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/LinearAlgebra/AffineSpace/AffineSubspace.lean | vectorSpan_eq_span_vsub_finset_right_ne | [
{
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1077,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1074,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.toOneHom_coe | [] | [
613,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
612,
1
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Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.pow_right_injective | [
{
"state_after": "α : Type ?u.956127\nR : Type u_1\ninst✝¹ : CancelCommMonoidWithZero R\ninst✝ : UniqueFactorizationMonoid R\na : R\nha0 : a ≠ 0\nha1 : ¬IsUnit a\nthis : DecidableEq R := Classical.decEq R\n⊢ Function.Injective ((fun x x_1 => x ^ x_1) a)",
"state_before": "α : Type ?u.956127\nR : Type u_1\ni... | [
941,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
931,
1
] |
Mathlib/Analysis/MeanInequalitiesPow.lean | NNReal.pow_sum_div_card_le_sum_pow | [
{
"state_after": "no goals",
"state_before": "ι : Type u\ns : Finset ι\nf : ι → ℝ≥0\nn : ℕ\n⊢ ↑((∑ x in s, f x) ^ (n + 1)) / ↑(card s) ^ n ≤ ↑(∑ x in s, f x ^ (n + 1))",
"tactic": "simpa only [← NNReal.coe_le_coe, NNReal.coe_sum, Nonneg.coe_div, NNReal.coe_pow] using\n @Real.pow_sum_div_card_le_sum_pow... | [
133,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | Measurable.fst | [] | [
656,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
1
] |
Mathlib/Analysis/Calculus/Deriv/Add.lean | HasDerivAt.add | [] | [
71,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
8
] |
Mathlib/GroupTheory/Perm/List.lean | List.support_formPerm_of_nodup | [
{
"state_after": "α : Type u_1\nβ : Type ?u.766003\ninst✝¹ : DecidableEq α\nl✝ : List α\nx : α\ninst✝ : Fintype α\nl : List α\nh : Nodup l\nh' : ∀ (x : α), l ≠ [x]\n⊢ ↑(support (formPerm l)) = ↑(toFinset l)",
"state_before": "α : Type u_1\nβ : Type ?u.766003\ninst✝¹ : DecidableEq α\nl✝ : List α\nx : α\ninst... | [
269,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.map_neg | [
{
"state_after": "no goals",
"state_before": "S : Type ?u.139031\nR : Type u_1\nR₁ : Type ?u.139037\nM : Type u_2\ninst✝³ : Ring R\ninst✝² : CommRing R₁\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nQ : QuadraticForm R M\nx : M\n⊢ ↑Q (-x) = ↑Q x",
"tactic": "rw [← @neg_one_smul R _ _ _ _ x, map_smul, ne... | [
254,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Geometry/Euclidean/Sphere/Basic.lean | EuclideanGeometry.Sphere.mem_coe | [] | [
91,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Data/Set/Intervals/WithBotTop.lean | WithTop.image_coe_Ioi | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : PartialOrder α\na b : α\n⊢ some '' Ioi a = Ioo ↑a ⊤",
"tactic": "rw [← preimage_coe_Ioi, image_preimage_eq_inter_range, range_coe, Ioi_inter_Iio]"
}
] | [
91,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Topology/ContinuousOn.lean | insert_mem_nhds_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.21904\nγ : Type ?u.21907\nδ : Type ?u.21910\ninst✝ : TopologicalSpace α\na : α\ns : Set α\n⊢ insert a s ∈ 𝓝 a ↔ s ∈ 𝓝[{a}ᶜ] a",
"tactic": "simp only [nhdsWithin, mem_inf_principal, mem_compl_iff, mem_singleton_iff, or_iff_not_imp_... | [
300,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | DoubleQuot.coe_quotQuotEquivQuotSupₐ_symm | [] | [
774,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
772,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.symm_linear | [] | [
211,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Topology/Instances/Matrix.lean | Continuous.matrix_cramer | [] | [
223,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Algebra/Star/Unitary.lean | unitary.mul_star_self | [] | [
101,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.sign_eq_of_continuousOn | [] | [
1056,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1052,
1
] |
Mathlib/Order/Concept.lean | extentClosure_anti | [] | [
164,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Order/Cover.lean | Covby.Icc_eq | [] | [
413,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/Topology/Algebra/Monoid.lean | Continuous.mul | [] | [
93,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.leadingCoeff_X_pow_sub_one | [] | [
1461,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1460,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.of_gt | [] | [
1052,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1050,
1
] |
Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.Completion.ofRat_div | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\ninst✝² : LinearOrderedField α\nβ : Type u_1\ninst✝¹ : DivisionRing β\nabv : β → α\ninst✝ : IsAbsoluteValue abv\nx y : β\n⊢ ofRat (x / y) = ofRat x / ofRat y",
"tactic": "simp only [div_eq_mul_inv, ofRat_inv, ofRat_mul]"
}
] | [
283,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.cos_arcsin_nonneg | [] | [
302,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Std/Data/Nat/Gcd.lean | Nat.coprime.mul_right | [] | [
295,
29
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
294,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Independent.lean | affineIndependent_iff_of_fintype | [
{
"state_after": "case mp\nk : Type u_2\nV : Type u_3\nP : Type u_4\ninst✝⁴ : Ring k\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AffineSpace V P\nι : Type u_1\ninst✝ : Fintype ι\np : ι → P\n⊢ AffineIndependent k p →\n ∀ (w : ι → k), ∑ i : ι, w i = 0 → ↑(Finset.weightedVSub Finset.univ p) w = 0 → ... | [
86,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | Localization.mk_sum | [] | [
943,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
941,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.smul_closedBall_subset | [
{
"state_after": "case intro.intro\nR : Type ?u.1191905\nR' : Type ?u.1191908\n𝕜 : Type u_1\n𝕜₂ : Type ?u.1191914\n𝕜₃ : Type ?u.1191917\n𝕝 : Type ?u.1191920\nE : Type u_2\nE₂ : Type ?u.1191926\nE₃ : Type ?u.1191929\nF : Type ?u.1191932\nG : Type ?u.1191935\nι : Type ?u.1191938\ninst✝² : NormedField 𝕜\ninst... | [
959,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
954,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.le_mk_iff_exists_set | [] | [
286,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.map_val_Iio_atBot | [] | [
1573,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1571,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | IsCompact.measure_zero_of_nhdsWithin | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.3763501\nγ : Type ?u.3763504\nδ : Type ?u.3763507\nι : Type ?u.3763510\nR : Type ?u.3763513\nR' : Type ?u.3763516\ninst✝¹ : TopologicalSpace α\ninst✝ : MeasurableSpace α\nμ : MeasureTheory.Measure α\ns : Set α\nhs : IsCompact s\n⊢ (∀ (a... | [
4492,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4490,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.bliminf_eq_iSup_biInf | [] | [
773,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
771,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIocDiv_sub | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\n⊢ toIocDiv hp a (b - p) = toIocDiv hp a b - 1",
"tactic": "simpa only [one_zsmul] using toIocDiv_sub_zsmul hp a b 1"
}
] | [
350,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.biUnion_eq_iUnion | [] | [
898,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
896,
1
] |
Mathlib/Combinatorics/SimpleGraph/Density.lean | Rel.edgeDensity_le_one | [
{
"state_after": "case h\n𝕜 : Type ?u.16981\nι : Type ?u.16984\nκ : Type ?u.16987\nα : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrderedField 𝕜\nr : α → β → Prop\ninst✝ : (a : α) → DecidablePred (r a)\ns✝ s₁ s₂ : Finset α\nt✝ t₁ t₂ : Finset β\na : α\nb : β\nδ : 𝕜\ns : Finset α\nt : Finset β\n⊢ ↑(card (interedge... | [
142,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Algebra/Category/Ring/Constructions.lean | CommRingCat.pushoutCocone_pt | [
{
"state_after": "R A B : CommRingCat\nf : R ⟶ A\ng : R ⟶ B\nthis : Algebra ↑R ↑A := RingHom.toAlgebra f\n⊢ CommRingCat",
"state_before": "R A B : CommRingCat\nf : R ⟶ A\ng : R ⟶ B\n⊢ CommRingCat",
"tactic": "letI := f.toAlgebra"
},
{
"state_after": "R A B : CommRingCat\nf : R ⟶ A\ng : R ⟶ B\nth... | [
82,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.le_bind | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.53011\nβ✝ : Type ?u.53014\nγ : Type ?u.53017\nδ : Type ?u.53020\na : α✝\ns t : Multiset α✝\nf✝ g : α✝ → Multiset β✝\nα : Type u_1\nβ : Type u_2\nf : α → Multiset β\nS : Multiset α\nx : α\nhx : x ∈ S\n⊢ f x ≤ bind S f",
"tactic": "classical\n rw... | [
220,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.map_comp_map | [] | [
652,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
647,
1
] |
Mathlib/Order/SymmDiff.lean | bihimp_snd | [] | [
842,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
840,
1
] |
Mathlib/Analysis/SpecialFunctions/CompareExp.lean | Complex.IsExpCmpFilter.isLittleO_cpow_mul_exp | [
{
"state_after": "l : Filter ℂ\nb₁ b₂ : ℝ\nhl : IsExpCmpFilter l\nhb : b₁ < b₂\na₁ a₂ z : ℂ\nhz : z ≠ 0\n⊢ z ^ a₁ * exp (↑b₁ * z) = z ^ a₂ * exp (↑b₁ * z) * z ^ (a₁ - a₂)",
"state_before": "l : Filter ℂ\nb₁ b₂ : ℝ\nhl : IsExpCmpFilter l\nhb : b₁ < b₂\na₁ a₂ z : ℂ\nhz : z ≠ 0\n⊢ (fun z => z ^ a₁ * exp (↑b₁ *... | [
203,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/RingTheory/WittVector/StructurePolynomial.lean | wittStructureRat_rec | [
{
"state_after": "p : ℕ\nR : Type ?u.533445\nidx : Type u_1\ninst✝ : CommRing R\nhp : Fact (Nat.Prime p)\nΦ : MvPolynomial idx ℚ\nn : ℕ\n⊢ wittStructureRat p Φ n = ↑C (1 / ↑p ^ n) * (wittStructureRat p Φ n * ↑C (↑p ^ n))",
"state_before": "p : ℕ\nR : Type ?u.533445\nidx : Type u_1\ninst✝ : CommRing R\nhp : ... | [
191,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Data/Set/Pointwise/ListOfFn.lean | Set.mem_prod_list_ofFn | [
{
"state_after": "case zero\nF : Type ?u.41\nα : Type u_1\nβ : Type ?u.47\nγ : Type ?u.50\ninst✝ : Monoid α\ns✝¹ t : Set α\na✝¹ : α\nm n : ℕ\na✝ : α\ns✝ : Fin n → Set α\na : α\ns : Fin Nat.zero → Set α\n⊢ a ∈ List.prod (List.ofFn s) ↔ ∃ f, List.prod (List.ofFn fun i => ↑(f i)) = a\n\ncase succ\nF : Type ?u.41\n... | [
34,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
29,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | Trivialization.coe_symmₗ | [] | [
225,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.degreeLT_eq_span_X_pow | [
{
"state_after": "case a\nR : Type u\nS : Type ?u.15171\ninst✝ : Semiring R\nn : ℕ\n⊢ degreeLT R n ≤ Submodule.span R ↑(image (fun n => X ^ n) (range n))\n\ncase a\nR : Type u\nS : Type ?u.15171\ninst✝ : Semiring R\nn : ℕ\n⊢ Submodule.span R ↑(image (fun n => X ^ n) (range n)) ≤ degreeLT R n",
"state_before... | [
132,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.disjoint_filter_filter | [] | [
2774,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2771,
1
] |
Mathlib/Dynamics/FixedPoints/Basic.lean | Function.Injective.isFixedPt_apply_iff | [] | [
127,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/RingTheory/Algebraic.lean | Algebra.isAlgebraic_of_larger_base_of_injective | [] | [
239,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | UniformContinuous₂.comp | [] | [
1723,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1721,
1
] |
Mathlib/Tactic/Abel.lean | Mathlib.Tactic.Abel.termg_eq | [] | [
398,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/NumberTheory/Padics/PadicNorm.lean | padicNorm.padicNorm_p_lt_one | [
{
"state_after": "p : ℕ\nhp : 1 < p\n⊢ ↑p ≤ 0 ∨ 1 < ↑p",
"state_before": "p : ℕ\nhp : 1 < p\n⊢ padicNorm p ↑p < 1",
"tactic": "rw [padicNorm_p hp, inv_lt_one_iff]"
},
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : 1 < p\n⊢ ↑p ≤ 0 ∨ 1 < ↑p",
"tactic": "exact_mod_cast Or.inr hp"... | [
113,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Order/WellFoundedSet.lean | IsAntichain.partiallyWellOrderedOn_iff | [] | [
302,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Data/QPF/Univariate/Basic.lean | Qpf.corecF_eq | [
{
"state_after": "no goals",
"state_before": "F : Type u → Type u\ninst✝ : Functor F\nq : Qpf F\nα : Type u\ng : α → F α\nx : α\n⊢ PFunctor.M.dest (corecF g x) = corecF g <$> repr (g x)",
"tactic": "rw [corecF, PFunctor.M.dest_corec]"
}
] | [
381,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/Data/Vector.lean | Vector.eq_nil | [] | [
209,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
11
] |
Mathlib/Topology/Inseparable.lean | SeparationQuotient.continuousAt_lift | [] | [
556,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
] |
Mathlib/GroupTheory/Submonoid/Inverses.lean | Submonoid.leftInv_le_isUnit | [] | [
132,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Topology/Constructions.lean | continuous_sigma_iff | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type ?u.528783\nδ : Type ?u.528786\nε : Type ?u.528789\nζ : Type ?u.528792\nι : Type u_1\nκ : Type ?u.528798\nσ : ι → Type u_2\nτ : κ → Type ?u.528808\ninst✝² : (i : ι) → TopologicalSpace (σ i)\ninst✝¹ : (k : κ) → TopologicalSpace (τ k)\ninst✝ : TopologicalSpace α\n... | [
1526,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1522,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | Padic.norm_le_one_iff_val_nonneg | [
{
"state_after": "case pos\np : ℕ\nhp : Fact (Nat.Prime p)\nx : ℚ_[p]\nhx : x = 0\n⊢ ‖x‖ ≤ 1 ↔ 0 ≤ valuation x\n\ncase neg\np : ℕ\nhp : Fact (Nat.Prime p)\nx : ℚ_[p]\nhx : ¬x = 0\n⊢ ‖x‖ ≤ 1 ↔ 0 ≤ valuation x",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nx : ℚ_[p]\n⊢ ‖x‖ ≤ 1 ↔ 0 ≤ valuation x",
"tac... | [
1186,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1182,
1
] |
Mathlib/Order/Bounded.lean | Set.bounded_le_Ioc | [] | [
238,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Analysis/LocallyConvex/Polar.lean | LinearMap.polar_eq_iInter | [
{
"state_after": "case h\n𝕜 : Type u_3\nE : Type u_1\nF : Type u_2\ninst✝⁴ : NormedCommRing 𝕜\ninst✝³ : AddCommMonoid E\ninst✝² : AddCommMonoid F\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\nB : E →ₗ[𝕜] F →ₗ[𝕜] 𝕜\ns : Set E\nx✝ : F\n⊢ x✝ ∈ polar B s ↔ x✝ ∈ ⋂ (x : E) (_ : x ∈ s), {y | ‖↑(↑B x) y‖ ≤ 1}",
... | [
79,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Data/Int/GCD.lean | Int.lcm_one_left | [
{
"state_after": "i : ℤ\n⊢ Nat.lcm (natAbs 1) (natAbs i) = natAbs i",
"state_before": "i : ℤ\n⊢ lcm 1 i = natAbs i",
"tactic": "rw [Int.lcm]"
},
{
"state_after": "no goals",
"state_before": "i : ℤ\n⊢ Nat.lcm (natAbs 1) (natAbs i) = natAbs i",
"tactic": "apply Nat.lcm_one_left"
}
] | [
468,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/LinearAlgebra/Ray.lean | exists_pos_right_iff_sameRay_and_ne_zero | [
{
"state_after": "R : Type u_2\ninst✝² : LinearOrderedField R\nM : Type u_1\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nx y : M\nhy : y ≠ 0\n⊢ (∃ r, 0 < r ∧ x = r • y) ↔ SameRay R y x ∧ x ≠ 0",
"state_before": "R : Type u_2\ninst✝² : LinearOrderedField R\nM : Type u_1\ninst✝¹ : AddCommGroup M\ninst✝ : Mod... | [
745,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
741,
1
] |
Mathlib/Topology/Semicontinuous.lean | Continuous.comp_lowerSemicontinuous_antitone | [] | [
363,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Analysis/Convex/Slope.lean | ConvexOn.secant_mono_aux2 | [
{
"state_after": "𝕜 : Type u_1\ninst✝ : LinearOrderedField 𝕜\ns : Set 𝕜\nf : 𝕜 → 𝕜\nhf : ConvexOn 𝕜 s f\nx y z : 𝕜\nhx : x ∈ s\nhz : z ∈ s\nhxy : x < y\nhyz : y < z\nhxy' : 0 < y - x\n⊢ (f y - f x) / (y - x) ≤ (f z - f x) / (z - x)",
"state_before": "𝕜 : Type u_1\ninst✝ : LinearOrderedField 𝕜\ns : ... | [
266,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot_mk_of | [] | [
830,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
827,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iInter₂_mono | [] | [
391,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_fin | [
{
"state_after": "no goals",
"state_before": "α β : Type u\nn : ℕ\n⊢ (#Fin n) = ↑n",
"tactic": "simp"
}
] | [
1278,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1278,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | isDedekindDomainInv_iff | [
{
"state_after": "R : Type ?u.96084\nA : Type u_1\nK : Type u_2\ninst✝⁵ : CommRing R\ninst✝⁴ : CommRing A\ninst✝³ : Field K\ninst✝² : IsDomain A\ninst✝¹ : Algebra A K\ninst✝ : IsFractionRing A K\nh : FractionalIdeal A⁰ (FractionRing A) ≃+* FractionalIdeal A⁰ K := mapEquiv (FractionRing.algEquiv A K)\n⊢ IsDedeki... | [
264,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.nat_mul_sub_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.102914\nf g : α → β\nc c₁ c₂ x : α\ninst✝ : Ring α\nh : Periodic f c\nn : ℕ\n⊢ f (↑n * c - x) = f (-x)",
"tactic": "simpa only [sub_eq_neg_add] using h.nat_mul n (-x)"
}
] | [
231,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/Algebra/GeomSum.lean | neg_one_geom_sum | [
{
"state_after": "case zero\nα : Type u\ninst✝ : Ring α\n⊢ ∑ i in range Nat.zero, (-1) ^ i = if Even Nat.zero then 0 else 1\n\ncase succ\nα : Type u\ninst✝ : Ring α\nk : ℕ\nhk : ∑ i in range k, (-1) ^ i = if Even k then 0 else 1\n⊢ ∑ i in range (Nat.succ k), (-1) ^ i = if Even (Nat.succ k) then 0 else 1",
"... | [
143,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.smul_imJ | [] | [
371,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
9
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.dotProduct_comm | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.122679\nm : Type u_1\nn : Type ?u.122685\no : Type ?u.122688\nm' : o → Type ?u.122693\nn' : o → Type ?u.122698\nR : Type ?u.122701\nS : Type ?u.122704\nα : Type v\nβ : Type w\nγ : Type ?u.122711\ninst✝³ : Fintype m\ninst✝² : Fintype n\ninst✝¹ : AddCo... | [
724,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
723,
1
] |
Mathlib/Tactic/NormNum/Prime.lean | Mathlib.Meta.NormNum.isNat_prime_2 | [] | [
180,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.inv_mul_cancel | [] | [
297,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
11
] |
Std/Logic.lean | iff_false_left | [] | [
67,
89
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
67,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidWithZeroHom.coe_orderMonoidHom | [] | [
633,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
632,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | uniformContinuous_comap | [] | [
1311,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1309,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.ppow_succ' | [
{
"state_after": "case h\nR : Type u_1\ninst✝ : Semiring R\nf : ArithmeticFunction R\nk : ℕ\nkpos : 0 < k\nx : ℕ\n⊢ ↑(ppow f (k + 1)) x = ↑(pmul (ppow f k) f) x",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nf : ArithmeticFunction R\nk : ℕ\nkpos : 0 < k\n⊢ ppow f (k + 1) = pmul (ppow f k) f",
"tac... | [
573,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.log_div | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\nhx : x ≠ 0\nhy : y ≠ 0\n⊢ exp (log (x / y)) = exp (log x - log y)",
"tactic": "rw [exp_log_eq_abs (div_ne_zero hx hy), exp_sub, exp_log_eq_abs hx, exp_log_eq_abs hy, abs_div]"
}
] | [
136,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | isConnected_Ioc | [] | [
490,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Std/Data/String/Lemmas.lean | String.lt_next' | [] | [
260,
69
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
260,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.mem_toSubsemiring | [] | [
213,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.AECover.ae_tendsto_indicator | [] | [
302,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.iterate_derivative_X | [] | [
266,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Data/List/AList.lean | AList.perm_insert | [
{
"state_after": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb : β a\ns₁ s₂ : AList β\np : s₁.entries ~ s₂.entries\n⊢ { fst := a, snd := b } :: kerase a s₁.entries ~ { fst := a, snd := b } :: kerase a s₂.entries",
"state_before": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb : ... | [
300,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/Topology/Category/TopCat/Opens.lean | TopologicalSpace.Opens.map_id_obj | [] | [
167,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | IsLUB.mul_left | [
{
"state_after": "case inl\nι : Type ?u.190062\nα : Type u_1\nβ : Type ?u.190068\ninst✝ : LinearOrderedField α\na b c d : α\nn : ℤ\ns : Set α\nha✝ : 0 ≤ a\nhs : IsLUB s b\nha : 0 < a\n⊢ IsLUB ((fun b => a * b) '' s) (a * b)\n\ncase inr\nι : Type ?u.190062\nα : Type u_1\nβ : Type ?u.190068\ninst✝ : LinearOrdered... | [
944,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
938,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiffOn_top_iff_fderiv_of_open | [
{
"state_after": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nX : Type uX\ninst✝¹ : NormedAdd... | [
1179,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1176,
1
] |
Mathlib/Order/Max.lean | IsMax.fst | [] | [
440,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/Data/Set/Basic.lean | Set.diff_subset_diff_left | [] | [
1885,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1884,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.card_support_extend_domain | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝⁴ : DecidableEq α\ninst✝³ : Fintype α\nf✝ g✝ : Perm α\nβ : Type u_2\ninst✝² : DecidableEq β\ninst✝¹ : Fintype β\np : β → Prop\ninst✝ : DecidablePred p\nf : α ≃ Subtype p\ng : Perm α\n⊢ card (support (extendDomain g f)) = card (support g)",
... | [
572,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.AbsTheory.re_le_abs | [] | [
921,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
920,
9
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.inclusion_self | [] | [
559,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
] |
Mathlib/Algebra/Module/LocalizedModule.lean | LocalizedModule.lift_unique | [
{
"state_after": "case h\nR : Type u_1\ninst✝⁶ : CommRing R\nS : Submonoid R\nM : Type u_2\nM' : Type ?u.570900\nM'' : Type u_3\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : AddCommMonoid M'\ninst✝³ : AddCommMonoid M''\ninst✝² : Module R M\ninst✝¹ : Module R M'\ninst✝ : Module R M''\nf : M →ₗ[R] M'\ng✝ g : M →ₗ[R] M''\nh... | [
683,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
675,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.list_prod_mem | [] | [
373,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
11
] |
Mathlib/GroupTheory/DoubleCoset.lean | Doset.rel_iff | [] | [
91,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.Integrable.swap | [] | [
229,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.commute_X | [] | [
615,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
614,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | Valuation.IsEquiv.val_eq | [
{
"state_after": "no goals",
"state_before": "K : Type ?u.2929625\nF : Type ?u.2929628\nR : Type u_1\ninst✝⁴ : DivisionRing K\nΓ₀ : Type u_2\nΓ'₀ : Type u_3\nΓ''₀ : Type ?u.2929643\ninst✝³ : LinearOrderedCommMonoidWithZero Γ''₀\ninst✝² : Ring R\ninst✝¹ : LinearOrderedCommMonoidWithZero Γ₀\ninst✝ : LinearOrd... | [
405,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Algebra/Order/Rearrangement.lean | Antivary.sum_smul_eq_sum_smul_comp_perm_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝⁴ : LinearOrderedRing α\ninst✝³ : LinearOrderedAddCommGroup β\ninst✝² : Module α β\ninst✝¹ : OrderedSMul α β\ns : Finset ι\nσ : Perm ι\nf : ι → α\ng : ι → β\ninst✝ : Fintype ι\nhfg : Antivary f g\n⊢ ∑ i : ι, f i • g... | [
303,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.sin_ne_zero_of_not_collinear | [] | [
527,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Real.ball_eq_Ioo | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.198627\nι : Type ?u.198630\ninst✝ : PseudoMetricSpace α\nx r y : ℝ\n⊢ y ∈ ball x r ↔ y ∈ Ioo (x - r) (x + r)",
"tactic": "rw [mem_ball, dist_comm, Real.dist_eq, abs_sub_lt_iff, mem_Ioo, ← sub_lt_iff_lt_add',\n sub_lt_comm... | [
1396,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1393,
1
] |
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