file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/List/Card.lean | List.mem_remove_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Sort ?u.8992\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\na b : α\nas : List α\n⊢ b ∈ remove a as ↔ b ∈ as ∧ b ≠ a",
"tactic": "induction as with\n| nil => simp [remove]\n| cons a' as ih =>\n simp [remove]\n cases Decidable.em (a = a')... | [
61,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Combinatorics/Pigeonhole.lean | Finset.exists_sum_fiber_le_of_sum_fiber_nonneg_of_sum_le_nsmul | [] | [
206,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.scanl_nil | [] | [
320,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | fderivWithin_sinh | [] | [
1160,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1158,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.secondCountableTopology_source | [] | [
1233,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1231,
1
] |
Mathlib/Analysis/Complex/ReImTopology.lean | Complex.interior_setOf_im_le | [
{
"state_after": "no goals",
"state_before": "a : ℝ\n⊢ interior {z | z.im ≤ a} = {z | z.im < a}",
"tactic": "simpa only [interior_Iic] using interior_preimage_im (Iic a)"
}
] | [
103,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Data/Polynomial/EraseLead.lean | Polynomial.eraseLead_coeff | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nf : R[X]\ni : ℕ\n⊢ coeff (eraseLead f) i = if i = natDegree f then 0 else coeff f i",
"tactic": "simp only [eraseLead, coeff_erase]"
}
] | [
50,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.typein_injective | [] | [
494,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/Topology/UniformSpace/Equicontinuity.lean | EquicontinuousAt.comp | [] | [
189,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Topology/MetricSpace/Completion.lean | Isometry.completion_extension | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝² : PseudoMetricSpace α\ninst✝¹ : MetricSpace β\ninst✝ : CompleteSpace β\nf : α → β\nh : Isometry f\nx y : Completion α\n⊢ Continuous fun x => dist (Completion.extension f x.fst) (Completion.extension f x.snd)",
"tactic": "contin... | [
211,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toNNReal_add | [
{
"state_after": "case intro\nα : Type ?u.80550\nβ : Type ?u.80553\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nr₂ : ℝ≥0∞\nh₂ : r₂ ≠ ⊤\nr₁ : ℝ≥0\n⊢ ENNReal.toNNReal (↑r₁ + r₂) = ENNReal.toNNReal ↑r₁ + ENNReal.toNNReal r₂",
"state_before": "α : Type ?u.80550\nβ : Type ?u.80553\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nr₁ r₂ : ℝ≥0∞\nh₁... | [
540,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
536,
1
] |
Mathlib/Data/Set/Finite.lean | Finite.Set.finite_biUnion | [
{
"state_after": "α : Type u\nβ : Type v\nι✝ : Sort w\nγ : Type x\nι : Type u_1\ns : Set ι\ninst✝ : Finite ↑s\nt : ι → Set α\nH : ∀ (i : ι), i ∈ s → Finite ↑(t i)\n⊢ Finite ↑(⋃ (x : ↑s), t ↑x)",
"state_before": "α : Type u\nβ : Type v\nι✝ : Sort w\nγ : Type x\nι : Type u_1\ns : Set ι\ninst✝ : Finite ↑s\nt :... | [
639,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
635,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.subset_le_of_restrict_le_restrict | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.543897\nm : MeasurableSpace α\nM : Type u_2\ninst✝² : TopologicalSpace M\ninst✝¹ : AddCommMonoid M\ninst✝ : PartialOrder M\nv w : VectorMeasure α M\ni : Set α\nhi : MeasurableSet i\nhi₂ : restrict v i ≤ restrict w i\nj : Set α\nhj : j ⊆ i\nhj₁ : MeasurableSe... | [
884,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
880,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.injective_valMinAbs | [] | [
928,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
927,
1
] |
Mathlib/Algebra/Ring/BooleanRing.lean | ofBoolRing_one | [] | [
500,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.sinh_pos_iff | [
{
"state_after": "no goals",
"state_before": "x y z : ℝ\n⊢ 0 < sinh x ↔ 0 < x",
"tactic": "simpa only [sinh_zero] using @sinh_lt_sinh 0 x"
}
] | [
705,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
705,
1
] |
Mathlib/Data/Set/Function.lean | Set.surjOn_image | [] | [
777,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
776,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.pushforward_monotone | [] | [
520,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.map_source | [] | [
148,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean | TopCat.snd_embedding_of_left_embedding | [
{
"state_after": "case h.e'_5.h\nJ : Type v\ninst✝ : SmallCategory J\nX✝ Y✝ Z : TopCat\nX Y S : TopCat\nf : X ⟶ S\nH : Embedding ((forget TopCat).map f)\ng : Y ⟶ S\ne_2✝ : (forget TopCat).obj Y = ↑Y\n⊢ (forget TopCat).map pullback.snd =\n ↑(homeoOfIso (asIso pullback.snd)) ∘\n (forget TopCat).map (pullb... | [
296,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Data/Fintype/Card.lean | Fin.cast_eq_cast' | [
{
"state_after": "case refl\nα : Type ?u.10869\nβ : Type ?u.10872\nγ : Type ?u.10875\nn : ℕ\nh : Fin n = Fin n\n⊢ _root_.cast h = ↑(cast (_ : n = n))",
"state_before": "α : Type ?u.10869\nβ : Type ?u.10872\nγ : Type ?u.10875\nn m : ℕ\nh : Fin n = Fin m\n⊢ _root_.cast h = ↑(cast (_ : n = m))",
"tactic": ... | [
320,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.add''_char | [
{
"state_after": "R : Type u_1\ninst✝¹ : Semiring R\nS : Submonoid R\ninst✝ : OreSet S\nr₁ : R\ns₁ : { x // x ∈ S }\nr₂ : R\ns₂ : { x // x ∈ S }\nrb : R\nsb : { x // x ∈ S }\nhb : ↑s₁ * ↑sb = ↑s₂ * rb\n⊢ (r₁ * ↑(oreDenom (↑s₁) s₂) + r₂ * oreNum (↑s₁) s₂) /ₒ (s₁ * oreDenom (↑s₁) s₂) = (r₁ * ↑sb + r₂ * rb) /ₒ (s₁... | [
529,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
500,
9
] |
Std/Data/BinomialHeap.lean | Std.BinomialHeapImp.Heap.WellFormed.of_rankGT | [] | [
344,
52
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
340,
1
] |
Mathlib/Combinatorics/SimpleGraph/Coloring.lean | SimpleGraph.Coloring.mem_colorClass | [] | [
99,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/GroupTheory/Subgroup/ZPowers.lean | Subgroup.forall_zpowers | [] | [
65,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Submodule.ideal_span_singleton_smul | [
{
"state_after": "R : Type u\nM : Type v\nF : Type ?u.87328\nG : Type ?u.87331\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nI J : Ideal R\nN✝ P : Submodule R M\nS : Set R\nT : Set M\nr : R\nN : Submodule R M\nthis : span R (⋃ (t : M) (_ : t ∈ N), {r • t}) = r • N\n⊢ Ideal.span {r} • N... | [
249,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Order/Disjoint.lean | Disjoint.eq_bot_of_le | [] | [
95,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.mapDomain_comapDomain | [
{
"state_after": "case h\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.311579\nι : Type ?u.311582\nM : Type u_3\nM' : Type ?u.311588\nN : Type ?u.311591\nP : Type ?u.311594\nG : Type ?u.311597\nH : Type ?u.311600\nR : Type ?u.311603\nS : Type ?u.311606\ninst✝ : AddCommMonoid M\nf : α → β\nhf : Injective f\nl : β →₀ ... | [
794,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
786,
1
] |
Mathlib/RingTheory/GradedAlgebra/Basic.lean | DirectSum.decompose_mul | [] | [
96,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.st_le_of_le | [] | [
420,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelEmbedding.isPartialOrder | [] | [
371,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
11
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.zero_trim | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.697802\nm : MeasurableSpace α\nL : Type ?u.697808\nM : Type u_2\nN : Type ?u.697814\ninst✝⁵ : AddCommMonoid L\ninst✝⁴ : TopologicalSpace L\ninst✝³ : AddCommMonoid M\ninst✝² : TopologicalSpace M\ninst✝¹ : AddCommMonoid N\ninst✝ : TopologicalSpace N\nn : Measura... | [
1302,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1300,
1
] |
Mathlib/Topology/Separation.lean | tendsto_const_nhds_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝² : TopologicalSpace α\ninst✝¹ : T1Space α\nl : Filter β\ninst✝ : NeBot l\nc d : α\n⊢ Tendsto (fun x => c) l (𝓝 d) ↔ c = d",
"tactic": "simp_rw [Tendsto, Filter.map_const, pure_le_nhds_iff]"
}
] | [
763,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
762,
1
] |
Mathlib/Data/Multiset/FinsetOps.lean | Multiset.mem_ndinsert | [] | [
59,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.map_decode_iff | [
{
"state_after": "α : Type u_1\nβ : Type u_3\nγ : Type ?u.126196\nδ : Type ?u.126199\nσ : Type u_2\ninst✝⁴ : Primcodable α\ninst✝³ : Primcodable β\ninst✝² : Primcodable γ\ninst✝¹ : Primcodable δ\ninst✝ : Primcodable σ\nf : α → β → σ\n⊢ (Primrec₂ fun a n => Option.bind (decode n) (some ∘ f a)) ↔ Primrec₂ f",
... | [
664,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
661,
1
] |
Mathlib/RingTheory/Valuation/Integral.lean | Valuation.Integers.integralClosure | [] | [
54,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
11
] |
Mathlib/Algebra/Algebra/Basic.lean | Algebra.coe_algebraMap_ofSubring | [] | [
542,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
1
] |
Mathlib/Order/Ideal.lean | Order.Ideal.top_toLowerSet | [] | [
212,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Data/Sign.lean | SignType.univ_eq | [
{
"state_after": "no goals",
"state_before": "⊢ Finset.univ = {0, -1, 1}",
"tactic": "decide"
}
] | [
287,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Order/RelIso/Set.lean | Subrel.relEmbedding_apply | [] | [
75,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.degree_spanningCoe | [
{
"state_after": "ι : Sort ?u.203693\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : Subgraph G\na b : V\nG' : Subgraph G\nv : V\ninst✝¹ : Fintype ↑(neighborSet G' v)\ninst✝ : Fintype ↑(SimpleGraph.neighborSet (Subgraph.spanningCoe G') v)\n⊢ Fintype.card ↑(SimpleGraph.neighborSet (Subgraph.spanningCoe G') v... | [
829,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
826,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIxxMod_total | [] | [
906,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
904,
9
] |
Mathlib/Algebra/Group/Basic.lean | div_div_div_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.44922\nG : Type ?u.44925\ninst✝ : DivisionCommMonoid α\na b c d : α\n⊢ a / b / (c / d) = a / c / (b / d)",
"tactic": "simp"
}
] | [
590,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
590,
1
] |
Mathlib/Data/Finsupp/Multiset.lean | Finsupp.card_toMultiset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.15299\nι : Type ?u.15302\nf : α →₀ ℕ\n⊢ ↑Multiset.card (↑toMultiset f) = sum f fun x => id",
"tactic": "simp [toMultiset_apply, map_finsupp_sum, Function.id_def]"
}
] | [
85,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Analysis/Asymptotics/AsymptoticEquivalent.lean | Asymptotics.IsEquivalent.tendsto_nhds | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type u_2\ninst✝ : NormedAddCommGroup β\nu v w : α → β\nl : Filter α\nc : β\nhuv : u ~[l] v\nhu : Tendsto u l (𝓝 c)\nh : c = 0\n⊢ Tendsto v l (𝓝 c)\n\ncase neg\nα : Type u_1\nβ : Type u_2\ninst✝ : NormedAddCommGroup β\nu v w : α → β\nl : Filter α\nc : β\nhuv : u ~[... | [
160,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/MeasureTheory/Function/L2Space.lean | MeasureTheory.Memℒp.integrable_sq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nF : Type ?u.1981\nm : MeasurableSpace α\nμ : Measure α\ninst✝ : NormedAddCommGroup F\nf : α → ℝ\nh : Memℒp f 2\n⊢ Integrable fun x => f x ^ 2",
"tactic": "simpa [← memℒp_one_iff_integrable] using h.norm_rpow two_ne_zero ENNReal.two_ne_top"
}
... | [
48,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.coe_eq_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.30150\nγ : Type ?u.30153\ns✝ : Finset α\na✝ b : α\ns : Finset α\na : α\n⊢ ↑s = {a} ↔ s = {a}",
"tactic": "rw [← coe_singleton, coe_inj]"
}
] | [
735,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
734,
1
] |
Mathlib/CategoryTheory/Limits/ConcreteCategory.lean | CategoryTheory.Limits.Concrete.to_product_injective_of_isLimit | [
{
"state_after": "C : Type u\ninst✝³ : Category C\ninst✝² : ConcreteCategory C\nJ : Type w\ninst✝¹ : SmallCategory J\nF : J ⥤ C\ninst✝ : PreservesLimit F (forget C)\nD : Cone F\nhD : IsLimit D\nE : Cone (F ⋙ forget C) := (forget C).mapCone D\n⊢ Function.Injective fun x j => (forget C).map (D.π.app j) x",
"s... | [
50,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/Data/Fintype/Card.lean | Finset.exists_maximal | [] | [
971,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
969,
1
] |
Mathlib/Algebra/Order/Sub/Canonical.lean | AddLECancellable.lt_of_tsub_lt_tsub_left_of_le | [
{
"state_after": "α : Type u_1\ninst✝⁶ : AddCommSemigroup α\ninst✝⁵ : PartialOrder α\ninst✝⁴ : ExistsAddOfLE α\ninst✝³ : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1\ninst✝² : Sub α\ninst✝¹ : OrderedSub α\na b c d : α\ninst✝ : ContravariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x < x_1\... | [
164,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
11
] |
Mathlib/Data/List/Basic.lean | List.splitOnP_ne_nil | [] | [
2933,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2933,
1
] |
Mathlib/Data/Set/BoolIndicator.lean | Set.preimage_boolIndicator | [
{
"state_after": "α : Type u_1\ns : Set α\nt : Set Bool\n⊢ ((if true ∈ t then s else ∅) ∪ if false ∈ t then sᶜ else ∅) = univ ∨\n ((if true ∈ t then s else ∅) ∪ if false ∈ t then sᶜ else ∅) = s ∨\n ((if true ∈ t then s else ∅) ∪ if false ∈ t then sᶜ else ∅) = sᶜ ∨\n ((if true ∈ t then s else ∅) ∪... | [
61,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
src/lean/Init/Core.lean | Quot.liftIndepPr1 | [
{
"state_after": "case mk\na b c d : Prop\nα : Sort u\nr : α → α → Prop\nmotive : Quot r → Sort v\nf : (a : α) → motive (mk r a)\nh : ∀ (a b : α) (p : r a b), Eq.ndrec (f a) (_ : mk r a = mk r b) = f b\na✝ : α\n⊢ (lift (Quot.indep f) (_ : ∀ (a b : α), r a b → Quot.indep f a = Quot.indep f b) (mk r a✝)).fst = mk... | [
1264,
11
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1258,
11
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.subtypeDomain_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.487267\nγ : Type ?u.487270\nι : Type ?u.487273\nM : Type u_2\nM' : Type ?u.487279\nN : Type ?u.487282\nP : Type ?u.487285\nG : Type ?u.487288\nH✝ : Type ?u.487291\nR : Type ?u.487294\nS : Type ?u.487297\ninst✝ : Zero M\np : α → Prop\nf ... | [
1057,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1051,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.proj_apply | [] | [
618,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
617,
1
] |
Mathlib/Algebra/Associated.lean | Prime.left_dvd_or_dvd_right_of_dvd_mul | [
{
"state_after": "case intro\nα : Type u_1\nβ : Type ?u.29194\nγ : Type ?u.29197\nδ : Type ?u.29200\ninst✝ : CancelCommMonoidWithZero α\np : α\nhp : Prime p\na b c : α\nhc : p * b = a * c\n⊢ p ∣ a ∨ a ∣ b",
"state_before": "α : Type u_1\nβ : Type ?u.29194\nγ : Type ?u.29197\nδ : Type ?u.29200\ninst✝ : Cance... | [
107,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | totallyBounded_Icc | [] | [
1420,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1419,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | summable_of_sum_range_le | [
{
"state_after": "α : Type ?u.348849\nβ : Type ?u.348852\nγ : Type ?u.348855\nf : ℕ → ℝ\nc : ℝ\nhf : ∀ (n : ℕ), 0 ≤ f n\nh : ∀ (n : ℕ), ∑ i in Finset.range n, f i ≤ c\nH : Tendsto (fun n => ∑ i in Finset.range n, f i) atTop atTop\n⊢ False",
"state_before": "α : Type ?u.348849\nβ : Type ?u.348852\nγ : Type ?... | [
1353,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1349,
1
] |
src/lean/Init/Data/Array/Basic.lean | Array.data_toArray | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nas : List α\n⊢ (List.toArray as).data = as",
"tactic": "simp [List.toArray, toArrayAux_eq, Array.mkEmpty]"
}
] | [
742,
52
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
741,
1
] |
Mathlib/RingTheory/Polynomial/Quotient.lean | Polynomial.quotientSpanXSubCAlgEquiv_symm_apply | [] | [
55,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Combinatorics/Composition.lean | Composition.toCompositionAsSet_boundaries | [] | [
1065,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1063,
1
] |
Mathlib/Analysis/Convex/Join.lean | convexJoin_segment_singleton | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.141835\n𝕜 : Type u_2\nE : Type u_1\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\ns t u : Set E\nx y a b c : E\n⊢ convexJoin 𝕜 (segment 𝕜 a b) {c} = ↑(convexHull 𝕜).toOrderHom {a, b, c}",
"tactic": "rw [← pair_... | [
221,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.bounded_range_iff | [] | [
2420,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2419,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.real_smul_ofReal | [] | [
270,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Topology/Order/Basic.lean | nhdsWithin_Ioo_eq_nhdsWithin_Iio | [
{
"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 : OrderClosedTopology α\na✝ b✝ : α\ninst✝ : TopologicalSpace γ\na b : α\nh : a < b\n⊢ 𝓝[Ioo a b] b = 𝓝[Iio b] b",
"tactic": "simpa only [dual_Ioo] using nhdsWit... | [
500,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.add_moveRight_inl | [
{
"state_after": "case mk\ny : PGame\nα✝ β✝ : Type u_1\na✝¹ : α✝ → PGame\na✝ : β✝ → PGame\ni : RightMoves (mk α✝ β✝ a✝¹ a✝)\n⊢ moveRight (mk α✝ β✝ a✝¹ a✝ + y) (↑toRightMovesAdd (Sum.inl i)) = moveRight (mk α✝ β✝ a✝¹ a✝) i + y",
"state_before": "x y : PGame\ni : RightMoves x\n⊢ moveRight (x + y) (↑toRightMov... | [
1526,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1522,
1
] |
Mathlib/Order/BooleanAlgebra.lean | compl_involutive | [] | [
646,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
645,
1
] |
Mathlib/Topology/ContinuousFunction/Basic.lean | ContinuousMap.coe_const | [] | [
211,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/RingTheory/PowerBasis.lean | PowerBasis.equivOfMinpoly_aeval | [] | [
407,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Data/Prod/Basic.lean | Prod.map_involutive | [] | [
409,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | Summable.toNNReal | [
{
"state_after": "α : Type u_1\nβ : Type ?u.340703\nγ : Type ?u.340706\nf : α → ℝ\nhf : Summable f\n⊢ Summable fun a => ↑(Real.toNNReal (f a))",
"state_before": "α : Type u_1\nβ : Type ?u.340703\nγ : Type ?u.340706\nf : α → ℝ\nhf : Summable f\n⊢ Summable fun n => Real.toNNReal (f n)",
"tactic": "apply N... | [
1305,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1302,
1
] |
Mathlib/Algebra/Associated.lean | Associates.irreducible_iff_prime_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.327284\nγ : Type ?u.327287\nδ : Type ?u.327290\ninst✝ : CommMonoidWithZero α\n⊢ (∀ (a : α), Irreducible a ↔ Prime a) ↔ ∀ (a : Associates α), Irreducible a ↔ Prime a",
"tactic": "simp_rw [forall_associated, irreducible_mk, prime_mk]"... | [
1080,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1078,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.comap_iSup_map_of_injective | [] | [
594,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/RingTheory/Localization/Integral.lean | is_integral_localization_at_leadingCoeff | [] | [
224,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_periodic | [] | [
234,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_restrict₀ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.289512\nγ : Type ?u.289515\nδ : Type ?u.289518\nι : Type ?u.289521\nR : Type ?u.289524\nR' : Type ?u.289527\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set ... | [
1634,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1630,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_indicator₀ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.952259\nγ : Type ?u.952262\nδ : Type ?u.952265\nm : MeasurableSpace α\nμ ν : Measure α\nf : α → ℝ≥0∞\ns : Set α\nhs : NullMeasurableSet s\n⊢ (∫⁻ (a : α), indicator s f a ∂μ) = ∫⁻ (a : α) in s, f a ∂μ",
"tactic": "rw [← lintegral_con... | [
788,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.leadingCoeffHom_apply | [] | [
1557,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1556,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.einfsep_pos | [
{
"state_after": "α : Type u_1\nβ : Type ?u.5645\ninst✝ : EDist α\nx y : α\ns t : Set α\n⊢ (¬∀ (C : ℝ≥0∞), 0 < C → ∃ x x_1 y x_2 _hxy, edist x y < C) ↔\n ∃ C _hC, ∀ (x : α), x ∈ s → ∀ (y : α), y ∈ s → x ≠ y → C ≤ edist x y",
"state_before": "α : Type u_1\nβ : Type ?u.5645\ninst✝ : EDist α\nx y : α\ns t :... | [
68,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Analysis/Convex/Basic.lean | Submodule.convex | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.283563\nβ : Type ?u.283566\ninst✝² : OrderedSemiring 𝕜\ninst✝¹ : AddCommMonoid E\ninst✝ : Module 𝕜 E\nK : Submodule 𝕜 E\nx✝ : E\na✝⁵ : x✝ ∈ ↑K\ny✝ : E\na✝⁴ : y✝ ∈ ↑K\na✝³ b✝ : 𝕜\na✝² : 0 ≤ a✝³\na✝¹ : 0 ≤ b✝\na✝ : a✝³ + b✝ = 1\n⊢ a✝³ • x✝ + b✝ • y✝ ∈... | [
600,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
11
] |
Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.exists_mem_range | [
{
"state_after": "p : ℕ\nhp_prime : Fact (Nat.Prime p)\nr : ℚ\nx : ℤ_[p]\n⊢ ∃ n, n < p ∧ ‖x - ↑n‖ < 1",
"state_before": "p : ℕ\nhp_prime : Fact (Nat.Prime p)\nr : ℚ\nx : ℤ_[p]\n⊢ ∃ n, n < p ∧ x - ↑n ∈ maximalIdeal ℤ_[p]",
"tactic": "simp only [maximalIdeal_eq_span_p, Ideal.mem_span_singleton, ← norm_lt_... | [
193,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.IsInaccessible.mk | [] | [
1214,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1212,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.mul_one | [
{
"state_after": "no goals",
"state_before": "σ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nm n✝ : σ →₀ ℕ\nφ ψ : MvPowerSeries σ R\nn : σ →₀ ℕ\n⊢ ↑(coeff R n) (φ * 1) = ↑(coeff R n) φ",
"tactic": "simpa using coeff_add_mul_monomial n 0 φ 1"
}
] | [
274,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
11
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.basisFun_equivFun | [] | [
981,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
980,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.multiset_prod_mem | [] | [
384,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
11
] |
Mathlib/Combinatorics/Composition.lean | Composition.mem_range_embedding | [
{
"state_after": "n : ℕ\nc : Composition n\nj : Fin n\nthis : ↑(embedding c (index c j)) (invEmbedding c j) ∈ Set.range ↑(embedding c (index c j))\n⊢ j ∈ Set.range ↑(embedding c (index c j))",
"state_before": "n : ℕ\nc : Composition n\nj : Fin n\n⊢ j ∈ Set.range ↑(embedding c (index c j))",
"tactic": "h... | [
420,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.Reaches₀.head | [] | [
797,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
795,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.le_trailingDegree_monomial | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nha : a = 0\n⊢ ↑n ≤ trailingDegree (↑(monomial n) a)",
"tactic": "simp [ha]"
}
] | [
217,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Logic/Relation.lean | Relation.join_of_equivalence | [] | [
652,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
650,
1
] |
Mathlib/Topology/Order/Basic.lean | mem_nhdsWithin_Ici_iff_exists_Ico_subset | [] | [
1773,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1770,
1
] |
Mathlib/GroupTheory/GroupAction/Defs.lean | mul_smul_comm | [] | [
411,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/Init/Function.lean | Function.bijective_id | [] | [
127,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Topology/Instances/Rat.lean | Rat.dist_eq | [] | [
31,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
31,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | borel_eq_generateFrom_Iio | [
{
"state_after": "case refine'_1\nα : Type u_1\nβ : Type ?u.82061\nγ : Type ?u.82064\nγ₂ : Type ?u.82067\nδ : Type ?u.82070\nι : Sort y\ns t u : Set α\ninst✝³ : TopologicalSpace α\ninst✝² : SecondCountableTopology α\ninst✝¹ : LinearOrder α\ninst✝ : OrderTopology α\n⊢ borel α ≤ MeasurableSpace.generateFrom (rang... | [
153,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.rightUnitor_tensor | [
{
"state_after": "no goals",
"state_before": "C✝ : Type u\n𝒞 : Category C✝\ninst✝² : MonoidalCategory C✝\nC : Type u\ninst✝¹ : Category C\ninst✝ : MonoidalCategory C\nU V W X✝ Y✝ Z X Y : C\n⊢ (ρ_ (X ⊗ Y)).hom = (α_ X Y (𝟙_ C)).hom ≫ (𝟙 X ⊗ (ρ_ Y).hom)",
"tactic": "rw [← tensor_right_iff, comp_tensor_... | [
295,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/Data/MvPolynomial/CommRing.lean | MvPolynomial.support_sub | [] | [
93,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Algebra/Module/Equiv.lean | AddEquiv.toIntLinearEquiv_trans | [] | [
881,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
879,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | HomogeneousLocalization.NumDenSameDeg.deg_mul | [] | [
170,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | WithSeminorms.topologicalAddGroup | [
{
"state_after": "𝕜 : Type u_1\n𝕜₂ : Type ?u.180765\n𝕝 : Type ?u.180768\n𝕝₂ : Type ?u.180771\nE : Type u_2\nF : Type ?u.180777\nG : Type ?u.180780\nι : Type u_3\nι' : Type ?u.180786\ninst✝⁴ : NormedField 𝕜\ninst✝³ : AddCommGroup E\ninst✝² : Module 𝕜 E\ninst✝¹ : Nonempty ι\ninst✝ : TopologicalSpace E\np : ... | [
288,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Order/Disjoint.lean | Disjoint.ne | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : OrderBot α\na b c d : α\nha : a ≠ ⊥\nhab : Disjoint a b\nh : a = b\n⊢ Disjoint a a",
"tactic": "rwa [← h] at hab"
}
] | [
91,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
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