_app | [
{
"state_after": "C : Type u\ninst✝² : Category C\nM : Type u_2\ninst✝¹ : Category M\ninst✝ : MonoidalCategory M\nF : MonoidalFunctor M (C ⥤ C)\nm₁ m₂ m₃ : M\nX : C\n⊢ (F.obj m₃).map ((LaxMonoidalFunctor.μ F.toLaxMonoidalFunctor m₁ m₂).app X) =\n (F.obj m₃).map ((LaxMonoidalFunctor.μ F.toLaxMonoidalFunctor m... | [
259,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.mul_def | [] | [
168,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
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Mathlib/Topology/UniformSpace/Cauchy.lean | isCompact_of_totallyBounded_isClosed | [] | [
605,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
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Mathlib/Algebra/BigOperators/Order.lean | Finset.card_le_mul_card_image_of_maps_to | [
{
"state_after": "no goals",
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291,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.antilipschitz_of_embedding | [] | [
1515,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1513,
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Mathlib/RepresentationTheory/Basic.lean | Representation.asModuleEquiv_symm_map_smul | [
{
"state_after": "k : Type u_2\nG : Type u_3\nV : Type u_1\ninst✝³ : CommSemiring k\ninst✝² : Monoid G\ninst✝¹ : AddCommMonoid V\ninst✝ : Module k V\nρ : Representation k G V\nr : k\nx : V\n⊢ ↑(asModuleEquiv ρ) (↑(AddEquiv.symm (asModuleEquiv ρ)) (r • x)) =\n ↑(asModuleEquiv ρ) (↑(algebraMap k (MonoidAlgebra... | [
149,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Basic.lean | lt_of_le_of_lt' | [] | [
83,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
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Mathlib/Topology/PathConnected.lean | Path.reparam_id | [
{
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"state_before": "X : Type u_1\nY : Type ?u.52... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/List/Cycle.lean | List.nextOr_nil | [] | [
45,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
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Mathlib/Algebra/Hom/Ring.lean | NonUnitalRingHom.coe_addMonoidHom_id | [] | [
235,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioi_injective | [] | [
1116,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1115,
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Mathlib/Topology/FiberBundle/Basic.lean | FiberPrebundle.continuous_totalSpaceMk | [
{
"state_after": "ι : Type ?u.62801\nB : Type u_2\nF : Type u_3\nX : Type ?u.62810\ninst✝³ : TopologicalSpace X\nE : B → Type u_1\ninst✝² : TopologicalSpace B\ninst✝¹ : TopologicalSpace F\ninst✝ : (x : B) → TopologicalSpace (E x)\na : FiberPrebundle F E\ne : Pretrivialization F TotalSpace.proj\nb : B\nthis : To... | [
874,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Order/Sub/Canonical.lean | AddLECancellable.tsub_inj_right | [
{
"state_after": "α : Type u_1\ninst✝⁵ : AddCommSemigroup α\ninst✝⁴ : PartialOrder α\ninst✝³ : ExistsAddOfLE α\ninst✝² : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\na b c d : α\nhab : AddLECancellable (a - b)\nh₁ : b ≤ a\nh₂ : c ≤ a\nh₃ : a - b = a - c\n... | [
158,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
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] |
Mathlib/Order/Filter/Prod.lean | Filter.Eventually.diag_of_prod_right | [
{
"state_after": "α : Type u_1\nβ : Type ?u.10420\nγ : Type u_2\nδ : Type ?u.10426\nι : Sort ?u.10429\ns : Set α\nt : Set β\nf✝ : Filter α\ng✝ : Filter β\nf : Filter α\ng : Filter γ\np : α × γ × γ → Prop\nh : ∀ᶠ (x : α × γ × γ) in f ×ˢ g ×ˢ g, p x\n⊢ ∀ᶠ (x : α × γ) in f ×ˢ g, p (x.fst, x.snd, x.snd)",
"stat... | [
209,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
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Mathlib/Topology/Algebra/UniformGroup.lean | uniformity_eq_comap_nhds_one | [
{
"state_after": "α : Type u_1\nβ : Type ?u.159712\ninst✝² : UniformSpace α\ninst✝¹ : Group α\ninst✝ : UniformGroup α\n⊢ 𝓤 α = comap (Prod.mk 1 ∘ fun x => x.snd / x.fst) (𝓤 α)",
"state_before": "α : Type u_1\nβ : Type ?u.159712\ninst✝² : UniformSpace α\ninst✝¹ : Group α\ninst✝ : UniformGroup α\n⊢ 𝓤 α = c... | [
278,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
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Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.aleph_pos | [] | [
301,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
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Mathlib/GroupTheory/Submonoid/Pointwise.lean | Submonoid.inv_bot | [] | [
192,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Data/List/AList.lean | AList.insert_insert | [
{
"state_after": "case a\nα : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb b' : β a\ns : AList β\n⊢ (insert a b' (insert a b s)).entries = (insert a b' s).entries",
"state_before": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb b' : β a\ns : AList β\n⊢ insert a b' (insert a b s) = i... | [
322,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
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Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | HasFDerivWithinAt.mapsTo_tangent_cone | [
{
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493,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
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Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.remainder_lt_aux | [
{
"state_after": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝ : Field R\np✝ q p : R[X]\nhq : q ≠ 0\n⊢ degree (mod p q) < degree (q * ↑C (leadingCoeff q)⁻¹)",
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186,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.span_singleton_inf_orthogonal_eq_bot | [
{
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Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.sum_mem | [] | [
361,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
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Mathlib/Topology/Constructions.lean | OpenEmbedding.prod | [] | [
838,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.ext | [] | [
584,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
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Mathlib/Data/Set/Basic.lean | Set.mem_dite | [
{
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2187,
77
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2183,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.two_zsmul_toReal_eq_two_mul_add_two_pi | [
{
"state_after": "no goals",
"state_before": "θ : Angle\n⊢ toReal (2 • θ) = 2 * toReal θ + 2 * π ↔ toReal θ ≤ -π / 2",
"tactic": "rw [two_zsmul, ← two_nsmul, two_nsmul_toReal_eq_two_mul_add_two_pi]"
}
] | [
723,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
] |
Mathlib/Data/Finset/Basic.lean | Directed.exists_mem_subset_of_finset_subset_biUnion | [
{
"state_after": "α✝ : Type ?u.168635\nβ : Type ?u.168638\nγ : Type ?u.168641\ninst✝ : DecidableEq α✝\ns✝ s₁ s₂ t t₁ t₂ u v : Finset α✝\na b : α✝\nα : Type u_1\nι : Type u_2\nhn : Nonempty ι\nf : ι → Set α\nh : Directed (fun x x_1 => x ⊆ x_1) f\ns : Finset α\n⊢ (↑s ⊆ ⋃ (i : ι), f i) → ∃ i, ↑s ⊆ f i",
"state... | [
1543,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1529,
1
] |
Mathlib/Order/Filter/SmallSets.lean | Filter.smallSets_top | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.2978\nι : Sort ?u.2981\nl l' la : Filter α\nlb : Filter β\n⊢ smallSets ⊤ = ⊤",
"tactic": "rw [smallSets, lift'_top, powerset_univ, principal_univ]"
}
] | [
105,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.mkOfCompact_neg | [] | [
962,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
962,
1
] |
Mathlib/Order/Lattice.lean | inf_le_of_left_le | [] | [
412,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atTop_atTop_of_monotone' | [
{
"state_after": "ι : Type u_1\nι' : Type ?u.347734\nα : Type u_2\nβ : Type ?u.347740\nγ : Type ?u.347743\ninst✝¹ : Preorder ι\ninst✝ : LinearOrder α\nu : ι → α\nh : Monotone u\nH : ¬BddAbove (range u)\n⊢ ∀ (b : α), ∃ a, b ≤ u a",
"state_before": "ι : Type u_1\nι' : Type ?u.347734\nα : Type u_2\nβ : Type ?u... | [
1681,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1676,
1
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Mathlib/Analysis/Convex/Strict.lean | strictConvex_Ioo | [] | [
193,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Data/Multiset/Lattice.lean | Multiset.sup_ndunion | [
{
"state_after": "α : Type u_1\ninst✝² : SemilatticeSup α\ninst✝¹ : OrderBot α\ninst✝ : DecidableEq α\ns₁ s₂ : Multiset α\n⊢ ∀ (a : α), a ∈ ndunion s₁ s₂ ↔ a ∈ s₁ + s₂",
"state_before": "α : Type u_1\ninst✝² : SemilatticeSup α\ninst✝¹ : OrderBot α\ninst✝ : DecidableEq α\ns₁ s₂ : Multiset α\n⊢ sup (ndunion s... | [
83,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.xy_modEq_yn | [
{
"state_after": "no goals",
"state_before": "a : ℕ\na1 : 1 < a\nn : ℕ\n⊢ xn a1 (n * 0) ≡ xn a1 n ^ 0 [MOD yn a1 n ^ 2] ∧ yn a1 (n * 0) ≡ 0 * xn a1 n ^ (0 - 1) * yn a1 n [MOD yn a1 n ^ 3]",
"tactic": "constructor <;> simp <;> exact Nat.ModEq.refl _"
},
{
"state_after": "a : ℕ\na1 : 1 < a\nn k : ... | [
487,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.aleph0_lt_aleph_one | [
{
"state_after": "⊢ ℵ₀ < succ ℵ₀",
"state_before": "⊢ ℵ₀ < aleph 1",
"tactic": "rw [← succ_aleph0]"
},
{
"state_after": "no goals",
"state_before": "⊢ ℵ₀ < succ ℵ₀",
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}
] | [
348,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.coe_list_prod | [] | [
909,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
908,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.sum_div | [] | [
777,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
775,
1
] |
Std/Data/Int/Lemmas.lean | Int.neg_add_le_right_of_le_add | [
{
"state_after": "a b c : Int\nh : a ≤ c + b\n⊢ -c + a ≤ b",
"state_before": "a b c : Int\nh : a ≤ b + c\n⊢ -c + a ≤ b",
"tactic": "rw [Int.add_comm] at h"
},
{
"state_after": "no goals",
"state_before": "a b c : Int\nh : a ≤ c + b\n⊢ -c + a ≤ b",
"tactic": "exact Int.neg_add_le_left_of_... | [
1012,
40
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1010,
11
] |
Mathlib/Topology/UniformSpace/AbstractCompletion.lean | AbstractCompletion.extend_comp_coe | [] | [
171,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.Tendsto.congr | [] | [
2905,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2903,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | mul_lt_of_lt_of_lt_one | [] | [
584,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
578,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.abs_one_sub_fract | [] | [
900,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
899,
1
] |
Mathlib/Analysis/Convex/Basic.lean | convex_iff_div | [] | [
532,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.Chain.mem_map_iff | [
{
"state_after": "case intro.intro\nα : Type u\nβ : Type v\nγ : Type ?u.3585\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : Preorder γ\nc c' : Chain α\nf : α →o β\ng : β →o γ\nb : β\nw : α\nh : w ∈ c\nh' : ↑f w = b\n⊢ b ∈ map c f",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.3585\ninst✝² : Preo... | [
135,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | totallyBounded_iff_subset | [] | [
481,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_add_C | [] | [
712,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
711,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.sumArrowEquivProdArrow_apply_fst | [] | [
880,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
878,
1
] |
Mathlib/Algebra/Hom/GroupAction.lean | DistribMulActionHom.comp_apply | [] | [
373,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/Data/List/Basic.lean | List.map₂Left_nil_right | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.465146\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf : α → Option β → γ\nas : List α\n⊢ map₂Left f as [] = map (fun a => f a none) as",
"tactic": "cases as <;> rfl"
}
] | [
4107,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4107,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.Red.Step.to_red | [] | [
229,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Combinatorics/Young/SemistandardTableau.lean | Ssyt.highestWeight_apply | [] | [
157,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Hom.range_le_iff_comap | [
{
"state_after": "no goals",
"state_before": "L : Language\nM : Type w\nN : Type u_1\nP : Type ?u.984407\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nS : Substructure L M\nf : M →[L] N\np : Substructure L N\n⊢ range f ≤ p ↔ comap f p = ⊤",
"tactic": "rw [range_eq_map, map_le_i... | [
864,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
863,
1
] |
Mathlib/Data/PNat/Prime.lean | PNat.gcd_dvd_right | [] | [
83,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Topology/ContinuousFunction/Units.lean | ContinuousMap.isUnit_iff_forall_ne_zero | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\nM : Type ?u.396272\nR : Type ?u.396275\n𝕜 : Type u_2\ninst✝² : TopologicalSpace X\ninst✝¹ : NormedField 𝕜\ninst✝ : CompleteSpace 𝕜\nf : C(X, 𝕜)\n⊢ IsUnit f ↔ ∀ (x : X), ↑f x ≠ 0",
"tactic": "simp_rw [f.isUnit_iff_forall_isUnit, isUnit_iff_n... | [
112,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Analysis/Complex/Liouville.lean | Complex.norm_deriv_le_aux | [
{
"state_after": "E : Type u\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℂ E\nF : Type v\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℂ F\ninst✝ : CompleteSpace F\nc : ℂ\nR C : ℝ\nf : ℂ → F\nhR : 0 < R\nhf : DiffContOnCl ℂ f (ball c R)\nhC : ∀ (z : ℂ), z ∈ sphere c R → ‖f z‖ ≤ C\nthis : ∀ (z : ... | [
71,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.coe_eq_zero | [] | [
49,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Data/Rat/Lemmas.lean | Rat.inv_coe_int_num_of_pos | [
{
"state_after": "a : ℤ\nha0 : 0 < a\n⊢ (↑1 / ↑a).num = 1",
"state_before": "a : ℤ\nha0 : 0 < a\n⊢ (↑a)⁻¹.num = 1",
"tactic": "rw [← ofInt_eq_cast, ofInt, mk_eq_divInt, Rat.inv_def', divInt_eq_div, Nat.cast_one]"
},
{
"state_after": "a : ℤ\nha0 : 0 < a\n⊢ Nat.coprime (Int.natAbs 1) (Int.natAbs a... | [
262,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Order/Minimal.lean | inter_minimals_subset | [] | [
173,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.einfsep_eq_top_iff | [] | [
262,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Data/Set/Basic.lean | Set.subset_insert_diff_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns✝ s₁ s₂ t t₁ t₂ u : Set α\nx : α\ns : Set α\n⊢ s ⊆ insert x (s \\ {x})",
"tactic": "rw [← diff_singleton_subset_iff]"
}
] | [
1947,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1946,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Summable.add | [] | [
318,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Algebra/Invertible.lean | mul_invOf_mul_self_cancel' | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Monoid α\na b : α\nx✝ : Invertible b\n⊢ a * ⅟b * b = a",
"tactic": "simp [mul_assoc]"
}
] | [
136,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Topology/Semicontinuous.lean | lowerSemicontinuousOn_iSup | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝³ : TopologicalSpace α\nβ : Type ?u.123063\ninst✝² : Preorder β\nf✝ g : α → β\nx : α\ns t : Set α\ny z : β\nι : Sort u_3\nδ : Type u_2\nδ' : Type ?u.123095\ninst✝¹ : CompleteLinearOrder δ\ninst✝ : ConditionallyCompleteLinearOrder δ'\nf : ι → α... | [
603,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
601,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.le_of_op_norm_le | [] | [
353,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.refl_trans | [] | [
823,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
822,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.smul_single | [] | [
1588,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1586,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.diagonal_apply_eq | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.44950\nm : Type ?u.44953\nn : Type u_1\no : Type ?u.44959\nm' : o → Type ?u.44964\nn' : o → Type ?u.44969\nR : Type ?u.44972\nS : Type ?u.44975\nα : Type v\nβ : Type w\nγ : Type ?u.44982\ninst✝¹ : DecidableEq n\ninst✝ : Zero α\nd : n → α\ni : n\n⊢ di... | [
435,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.coe_mapAlgHom_eq_coe_map | [] | [
951,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
949,
1
] |
Mathlib/Data/Set/Intervals/Monotone.lean | Monotone.Ico | [] | [
126,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
11
] |
Mathlib/Order/Filter/NAry.lean | Filter.map₂_distrib_le_left | [
{
"state_after": "case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.intro\nα : Type u_2\nα' : Type ?u.41440\nβ : Type u_4\nβ' : Type u_6\nγ : Type u_5\nγ' : Type u_7\nδ : Type u_3\nδ' : Type ?u.41458\nε : Type u_1\nε' : Type ?u.41464\nm✝ : α → β → γ\nf f₁ f₂ : Filter α\ng g₁ g₂ : Filter β\n... | [
364,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | differentiable_snd | [] | [
288,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Complex.lean | Complex.inv_cpow_eq_ite | [
{
"state_after": "x n : ℂ\n⊢ (if x = 0 then if n = 0 then 1 else 0\n else if arg x = π then (exp (↑(starRingEnd ℂ) (log x) * n))⁻¹ else (exp (log x * n))⁻¹) =\n if arg x = π then if x = 0 then if n = 0 then 1 else 0 else (exp (↑(starRingEnd ℂ) (log x) * n))⁻¹\n else if x = 0 then if n = 0 then 1 else 0... | [
186,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ext_on_measurableSpace_of_generate_finite | [
{
"state_after": "α✝ : Type ?u.846775\nβ : Type ?u.846778\nγ : Type ?u.846781\nδ : Type ?u.846784\nι : Type ?u.846787\nR : Type ?u.846790\nR' : Type ?u.846793\nm0 : MeasurableSpace α✝\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\nμ✝ μ₁ μ₂ μ₃ ν✝ ν' ν₁ ν₂ : Measure α✝\ns✝ s' t : Set α✝\nα : Type u_1\nm... | [
4055,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4040,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.le_einfsep_image_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\ninst✝ : EDist α\nx y : α\ns✝ t : Set α\nd : ℝ≥0∞\nf : β → α\ns : Set β\n⊢ d ≤ einfsep (f '' s) ↔ ∀ (x : β), x ∈ s → ∀ (y : β), y ∈ s → f x ≠ f y → d ≤ edist (f x) (f y)",
"tactic": "simp_rw [le_einfsep_iff, ball_image_iff]"
}
] | [
107,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Logic/Relation.lean | Relation.TransGen.trans | [] | [
369,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.map_smul | [] | [
113,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | vectorSpan_empty | [
{
"state_after": "no goals",
"state_before": "k : Type u_2\nV : Type u_1\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\n⊢ vectorSpan k ∅ = ⊥",
"tactic": "rw [vectorSpan_def, vsub_empty, Submodule.span_empty]"
}
] | [
83,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/GroupTheory/Subsemigroup/Basic.lean | Subsemigroup.mem_mk | [] | [
120,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
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