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/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.innerContent_mono' | [] | [
245,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
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Mathlib/Combinatorics/Hall/Basic.lean | Finset.all_card_le_biUnion_card_iff_exists_injective | [
{
"state_after": "case mp\nι : Type u\nα : Type v\ninst✝ : DecidableEq α\nt : ι → Finset α\n⊢ (∀ (s : Finset ι), card s ≤ card (Finset.biUnion s t)) → ∃ f, Function.Injective f ∧ ∀ (x : ι), f x ∈ t x\n\ncase mpr\nι : Type u\nα : Type v\ninst✝ : DecidableEq α\nt : ι → Finset α\n⊢ (∃ f, Function.Injective f ∧ ∀ (... | [
166,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
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Mathlib/Tactic/LinearCombination.lean | Mathlib.Tactic.LinearCombination.pf_add_c | [] | [
37,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
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Mathlib/Deprecated/Subgroup.lean | Group.normalClosure_subset | [
{
"state_after": "case basic\nG : Type u_1\nH : Type ?u.145368\nA : Type ?u.145371\na✝ a₁ a₂ b c : G\ns✝ : Set G\ninst✝ : Group G\ns t : Set G\nht : IsNormalSubgroup t\nh : s ⊆ t\na x : G\nhx : x ∈ conjugatesOfSet s\n⊢ x ∈ t\n\ncase one\nG : Type u_1\nH : Type ?u.145368\nA : Type ?u.145371\na✝ a₁ a₂ b c : G\ns✝... | [
736,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
730,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Ioi_ae_eq_Ici | [] | [
3336,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3335,
1
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Mathlib/Topology/FiberBundle/Basic.lean | FiberBundleCore.isOpenMap_proj | [] | [
774,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
773,
8
] |
Mathlib/GroupTheory/Index.lean | Subgroup.index_map_dvd | [
{
"state_after": "G : Type u_2\ninst✝¹ : Group G\nH K L : Subgroup G\nG' : Type u_1\ninst✝ : Group G'\nf : G →* G'\nhf : Function.Surjective ↑f\n⊢ index (H ⊔ MonoidHom.ker f) ∣ index H",
"state_before": "G : Type u_2\ninst✝¹ : Group G\nH K L : Subgroup G\nG' : Type u_1\ninst✝ : Group G'\nf : G →* G'\nhf : F... | [
338,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
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Mathlib/Data/Nat/Order/Basic.lean | Nat.bit_lt_bit0 | [] | [
712,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
710,
1
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Mathlib/Algebra/GroupPower/Lemmas.lean | strictMono_pow_bit1 | [
{
"state_after": "α : Type ?u.310657\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : LinearOrderedRing R\na✝ : R\nn✝ n : ℕ\na b : R\nhab : a < b\n⊢ (fun a => a ^ bit1 n) a < (fun a => a ^ bit1 n) b",
"state_before": "α : Type ?u.310657\nM : Type u\n... | [
752,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
745,
1
] |
Mathlib/Algebra/MonoidAlgebra/Division.lean | AddMonoidAlgebra.modOf_apply_self_add | [] | [
154,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Logic/Basic.lean | forall_apply_eq_imp_iff' | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.18928\nα : Sort ?u.18933\nκ : ι → Sort ?u.18930\np✝ q : α → Prop\nβ : Sort u_1\nf : α → β\np : β → Prop\n⊢ (∀ (b : β) (a : α), f a = b → p b) ↔ ∀ (a : α), p (f a)",
"tactic": "simp [forall_swap]"
}
] | [
807,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
806,
9
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.equalizer.fork_ι | [] | [
771,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
770,
1
] |
Mathlib/Topology/Instances/Int.lean | Int.preimage_ball | [] | [
56,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | FiniteDimensional.finrank_zero_iff | [
{
"state_after": "K : Type u\nV : Type v\ninst✝⁵ : DivisionRing K\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module K V\nV₂ : Type v'\ninst✝² : AddCommGroup V₂\ninst✝¹ : Module K V₂\ninst✝ : FiniteDimensional K V\n⊢ finrank K V = 0 ↔ ↑(finrank K V) = 0",
"state_before": "K : Type u\nV : Type v\ninst✝⁵ : DivisionRin... | [
347,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | Isometry.prod_map | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.2341\nα : Type u\nβ : Type v\nγ : Type w\ninst✝³ : PseudoEMetricSpace α\ninst✝² : PseudoEMetricSpace β\ninst✝¹ : PseudoEMetricSpace γ\nf✝ : α → β\nx✝ y✝ z : α\ns : Set α\nδ : Type u_1\ninst✝ : PseudoEMetricSpace δ\nf : α → β\ng : γ → δ\nhf : Isometry... | [
104,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Algebra/Parity.lean | Odd.sub_odd | [
{
"state_after": "F : Type ?u.105241\nα : Type u_1\nβ : Type ?u.105247\nR : Type ?u.105250\ninst✝ : Ring α\na b : α\nn : ℕ\nha : Odd a\nhb : Odd b\n⊢ Even (a + -b)",
"state_before": "F : Type ?u.105241\nα : Type u_1\nβ : Type ?u.105247\nR : Type ?u.105250\ninst✝ : Ring α\na b : α\nn : ℕ\nha : Odd a\nhb : Od... | [
455,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | integral_re_add_im | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.3500341\nE : Type ?u.3500344\nF : Type ?u.3500347\ninst✝⁹ : MeasurableSpace α\nι : Type ?u.3500353\ninst✝⁸ : NormedAddCommGroup E\nμ : MeasureTheory.Measure α\n𝕜 : Type u_1\ninst✝⁷ : IsROrC 𝕜\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : Norme... | [
1183,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1180,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.principal_bind | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.299672\nι : Sort x\ns : Set α\nf : α → Filter β\n⊢ join (map f (𝓟 s)) = ⨆ (x : α) (_ : x ∈ s), f x",
"tactic": "simp only [sSup_image, join_principal_eq_sSup, map_principal, eq_self_iff_true]"
}
] | [
2771,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2769,
1
] |
Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean | SimpleGraph.incMatrix_apply_eq_one_iff | [
{
"state_after": "R : Type u_1\nα : Type u_2\nG : SimpleGraph α\ninst✝¹ : MulZeroOneClass R\na b : α\ne : Sym2 α\ninst✝ : Nontrivial R\n⊢ (let x := e;\n if x ∈ incidenceSet G a then OfNat.ofNat 1 x else 0) =\n 1 ↔\n e ∈ incidenceSet G a",
"state_before": "R : Type u_1\nα : Type u_2\nG : SimpleG... | [
114,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.range_mem_map | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.221604\nι : Sort x\nf : Filter α\nm : α → β\nm' : β → γ\ns : Set α\nt : Set β\n⊢ m '' univ ∈ map m f",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.221604\nι : Sort x\nf : Filter α\nm : α → β\nm' : β → γ\ns : Set α\nt : Se... | [
1847,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1845,
1
] |
Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.relabel_sum_inl | [
{
"state_after": "L : Language\nL' : Language\nM : Type w\nN : Type ?u.98243\nP : Type ?u.98246\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nγ : Type ?u.98274\nn : ℕ\nφ : BoundedFormula L α n\n⊢ mapTermRel (fun x t => Term.relabel (Sum.map id ↑(natAdd 0)) t) ... | [
647,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
639,
1
] |
Mathlib/Data/Set/Image.lean | Set.image_eta | [] | [
217,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Analysis/SpecificLimits/Normed.lean | tendsto_pow_atTop_nhds_0_of_abs_lt_1 | [] | [
276,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Data/Set/Intervals/Monoid.lean | Set.Ico_add_bij | [
{
"state_after": "M : Type u_1\ninst✝¹ : OrderedCancelAddCommMonoid M\ninst✝ : ExistsAddOfLE M\na b c d : M\n⊢ BijOn (fun x => x + d) (Ici a ∩ Iio b) (Ici (a + d) ∩ Iio (b + d))",
"state_before": "M : Type u_1\ninst✝¹ : OrderedCancelAddCommMonoid M\ninst✝ : ExistsAddOfLE M\na b c d : M\n⊢ BijOn (fun x => x ... | [
72,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/MeasureTheory/Lattice.lean | AEMeasurable.inf' | [] | [
221,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.exp_nat_mul | [
{
"state_after": "no goals",
"state_before": "x✝ y x : ℝ\nn : ℕ\n⊢ ↑(exp (↑n * x)) = ↑(exp x ^ n)",
"tactic": "simp [exp_nat_mul]"
}
] | [
1161,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1160,
8
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.cons_coe | [] | [
138,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/CategoryTheory/Sites/Grothendieck.lean | CategoryTheory.GrothendieckTopology.intersection_covering_iff | [] | [
170,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Computability/NFA.lean | NFA.toDFA_correct | [
{
"state_after": "case h\nα : Type u\nσ σ' : Type v\nM : NFA α σ\nx : List α\n⊢ x ∈ DFA.accepts (toDFA M) ↔ x ∈ accepts M",
"state_before": "α : Type u\nσ σ' : Type v\nM : NFA α σ\n⊢ DFA.accepts (toDFA M) = accepts M",
"tactic": "ext x"
},
{
"state_after": "case h\nα : Type u\nσ σ' : Type v\nM :... | [
126,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Topology/Order/Basic.lean | Dense.exists_ge' | [] | [
786,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
1
] |
Mathlib/Computability/Partrec.lean | Partrec₂.unpaired' | [] | [
508,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/FieldTheory/Separable.lean | Polynomial.count_roots_le_one | [
{
"state_after": "R : Type u\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np : R[X]\nhsep : Separable p\nx : R\n⊢ rootMultiplicity x p ≤ 1",
"state_before": "R : Type u\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np : R[X]\nhsep : Separable p\nx : R\n⊢ Multiset.count x (roots p) ≤ 1",
"tactic": "rw [count_root... | [
264,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/CategoryTheory/Sites/CoverPreserving.lean | CategoryTheory.Presieve.FamilyOfElements.Compatible.functorPushforward | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nA : Type u₃\ninst✝ : Category A\nJ : GrothendieckTopology C\nK : GrothendieckTopology D\nL : GrothendieckTopology A\nG : C ⥤ D\nhG : CompatiblePreserving K G\nℱ : SheafOfTypes K\nZ : C\nT : Presieve Z\nx : FamilyOfElements (Fu... | [
113,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Order/SymmDiff.lean | symmDiff_left_comm | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.72219\nα : Type u_1\nβ : Type ?u.72225\nπ : ι → Type ?u.72230\ninst✝ : GeneralizedBooleanAlgebra α\na b c d : α\n⊢ a ∆ (b ∆ c) = b ∆ (a ∆ c)",
"tactic": "simp_rw [← symmDiff_assoc, symmDiff_comm]"
}
] | [
486,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.findGreatest_succ | [] | [
891,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
889,
1
] |
Std/Data/Int/Lemmas.lean | Int.lt_of_lt_of_le | [] | [
678,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
677,
11
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | Measurable.pow | [] | [
221,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Topology/Basic.lean | isClosed_univ | [] | [
211,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
9
] |
Mathlib/Order/Antisymmetrization.lean | ofAntisymmetrization_le_ofAntisymmetrization_iff | [] | [
197,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Cardinal.ord_univ | [
{
"state_after": "α : Type ?u.234443\nβ : Type ?u.234446\nγ : Type ?u.234449\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no : Ordinal\nh : o < Ordinal.univ\n⊢ card o < univ",
"state_before": "α : Type ?u.234443\nβ : Type ?u.234446\nγ : Type ?u.234449\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ ... | [
1519,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1514,
1
] |
Mathlib/CategoryTheory/Pi/Basic.lean | CategoryTheory.Pi.isoApp_symm | [] | [
208,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup_eq_biUnion | [
{
"state_after": "case a\nF : Type ?u.416235\nα✝ : Type ?u.416238\nβ✝ : Type ?u.416241\nγ : Type ?u.416244\nι : Type ?u.416247\nκ : Type ?u.416250\nα : Type u_1\nβ : Type u_2\ninst✝ : DecidableEq β\ns : Finset α\nt : α → Finset β\na✝ : β\n⊢ a✝ ∈ sup s t ↔ a✝ ∈ Finset.biUnion s t",
"state_before": "F : Type ... | [
1790,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1787,
1
] |
Mathlib/Order/Bounded.lean | Set.unbounded_ge_iff_unbounded_inter_ge | [] | [
422,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.choose_eq_zero_of_lt | [
{
"state_after": "n k : ℕ\nhk : n + 1 < k + 1\nhnk : n < k\n⊢ choose (n + 1) (k + 1) = 0",
"state_before": "n k : ℕ\nhk : n + 1 < k + 1\n⊢ choose (n + 1) (k + 1) = 0",
"tactic": "have hnk : n < k := lt_of_succ_lt_succ hk"
},
{
"state_after": "n k : ℕ\nhk : n + 1 < k + 1\nhnk : n < k\nhnk1 : n < ... | [
77,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | ContinuousOn.rpow | [] | [
303,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.den_one | [] | [
436,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Monad.lean | Pmf.bind_bind | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type u_2\nγ : Type u_1\np : Pmf α\nf : α → Pmf β\ng : β → Pmf γ\nb : γ\n⊢ ↑(bind (bind p f) g) b = ↑(bind p fun a => bind (f a) g) b",
"tactic": "simpa only [ENNReal.coe_eq_coe.symm, bind_apply, ENNReal.tsum_mul_left.symm,\n ENNReal.tsum_m... | [
157,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_add_of_nonneg | [
{
"state_after": "case inl\nx z : ℝ\nhx : 0 ≤ x\nhz : 0 ≤ z\nhy : 0 ≤ 0\n⊢ x ^ (0 + z) = x ^ 0 * x ^ z\n\ncase inr\nx y z : ℝ\nhx : 0 ≤ x\nhy✝ : 0 ≤ y\nhz : 0 ≤ z\nhy : 0 < y\n⊢ x ^ (y + z) = x ^ y * x ^ z",
"state_before": "x y z : ℝ\nhx : 0 ≤ x\nhy : 0 ≤ y\nhz : 0 ≤ z\n⊢ x ^ (y + z) = x ^ y * x ^ z",
... | [
192,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.star_fst | [] | [
441,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.cosh_sq_sub_sinh_sq | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ cosh x ^ 2 - sinh x ^ 2 = 1",
"tactic": "rw [sq_sub_sq, cosh_add_sinh, cosh_sub_sinh, ← exp_add, add_neg_self, exp_zero]"
}
] | [
756,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
755,
1
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Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.mem_coe | [] | [
168,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
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Mathlib/Computability/Primrec.lean | Nat.Primrec'.if_lt | [
{
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1475,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1470,
1
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.ae_eq_trim_of_stronglyMeasurable | [
{
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1801,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1797,
1
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Mathlib/Algebra/Algebra/Spectrum.lean | spectrum.inv_mem_resolventSet | [
{
"state_after": "R : Type u\nA : Type v\ninst✝² : CommSemiring R\ninst✝¹ : Ring A\ninst✝ : Algebra R A\nr : Rˣ\na : Aˣ\nh : IsUnit (r • 1 - ↑a)\n⊢ IsUnit (r⁻¹ • 1 - ↑a⁻¹)",
"state_before": "R : Type u\nA : Type v\ninst✝² : CommSemiring R\ninst✝¹ : Ring A\ninst✝ : Algebra R A\nr : Rˣ\na : Aˣ\nh : ↑r ∈ resol... | [
189,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
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Mathlib/MeasureTheory/Constructions/Pi.lean | IsCountablySpanning.pi | [
{
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"s... | [
101,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
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Mathlib/MeasureTheory/MeasurableSpace.lean | Measurable.subtype_mk | [] | [
572,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
570,
1
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Mathlib/Data/Real/CauSeq.lean | CauSeq.const_mul | [] | [
308,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
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Mathlib/Order/SuccPred/Basic.lean | Order.lt_succ_bot_iff | [
{
"state_after": "no goals",
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"tactic": "rw [lt_succ_iff, le_bot_iff]"
}
] | [
543,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
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Mathlib/Data/Finset/Card.lean | List.toFinset_card_of_nodup | [] | [
205,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
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Mathlib/Data/Set/Lattice.lean | Set.image2_iUnion₂_right | [
{
"state_after": "no goals",
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1894,
35
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1892,
1
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Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.Measure.rnDeriv_lt_top | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.38973\nm : MeasurableSpace α\nμ✝ ν✝ μ ν : Measure α\ninst✝ : SigmaFinite μ... | [
222,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
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Mathlib/Data/Multiset/Basic.lean | Multiset.filter_cons_of_pos | [
{
"state_after": "no goals",
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}
] | [
1969,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1968,
1
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Mathlib/Analysis/Calculus/ContDiff.lean | ContinuousLinearEquiv.contDiffOn_comp_iff | [] | [
494,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearEquivClass.range | [] | [
2141,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2139,
11
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Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.option | [] | [
1198,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1195,
1
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Mathlib/Data/Finset/NAry.lean | Finset.image₂_comm | [
{
"state_after": "no goals",
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380,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
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Mathlib/Data/Matrix/Basic.lean | Matrix.one_dotProduct | [] | [
739,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
739,
1
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Mathlib/Algebra/Order/Group/Defs.lean | div_lt_div'' | [
{
"state_after": "α : Type u\ninst✝² : CommGroup α\ninst✝¹ : Preorder α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x < x_1\na b c d : α\nhab : a < b\nhcd : c < d\n⊢ a * c < b * d",
"state_before": "α : Type u\ninst✝² : CommGroup α\ninst✝¹ : Preorder α\ninst✝ : CovariantClass α α (fun x ... | [
1021,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1019,
1
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Mathlib/Logic/Function/Basic.lean | Function.funext_iff | [] | [
86,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.restrict_dirac' | [
{
"state_after": "case h\nα : Type u_1\nmα : MeasurableSpace α\na : α\ns : Set α\nhs : MeasurableSet s\ninst✝ : Decidable (a ∈ s)\nt : Set α\nht : MeasurableSet t\n⊢ ↑↑(Measure.restrict (Measure.dirac a) s) t = ↑↑(if a ∈ s then Measure.dirac a else 0) t",
"state_before": "α : Type u_1\nmα : MeasurableSpace ... | [
63,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Topology/Sheaves/SheafCondition/UniqueGluing.lean | TopCat.Sheaf.eq_of_locally_eq | [
{
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290,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.mod_to_nat | [
{
"state_after": "no goals",
"state_before": "⊢ ↑(0 % 0) = ↑0 % ↑0",
"tactic": "simp"
}
] | [
1671,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1667,
1
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Mathlib/Analysis/Normed/Order/Lattice.lean | isClosed_nonneg | [
{
"state_after": "α : Type ?u.119963\ninst✝¹ : NormedLatticeAddCommGroup α\nE : Type u_1\ninst✝ : NormedLatticeAddCommGroup E\n⊢ {x | 0 ≤ x} = NegPart.neg ⁻¹' {0}",
"state_before": "α : Type ?u.119963\ninst✝¹ : NormedLatticeAddCommGroup α\nE : Type u_1\ninst✝ : NormedLatticeAddCommGroup E\n⊢ IsClosed {x | 0... | [
223,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.multichoose_one | [
{
"state_after": "case zero\n\n⊢ multichoose 1 zero = 1\n\ncase succ\nk : ℕ\nIH : multichoose 1 k = 1\n⊢ multichoose 1 (succ k) = 1",
"state_before": "k : ℕ\n⊢ multichoose 1 k = 1",
"tactic": "induction' k with k IH"
},
{
"state_after": "no goals",
"state_before": "case succ\nk : ℕ\nIH : mul... | [
379,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Data/Set/Function.lean | StrictAntiOn.comp_strictMonoOn | [] | [
1572,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1569,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | Continuous.prod_mapL | [] | [
1074,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1072,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.norm_mkPiAlgebraFin_le_of_pos | [
{
"state_after": "case intro\n𝕜 : Type u\nι : Type v\nι' : Type v'\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nG : Type wG\nG' : Type wG'\ninst✝¹⁶ : Fintype ι\ninst✝¹⁵ : Fintype ι'\ninst✝¹⁴ : NontriviallyNormedField 𝕜\ninst✝¹³ : (i : ι) → NormedAddCommGroup (E i)\ninst✝¹² : (i : ι) → NormedSpace ... | [
855,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
852,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.aevalTower_comp_algebraMap | [] | [
1618,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1616,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_pi_div_eight | [
{
"state_after": "x : ℝ\n⊢ sin (π / 8) = sin (π / 2 ^ 3)\n\nx : ℝ\n⊢ sin (π / 2 ^ 3) = sqrt (2 - sqrt 2) / 2",
"state_before": "x : ℝ\n⊢ sin (π / 8) = sqrt (2 - sqrt 2) / 2",
"tactic": "trans sin (π / 2 ^ 3)"
},
{
"state_after": "case e_x.e_a\nx : ℝ\n⊢ 8 = 2 ^ 3\n\nx : ℝ\n⊢ sin (π / 2 ^ 3) = sqr... | [
809,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
805,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.preimage_ball | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.1037072\nα : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\nh✝ h : α ≃ᵢ β\nx : β\nr : ℝ\n⊢ ↑h ⁻¹' Metric.ball x r = Metric.ball (↑(IsometryEquiv.symm h) x) r",
"tactic": "rw [← h.isometry.preimage_ball ... | [
612,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
610,
1
] |
Mathlib/RingTheory/Derivation/Basic.lean | Derivation.toFun_eq_coe | [] | [
80,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.ofInt'_toZNum | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.860270\nn : ℕ\n⊢ toZNum ↑(n + 1) = ZNum.ofInt' ↑(n + 1)",
"tactic": "rw [Nat.cast_succ, Num.add_one, toZNum_succ, ofInt'_toZNum n, Nat.cast_succ, succ_ofInt',\n ZNum.add_one]"
}
] | [
1277,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1273,
1
] |
Mathlib/Topology/Order.lean | induced_id | [] | [
465,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Bounded.dual | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Preorder α\no₁ : WithBot α\no₂ : WithTop α\nh : Bounded nil o₁ o₂\n⊢ Bounded (Ordnode.dual nil) o₂ o₁",
"tactic": "cases o₁ <;> cases o₂ <;> trivial"
}
] | [
907,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
904,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.derivBFamily_isNormal | [] | [
366,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/AlgebraicTopology/DoldKan/GammaCompN.lean | AlgebraicTopology.DoldKan.N₁Γ₀_inv_app_f_f | [
{
"state_after": "C : Type u_2\ninst✝² : Category C\ninst✝¹ : Preadditive C\ninst✝ : HasFiniteCoproducts C\nK : ChainComplex C ℕ\nn : ℕ\n⊢ HomologicalComplex.Hom.f\n ((toKaroubi (ChainComplex C ℕ)).map (Γ₀NondegComplexIso K).inv ≫\n (Splitting.toKaroubiNondegComplexIsoN₁ (Γ₀.splitting K)).hom).f\n... | [
116,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Algebra/Order/Monoid/Canonical/Defs.lean | le_self_mul | [] | [
157,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.inl_mul_inl | [] | [
475,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
1
] |
Mathlib/AlgebraicTopology/ExtraDegeneracy.lean | CategoryTheory.Arrow.AugmentedCechNerve.ExtraDegeneracy.s_comp_π_0 | [
{
"state_after": "C : Type u_2\ninst✝¹ : Category C\nf : Arrow C\ninst✝ : ∀ (n : ℕ), HasWidePullback f.right (fun x => f.left) fun x => f.hom\nS : SplitEpi f.hom\nn : ℕ\n⊢ WidePullback.lift (WidePullback.base fun x => f.hom)\n (fun i =>\n if x : i = 0 then (WidePullback.base fun x => f.hom) ≫ S.... | [
286,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.inv_nonempty_iff | [] | [
235,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.toBasicOpen_mk' | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : CommRing R\ns f : R\ng : { x // x ∈ Submonoid.powers s }\n⊢ ↑(toOpen R (PrimeSpectrum.basicOpen s)) f =\n ↑(toOpen R (PrimeSpectrum.basicOpen s)) ↑g *\n const R f (↑g) (PrimeSpectrum.basicOpen s)\n (_ : ∀ (x : ↑(PrimeSpectrum.T... | [
631,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
627,
1
] |
Mathlib/Algebra/Support.lean | Function.mulSupport_inv' | [] | [
286,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/CategoryTheory/EssentiallySmall.lean | CategoryTheory.Discrete.essentiallySmallOfSmall | [] | [
83,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.coe_mul_rpow | [] | [
510,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.RightInverse.comp_eq_id | [] | [
336,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/Algebra/BigOperators/Intervals.lean | Finset.prod_Ico_eq_div | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns₂ s₁ s : Finset α\na : α\ng f✝ : α → β\ninst✝¹ : CommMonoid β\nδ : Type u_1\ninst✝ : CommGroup δ\nf : ℕ → δ\nm n : ℕ\nh : m ≤ n\n⊢ ∏ k in Ico m n, f k = (∏ k in range n, f k) / ∏ k in range m, f k",
"tactic": "simpa only ... | [
108,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Data/Polynomial/Reverse.lean | Polynomial.reflect_C_mul | [
{
"state_after": "case a\nR : Type u_1\ninst✝ : Semiring R\nf✝ f : R[X]\nr : R\nN n✝ : ℕ\n⊢ coeff (reflect N (↑C r * f)) n✝ = coeff (↑C r * reflect N f) n✝",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nf✝ f : R[X]\nr : R\nN : ℕ\n⊢ reflect N (↑C r * f) = ↑C r * reflect N f",
"tactic": "ext"
},
... | [
143,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.le_of_le_of_equiv | [] | [
780,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
779,
1
] |
Mathlib/Data/MvPolynomial/Rename.lean | MvPolynomial.killCompl_comp_rename | [
{
"state_after": "σ : Type u_1\nτ : Type u_3\nα : Type ?u.345007\nR : Type u_2\nS : Type ?u.345013\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S\nf : σ → τ\nhf : Injective f\ni : σ\n⊢ ↑(killCompl hf) (↑(rename f) (X i)) = X i",
"state_before": "σ : Type u_1\nτ : Type u_3\nα : Type ?u.345007\nR : Type u_2... | [
142,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.val_fin_lt | [] | [
304,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
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