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/NumberTheory/SumFourSquares.lean | Nat.sum_four_squares | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ ∃ a b c d, a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 = n",
"tactic": "induction n using Nat.recOnMul with\n| h0 => exact ⟨0, 0, 0, 0, rfl⟩\n| h1 => exact ⟨1, 0, 0, 0, rfl⟩\n| hp p hp => exact hp.sum_four_squares\n| h m n hm hn =>\n rcases hm with ⟨a, b, c, d, ... | [
239,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
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Mathlib/Data/Nat/Cast/Basic.lean | map_natCast' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.41556\nβ : Type ?u.41559\nA✝ : Type ?u.41562\nB : Type u_3\nF : Type u_2\ninst✝³ : AddMonoidWithOne B\ninst✝² : AddMonoidWithOne A✝\nA : Type u_1\ninst✝¹ : AddMonoidWithOne A\ninst✝ : AddMonoidHomClass F A B\nf : F\nh : ↑f 1 = 1\n⊢ ↑f ↑0 = ↑0",
"... | [
228,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
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Mathlib/Algebra/GCDMonoid/Basic.lean | Associates.normalize_out | [] | [
255,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
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Mathlib/RingTheory/Ideal/Operations.lean | Submodule.mem_annihilator_span_singleton | [
{
"state_after": "no goals",
"state_before": "R : Type u\nM : Type v\nF : Type ?u.20043\nG : Type ?u.20046\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nI J : Ideal R\nN P : Submodule R M\ng : M\nr : R\n⊢ r ∈ annihilator (span R {g}) ↔ r • g = 0",
"tactic": "simp [mem_annihilat... | [
81,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
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Mathlib/Data/Num/Lemmas.lean | PosNum.cast_one | [] | [
40,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
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Mathlib/Analysis/NormedSpace/CompactOperator.lean | isCompactOperator_iff_exists_mem_nhds_isCompact_closure_image | [
{
"state_after": "R₁ : Type ?u.2937\nR₂ : Type ?u.2940\ninst✝⁵ : Semiring R₁\ninst✝⁴ : Semiring R₂\nσ₁₂ : R₁ →+* R₂\nM₁ : Type u_2\nM₂ : Type u_1\ninst✝³ : TopologicalSpace M₁\ninst✝² : AddCommMonoid M₁\ninst✝¹ : TopologicalSpace M₂\ninst✝ : T2Space M₂\nf : M₁ → M₂\n⊢ (∃ V, V ∈ 𝓝 0 ∧ ∃ K, IsCompact K ∧ f '' V ... | [
92,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
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Mathlib/MeasureTheory/Measure/Haar/OfBasis.lean | parallelepiped_comp_equiv | [
{
"state_after": "ι : Type u_2\nι' : Type u_1\nE : Type u_3\nF : Type ?u.30696\ninst✝⁵ : Fintype ι\ninst✝⁴ : Fintype ι'\ninst✝³ : AddCommGroup E\ninst✝² : Module ℝ E\ninst✝¹ : AddCommGroup F\ninst✝ : Module ℝ F\nv : ι → E\ne : ι' ≃ ι\n⊢ (fun a => ∑ x : ι', a x • (v ∘ ↑e) x) '' Icc 0 1 = (fun t => ∑ i : ι, t i •... | [
84,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
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Mathlib/Data/Int/GCD.lean | Int.gcd_greatest | [] | [
405,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.mul_re | [] | [
174,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/CategoryTheory/Arrow.lean | CategoryTheory.Arrow.id_right | [] | [
67,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.liftRingHom_apply | [] | [
1360,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1358,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | DifferentiableOn.ccos | [] | [
331,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/Topology/Support.lean | tsupport_mul_subset_right | [] | [
97,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Order/SuccPred/Limit.lean | Order.not_isSuccLimit | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝³ : PartialOrder α\ninst✝² : SuccOrder α\na b : α\nC : α → Sort ?u.10097\ninst✝¹ : IsSuccArchimedean α\ninst✝ : NoMinOrder α\n⊢ ¬IsSuccLimit a",
"tactic": "simp"
}
] | [
229,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.IsMultiplicative.pmul | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : CommSemiring R\nf g : ArithmeticFunction R\nhf : IsMultiplicative f\nhg : IsMultiplicative g\n⊢ ↑(ArithmeticFunction.pmul f g) 1 = 1",
"tactic": "simp [hf, hg]"
},
{
"state_after": "R : Type u_1\ninst✝ : CommSemiring R\nf g : Ar... | [
698,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
694,
1
] |
Mathlib/GroupTheory/Coset.lean | mem_leftCoset_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Group α\ns : Set α\nx a : α\nx✝ : x ∈ a *l s\nb : α\nhb : b ∈ s\nEq : (fun x => a * x) b = x\n⊢ a⁻¹ * x ∈ s",
"tactic": "simp [Eq.symm, hb]"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Group α\ns :... | [
204,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.hasPullback_symmetry | [] | [
1509,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1507,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atTop_of_add_bdd_above_right' | [] | [
740,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
737,
1
] |
Mathlib/Data/Multiset/Lattice.lean | Multiset.nodup_sup_iff | [
{
"state_after": "case empty\nα✝ : Type ?u.22553\ninst✝³ : SemilatticeSup α✝\ninst✝² : OrderBot α✝\ninst✝¹ : DecidableEq α✝\nα : Type u_1\ninst✝ : DecidableEq α\n⊢ Nodup (sup 0) ↔ ∀ (a : Multiset α), a ∈ 0 → Nodup a\n\ncase cons\nα✝ : Type ?u.22553\ninst✝³ : SemilatticeSup α✝\ninst✝² : OrderBot α✝\ninst✝¹ : Dec... | [
102,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.of_prod_right | [] | [
922,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
921,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.card_roots_X_pow_sub_C | [] | [
767,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
761,
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] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_update | [
{
"state_after": "α : Type ?u.103718\nβ : Type ?u.103721\nγ : Type ?u.103724\nδ : Type u_1\nδ' : Type ?u.103730\nι : Sort uι\ns t u : Set α\nπ : δ → Type u_2\ninst✝³ : MeasurableSpace α\ninst✝² : (a : δ) → MeasurableSpace (π a)\ninst✝¹ : MeasurableSpace γ\nf : (a : δ) → π a\na : δ\ninst✝ : DecidableEq δ\nx : δ\... | [
870,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
866,
1
] |
Mathlib/Logic/Basic.lean | not_forall | [] | [
688,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
687,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.IsAlt.sub | [] | [
985,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
984,
11
] |
Mathlib/Topology/Order.lean | setOf_isOpen_iSup | [] | [
955,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
953,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.eleven_dvd_of_palindrome | [
{
"state_after": "n : ℕ\np : List.Palindrome (digits 10 n)\nh : Even (List.length (digits 10 n))\ndig : List ℤ := List.map Coe.coe (digits 10 n)\n⊢ 11 ∣ n",
"state_before": "n : ℕ\np : List.Palindrome (digits 10 n)\nh : Even (List.length (digits 10 n))\n⊢ 11 ∣ n",
"tactic": "let dig := (digits 10 n).map... | [
624,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
617,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.domDomCongr_eq_iff | [] | [
781,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
779,
1
] |
Mathlib/Data/Fintype/Parity.lean | Fintype.card_fin_even | [
{
"state_after": "α : Type ?u.497\nn : ℕ\n⊢ Even (bit0 n)",
"state_before": "α : Type ?u.497\nn : ℕ\n⊢ Even (card (Fin (bit0 n)))",
"tactic": "rw [Fintype.card_fin]"
},
{
"state_after": "no goals",
"state_before": "α : Type ?u.497\nn : ℕ\n⊢ Even (bit0 n)",
"tactic": "exact even_bit0 _"
... | [
34,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.Memℒp.memℒp_of_exponent_le | [
{
"state_after": "case intro\nα : Type u_1\nE : Type u_2\nF : Type ?u.5027535\nG : Type ?u.5027538\nm m0 : MeasurableSpace α\np✝ : ℝ≥0∞\nq✝ : ℝ\nμ ν : Measure α\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedAddCommGroup G\np q : ℝ≥0∞\ninst✝ : IsFiniteMeasure μ\nf : α → E\nhpq : p... | [
1202,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1176,
1
] |
Mathlib/Deprecated/Group.lean | IsMulHom.comp | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝² : Mul α\ninst✝¹ : Mul β\nγ : Type u_1\ninst✝ : Mul γ\nf : α → β\ng : β → γ\nhf : IsMulHom f\nhg : IsMulHom g\nx y : α\n⊢ (g ∘ f) (x * y) = (g ∘ f) x * (g ∘ f) y",
"tactic": "simp only [Function.comp, hf.map_mul, hg.map_mul]"
... | [
70,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.le.dest | [] | [
355,
83
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
347,
1
] |
Mathlib/RingTheory/DedekindDomain/Dvr.lean | IsLocalization.AtPrime.not_isField | [
{
"state_after": "R : Type ?u.41349\nA : Type u_1\nK : Type ?u.41355\ninst✝⁶ : CommRing R\ninst✝⁵ : CommRing A\ninst✝⁴ : IsDomain A\ninst✝³ : Field K\nP : Ideal A\nhP : P ≠ ⊥\npP : Ideal.IsPrime P\nAₘ : Type u_2\ninst✝² : CommRing Aₘ\ninst✝¹ : Algebra A Aₘ\ninst✝ : IsLocalization.AtPrime Aₘ P\nh : IsField Aₘ\n⊢... | [
132,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.lt_def | [] | [
1152,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1151,
1
] |
Mathlib/MeasureTheory/Measure/GiryMonad.lean | MeasureTheory.Measure.measurable_dirac | [
{
"state_after": "α : Type u_1\nβ : Type ?u.3729\ninst✝¹ : MeasurableSpace α\ninst✝ : MeasurableSpace β\ns : Set α\nhs : MeasurableSet s\n⊢ Measurable fun b => ↑↑(dirac b) s",
"state_before": "α : Type u_1\nβ : Type ?u.3729\ninst✝¹ : MeasurableSpace α\ninst✝ : MeasurableSpace β\n⊢ Measurable dirac",
"ta... | [
89,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
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] |
Mathlib/Analysis/Convex/Integral.lean | StrictConvexOn.ae_eq_const_or_map_average_lt | [
{
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313,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
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Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.set_integral_prod_mul | [
{
"state_after": "α : Type u_2\nα' : Type ?u.2467745\nβ : Type u_3\nβ' : Type ?u.2467751\nγ : Type ?u.2467754\nE : Type ?u.2467757\ninst✝¹³ : MeasurableSpace α\ninst✝¹² : MeasurableSpace α'\ninst✝¹¹ : MeasurableSpace β\ninst✝¹⁰ : MeasurableSpace β'\ninst✝⁹ : MeasurableSpace γ\nμ μ' : Measure α\nν ν' : Measure β... | [
530,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Interval.lean | Interval.dual_bot | [] | [
400,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | AffineIndependent.vectorSpan_eq_top_of_card_eq_finrank_add_one | [] | [
137,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.exists_subordinate_pairwise_disjoint | [
{
"state_after": "ι : Type u_1\nα : Type u_2\nβ : Type ?u.7332\nγ : Type ?u.7335\nm0 : MeasurableSpace α\nμ : Measure α\ns✝ t✝ : Set α\ninst✝ : Countable ι\ns : ι → Set α\nh : ∀ (i : ι), NullMeasurableSet (s i)\nhd : Pairwise (AEDisjoint μ on s)\nt : ι → Set α\nht_sub : ∀ (i : ι), t i ⊆ s i\nhtm : ∀ (i : ι), Me... | [
272,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
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] |
Mathlib/Algebra/Module/Torsion.lean | Submodule.torsionBy.mk_ideal_smul | [] | [
585,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.map_map | [
{
"state_after": "no goals",
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1251,
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Mathlib/Algebra/Ring/BooleanRing.lean | ofBoolRing_le_ofBoolRing_iff | [] | [
528,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_pi_div_four | [
{
"state_after": "x : ℝ\n⊢ sin (π / 4) = sin (π / 2 ^ 2)\n\nx : ℝ\n⊢ sin (π / 2 ^ 2) = sqrt 2 / 2",
"state_before": "x : ℝ\n⊢ sin (π / 4) = sqrt 2 / 2",
"tactic": "trans sin (π / 2 ^ 2)"
},
{
"state_after": "case e_x.e_a\nx : ℝ\n⊢ 4 = 2 ^ 2\n\nx : ℝ\n⊢ sin (π / 2 ^ 2) = sqrt 2 / 2",
"state_b... | [
793,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
789,
1
] |
Mathlib/MeasureTheory/Function/EssSup.lean | meas_essSup_lt | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nm : MeasurableSpace α\nμ ν : MeasureTheory.Measure α\ninst✝³ : ConditionallyCompleteLinearOrder β\nx : β\nf : α → β\ninst✝² : TopologicalSpace β\ninst✝¹ : FirstCountableTopology β\ninst✝ : OrderTopology β\nhf : autoParam (IsBoundedUnder (fun x x_1 => x ≤ x_1) (Measu... | [
133,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/LinearAlgebra/InvariantBasisNumber.lean | le_of_fin_surjective | [] | [
136,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
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Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.Pointed.mono | [] | [
364,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
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Mathlib/GroupTheory/Subgroup/Basic.lean | zpow_mem | [
{
"state_after": "G : Type ?u.5843\nG' : Type ?u.5846\ninst✝⁴ : Group G\ninst✝³ : Group G'\nA : Type ?u.5855\ninst✝² : AddGroup A\nM : Type u_1\nS : Type u_2\ninst✝¹ : DivInvMonoid M\ninst✝ : SetLike S M\nhSM : SubgroupClass S M\nH K : S\nx : M\nhx : x ∈ K\nn : ℕ\n⊢ x ^ n ∈ K",
"state_before": "G : Type ?u.... | [
157,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
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Mathlib/MeasureTheory/Constructions/Pi.lean | generateFrom_eq_pi | [
{
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139,
43
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136,
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_bit1 | [
{
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}
] | [
110,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
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Mathlib/Algebra/Module/Equiv.lean | AddEquiv.toIntLinearEquiv_toAddEquiv | [
{
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859,
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857,
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Mathlib/Analysis/Fourier/FourierTransform.lean | Real.fourierIntegral_eq_integral_exp_smul | [
{
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278,
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Mathlib/CategoryTheory/Limits/Shapes/Reflexive.lean | CategoryTheory.IsReflexivePair.common_section | [] | [
53,
76
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Mathlib/CategoryTheory/Monoidal/Free/Basic.lean | CategoryTheory.FreeMonoidalCategory.mk_l_hom | [] | [
226,
6
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225,
1
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Mathlib/Topology/Separation.lean | eqOn_closure₂ | [] | [
1213,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1209,
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Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.IsStrongLimit.isSuccLimit | [] | [
878,
92
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877,
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Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.coeff_mul_monomial | [
{
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244,
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237,
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Mathlib/GroupTheory/Congruence.lean | Con.induction_on_units | [
{
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1332,
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.aestronglyMeasurable | [] | [
135,
33
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132,
11
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Mathlib/Data/Set/Function.lean | Set.piecewise_mem_pi | [
{
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Mathlib/Analysis/SpecialFunctions/Complex/Log.lean | Complex.exp_eq_one_iff | [
{
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},
{
"state_after": "case mp\nx : ℂ\nh : exp x = 1\n⊢ ∃ n, x = ↑n... | [
152,
53
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143,
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Mathlib/Data/Complex/Module.lean | Complex.smul_im | [] | [
67,
88
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Mathlib/Data/List/MinMax.lean | List.argmax_mem | [
{
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{
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154,
78
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152,
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Mathlib/Data/Finset/Fold.lean | Finset.le_fold_max | [] | [
251,
32
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250,
1
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Mathlib/Topology/MetricSpace/IsometricSMul.lean | nndist_mul_left | [] | [
367,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
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Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.coe_det_isEmpty | [
{
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109,
20
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Mathlib/Data/Finset/Lattice.lean | Finset.sup_lt_iff | [
{
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708,
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705,
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Std/Data/Int/Lemmas.lean | Int.sub_le_of_sub_le | [] | [
1028,
59
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1027,
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Mathlib/MeasureTheory/Group/Prod.lean | MeasureTheory.inv_absolutelyContinuous | [] | [
186,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
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Mathlib/MeasureTheory/Integral/SetIntegral.lean | integral_conj | [] | [
1167,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1166,
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Mathlib/GroupTheory/OrderOfElement.lean | orderOf_eq_of_pow_and_pow_div_prime | [
{
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321,
39
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304,
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Mathlib/Algebra/GCDMonoid/Basic.lean | lcm_eq_one_iff | [
{
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"tact... | [
814,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
811,
1
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src/lean/Init/Data/Nat/Basic.lean | Nat.zero_sub | [
{
"state_after": "no goals",
"state_before": "n : Nat\n⊢ 0 - n = 0",
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},
{
"state_after": "no goals",
"state_before": "case zero\n\n⊢ 0 - zero = 0",
"tactic": "rfl"
},
{
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... | [
632,
41
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629,
19
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Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_le_one | [] | [
810,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
809,
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Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_neg_eq_logb | [
{
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"tactic": "rw [← logb_abs x, ← logb_abs (-x), abs_neg]"
}
] | [
65,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.isProbabilityMeasureSmul | [
{
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Mathlib/Data/Finset/Basic.lean | List.toFinset_surjective | [] | [
3277,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3275,
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Mathlib/Analysis/Calculus/ContDiff.lean | ContinuousLinearEquiv.contDiffAt_comp_iff | [
{
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486,
36
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483,
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Mathlib/Topology/Algebra/InfiniteSum/Order.lean | tsum_le_of_sum_range_le | [] | [
36,
56
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33,
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.ext_on | [] | [
545,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
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Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.inv_zero | [
{
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"state_before": "R : Type u_1\ninst✝³ : Ring R\ninst✝² : Nontrivial R\ninst✝¹ : Or... | [
933,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
931,
11
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Mathlib/Data/Set/Basic.lean | Set.Nontrivial.pair_subset | [] | [
2475,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2473,
1
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Mathlib/Data/Set/Sups.lean | Set.sups_right_comm | [] | [
207,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
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Mathlib/Order/CompleteLattice.lean | sInf_diff_singleton_top | [] | [
530,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/Algebra/Order/Sub/Defs.lean | add_tsub_le_right | [] | [
74,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
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Mathlib/Order/Hom/CompleteLattice.lean | sInfHom.ext | [] | [
412,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Order/RelClasses.lean | rel_of_subsingleton | [] | [
148,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.rel_map_left | [
{
"state_after": "no goals",
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"tactic": "simp"
},
{
"state_after": "no goals",
... | [
2767,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2765,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.mul_mem_mul | [
{
"state_after": "no goals",
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537,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
536,
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Mathlib/Order/ModularLattice.lean | inf_covby_of_covby_sup_right | [
{
"state_after": "α : Type u_1\ninst✝¹ : Lattice α\ninst✝ : IsLowerModularLattice α\na b : α\n⊢ b ⋖ b ⊔ a → b ⊓ a ⋖ a",
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"tactic": "rw [inf_comm, sup_comm]"
},
{
"state_after": "... | [
185,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
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Mathlib/CategoryTheory/Abelian/Exact.lean | CategoryTheory.Abelian.exact_iff_exact_image_ι | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\ninst✝ : Abelian C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\n⊢ Exact (Abelian.factorThruImage f ≫ image.ι f) g ↔ Exact (image.ι f) g",
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244,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.zoom_toList | [
{
"state_after": "α : Type u_1\ncut : α → Ordering\nt' : RBNode α\np' : Path α\nt : RBNode α\neq : zoom cut t root = (t', p')\n⊢ toList (fill root t) = toList t",
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488,
83
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
487,
1
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Mathlib/Order/CompleteLattice.lean | iSup_neg | [] | [
1091,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1090,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesOnBall.image_sub_sub_deriv_le | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.932002\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedS... | [
792,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
786,
1
] |
Mathlib/Data/List/Forall2.lean | List.Forall₂.imp | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.1154\nδ : Type ?u.1157\nR S : α → β → Prop\nP : γ → δ → Prop\nRₐ : α → α → Prop\nH : ∀ (a : α) (b : β), R a b → S a b\nl₁ : List α\nl₂ : List β\nh : Forall₂ R l₁ l₂\n⊢ Forall₂ S l₁ l₂",
"tactic": "induction h <;> const... | [
43,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/Analysis/Convex/Hull.lean | convexHull_convexHull_union_right | [] | [
149,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.mem_span_singleton | [
{
"state_after": "case refine_1\nR : Type u_2\nR₂ : Type ?u.115596\nK : Type ?u.115599\nM : Type u_1\nM₂ : Type ?u.115605\nV : Type ?u.115608\nS : Type ?u.115611\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nx : M\np p' : Submodule R M\ninst✝² : Semiring R₂\nσ₁₂ : R →+* R₂\ninst✝¹ : AddCo... | [
411,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Logic/Basic.lean | Iff.not_right | [] | [
277,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq1.map_pair | [] | [
925,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
925,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.zeroLocus_inf | [] | [
359,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/Topology/Separation.lean | nhdsWithin_of_mem_discrete | [] | [
823,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
821,
1
] |
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