file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/Num/Lemmas.lean | Num.to_of_nat | [
{
"state_after": "no goals",
"state_before": "⊢ ↑↑0 = 0",
"tactic": "rw [Nat.cast_zero, cast_zero]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ ↑↑(n + 1) = n + 1",
"tactic": "rw [Nat.cast_succ, add_one, succ_to_nat, to_of_nat n]"
}
] | [
492,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/Data/PNat/Interval.lean | PNat.card_fintype_Ico | [
{
"state_after": "no goals",
"state_before": "a b : ℕ+\n⊢ Fintype.card ↑(Set.Ico a b) = ↑b - ↑a",
"tactic": "rw [← card_Ico, Fintype.card_ofFinset]"
}
] | [
102,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | Algebra.IsIntegral.of_finite | [
{
"state_after": "case h\nR : Type u_1\nA : Type u_2\nB : Type ?u.630412\nS : Type ?u.630415\ninst✝⁵ : CommRing R\ninst✝⁴ : CommRing A\ninst✝³ : CommRing B\ninst✝² : CommRing S\ninst✝¹ : Algebra R A\ninst✝ : Algebra R B\nf : R →+* S\nh : Module.Finite R A\n⊢ RingHom.Finite (algebraMap R A)",
"state_before":... | [
450,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean | differentiableWithinAt_iff_restrictScalars | [
{
"state_after": "case mp\n𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\n𝕜' : Type u_4\ninst✝⁹ : NontriviallyNormedField 𝕜'\ninst✝⁸ : NormedAlgebra 𝕜 𝕜'\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : NormedSpace 𝕜' E\ninst✝⁴ : IsScalarTower 𝕜 𝕜' E\nF : Type u_3\n... | [
116,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | exists_associated_pow_of_mul_eq_pow | [
{
"state_after": "case inl\nα : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : GCDMonoid α\na b c : α\nhab : IsUnit (gcd a b)\nk : ℕ\nh : a * b = c ^ k\nh✝ : Subsingleton α\n⊢ ∃ d, Associated (d ^ k) a\n\ncase inr\nα : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : GCDMonoid α\na b c : α\nhab : ... | [
656,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
614,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.update_comp_eq_of_forall_ne' | [] | [
621,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
619,
1
] |
Mathlib/Algebra/GeomSum.lean | mul_geom_sum | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Ring α\nx : α\nn : ℕ\n⊢ op ((x - 1) * ∑ i in range n, x ^ i) = op (x ^ n - 1)",
"tactic": "simpa using geom_sum_mul (op x) n"
}
] | [
226,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/RingTheory/Localization/NumDen.lean | IsFractionRing.mk'_num_den | [] | [
71,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.HasColimit.mk | [] | [
649,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | InnerProductGeometry.norm_div_sin_angle_sub_of_inner_eq_zero | [
{
"state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : inner x (-y) = 0\nh0 : x = 0 ∨ y ≠ 0\n⊢ ‖y‖ / Real.sin (angle x (x - y)) = ‖x - y‖",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : inner x y ... | [
345,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.subtypeDomain_def | [
{
"state_after": "case h\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝² : (i : ι) → Zero (β i)\ninst✝¹ : (i : ι) → (x : β i) → Decidable (x ≠ 0)\np : ι → Prop\ninst✝ : DecidablePred p\nf : Π₀ (i : ι), β i\ni : Subtype p\n⊢ ↑(subtypeDomain p f) i = ↑(mk (... | [
1261,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1259,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | SubgroupClass.coe_inv | [] | [
229,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_sup_eq | [] | [
1234,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1232,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.toAddEquiv_toNatLinearEquiv | [] | [
818,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
816,
1
] |
Mathlib/Data/Finsupp/Order.lean | Finsupp.add_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : Type u_2\ninst✝ : CanonicallyOrderedAddMonoid α\nf g : ι →₀ α\n⊢ f + g = 0 ↔ f = 0 ∧ g = 0",
"tactic": "simp [FunLike.ext_iff, forall_and]"
}
] | [
154,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Topology/Maps.lean | IsOpenMap.preimage_frontier_subset_frontier_preimage | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.196325\nδ : Type ?u.196328\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\nf : α → β\nhf : IsOpenMap f\ns : Set β\n⊢ f ⁻¹' frontier s ⊆ frontier (f ⁻¹' s)",
"tactic": "simpa only ... | [
434,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/Data/Set/Pairwise/Basic.lean | Set.pairwiseDisjoint_image_right_iff | [
{
"state_after": "case refine'_1\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nι : Type ?u.40777\nι' : Type ?u.40780\nr p q : α → α → Prop\nf : α → β → γ\ns : Set α\nt : Set β\nhf : ∀ (a : α), a ∈ s → Injective (f a)\nhs : PairwiseDisjoint s fun a => f a '' t\nx : α × β\nhx : x ∈ s ×ˢ t\ny : α × β\nhy : y ∈ s ×ˢ t... | [
376,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.card_relations_sum | [
{
"state_after": "no goals",
"state_before": "L : Language\nL' : Language\ni : ℕ\n⊢ (#Relations (Language.sum L L') i) = lift (#Relations L i) + lift (#Relations L' i)",
"tactic": "simp [Language.sum]"
}
] | [
263,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Topology/PartitionOfUnity.lean | BumpCovering.toPouFun_zero_of_zero | [
{
"state_after": "no goals",
"state_before": "ι : Type u\nX : Type v\ninst✝ : TopologicalSpace X\ns : Set X\nf : BumpCovering ι X s\ni : ι\nx : X\nh : ↑(toFun s f i) x = 0\n⊢ toPouFun f i x = 0",
"tactic": "rw [toPouFun, h, MulZeroClass.zero_mul]"
}
] | [
382,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | mul_le_mul_of_nonneg_of_nonpos | [] | [
365,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/Data/List/Basic.lean | List.Sublist.antisymm | [] | [
1100,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1099,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.mem_centralizer_iff | [] | [
866,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
865,
1
] |
Mathlib/Order/Hom/Lattice.lean | LatticeHom.coe_id | [] | [
1091,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1090,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | Algebra.smul_leftMulMatrix | [
{
"state_after": "no goals",
"state_before": "R : Type u_3\nS : Type u_5\nT : Type u_4\ninst✝¹⁰ : CommRing R\ninst✝⁹ : CommRing S\ninst✝⁸ : Ring T\ninst✝⁷ : Algebra R S\ninst✝⁶ : Algebra S T\ninst✝⁵ : Algebra R T\ninst✝⁴ : IsScalarTower R S T\nm : Type u_1\nn : Type u_2\ninst✝³ : Fintype m\ninst✝² : Fintype... | [
932,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
928,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | ContinuousOn.intervalIntegrable | [] | [
359,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/Algebra/Homology/Homology.lean | HomologicalComplex.cycles_eq_kernelSubobject | [] | [
56,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Analysis/SumIntegralComparisons.lean | AntitoneOn.integral_le_sum | [
{
"state_after": "x₀ : ℝ\na b : ℕ\nf : ℝ → ℝ\nhf : AntitoneOn f (Icc x₀ (x₀ + ↑a))\nk : ℕ\nhk : k < a\n⊢ IntervalIntegrable f volume (x₀ + ↑k) (x₀ + ↑(k + 1))",
"state_before": "x₀ : ℝ\na b : ℕ\nf : ℝ → ℝ\nhf : AntitoneOn f (Icc x₀ (x₀ + ↑a))\n⊢ ∀ (k : ℕ), k < a → IntervalIntegrable f volume (x₀ + ↑k) (x₀ +... | [
76,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.subset_coe_filter_of_subset_forall | [] | [
2746,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2745,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.isBoundedUnder_ge_inv | [] | [
273,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.coe_filter | [] | [
1924,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1923,
1
] |
Mathlib/RingTheory/Filtration.lean | Ideal.Filtration.mem_submodule | [] | [
282,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Data/MvPolynomial/Division.lean | MvPolynomial.monomial_dvd_monomial | [
{
"state_after": "case mp\nσ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\nr s : R\ni j : σ →₀ ℕ\n⊢ ↑(monomial i) r ∣ ↑(monomial j) s → (s = 0 ∨ i ≤ j) ∧ r ∣ s\n\ncase mpr\nσ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\nr s : R\ni j : σ →₀ ℕ\n⊢ (s = 0 ∨ i ≤ j) ∧ r ∣ s → ↑(monomial i) r ∣ ↑(monomial j) ... | [
243,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Analysis/Normed/Group/Completion.lean | UniformSpace.Completion.norm_coe | [] | [
39,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/Computability/PartrecCode.lean | Nat.Partrec.Code.evaln_prim | [
{
"state_after": "x✝ : Unit\np : ℕ\n⊢ List.map\n (fun n =>\n Nat.rec Option.none\n (fun n_1 n_ih =>\n rec (some 0) (some (Nat.succ n)) (some (unpair n).fst) (some (unpair n).snd)\n (fun cf cg x x => do\n let x ←\n Nat.Partrec.Code.lup\... | [
1146,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1087,
1
] |
Mathlib/Logic/Equiv/List.lean | Denumerable.raise_sorted | [] | [
324,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.ext_iff | [] | [
177,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Data/Nat/Dist.lean | Nat.dist_mul_left | [
{
"state_after": "no goals",
"state_before": "k n m : ℕ\n⊢ dist (k * n) (k * m) = k * dist n m",
"tactic": "rw [mul_comm k n, mul_comm k m, dist_mul_right, mul_comm]"
}
] | [
108,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/CategoryTheory/Sites/Grothendieck.lean | CategoryTheory.GrothendieckTopology.Cover.Relation.map_fst | [] | [
550,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
] |
Mathlib/Order/Minimal.lean | maximals_swap | [] | [
77,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Std/Data/Int/DivMod.lean | Int.dvd_refl | [] | [
595,
74
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
595,
11
] |
Mathlib/GroupTheory/OrderOfElement.lean | orderOf_pow_dvd | [
{
"state_after": "no goals",
"state_before": "G : Type u\nA : Type v\nx y : G\na b : A\nn✝ m : ℕ\ninst✝¹ : Monoid G\ninst✝ : AddMonoid A\nn : ℕ\n⊢ orderOf (x ^ n) ∣ orderOf x",
"tactic": "rw [orderOf_dvd_iff_pow_eq_one, pow_right_comm, pow_orderOf_eq_one, one_pow]"
}
] | [
254,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/NumberTheory/VonMangoldt.lean | Nat.ArithmeticFunction.vonMangoldt_sum | [
{
"state_after": "case refine'_1\nn : ℕ\n⊢ ∑ i in divisors 0, ↑Λ i = Real.log ↑0\n\ncase refine'_2\nn : ℕ\n⊢ ∀ (p n : ℕ), Prime p → ∑ i in divisors (p ^ n), ↑Λ i = Real.log ↑(p ^ n)\n\ncase refine'_3\nn : ℕ\n⊢ ∀ (a b : ℕ),\n 1 < a →\n 1 < b →\n coprime a b →\n ∑ i in divisors a, ↑Λ i = R... | [
123,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Algebra/Order/SMul.lean | strictMono_smul_left | [] | [
142,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Std/Data/Int/Lemmas.lean | Int.add_neg_of_nonpos_of_neg | [] | [
841,
52
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
840,
11
] |
Mathlib/Order/Hom/CompleteLattice.lean | CompleteLatticeHom.symm_dual_id | [] | [
895,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
893,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.Multicofork.sigma_condition | [
{
"state_after": "case h\nC : Type u\ninst✝² : Category C\nI : MultispanIndex C\nK : Multicofork I\ninst✝¹ : HasCoproduct I.left\ninst✝ : HasCoproduct I.right\nb✝ : I.L\n⊢ Sigma.ι I.left b✝ ≫ MultispanIndex.fstSigmaMap I ≫ Sigma.desc (π K) =\n Sigma.ι I.left b✝ ≫ MultispanIndex.sndSigmaMap I ≫ Sigma.desc (π ... | [
610,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
608,
1
] |
Mathlib/Combinatorics/SimpleGraph/Coloring.lean | SimpleGraph.Colorable.mono_left | [] | [
322,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/Data/Set/Image.lean | Set.range_inl | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.78850\nι : Sort ?u.78853\nι' : Sort ?u.78856\nf : ι → α\ns t : Set α\n⊢ range Sum.inl = {x | Sum.isLeft x = true}",
"tactic": "ext (_|_) <;> simp"
}
] | [
884,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
884,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.eq_top_iff' | [] | [
946,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
945,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.ext_iff | [] | [
765,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
764,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.symm_trans_apply | [] | [
407,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.map_sub | [] | [
109,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/CategoryTheory/Adhesive.lean | CategoryTheory.Adhesive.van_kampen' | [] | [
236,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Localization.mk_left_injective | [
{
"state_after": "α : Type u_1\ninst✝ : CancelCommMonoid α\ns : Submonoid α\na₁ b₁ : α\na₂ b₂ b : { x // x ∈ s }\nc d : α\nh : (fun a => mk a b) c = (fun a => mk a b) d\nthis : Nonempty { x // x ∈ s }\n⊢ c = d",
"state_before": "α : Type u_1\ninst✝ : CancelCommMonoid α\ns : Submonoid α\na₁ b₁ : α\na₂ b₂ b :... | [
1889,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1886,
1
] |
Mathlib/Topology/Algebra/Module/Multilinear.lean | ContinuousMultilinearMap.neg_apply | [] | [
438,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.log_neg_eq_log | [
{
"state_after": "no goals",
"state_before": "x✝ y x : ℝ\n⊢ log (-x) = log x",
"tactic": "rw [← log_abs x, ← log_abs (-x), abs_neg]"
}
] | [
114,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
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Mathlib/Deprecated/Subgroup.lean | Group.subset_closure | [] | [
544,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
544,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | Left.pow_lt_one_iff | [] | [
349,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pushout.congrHom_inv | [
{
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"state_before": "C : Type u\ninst✝³ : Category C\nD : Type u₂\ninst✝² : Category D\nW X✝ Y✝ Z✝ X Y Z : C\nf₁ f₂ : X ⟶ Y\ng₁ g₂ : X ⟶ Z\nh₁ : f₁ = f₂\nh₂ : g₁ = g₂\ninst✝¹ : HasPushout f₁ g₁\ninst✝ : HasPushout f₂ g₂\n⊢ f₂ ≫ 𝟙 Y = 𝟙 X ≫ f₁",
"tactic": "simp [h₁]"
},
{
... | [
1420,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1408,
1
] |
Mathlib/Geometry/Euclidean/Sphere/Basic.lean | EuclideanGeometry.subset_sphere | [] | [
107,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Topology/MetricSpace/Completion.lean | Isometry.completion_map | [] | [
215,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | HasDerivAt.cpow_const | [] | [
190,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/MeasureTheory/PiSystem.lean | isPiSystem_Ioc | [] | [
194,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.comp | [
{
"state_after": "no goals",
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264,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.image_symmDiff | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.94769\ninst✝¹ : DecidableEq β\nf✝ g : α → β\ns✝ : Finset α\nt✝ : Finset β\na : α\nb c : β\ninst✝ : DecidableEq α\nf : α → β\ns t : Finset α\nhf : Injective f\n⊢ f '' ↑s ∆ ↑t = (f '' ↑s) ∆ (f '' ↑t)",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : T... | [
542,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
] |
src/lean/Init/SimpLemmas.lean | ite_self | [
{
"state_after": "no goals",
"state_before": "α : Sort u\nc : Prop\nd : Decidable c\na : α\n⊢ ite c a a = a",
"tactic": "cases d <;> rfl"
}
] | [
81,
113
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
81,
9
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.sub_coe_pi_eq_add_coe_pi | [
{
"state_after": "no goals",
"state_before": "θ : Angle\n⊢ θ - ↑π = θ + ↑π",
"tactic": "rw [sub_eq_add_neg, neg_coe_pi]"
}
] | [
161,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_add_zsmul | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\nm : ℤ\n⊢ b + m • p - (toIcoDiv hp a b • p + m • p) = b - toIcoDiv hp a b • p",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : ... | [
407,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | Associates.dvd_out_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizationMonoid α\na : α\nb : Associates α\n⊢ ∀ (a_1 : α),\n a ∣ Associates.out (Quotient.mk (Associated.setoid α) a_1) ↔ Associates.mk a ≤ Quotient.mk (Associated.setoid α) a_1",
"tactic": "s... | [
238,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Analysis/Convex/Gauge.lean | gauge_ball | [
{
"state_after": "case symmetric\n𝕜 : Type ?u.286698\nE : Type u_1\nF : Type ?u.286704\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\ns : Set E\nr : ℝ\nx✝ : E\nhr : 0 < r\nx : E\n⊢ ∀ (x : E), x ∈ Metric.ball 0 1 → -x ∈ Metric.ball 0 1",
"state_before": "𝕜 : Type ?u.286698\nE : Type u_1\nF : ... | [
464,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
1
] |
Mathlib/Algebra/Hom/Iterate.lean | RingHom.iterate_map_add | [] | [
140,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Algebra/Parity.lean | Even.mul_right | [] | [
287,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.associated_comp | [
{
"state_after": "case H\nS : Type u_3\nR : Type u_1\nR₁ : Type ?u.408596\nM : Type u_2\ninst✝⁹ : Ring R\ninst✝⁸ : CommRing R₁\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : Module R₁ M\ninst✝⁴ : CommSemiring S\ninst✝³ : Algebra S R\ninst✝² : Invertible 2\nB₁ : BilinForm R M\nQ : QuadraticForm R M\nN :... | [
793,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
790,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.isWf_empty | [] | [
192,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.polar_neg_left | [
{
"state_after": "no goals",
"state_before": "S : Type ?u.154687\nR : Type u_1\nR₁ : Type ?u.154693\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 y : M\n⊢ polar (↑Q) (-x) y = -polar (↑Q) x y",
"tactic": "rw [← neg_one_smul R x... | [
278,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Combinatorics/SimpleGraph/Metric.lean | SimpleGraph.dist_le | [] | [
69,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Topology/UniformSpace/CompleteSeparated.lean | DenseInducing.continuous_extend_of_cauchy | [] | [
48,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/Algebra/Lie/Solvable.lean | LieIdeal.derivedSeries_eq_bot_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u\nL : Type v\nM : Type w\nL' : Type w₁\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\ninst✝¹ : LieRing L'\ninst✝ : LieAlgebra R L'\nI J : LieIdeal R L\nf : L' →ₗ⁅R⁆ L\nk : ℕ\n⊢ derivedSeries R { x // x ∈ ↑I } k = ⊥ ↔ derivedSeriesOf... | [
171,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Data/Set/Basic.lean | Set.Subsingleton.anti | [] | [
2337,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2336,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.lintegral_add | [] | [
1046,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1045,
1
] |
Mathlib/Data/Int/Parity.lean | Int.ediv_two_mul_two_add_one_of_odd | [
{
"state_after": "case intro\nm c : ℤ\n⊢ (2 * c + 1) / 2 * 2 + 1 = 2 * c + 1",
"state_before": "m n : ℤ\n⊢ Odd n → n / 2 * 2 + 1 = n",
"tactic": "rintro ⟨c, rfl⟩"
},
{
"state_after": "case h.e'_2.h.e'_6\nm c : ℤ\n⊢ 1 = (2 * c + 1) % 2",
"state_before": "case intro\nm c : ℤ\n⊢ (2 * c + 1) / 2... | [
270,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/LinearAlgebra/Matrix/Trace.lean | Matrix.trace_smul | [] | [
65,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.monotone_filter_right | [] | [
2737,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2735,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_le_natDegree | [] | [
237,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/CategoryTheory/Abelian/Homology.lean | homology.hom_from_ext | [
{
"state_after": "A : Type u\ninst✝¹ : Category A\ninst✝ : Abelian A\nX Y Z : A\nf : X ⟶ Y\ng : Y ⟶ Z\nw : f ≫ g = 0\nW : A\na b : homology f g w ⟶ W\nh :\n (cokernel.π (kernel.lift g f w) ≫ (homologyIsoCokernelLift f g w).inv) ≫ a =\n (cokernel.π (kernel.lift g f w) ≫ (homologyIsoCokernelLift f g w).inv) ≫... | [
175,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/GroupTheory/GroupAction/Prod.lean | Prod.pow_snd | [] | [
99,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.Subsingleton.stronglyMeasurable | [
{
"state_after": "case refine_2\nα✝ : Type ?u.13198\nβ✝ : Type ?u.13201\nγ : Type ?u.13204\nι : Type ?u.13207\ninst✝³ : Countable ι\nα : Type u_1\nβ : Type u_2\ninst✝² : MeasurableSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : Subsingleton β\nf : α → β\nf_sf : α →ₛ β :=\n { toFun := f, measurableSet_fiber' := (... | [
147,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.BoundedFormula.realize_all_liftAt_one_self | [
{
"state_after": "L : Language\nL' : Language\nM : Type w\nN : Type ?u.165049\nP : Type ?u.165052\ninst✝³ : Structure L M\ninst✝² : Structure L N\ninst✝¹ : Structure L P\nα : Type u'\nβ : Type v'\nn✝ l : ℕ\nφ✝ ψ : BoundedFormula L α l\nθ : BoundedFormula L α (Nat.succ l)\nv✝ : α → M\nxs✝ : Fin l → M\ninst✝ : No... | [
509,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/CategoryTheory/Preadditive/Biproducts.lean | CategoryTheory.Limits.inr_of_isLimit | [
{
"state_after": "case x\nC : Type u\ninst✝² : Category C\ninst✝¹ : Preadditive C\nJ : Type\ninst✝ : Fintype J\nX Y : C\nt : BinaryBicone X Y\nht : IsLimit (BinaryBicone.toCone t)\n⊢ ∀ (j : Discrete WalkingPair), t.inr ≫ (BinaryBicone.toCone t).π.app j = (BinaryFan.mk 0 (𝟙 Y)).π.app j",
"state_before": "C ... | [
357,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | map_mul_right_nhds_one | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝³ : TopologicalSpace G\ninst✝² : Group G\ninst✝¹ : TopologicalGroup G\ninst✝ : TopologicalSpace α\nf : α → G\ns : Set α\nx✝ : α\nx : G\n⊢ map (fun y => y * x) (𝓝 1) = 𝓝 x",
"tactic": "simp"
}
] | [
837,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
837,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.extend_injective | [
{
"state_after": "α : Sort u_1\nβ : Sort u_2\nγ : Sort u_3\nf : α → β\nhf : Injective f\ne' : β → γ\ng₁ g₂ : α → γ\nhg : (fun g => extend f g e') g₁ = (fun g => extend f g e') g₂\n⊢ g₁ = g₂",
"state_before": "α : Sort u_1\nβ : Sort u_2\nγ : Sort u_3\nf : α → β\nhf : Injective f\ne' : β → γ\n⊢ Injective fun ... | [
771,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
766,
1
] |
Mathlib/Data/Set/Basic.lean | Set.union_subset_union_left | [] | [
838,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
837,
1
] |
Mathlib/Data/Set/Image.lean | Set.preimage_id' | [] | [
130,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.range | [] | [
2135,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2134,
11
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.sin_coe_pi | [
{
"state_after": "no goals",
"state_before": "⊢ sin ↑π = 0",
"tactic": "rw [sin_coe, Real.sin_pi]"
}
] | [
362,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.closure_mono | [] | [
293,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/RingTheory/Polynomial/Pochhammer.lean | Polynomial.mul_X_add_nat_cast_comp | [
{
"state_after": "no goals",
"state_before": "S : Type u\ninst✝ : Semiring S\np q : S[X]\nn : ℕ\n⊢ comp (p * (X + ↑n)) q = comp p q * (q + ↑n)",
"tactic": "rw [mul_add, add_comp, mul_X_comp, ← Nat.cast_comm, nat_cast_mul_comp, Nat.cast_comm, mul_add]"
}
] | [
134,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.mem_iInf_of_mem | [] | [
586,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.forall_measure_inter_spanningSets_eq_zero | [
{
"state_after": "α : Type u_1\nβ : Type ?u.732836\nγ : Type ?u.732839\nδ : Type ?u.732842\nι : Type ?u.732845\nR : Type ?u.732848\nR' : Type ?u.732851\nm0 : MeasurableSpace α\ninst✝³ : MeasurableSpace β\ninst✝² : MeasurableSpace γ\nμ✝ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t : Set α\ninst✝¹ : MeasurableSpace α... | [
3560,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3556,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.cosh_neg | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ ↑(cosh (-x)) = ↑(cosh x)",
"tactic": "simp"
}
] | [
1370,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1369,
1
] |
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