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/Rat/Lemmas.lean | Rat.add_num_den | [
{
"state_after": "q r : ℚ\nhqd : ↑q.den ≠ 0\n⊢ q + r = (q.num * ↑r.den + ↑q.den * r.num) /. (↑q.den * ↑r.den)",
"state_before": "q r : ℚ\n⊢ q + r = (q.num * ↑r.den + ↑q.den * r.num) /. (↑q.den * ↑r.den)",
"tactic": "have hqd : (q.den : ℤ) ≠ 0 := Int.coe_nat_ne_zero_iff_pos.2 q.den_pos"
},
{
"sta... | [
115,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_eq_zero_iff' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.971808\nγ : Type ?u.971811\nδ : Type ?u.971814\nm : MeasurableSpace α\nμ ν : Measure α\nf : α → ℝ≥0∞\nhf : AEMeasurable f\n⊢ (∫⁻ (x : α), 0 ∂μ) ≠ ⊤",
"tactic": "simp [lintegral_zero, zero_ne_top]"
}
] | [
878,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
872,
1
] |
Mathlib/Algebra/CharP/Basic.lean | ringChar.dvd | [] | [
234,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Data/Erased.lean | Erased.map_out | [
{
"state_after": "no goals",
"state_before": "α : Sort u_1\nβ : Sort u_2\nf : α → β\na : Erased α\n⊢ out (map f a) = f (out a)",
"tactic": "simp [map]"
}
] | [
135,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isNat_lt_false | [] | [
689,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
687,
1
] |
Mathlib/Data/Nat/Parity.lean | Nat.mod_two_add_add_odd_mod_two | [
{
"state_after": "no goals",
"state_before": "m✝ n✝ m n : ℕ\nhn : Odd n\nhm : Even m\n⊢ m % 2 + (m + n) % 2 = 1",
"tactic": "rw [even_iff.1 hm, odd_iff.1 (hm.add_odd hn)]"
},
{
"state_after": "no goals",
"state_before": "m✝ n✝ m n : ℕ\nhn : Odd n\nhm : Odd m\n⊢ m % 2 + (m + n) % 2 = 1",
... | [
98,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Algebra/Order/Field/Power.lean | Nat.cast_le_pow_sub_div_sub | [] | [
230,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_sin_pow_odd | [
{
"state_after": "case zero\na b : ℝ\nn : ℕ\n⊢ (∫ (x : ℝ) in 0 ..π, sin x ^ (2 * zero + 1)) = 2 * ∏ i in Finset.range zero, (2 * ↑i + 2) / (2 * ↑i + 3)\n\ncase succ\na b : ℝ\nn k : ℕ\nih : (∫ (x : ℝ) in 0 ..π, sin x ^ (2 * k + 1)) = 2 * ∏ i in Finset.range k, (2 * ↑i + 2) / (2 * ↑i + 3)\n⊢ (∫ (x : ℝ) in 0 ..π, ... | [
671,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
666,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | hasFPowerSeriesAt_iff | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.2373770\nG : Type ?u.2373773\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\np : FormalMul... | [
1414,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1393,
1
] |
Mathlib/Algebra/Category/GroupCat/Colimits.lean | AddCommGroupCat.Colimits.cocone_naturality_components | [
{
"state_after": "J : Type v\ninst✝ : SmallCategory J\nF : J ⥤ AddCommGroupCat\nj j' : J\nf : j ⟶ j'\nx : ↑(F.obj j)\n⊢ ↑(coconeMorphism F j') (↑(F.map f) x) = ↑(F.map f ≫ coconeMorphism F j') x",
"state_before": "J : Type v\ninst✝ : SmallCategory J\nF : J ⥤ AddCommGroupCat\nj j' : J\nf : j ⟶ j'\nx : ↑(F.ob... | [
226,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.smul_le_smul | [
{
"state_after": "R : Type ?u.474477\nR' : Type ?u.474480\n𝕜 : Type u_1\n𝕜₂ : Type ?u.474486\n𝕜₃ : Type ?u.474489\n𝕝 : Type ?u.474492\nE : Type u_2\nE₂ : Type ?u.474498\nE₃ : Type ?u.474501\nF : Type ?u.474504\nG : Type ?u.474507\nι : Type ?u.474510\ninst✝¹⁸ : SeminormedRing 𝕜\ninst✝¹⁷ : SeminormedRing 𝕜₂... | [
390,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.ofReal_cos | [] | [
961,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
960,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.extraction_of_frequently_atTop' | [
{
"state_after": "ι : Type ?u.57426\nι' : Type ?u.57429\nα : Type ?u.57432\nβ : Type ?u.57435\nγ : Type ?u.57438\nP : ℕ → Prop\nu : ℕ → ℕ\nhu : ∀ (N : ℕ), u N > N\nhu' : ∀ (N : ℕ), P (u N)\n⊢ ∃ φ, StrictMono φ ∧ ∀ (n : ℕ), P (φ n)",
"state_before": "ι : Type ?u.57426\nι' : Type ?u.57429\nα : Type ?u.57432\n... | [
464,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/Topology/Separation.lean | isOpen_compl_singleton | [] | [
380,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/GroupTheory/PGroup.lean | IsPGroup.powEquiv_symm_apply | [
{
"state_after": "p : ℕ\nG : Type u_1\ninst✝ : Group G\nhG : IsPGroup p G\nn : ℕ\nhn : Nat.coprime p n\ng : G\n⊢ ↑(powEquiv hG hn).symm g = g ^ Nat.gcdB (Nat.card { x // x ∈ Subgroup.zpowers g }) n",
"state_before": "p : ℕ\nG : Type u_1\ninst✝ : Group G\nhG : IsPGroup p G\nn : ℕ\nhn : Nat.coprime p n\ng : G... | [
127,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Topology/Order/Basic.lean | StrictMono.induced_topology_eq_preorder | [
{
"state_after": "case refine_1\nα✝ : Type u\nβ✝ : Type v\nγ : Type w\nα : Type u_1\nβ : Type u_2\ninst✝² : LinearOrder α\ninst✝¹ : LinearOrder β\nt : TopologicalSpace β\ninst✝ : OrderTopology β\nf : α → β\nhf : StrictMono f\nhc : OrdConnected (range f)\na✝ : α\nb✝ : β\nx✝ : α\nh₁ : b✝ < f a✝\nh₂ : ¬b✝ < f x✝\n... | [
1066,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1059,
8
] |
Mathlib/Algebra/Order/Floor.lean | Int.ceil_le_floor_add_one | [
{
"state_after": "F : Type ?u.210054\nα : Type u_1\nβ : Type ?u.210060\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na✝ a : α\n⊢ a ≤ ↑⌊a⌋ + 1",
"state_before": "F : Type ?u.210054\nα : Type u_1\nβ : Type ?u.210060\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na✝ a : α\n⊢ ⌈a⌉ ≤ ⌊a⌋ ... | [
1122,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1120,
1
] |
Mathlib/Algebra/Hom/Ring.lean | RingHom.codomain_trivial_iff_range_eq_singleton_zero | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.88572\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.88581\nx✝³ : NonAssocSemiring α\nx✝² : NonAssocSemiring β\nf : α →+* β\nx✝¹ y✝ : α\nh : ∀ (x : α), ↑f x = 0\ny : β\nx✝ : y ∈ Set.range ↑f\nx : α\nhx : ↑f x = y\n⊢ y ∈ {0}",
"tactic": "simp [← hx, h x... | [
613,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
1
] |
Mathlib/Data/Int/Cast/Lemmas.lean | Int.cast_mul | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.1324\nι : Type ?u.1327\nα : Type u_1\nβ : Type ?u.1333\ninst✝ : NonAssocRing α\nm : ℤ\n⊢ ∀ (n : ℤ), ↑(0 * n) = ↑0 * ↑n",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "F : Type ?u.1324\nι : Type ?u.1327\nα : Type u_... | [
64,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Algebra/GroupWithZero/Defs.lean | mul_eq_zero | [] | [
251,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Algebra/Group/Commute.lean | Commute.right_comm | [
{
"state_after": "no goals",
"state_before": "G : Type ?u.1760\nS : Type u_1\ninst✝ : Semigroup S\na✝ b c : S\nh : Commute b c\na : S\n⊢ a * b * c = a * c * b",
"tactic": "simp only [mul_assoc, h.eq]"
}
] | [
118,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
11
] |
Mathlib/Combinatorics/SimpleGraph/Trails.lean | SimpleGraph.Walk.IsTrail.isEulerian_of_forall_mem | [] | [
119,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | Ideal.mul_homogeneous_element_mem_of_mem | [
{
"state_after": "ι : Type u_2\nσ : Type u_3\nR : Type ?u.63833\nA : Type u_1\ninst✝⁵ : Semiring A\ninst✝⁴ : SetLike σ A\ninst✝³ : AddSubmonoidClass σ A\n𝒜 : ι → σ\ninst✝² : DecidableEq ι\ninst✝¹ : AddMonoid ι\ninst✝ : GradedRing 𝒜\nI✝ I : Ideal A\nr x : A\nhx₁ : Homogeneous 𝒜 x\nhx₂ : x ∈ I\nj : ι\n⊢ ∑ x_1 ... | [
164,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.factorization_mul_support | [
{
"state_after": "case a\na b : ℕ\nha : a ≠ 0\nhb : b ≠ 0\nq : ℕ\n⊢ q ∈ (factorization (a * b)).support ↔ q ∈ (factorization a).support ∪ (factorization b).support",
"state_before": "a b : ℕ\nha : a ≠ 0\nhb : b ≠ 0\n⊢ (factorization (a * b)).support = (factorization a).support ∪ (factorization b).support",
... | [
233,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | MulSemiringAction.toAlgEquiv_injective | [] | [
808,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
806,
1
] |
Std/Data/List/Basic.lean | List.filterMap_eq_filterMapTR | [
{
"state_after": "case h.h.h.h\nα : Type u_2\nβ : Type u_1\nf : α → Option β\nl : List α\n⊢ filterMap f l = filterMapTR f l",
"state_before": "⊢ @filterMap = @filterMapTR",
"tactic": "funext α β f l"
},
{
"state_after": "case h.h.h.h\nα : Type u_2\nβ : Type u_1\nf : α → Option β\nl : List α\n⊢ f... | [
108,
24
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
103,
10
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.TrailingMonic.trailingCoeff | [] | [
83,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Order/Monotone/Odd.lean | antitone_of_odd_of_monotoneOn_nonneg | [] | [
56,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_apply | [] | [
1323,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1321,
1
] |
Mathlib/Topology/Algebra/Order/LeftRight.lean | nhds_left_sup_nhds_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1151\ninst✝² : TopologicalSpace α\ninst✝¹ : LinearOrder α\ninst✝ : TopologicalSpace β\na : α\n⊢ 𝓝[Iic a] a ⊔ 𝓝[Ici a] a = 𝓝 a",
"tactic": "rw [← nhdsWithin_union, Iic_union_Ici, nhdsWithin_univ]"
}
] | [
62,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.lt_iff' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.145326\nγ : Type ?u.145329\nδ : Type ?u.145332\nι : Type ?u.145335\nR : Type ?u.145338\nR' : Type ?u.145341\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set ... | [
985,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
984,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_inv_le_iff_of_neg | [
{
"state_after": "no goals",
"state_before": "x y z : ℝ\nhx : 0 < x\nhy : 0 < y\nhz : z < 0\n⊢ x ^ z⁻¹ ≤ y ↔ y ^ z ≤ x",
"tactic": "convert le_rpow_inv_iff_of_neg (Real.rpow_pos_of_pos hx z⁻¹) (Real.rpow_pos_of_pos hy z) hz <;>\nsimp [← Real.rpow_mul hx.le, ← Real.rpow_mul hy.le, ne_of_lt hz]"
}
] | [
467,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.chaar_sup_eq | [
{
"state_after": "case intro.intro.intro.intro.intro.intro\nG : Type u_1\ninst✝³ : Group G\ninst✝² : TopologicalSpace G\ninst✝¹ : TopologicalGroup G\ninst✝ : T2Space G\nK₀ : PositiveCompacts G\nK₁ K₂ : Compacts G\nh : Disjoint K₁.carrier K₂.carrier\nU₁ U₂ : Set G\nh1U₁ : IsOpen U₁\nh1U₂ : IsOpen U₂\nh2U₁ : K₁.c... | [
517,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
1
] |
Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | norm_withSeminorms | [
{
"state_after": "𝕜✝ : Type ?u.457423\n𝕜₂ : Type ?u.457426\n𝕝 : Type ?u.457429\n𝕝₂ : Type ?u.457432\nE✝ : Type ?u.457435\nF : Type ?u.457438\nG : Type ?u.457441\nι : Type ?u.457444\nι' : Type ?u.457447\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NormedField 𝕜\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSp... | [
508,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPullback.of_map_of_faithful | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝³ : Category C\nD : Type u₂\ninst✝² : Category D\nF : C ⥤ D\nW X Y Z : C\nf : W ⟶ X\ng : W ⟶ Y\nh : X ⟶ Z\ni : Y ⟶ Z\ninst✝¹ : ReflectsLimit (cospan h i) F\ninst✝ : Faithful F\nH : IsPullback (F.map f) (F.map g) (F.map h) (F.map i)\n⊢ F.map (f ... | [
1040,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1038,
1
] |
Mathlib/Logic/Equiv/Set.lean | Equiv.ofLeftInverse'_eq_ofInjective | [
{
"state_after": "case H.a\nα✝ : Sort u\nβ✝ : Sort v\nγ : Sort w\nα : Type u_1\nβ : Type u_2\nf : α → β\nf_inv : β → α\nhf : LeftInverse f_inv f\nx✝ : α\n⊢ ↑(↑(ofLeftInverse' f f_inv hf) x✝) = ↑(↑(ofInjective f (_ : Injective f)) x✝)",
"state_before": "α✝ : Sort u\nβ✝ : Sort v\nγ : Sort w\nα : Type u_1\nβ :... | [
649,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
646,
1
] |
Mathlib/Analysis/Convex/Body.lean | ConvexBody.coe_zero | [] | [
125,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Data/Set/Function.lean | Set.injOn_union | [
{
"state_after": "case refine'_1\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.28155\nι : Sort ?u.28158\nπ : α → Type ?u.28163\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\np : Set γ\nf f₁ f₂ f₃ : α → β\ng g₁ g₂ : β → γ\nf' f₁' f₂' : β → α\ng' : γ → β\na : α\nb : β\nh : Disjoint s₁ s₂\nH : InjOn f (s₁ ∪ s₂)\n⊢ ∀ (x : α), x ∈ s... | [
640,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
632,
1
] |
Mathlib/Order/Chain.lean | IsChain.superChain_succChain | [
{
"state_after": "α : Type u_1\nβ : Type ?u.8828\nr : α → α → Prop\nc c₁ c₂ c₃ s t : Set α\na b x y : α\nhs₁ : IsChain r s\nhs₂ : IsChain r s → ∃ x, IsChain r x ∧ s ⊆ x ∧ ¬s = x\n⊢ SuperChain r s (SuccChain r s)",
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183,
65
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179,
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Mathlib/Data/MvPolynomial/Rename.lean | MvPolynomial.eval₂_cast_comp | [
{
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290,
98
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286,
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Mathlib/CategoryTheory/Sites/Sheaf.lean | CategoryTheory.Presheaf.subsingleton_iff_isSeparatedFor | [
{
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168,
45
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149,
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Mathlib/RingTheory/PolynomialAlgebra.lean | PolyEquivTensor.toFunAlgHom_apply_tmul | [] | [
132,
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.subtypeDomain_neg | [] | [
549,
28
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547,
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Mathlib/Analysis/SpecificLimits/FloorPow.lean | sum_div_pow_sq_le_div_sq | [
{
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Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.map_add_int | [] | [
368,
24
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367,
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Mathlib/Data/List/Chain.lean | List.chain_append_singleton_iff_forall₂ | [
{
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] | [
82,
30
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81,
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Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.smulRight_apply | [] | [
1046,
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1044,
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Mathlib/Data/Rat/Lemmas.lean | Rat.pnatDen_eq_iff_den_eq | [] | [
337,
18
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Mathlib/Data/Rel.lean | Rel.image_subset_iff | [] | [
253,
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Mathlib/Data/Finset/Lattice.lean | Finset.sup_sup | [
{
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Mathlib/Algebra/Hom/Freiman.lean | FreimanHom.FreimanHomClass_of_le | [] | [
544,
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Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.count_reducible | [] | [
1309,
13
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1307,
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Mathlib/Topology/LocalExtr.lean | IsLocalMinOn.isLocalMin | [] | [
146,
39
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144,
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Mathlib/Order/Monotone/Monovary.lean | Monovary.comp_right | [] | [
148,
23
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.vsub_iUnion | [] | [
721,
28
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720,
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Mathlib/Analysis/SpecificLimits/Normed.lean | tendsto_pow_const_mul_const_pow_of_lt_one | [] | [
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96
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Mathlib/Analysis/Convex/Side.lean | AffineSubspace.wOppSide_self_iff | [
{
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430,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Bounds.lean | Real.cos_lt_one_div_sqrt_sq_add_one | [
{
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... | [
150,
72
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Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.codeSupp_supports | [] | [
2062,
91
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2061,
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Mathlib/Order/SuccPred/Relation.lean | transGen_of_succ_of_ne | [] | [
82,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.angle_eq_pi_iff | [
{
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221,
68
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219,
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Mathlib/Data/Set/Sups.lean | Set.infs_union_left | [] | [
316,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
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Mathlib/Data/Set/Lattice.lean | Set.iUnion_mono' | [] | [
396,
15
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394,
1
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Mathlib/Algebra/GeomSum.lean | geom_sum_succ | [
{
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51,
61
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Mathlib/Order/Filter/NAry.lean | Filter.map₂_swap | [
{
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Mathlib/CategoryTheory/Limits/Lattice.lean | CategoryTheory.Limits.CompleteLattice.pushout_eq_sup | [
{
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.neg_comp | [] | [
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1275,
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Mathlib/Order/WithBot.lean | WithBot.unbot'_coe | [] | [
128,
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127,
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Mathlib/MeasureTheory/Measure/Haar/InnerProductSpace.lean | OrthonormalBasis.volume_parallelepiped | [
{
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Mathlib/GroupTheory/SemidirectProduct.lean | SemidirectProduct.lift_unique | [
{
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Mathlib/Control/Fold.lean | Traversable.Free.map_eq_map | [] | [
270,
6
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268,
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Mathlib/LinearAlgebra/Span.lean | Submodule.span_singleton_eq_span_singleton | [
{
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571,
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Mathlib/Topology/Algebra/Order/LeftRightLim.lean | leftLim_eq_of_eq_bot | [
{
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"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrder α\ninst✝ : TopologicalSpace β\nhα :... | [
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37
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Mathlib/AlgebraicTopology/SimplexCategory.lean | SimplexCategory.le_of_mono | [] | [
505,
17
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504,
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_finset_product' | [] | [
614,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
611,
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Mathlib/LinearAlgebra/TensorPower.lean | TensorPower.cast_tprod | [] | [
114,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
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Mathlib/Data/Finset/NoncommProd.lean | Multiset.noncommProd_map_aux | [
{
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186,
35
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11
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Mathlib/Data/PEquiv.lean | PEquiv.trans_eq_some | [] | [
157,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
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Mathlib/Combinatorics/Pigeonhole.lean | Finset.exists_le_sum_fiber_of_sum_fiber_nonpos_of_nsmul_le_sum | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nM : Type w\ninst✝¹ : DecidableEq β\ns : Finset α\nt : Finset β\nf : α → β\nw : α → M\nb : M\nn : ℕ\ninst✝ : LinearOrderedCancelAddCommMonoid M\nhf : ∀ (y : β), ¬y ∈ t → ∑ x in filter (fun x => f x = y) s, w x ≤ 0\nht : Finset.Nonempty t\n... | [
195,
52
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188,
1
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Mathlib/Computability/Partrec.lean | Computable.list_append | [] | [
358,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
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Mathlib/Topology/LocalExtr.lean | IsLocalMinOn.not_nhds_le_map | [] | [
174,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
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Mathlib/Topology/MetricSpace/GromovHausdorffRealized.lean | GromovHausdorff.candidates_refl | [] | [
130,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
9
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.le_trailingDegree_X | [] | [
292,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
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Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.zero_rpow | [
{
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}
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106,
81
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106,
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Mathlib/Algebra/Algebra/Spectrum.lean | AlgHom.apply_mem_spectrum | [
{
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"state_bef... | [
428,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.symm_source | [] | [
342,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.monic_one | [] | [
842,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
1
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Mathlib/Init/Algebra/Order.lean | lt_of_le_not_le | [] | [
69,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
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Mathlib/RingTheory/HahnSeries.lean | HahnSeries.eq_of_mem_support_single | [] | [
183,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.erase_add | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.310309\nγ : Type ?u.310312\nι : Type ?u.310315\nM : Type u_2\nM' : Type ?u.310321\nN : Type ?u.310324\nP : Type ?u.310327\nG : Type ?u.310330\nH : Type ?u.310333\nR : Type ?u.310336\nS : Type ?u.310339\ninst✝ : AddZeroClass M\na : α\nf f' : α →₀ M\ns : α\n⊢ ↑(... | [
1071,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1068,
1
] |
Mathlib/Init/Data/Nat/Bitwise.lean | Nat.div2_one | [] | [
110,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Topology/Separation.lean | isClosedMap_const | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u\nβ✝ : Type v\ninst✝³ : TopologicalSpace α✝\nα : Type u_1\nβ : Type u_2\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : T1Space β\ny : β\ns : Set α\nx✝ : IsClosed s\nh2s : Set.Nonempty s\n⊢ IsClosed (const α y '' s)",
"tactic": ... | [
643,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.zeroLocus_union | [] | [
330,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/Analysis/Calculus/Inverse.lean | HasStrictFDerivAt.to_local_left_inverse | [] | [
677,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
675,
1
] |
Mathlib/Data/List/Basic.lean | List.map_concat | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.132558\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf : α → β\na : α\nl : List α\n⊢ map f (concat l a) = concat (map f l) (f a)",
"tactic": "induction l <;> [rfl; simp only [*, concat_eq_append, cons_append, map, map_append]]"... | [
1790,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1788,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | lt_mul_of_lt_mul_of_nonneg_right | [] | [
268,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.coe_trans_symm | [] | [
697,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPullback.zero_left | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝² : Category C\nP X✝ Y Z : C\nfst : P ⟶ X✝\nsnd : P ⟶ Y\nf : X✝ ⟶ Z\ng : Y ⟶ Z\ninst✝¹ : HasZeroObject C\ninst✝ : HasZeroMorphisms C\nX : C\n⊢ 0 ≫ 𝟙 X = 0 ≫ 0",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "... | [
479,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.map_swap4_eq_comap | [] | [
2553,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2550,
1
] |
Mathlib/MeasureTheory/Measure/Stieltjes.lean | StieltjesFunction.iInf_Ioi_eq | [
{
"state_after": "f✝ f : StieltjesFunction\nx : ℝ\n⊢ rightLim (↑f) x = ⨅ (r : ↑(Ioi x)), ↑f ↑r",
"state_before": "f✝ f : StieltjesFunction\nx : ℝ\n⊢ (⨅ (r : ↑(Ioi x)), ↑f ↑r) = ↑f x",
"tactic": "suffices Function.rightLim f x = ⨅ r : Ioi x, f r by rw [← this, f.rightLim_eq]"
},
{
"state_after": ... | [
242,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
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