file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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|---|---|---|---|---|---|---|
Mathlib/Data/Set/Image.lean | Set.image_eq_empty | [
{
"state_after": "α✝ : Type ?u.37986\nβ✝ : Type ?u.37989\nγ : Type ?u.37992\nι : Sort ?u.37995\nι' : Sort ?u.37998\nf✝ : α✝ → β✝\ns✝ t : Set α✝\nα : Type u_1\nβ : Type u_2\nf : α → β\ns : Set α\n⊢ (∀ (x : β), ¬x ∈ f '' s) ↔ ∀ (x : α), ¬x ∈ s",
"state_before": "α✝ : Type ?u.37986\nβ✝ : Type ?u.37989\nγ : Typ... | [
357,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
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Mathlib/LinearAlgebra/Matrix/Symmetric.lean | Matrix.IsSymm.eq | [] | [
40,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
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Mathlib/Topology/Homotopy/HomotopyGroup.lean | Cube.head.continuous | [] | [
86,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
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Mathlib/Order/Bounds/Basic.lean | BddBelow.image2 | [
{
"state_after": "case intro.intro\nα : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : Preorder γ\nf : α → β → γ\ns : Set α\nt : Set β\na✝ : α\nb✝ : β\nh₀ : ∀ (b : β), Monotone (swap f b)\nh₁ : ∀ (a : α), Monotone (f a)\na : α\nha : a ∈ lowerBounds s\nb : β\nhb : b... | [
1387,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1385,
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Mathlib/Topology/LocalExtr.lean | IsLocalExtrOn.isLocalExtr | [] | [
155,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
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Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.monotone_rpow_of_nonneg | [
{
"state_after": "no goals",
"state_before": "z : ℝ\nh : 0 ≤ z\nh0 : 0 = z\n⊢ Monotone fun x => x ^ 0",
"tactic": "simp only [rpow_zero, monotone_const]"
}
] | [
546,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
544,
1
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Mathlib/SetTheory/Ordinal/Basic.lean | Cardinal.ord_mono | [] | [
1408,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1407,
1
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Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.SignedMeasure.rnDeriv_neg | [
{
"state_after": "α : Type u_1\nβ : Type ?u.646293\nm : MeasurableSpace α\nμ✝ ν : Measure α\ns✝ t s : SignedMeasure α\nμ : Measure α\ninst✝ : HaveLebesgueDecomposition s μ\n⊢ withDensityᵥ μ (rnDeriv (-s) μ) = withDensityᵥ μ (-rnDeriv s μ)",
"state_before": "α : Type u_1\nβ : Type ?u.646293\nm : MeasurableSp... | [
1152,
45
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1146,
1
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Mathlib/Analysis/Calculus/Conformal/NormedSpace.lean | conformalAt_iff_isConformalMap_fderiv | [
{
"state_after": "case mp\nX : Type u_1\nY : Type u_2\nZ : Type ?u.68199\ninst✝⁵ : NormedAddCommGroup X\ninst✝⁴ : NormedAddCommGroup Y\ninst✝³ : NormedAddCommGroup Z\ninst✝² : NormedSpace ℝ X\ninst✝¹ : NormedSpace ℝ Y\ninst✝ : NormedSpace ℝ Z\nf : X → Y\nx : X\n⊢ ConformalAt f x → IsConformalMap (fderiv ℝ f x)\... | [
88,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
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Mathlib/CategoryTheory/Whiskering.lean | CategoryTheory.whiskerRight_id | [] | [
134,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
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Mathlib/Data/LazyList/Basic.lean | LazyList.append_nil | [
{
"state_after": "case nil\nα : Type u_1\n⊢ append nil (Thunk.pure nil) = nil\n\ncase cons\nα : Type u_1\nxs : LazyList α\nhd✝ : α\ntl✝ : Thunk (LazyList α)\ntl_ih✝ : ?m.62837 tl✝\n⊢ append (cons hd✝ tl✝) (Thunk.pure nil) = cons hd✝ tl✝\n\ncase mk\nα : Type u_1\nxs : LazyList α\nfn✝ : Unit → LazyList α\nih : ∀ ... | [
170,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
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Mathlib/Computability/Language.lean | Language.add_def | [] | [
78,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.All_def | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\np : α → Prop\nt : RBNode α\n⊢ All p t ↔ ∀ (x : α), x ∈ t → p x",
"tactic": "induction t <;> simp [or_imp, forall_and, *]"
}
] | [
101,
47
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
100,
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Mathlib/CategoryTheory/Quotient.lean | CategoryTheory.Quotient.lift.isLift_hom | [] | [
209,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
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Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_add_right | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1221416\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx y z : E\n⊢ ↑(starRingEnd 𝕜) (inner y x) + ↑(starRingEnd 𝕜) (inner z x) ... | [
466,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
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Mathlib/Topology/DenseEmbedding.lean | isClosed_property2 | [] | [
324,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
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Mathlib/Logic/Equiv/Basic.lean | Equiv.swap_apply_left | [] | [
1564,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1563,
1
] |
Mathlib/Probability/Integration.lean | ProbabilityTheory.lintegral_mul_indicator_eq_lintegral_mul_lintegral_indicator | [
{
"state_after": "Ω : Type u_1\nmΩ✝ : MeasurableSpace Ω\nμ✝ : MeasureTheory.Measure Ω\ng : Ω → ℝ≥0∞\nX Y : Ω → ℝ\nMf mΩ : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\nhMf : Mf ≤ mΩ\nc : ℝ≥0∞\nT : Set Ω\nh_meas_T : MeasurableSet T\nh_ind : IndepSets {s | MeasurableSet s} {T}\n⊢ ∀ {f : Ω → ℝ≥0∞},\n Measurab... | [
75,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
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Mathlib/Data/Nat/ModEq.lean | Dvd.dvd.modEq_zero_nat | [] | [
83,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
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Mathlib/Data/Multiset/Basic.lean | Multiset.le_replicate_iff | [] | [
976,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
972,
1
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Mathlib/Order/SuccPred/Limit.lean | Order.isSuccLimitRecOn_limit | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : SuccOrder α\na b : α\nC : α → Sort u_2\nhs : (a : α) → ¬IsMax a → C (succ a)\nhl : (a : α) → IsSuccLimit a → C a\nhb : IsSuccLimit b\n⊢ isSuccLimitRecOn b hs hl = hl b hb",
"tactic": "classical exact dif_pos hb"... | [
177,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
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Mathlib/Computability/Partrec.lean | Computable.option_bind | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type u_1\nγ : Type ?u.184893\nσ : Type u_2\ninst✝³ : Primcodable α\ninst✝² : Primcodable β\ninst✝¹ : Primcodable γ\ninst✝ : Primcodable σ\nf : α → Option β\ng : α → β → Option σ\nhf : Computable f\nhg : Computable₂ g\na : α\n⊢ Option.casesOn (f... | [
694,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
1
] |
Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | MvPolynomial.mem_weightedHomogeneousSubmodule | [] | [
160,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Order/Bounds/Basic.lean | BddBelow.mono | [] | [
224,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/CategoryTheory/Monad/Basic.lean | CategoryTheory.Monad.left_unit | [] | [
151,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPushout.of_right | [] | [
749,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
745,
1
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Std/Data/Nat/Gcd.lean | Nat.not_coprime_of_dvd_of_dvd | [
{
"state_after": "d m n : Nat\ndgt1 : 1 < d\nHm : d ∣ m\nHn : d ∣ n\nco : coprime m n\n⊢ d ∣ gcd m n",
"state_before": "d m n : Nat\ndgt1 : 1 < d\nHm : d ∣ m\nHn : d ∣ n\nco : coprime m n\n⊢ d ∣ 1",
"tactic": "rw [← co.gcd_eq_one]"
},
{
"state_after": "no goals",
"state_before": "d m n : Nat... | [
279,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
277,
1
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Mathlib/Data/Set/Pointwise/Basic.lean | Set.iInter_inv | [] | [
218,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
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Mathlib/Data/Multiset/Basic.lean | Multiset.not_mem_zero | [] | [
262,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
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Mathlib/Topology/Separation.lean | lim_nhds | [] | [
1072,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1071,
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Mathlib/Order/Minimal.lean | minimals_inter_subset | [] | [
165,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | circleIntegral.integral_sub_inv_of_mem_ball | [
{
"state_after": "E : Type ?u.901462\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nc w : ℂ\nR : ℝ\nhw : w ∈ ball c R\nhR : 0 < R\n⊢ (∮ (z : ℂ) in C(c, R), (z - w)⁻¹) = 2 * ↑π * I",
"state_before": "E : Type ?u.901462\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ... | [
666,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
650,
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurableSet_Icc | [] | [
448,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.inf_eq_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\na b : CauSeq α abs\nh : a ≤ b\n⊢ a ⊓ b ≈ a",
"tactic": "simpa only [CauSeq.inf_comm] using CauSeq.inf_eq_right h"
}
] | [
948,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
947,
11
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Mathlib/Order/Minimal.lean | minimals_mono | [
{
"state_after": "α : Type u_1\nr r₁ r₂ : α → α → Prop\ns t : Set α\na✝ b✝ : α\ninst✝ : IsAntisymm α r₂\nh : ∀ (a b : α), r₁ a b → r₂ a b\na : α\nha : a ∈ minimals r₂ s\nb : α\nhb : b ∈ s\nhab : r₁ b a\nthis : a = b\n⊢ r₁ a b",
"state_before": "α : Type u_1\nr r₁ r₂ : α → α → Prop\ns t : Set α\na✝ b✝ : α\ni... | [
146,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
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Mathlib/Topology/Algebra/Star.lean | ContinuousAt.star | [] | [
66,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
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Mathlib/Logic/Equiv/TransferInstance.lean | Equiv.smul_def | [] | [
115,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
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Mathlib/Topology/Order.lean | induced_inf | [] | [
438,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.natDegree_cyclotomic | [
{
"state_after": "n : ℕ\nR : Type u_1\ninst✝¹ : Ring R\ninst✝ : Nontrivial R\n⊢ WithBot.unbot' 0 ↑(Nat.totient n) = Nat.totient n",
"state_before": "n : ℕ\nR : Type u_1\ninst✝¹ : Ring R\ninst✝ : Nontrivial R\n⊢ natDegree (cyclotomic n R) = Nat.totient n",
"tactic": "rw [natDegree, degree_cyclotomic]"
... | [
353,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
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Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Iso.refl_trans | [
{
"state_after": "case w\nC : Type u\ninst✝ : Category C\nX Y Z : C\nα : X ≅ Y\n⊢ (refl X ≪≫ α).hom = α.hom",
"state_before": "C : Type u\ninst✝ : Category C\nX Y Z : C\nα : X ≅ Y\n⊢ refl X ≪≫ α = α",
"tactic": "ext"
},
{
"state_after": "no goals",
"state_before": "case w\nC : Type u\ninst✝ ... | [
194,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Computability/EpsilonNFA.lean | εNFA.start_zero | [] | [
245,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
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Mathlib/CategoryTheory/Limits/Shapes/ZeroObjects.lean | CategoryTheory.Limits.IsZero.op | [] | [
133,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.comm_symm_tmul | [] | [
659,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
658,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | HasDerivAt.rpow_const | [
{
"state_after": "f g : ℝ → ℝ\nf' g' x y p : ℝ\ns : Set ℝ\nhf : HasDerivWithinAt f f' Set.univ x\nhx : f x ≠ 0 ∨ 1 ≤ p\n⊢ HasDerivWithinAt (fun y => f y ^ p) (f' * p * f x ^ (p - 1)) Set.univ x",
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589,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
586,
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Mathlib/SetTheory/ZFC/Basic.lean | PSet.Equiv.comm | [] | [
197,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
11
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Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.coeff_X_pow | [
{
"state_after": "no goals",
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"tactic": "rw [X_pow_eq s n, coeff_monomial]"
}
] | [
443,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
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Mathlib/Data/Matrix/Basic.lean | Matrix.sub_mul | [
{
"state_after": "no goals",
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70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.cokernelComparison_map_desc | [
{
"state_after": "no goals",
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1147,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1143,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.nat_cast_sub | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.173725\nβ : Type ?u.173728\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nm n : ℕ\n⊢ ↑(m - n) = ↑m - ↑n",
"tactic": "rw [← coe_nat, Nat.cast_tsub, coe_sub, coe_nat, coe_nat]"
}
] | [
1120,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1119,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.ofReal_mul_re | [
{
"state_after": "no goals",
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"tactic": "simp [ofReal']"
}
] | [
281,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean | Matrix.SpecialLinearGroup.coe_neg | [] | [
271,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Data/Nat/GCD/Basic.lean | Nat.coprime_self_add_right | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\n⊢ coprime m (m + n) ↔ coprime m n",
"tactic": "rw [add_comm, coprime_add_self_right]"
}
] | [
139,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | MeasureTheory.Integrable.continuous_primitive | [] | [
1253,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1251,
8
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.wSameSide_and_wOppSide_iff | [
{
"state_after": "case mp\nR : Type u_1\nV : Type u_2\nV' : Type ?u.316087\nP : Type u_3\nP' : Type ?u.316093\ninst✝⁶ : LinearOrderedField R\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddTorsor V P\ninst✝² : AddCommGroup V'\ninst✝¹ : Module R V'\ninst✝ : AddTorsor V' P'\ns : AffineSubspace R P\nx y... | [
634,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
624,
1
] |
Mathlib/CategoryTheory/GlueData.lean | CategoryTheory.GlueData.glue_condition | [] | [
210,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
src/lean/Init/Data/List/BasicAux.lean | List.append_cancel_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nas bs cs : List α\nh : as ++ bs = cs ++ bs\n⊢ as = cs",
"tactic": "match as, cs with\n| [], [] => rfl\n| [], c::cs => have aux := congrArg length h; simp_arith at aux\n| a::as, [] => have aux := congrArg length h; simp_arith at aux\... | [
148,
82
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
143,
1
] |
Mathlib/Algebra/Group/Basic.lean | div_div_cancel | [] | [
943,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
942,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.sum_const | [] | [
878,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
872,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.nodup_iff_injective_get | [
{
"state_after": "case mk\nn : ℕ\nα : Type u_1\nl : List α\nhl : List.length l = n\n⊢ List.Nodup (toList { val := l, property := hl }) ↔ Function.Injective (get { val := l, property := hl })",
"state_before": "n : ℕ\nα : Type u_1\nv : Vector α n\n⊢ List.Nodup (toList v) ↔ Function.Injective (get v)",
"t... | [
232,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.map_val_Ici_atTop | [] | [
1543,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1542,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.fromBlocks_one | [
{
"state_after": "case a.h\nl : Type u_1\nm : Type u_2\nn : Type ?u.123200\no : Type ?u.123203\np : Type ?u.123206\nq : Type ?u.123209\nm' : o → Type ?u.123214\nn' : o → Type ?u.123219\np' : o → Type ?u.123224\nR : Type ?u.123227\nS : Type ?u.123230\nα : Type u_3\nβ : Type ?u.123236\ninst✝³ : DecidableEq l\nins... | [
315,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Continuous.aemeasurable | [] | [
825,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
824,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.map_comap_eq_self | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nG' : Type ?u.569964\ninst✝³ : Group G\ninst✝² : Group G'\nA : Type ?u.569973\ninst✝¹ : AddGroup A\nN : Type u_2\ninst✝ : Group N\nf✝ f : G →* N\nH : Subgroup N\nh : H ≤ range f\n⊢ map f (comap f H) = H",
"tactic": "rwa [map_comap_eq, inf_eq_rig... | [
3025,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3024,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.hasSum_re | [] | [
607,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
606,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.Set.EqOn.restr_eqOn_source | [
{
"state_after": "case left\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.81218\nδ : Type ?u.81221\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ne✝ : LocalHomeomorph α β\ne'✝ : LocalHomeomorph β γ\ne e' : LocalHomeomorph α β\nh : EqOn (↑e) (↑e') (... | [
990,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
983,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.ceil_int | [] | [
1597,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1596,
1
] |
Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.IsFundamentalDomain.measure_eq | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nH : Type ?u.302877\nα : Type u_2\nβ : Type ?u.302883\nE : Type ?u.302886\ninst✝¹⁰ : Group G\ninst✝⁹ : Group H\ninst✝⁸ : MulAction G α\ninst✝⁷ : MeasurableSpace α\ninst✝⁶ : MulAction H β\ninst✝⁵ : MeasurableSpace β\ninst✝⁴ : NormedAddCommGroup E\ns ... | [
355,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
11
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | intermediate_value_Ico' | [] | [
562,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.nonUnitalAlgHom_ext' | [] | [
1778,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1776,
1
] |
Mathlib/Analysis/Convex/Between.lean | wbtw_swap_left_iff | [
{
"state_after": "case mp\nR : Type u_1\nV : Type u_2\nV' : Type ?u.181718\nP : Type u_3\nP' : Type ?u.181724\ninst✝⁷ : OrderedRing R\ninst✝⁶ : AddCommGroup V\ninst✝⁵ : Module R V\ninst✝⁴ : AddTorsor V P\ninst✝³ : AddCommGroup V'\ninst✝² : Module R V'\ninst✝¹ : AddTorsor V' P'\ninst✝ : NoZeroSMulDivisors R V\nx... | [
376,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.coe_copy | [] | [
229,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/RingTheory/Derivation/Basic.lean | Derivation.coe_mk' | [] | [
364,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/Algebra/Support.lean | Function.mulSupport_nat_cast | [] | [
329,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/Data/Rat/NNRat.lean | NNRat.coe_eq_zero | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.14941\np q : ℚ≥0\n⊢ ↑q = 0 ↔ q = 0",
"tactic": "norm_cast"
}
] | [
158,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Data/Real/Basic.lean | Real.ofCauchy_add | [] | [
124,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Topology/LocallyConstant/Algebra.lean | LocallyConstant.coe_div | [] | [
135,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.map_div | [
{
"state_after": "case pos\nR : Type ?u.1232681\ninst✝⁹ : CommRing R\nS : Submonoid R\nP : Type ?u.1232888\ninst✝⁸ : CommRing P\ninst✝⁷ : Algebra R P\nloc : IsLocalization S P\nR₁ : Type u_1\ninst✝⁶ : CommRing R₁\nK : Type u_2\ninst✝⁵ : Field K\ninst✝⁴ : Algebra R₁ K\nfrac : IsFractionRing R₁ K\ninst✝³ : IsDoma... | [
1199,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1193,
1
] |
Mathlib/Topology/Order/Lattice.lean | Filter.Tendsto.inf_right_nhds | [] | [
130,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/RingTheory/Nilpotent.lean | LinearMap.isNilpotent_mulLeft_iff | [
{
"state_after": "no goals",
"state_before": "R S : Type u\nx y : R\nA : Type v\ninst✝² : CommSemiring R\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\na : A\n⊢ IsNilpotent (mulLeft R a) ↔ IsNilpotent a",
"tactic": "constructor <;> rintro ⟨n, hn⟩ <;> use n <;>\n simp only [mulLeft_eq_zero_iff, pow_mulLef... | [
228,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Data/List/Sublists.lean | List.length_of_sublistsLen | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u\nβ : Type v\nγ : Type w\nα : Type u_1\nl l' : List α\nh : l' ∈ sublistsLen 0 l\n⊢ length l' = 0",
"tactic": "simp_all"
},
{
"state_after": "α✝ : Type u\nβ : Type v\nγ : Type w\nα : Type u_1\nn : ℕ\na : α\nl l' : List α\nh : l' ∈ sublistsL... | [
316,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.mem_sInf | [] | [
156,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.get_pure | [] | [
547,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.upper_mem | [] | [
129,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mk_le_mk | [] | [
430,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.mul_sub | [
{
"state_after": "α : Type ?u.198618\nβ : Type ?u.198621\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nh : 0 < c → c < b → a ≠ ⊤\n⊢ (b - c) * a = b * a - c * a",
"state_before": "α : Type ?u.198618\nβ : Type ?u.198621\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nh : 0 < c → c < b → a ≠ ⊤\n⊢ a * (b - c) = a * b - a * c",
"tactic": "si... | [
1206,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1204,
1
] |
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | IsBoundedLinearMap.isBigO_comp | [] | [
197,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | div_le_one' | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Group α\ninst✝¹ : LE α\ninst✝ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b c d : α\n⊢ a / b ≤ 1 ↔ a ≤ b",
"tactic": "rw [← mul_le_mul_iff_right b, one_mul, div_eq_mul_inv, inv_mul_cancel_right]"
}
] | [
738,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
737,
1
] |
Mathlib/MeasureTheory/Covering/Differentiation.lean | VitaliFamily.mul_measure_le_of_subset_lt_limRatioMeas | [
{
"state_after": "α : Type u_1\ninst✝⁵ : MetricSpace α\nm0 : MeasurableSpace α\nμ : MeasureTheory.Measure α\nv : VitaliFamily μ\nE : Type ?u.3960181\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : SecondCountableTopology α\ninst✝² : BorelSpace α\ninst✝¹ : IsLocallyFiniteMeasure μ\nρ : MeasureTheory.Measure α\ninst✝ : ... | [
492,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Data/Nat/PSub.lean | Nat.pred_eq_ppred | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ pred n = Option.getD (ppred n) 0",
"tactic": "cases n <;> rfl"
}
] | [
57,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.log_one | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ exp (log 1) = exp 0",
"tactic": "rw [exp_log zero_lt_one, exp_zero]"
}
] | [
103,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.Iio_succ_eq_insert | [] | [
504,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/Topology/Order/Basic.lean | mem_nhdsWithin_Ici_iff_exists_Icc_subset | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝⁴ : TopologicalSpace α\ninst✝³ : LinearOrder α\ninst✝² : OrderTopology α\ninst✝¹ : NoMaxOrder α\ninst✝ : DenselyOrdered α\na : α\ns : Set α\n⊢ (∃ u, u ∈ Ioi a ∧ Ico a u ⊆ s) ↔ ∃ u, a < u ∧ Icc a u ⊆ s",
"state_before": "α : Type u\nβ : Type v\nγ : T... | [
1791,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1783,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.single_vecMul | [] | [
1795,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1793,
1
] |
Mathlib/Data/String/Basic.lean | List.asString_eq | [
{
"state_after": "no goals",
"state_before": "l : List Char\ns : String\n⊢ asString l = s ↔ l = toList s",
"tactic": "rw [← asString_inv_toList s, asString_inj, asString_inv_toList s]"
}
] | [
203,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Data/Quot.lean | Quotient.inductionOn₂' | [] | [
679,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
676,
11
] |
Mathlib/Topology/Homotopy/Path.lean | Path.Homotopic.equivalence | [] | [
285,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.sum_basis | [
{
"state_after": "case refine'_1\nF : Type u_2\ninst✝¹ : Field F\nι : Type u_1\ninst✝ : DecidableEq ι\ns : Finset ι\nv : ι → F\ni j : ι\nhvs : Set.InjOn v ↑s\nhs : Finset.Nonempty s\n⊢ (sup s fun b => degree (Lagrange.basis s v b)) < ↑(card s)\n\ncase refine'_2\nF : Type u_2\ninst✝¹ : Field F\nι : Type u_1\nins... | [
272,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Topology/ContinuousOn.lean | ContinuousOn.prod | [] | [
1067,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1065,
1
] |
Mathlib/Analysis/SpecificLimits/Normed.lean | Antitone.cauchySeq_series_mul_of_tendsto_zero_of_bounded | [
{
"state_after": "α : Type ?u.1506622\nβ : Type ?u.1506625\nι : Type ?u.1506628\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nb : ℝ\nf : ℕ → ℝ\nz : ℕ → E\nhfa : Antitone f\nhf0 : Tendsto f atTop (𝓝 0)\nhzb : ∀ (n : ℕ), ‖∑ i in Finset.range n, z i‖ ≤ b\nhfa' : Monotone fun n => -f n\n⊢ ... | [
610,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
601,
1
] |
Mathlib/GroupTheory/GroupAction/Basic.lean | MulAction.mem_fixedPoints' | [] | [
152,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
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