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/Analysis/Normed/Group/InfiniteSum.lean | tsum_of_nnnorm_bounded | [
{
"state_after": "ι : Type u_1\nα : Type ?u.20330\nE : Type u_2\nF : Type ?u.20336\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : SeminormedAddCommGroup F\nf : ι → E\ng : ι → ℝ≥0\na : ℝ≥0\nhg : HasSum (fun a => ↑(g a)) ↑a\nh : ∀ (i : ι), ‖f i‖ ≤ ↑(g i)\n⊢ ‖∑' (i : ι), f i‖ ≤ ↑a",
"state_before": "ι : Type u_1\... | [
151,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Std/Data/RBMap/Alter.lean | Std.RBNode.find?_eq_zoom | [
{
"state_after": "α : Type u_1\ncut : α → Ordering\nc✝ : RBColor\nl✝ : RBNode α\nv✝ : α\nr✝ : RBNode α\nx✝ : optParam (Path α) Path.root\n⊢ (match cut v✝ with\n | Ordering.lt => find? cut l✝\n | Ordering.gt => find? cut r✝\n | Ordering.eq => some v✝) =\n root?\n (match cut v✝ with\n | Or... | [
407,
99
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
405,
1
] |
Mathlib/Data/List/Destutter.lean | List.destutter'_eq_self_iff | [
{
"state_after": "α : Type u_1\nl : List α\nR : α → α → Prop\ninst✝ : DecidableRel R\na✝ b a : α\nh : destutter' R a l = a :: l\n⊢ Chain' R (a :: l)",
"state_before": "α : Type u_1\nl : List α\nR : α → α → Prop\ninst✝ : DecidableRel R\na✝ b a : α\nh : destutter' R a l = a :: l\n⊢ Chain R a l",
"tactic":... | [
117,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Data/Polynomial/Div.lean | Polynomial.divByMonic_one | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\ninst✝ : CommRing R\np✝ q p : R[X]\n⊢ p /ₘ 1 = p",
"tactic": "conv_rhs => rw [← modByMonic_add_div p monic_one]; simp"
}
] | [
420,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
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Mathlib/Analysis/Calculus/Inverse.lean | ApproximatesLinearOn.exists_homeomorph_extension | [
{
"state_after": "case intro.intro\n𝕜 : Type ?u.461349\ninst✝¹⁴ : NontriviallyNormedField 𝕜\nE✝ : Type ?u.461355\ninst✝¹³ : NormedAddCommGroup E✝\ninst✝¹² : NormedSpace 𝕜 E✝\nF✝ : Type ?u.461465\ninst✝¹¹ : NormedAddCommGroup F✝\ninst✝¹⁰ : NormedSpace 𝕜 F✝\nG : Type ?u.461568\ninst✝⁹ : NormedAddCommGroup G\n... | [
493,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.relindex_self | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝ : Group G\nH K L : Subgroup G\n⊢ relindex H H = 1",
"tactic": "rw [relindex, subgroupOf_self, index_top]"
}
] | [
272,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | Trivialization.coordChangeL_symm_apply | [] | [
367,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalMinOn.sub | [] | [
432,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
8
] |
src/lean/Init/Prelude.lean | decide_eq_true | [] | [
849,
35
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
847,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.uncurry_curryLeft | [
{
"state_after": "case H\nR : Type u\nι : Type u'\nn : ℕ\nM : Fin (Nat.succ n) → Type v\nM₁ : ι → Type v₁\nM₂ : Type v₂\nM₃ : Type v₃\nM' : Type v'\ninst✝⁶ : CommSemiring R\ninst✝⁵ : (i : Fin (Nat.succ n)) → AddCommMonoid (M i)\ninst✝⁴ : AddCommMonoid M'\ninst✝³ : AddCommMonoid M₂\ninst✝² : (i : Fin (Nat.succ n... | [
1285,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1282,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.min_eq_min | [] | [
168,
70
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
168,
11
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.continuous_testAgainstNN_eval | [
{
"state_after": "Ω : Type u_1\ninst✝⁶ : MeasurableSpace Ω\nR : Type ?u.105418\ninst✝⁵ : SMul R ℝ≥0\ninst✝⁴ : SMul R ℝ≥0∞\ninst✝³ : IsScalarTower R ℝ≥0 ℝ≥0∞\ninst✝² : IsScalarTower R ℝ≥0∞ ℝ≥0∞\ninst✝¹ : TopologicalSpace Ω\ninst✝ : OpensMeasurableSpace Ω\nf : Ω →ᵇ ℝ≥0\n⊢ Continuous ((fun φ => ↑φ f) ∘ toWeakDualB... | [
476,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/GroupTheory/SpecificGroups/Dihedral.lean | DihedralGroup.sr_mul_self | [
{
"state_after": "no goals",
"state_before": "n : ℕ\ni : ZMod n\n⊢ sr i * sr i = 1",
"tactic": "rw [sr_mul_sr, sub_self, one_def]"
}
] | [
148,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Data/MvPolynomial/Counit.lean | MvPolynomial.ACounit_C | [] | [
58,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/GroupTheory/SemidirectProduct.lean | SemidirectProduct.lift_inl | [
{
"state_after": "no goals",
"state_before": "N : Type u_2\nG : Type u_3\nH : Type u_1\ninst✝² : Group N\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* MulAut N\nf₁ : N →* H\nf₂ : G →* H\nh :\n ∀ (g : G),\n MonoidHom.comp f₁ (MulEquiv.toMonoidHom (↑φ g)) = MonoidHom.comp (MulEquiv.toMonoidHom (↑MulAut.con... | [
232,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Order/Disjoint.lean | Disjoint.inf_right | [] | [
163,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.mem_transpose | [
{
"state_after": "no goals",
"state_before": "μ : YoungDiagram\nc : ℕ × ℕ\n⊢ c ∈ transpose μ ↔ Prod.swap c ∈ μ",
"tactic": "simp [transpose]"
}
] | [
219,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | Real.tendsto_exp_atBot | [] | [
197,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_fin2 | [
{
"state_after": "no goals",
"state_before": "ι : Type u'\nι' : Type ?u.1252914\nR : Type ?u.1252917\nK : Type u_1\nM : Type ?u.1252923\nM' : Type ?u.1252926\nM'' : Type ?u.1252929\nV : Type u\nV' : Type ?u.1252934\ninst✝⁴ : DivisionRing K\ninst✝³ : AddCommGroup V\ninst✝² : AddCommGroup V'\ninst✝¹ : Module ... | [
1267,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1264,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.liftRel_map | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type u_1\nR : α → β → Prop\nS : γ → δ → Prop\ns1✝ : WSeq α\ns2✝ : WSeq β\nf1 : α → γ\nf2 : β → δ\nh1 : LiftRel R s1✝ s2✝\nh2 : ∀ {a : α} {b : β}, R a b → S (f1 a) (f2 b)\ns1 : WSeq γ\ns2 : WSeq δ\nh✝ : (fun s1 s2 => ∃ s t, s1 = map f1 s ∧ s2 = map f2 t ∧... | [
1509,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1495,
1
] |
Mathlib/Order/Basic.lean | update_lt_update_iff | [] | [
882,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
881,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Ring.lean | summable_div_const_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nκ : Type ?u.15580\nR : Type ?u.15583\nα : Type u_1\ninst✝² : DivisionSemiring α\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSemiring α\nf g : ι → α\na a₁ a₂ : α\nh : a ≠ 0\n⊢ (Summable fun i => f i / a) ↔ Summable f",
"tactic": "simpa only... | [
113,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Analysis/NormedSpace/AddTorsor.lean | eventually_homothety_image_subset_of_finite_subset_interior | [
{
"state_after": "α : Type ?u.95109\nV : Type ?u.95112\nP : Type ?u.95115\nW : Type u_3\nQ : Type u_1\ninst✝⁸ : SeminormedAddCommGroup V\ninst✝⁷ : PseudoMetricSpace P\ninst✝⁶ : NormedAddTorsor V P\ninst✝⁵ : NormedAddCommGroup W\ninst✝⁴ : MetricSpace Q\ninst✝³ : NormedAddTorsor W Q\n𝕜 : Type u_2\ninst✝² : Norme... | [
259,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Std/Data/RBMap/WF.lean | Std.RBNode.RedRed.balance1 | [
{
"state_after": "α : Type u_1\np : Prop\nn : Nat\nc : RBColor\nl : RBNode α\nv : α\nr : RBNode α\nhl : RedRed p l n\nhr : Balanced r c n\n⊢ ∃ c,\n Balanced\n (match l, v, r with\n | node red (node red a x b) y c, z, d => node red (node black a x b) y (node black c z d)\n | node red a x (node ... | [
163,
66
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
154,
11
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_const_const_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.611781\nE : Type ?u.611784\nF : Type ?u.611787\nG : Type ?u.611790\nE' : Type ?u.611793\nF' : Type ?u.611796\nG' : Type ?u.611799\nE'' : Type u_2\nF'' : Type u_3\nG'' : Type ?u.611808\nR : Type ?u.611811\nR' : Type ?u.611814\n𝕜 : Type ?u.611817\n𝕜' : Type ?u.611820\... | [
1869,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1864,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.RespectsIso.cancel_right_isIso | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\nD : Type ?u.14744\ninst✝¹ : Category D\nP : MorphismProperty C\nhP : RespectsIso P\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\ninst✝ : IsIso g\nh : P (f ≫ g)\n⊢ P f",
"tactic": "simpa using hP.2 (asIso g).symm (f ≫ g) h"
}
] | [
161,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Data/List/Intervals.lean | List.Ico.bagInter_consecutive | [] | [
118,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/NumberTheory/Padics/PadicVal.lean | padicValInt.one | [
{
"state_after": "no goals",
"state_before": "p : ℕ\n⊢ padicValInt p 1 = 0",
"tactic": "simp [padicValInt]"
}
] | [
129,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
11
] |
Std/Data/Int/Lemmas.lean | Int.max_le | [
{
"state_after": "a b c : Int\nx✝ : a ≤ c ∧ b ≤ c\nh₁ : a ≤ c\nh₂ : b ≤ c\n⊢ (if a ≤ b then b else a) ≤ c",
"state_before": "a b c : Int\nx✝ : a ≤ c ∧ b ≤ c\nh₁ : a ≤ c\nh₂ : b ≤ c\n⊢ max a b ≤ c",
"tactic": "rw [Int.max_def]"
},
{
"state_after": "no goals",
"state_before": "a b c : Int\nx✝ ... | [
720,
62
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
718,
11
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.trans_target' | [] | [
842,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
1
] |
Mathlib/Analysis/Calculus/DiffContOnCl.lean | Differentiable.comp_diffContOnCl | [] | [
147,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Combinatorics/Hall/Basic.lean | hallMatchingsOn.nonempty | [
{
"state_after": "no goals",
"state_before": "ι : Type u\nα : Type v\ninst✝ : DecidableEq α\nt : ι → Finset α\nh : ∀ (s : Finset ι), card s ≤ card (Finset.biUnion s t)\nι' : Finset ι\n⊢ Nonempty ↑(hallMatchingsOn t ι')",
"tactic": "classical\n refine' ⟨Classical.indefiniteDescription _ _⟩\n apply (all... | [
89,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/MeasureTheory/Function/ContinuousMapDense.lean | MeasureTheory.exists_continuous_snorm_sub_le_of_closed | [
{
"state_after": "α : Type u_1\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : NormalSpace α\ninst✝³ : BorelSpace α\nE : Type u_2\ninst✝² : NormedAddCommGroup E\nμ : Measure α\np : ℝ≥0∞\ninst✝¹ : NormedSpace ℝ E\ninst✝ : Measure.OuterRegular μ\nhp : p ≠ ⊤\ns u : Set α\ns_closed : IsClosed s\n... | [
139,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Algebra/CharP/ExpChar.lean | expChar_one_of_char_zero | [
{
"state_after": "case zero\nR : Type u\ninst✝ : Semiring R\nhp : CharP R 0\nq : CharZero R\n⊢ 1 = 1\n\ncase prime\nR : Type u\ninst✝ : Semiring R\nq : ℕ\nhp : CharP R 0\nhq_prime : Nat.Prime q\nhq_hchar : CharP R q\n⊢ q = 1",
"state_before": "R : Type u\ninst✝ : Semiring R\nq : ℕ\nhp : CharP R 0\nhq : ExpC... | [
55,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_union_Ico_eq_Ico | [] | [
1643,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1640,
1
] |
Mathlib/GroupTheory/GroupAction/Quotient.lean | MulAction.ofQuotientStabilizer_mk | [] | [
166,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.rootMultiplicity_mul | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np✝ q✝ p q : R[X]\nx : R\nhpq : p * q ≠ 0\nhp : p ≠ 0\n⊢ rootMultiplicity x (p * q) = rootMultiplicity x p + rootMultiplicity x q",
"state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ... | [
450,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
Mathlib/Data/Setoid/Partition.lean | Setoid.eqv_class_mem | [] | [
155,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.disjoint_range_addRightEmbedding | [
{
"state_after": "α : Type ?u.49249\nβ : Type ?u.49252\nγ : Type ?u.49255\nf : α ↪ β\ns : Finset α\na b : ℕ\n⊢ range a ⊓ map (addRightEmbedding a) (range b) ≤ ⊥",
"state_before": "α : Type ?u.49249\nβ : Type ?u.49252\nγ : Type ?u.49255\nf : α ↪ β\ns : Finset α\na b : ℕ\n⊢ _root_.Disjoint (range a) (map (add... | [
274,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.assoc_tmul | [] | [
854,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
851,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.mem_Ici_of_Ioi | [] | [
675,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
1
] |
Mathlib/RingTheory/Filtration.lean | Ideal.Filtration.submodule_closure_single | [
{
"state_after": "case a\nR M : Type u\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nI : Ideal R\nF F' : Filtration I M\nh : Stable F\n⊢ AddSubmonoid.closure (⋃ (i : ℕ), ↑(single R i) '' ↑(N F i)) ≤ (Filtration.submodule F).toAddSubmonoid\n\ncase a\nR M : Type u\ninst✝² : CommRing R\ninst✝¹... | [
314,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Std/Data/List/Lemmas.lean | List.isPrefix.trans | [] | [
1592,
75
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1591,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.hasSum_ofReal | [] | [
593,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/Data/Set/Basic.lean | Set.singleton_injective | [] | [
1286,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1285,
1
] |
Mathlib/Data/Matrix/Basis.lean | Matrix.stdBasisMatrix_zero | [
{
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Mathlib/LinearAlgebra/FiniteDimensional.lean | FiniteDimensional.finite_of_finite | [
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138,
17
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135,
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Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.deleteVerts_anti | [] | [
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57
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_subset_Ici_self | [] | [
475,
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475,
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Mathlib/Order/CompactlyGenerated.lean | CompleteLattice.setIndependent_iff_finite | [
{
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Mathlib/Data/Set/Countable.lean | Set.countable_empty | [] | [
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74
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128,
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Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.mk_toWord | [
{
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Mathlib/Data/Finset/Interval.lean | Finset.Icc_eq_filter_powerset | [] | [
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Mathlib/Data/Analysis/Filter.lean | Filter.Realizer.mem_sets | [
{
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Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.MultispanIndex.multispan_map_fst | [] | [
281,
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.range_indicator | [
{
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Mathlib/GroupTheory/Finiteness.lean | AddSubmonoid.fg_iff_mul_fg | [
{
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Mathlib/NumberTheory/RamificationInertia.lean | Ideal.IsDedekindDomain.ramificationIdx_eq_normalizedFactors_count | [
{
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Mathlib/Data/Stream/Init.lean | Stream'.nth_map | [] | [
153,
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Mathlib/Analysis/InnerProductSpace/Basic.lean | real_inner_self_eq_norm_mul_norm | [
{
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1019,
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Mathlib/Data/Num/Lemmas.lean | Num.cast_to_nat | [] | [
305,
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | fderivWithin_inter | [
{
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640,
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Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.map_le_map_iff_of_injective | [] | [
432,
30
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431,
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Std/Data/List/Lemmas.lean | List.getLast?_cons | [
{
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477,
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Mathlib/Data/Finset/Sups.lean | Finset.sups_nonempty | [] | [
119,
22
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118,
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Mathlib/Topology/Semicontinuous.lean | lowerSemicontinuousAt_tsum | [
{
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648,
43
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645,
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Mathlib/Data/Matrix/Basic.lean | Matrix.diagonal_eq_diagonal_iff | [
{
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451,
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Mathlib/Data/Finset/Lattice.lean | Finset.min_mem_insert_top_image_coe | [] | [
1540,
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1538,
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Mathlib/FieldTheory/Subfield.lean | Subfield.coe_sInf | [
{
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Mathlib/Algebra/Order/Interval.lean | NonemptyInterval.fst_one | [] | [
62,
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Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.coeff_zero_C | [] | [
389,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
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Mathlib/Topology/Basic.lean | preimage_interior_subset_interior_preimage | [] | [
1624,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1622,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.of_bound' | [
{
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127,
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Mathlib/MeasureTheory/Covering/Besicovitch.lean | Besicovitch.exist_disjoint_covering_families | [
{
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533,
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Mathlib/Data/Multiset/Powerset.lean | Multiset.powerset_cons | [
{
"state_after": "α : Type u_1\na : α\ns : Multiset α\nl : List α\n⊢ List.map ofList (sublists' l) ++ List.map (ofList ∘ List.cons a) (sublists' l) ~\n List.map ofList (sublists' l) ++ List.map ((fun x => a ::ₘ x) ∘ ofList) (sublists' l)",
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106,
47
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105,
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Mathlib/Data/Finset/Pointwise.lean | Finset.union_div_inter_subset_union | [] | [
692,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
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Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.MutuallySingular.neg_left_iff | [] | [
1262,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1260,
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Mathlib/Analysis/LocallyConvex/WeakDual.lean | LinearMap.toSeminorm_ball_zero | [
{
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73,
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.length_toList | [
{
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] | [
562,
42
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561,
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Mathlib/Order/Filter/Lift.lean | Filter.prod_def | [
{
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426,
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423,
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Mathlib/AlgebraicTopology/DoldKan/SplitSimplicialObject.lean | SimplicialObject.Splitting.ιSummand_comp_PInfty_eq_zero | [
{
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100,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
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Mathlib/Order/Ideal.lean | Order.Ideal.carrier_eq_coe | [] | [
120,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
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Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSet.coe_empty | [] | [
1790,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1789,
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Mathlib/Data/Set/Basic.lean | Set.subset_ite | [
{
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2322,
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Mathlib/Analysis/NormedSpace/Banach.lean | ContinuousLinearMap.range_eq_map_coprodSubtypeLEquivOfIsCompl | [
{
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428,
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421,
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Mathlib/Order/Closure.lean | LowerAdjoint.ext | [
{
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339,
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337,
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Mathlib/Order/Monotone/Basic.lean | Int.exists_strictAnti | [] | [
1093,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1092,
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Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.parallelPair_functor_obj | [
{
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244,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
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Mathlib/Data/Nat/Choose/Multinomial.lean | Finset.sum_pow_of_commute | [
{
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277,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Algebra/Symmetrized.lean | SymAlg.unsym_mul_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : Semiring α\ninst✝ : Invertible 2\na : αˢʸᵐ\n⊢ ↑unsym (a * a) = ↑unsym a * ↑unsym a",
"tactic": "rw [mul_def, unsym_sym, ← two_mul, invOf_mul_self_assoc]"
}
] | [
331,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/MeasureTheory/Measure/Doubling.lean | IsUnifLocDoublingMeasure.eventually_measure_le_scaling_constant_mul' | [
{
"state_after": "case h.e'_2.h.h.h.e'_3.h.e'_3.h.e'_4\nα : Type u_1\ninst✝² : MetricSpace α\ninst✝¹ : MeasurableSpace α\nμ : MeasureTheory.Measure α\ninst✝ : IsUnifLocDoublingMeasure μ\nK : ℝ\nhK : 0 < K\nx✝ : ℝ\na✝ : α\n⊢ x✝ = K⁻¹ * (K * x✝)",
"state_before": "α : Type u_1\ninst✝² : MetricSpace α\ninst✝¹ ... | [
149,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.cons_induction | [
{
"state_after": "no goals",
"state_before": "case empty\nα✝ : Type ?u.115585\nβ : Type ?u.115588\nγ : Type ?u.115591\ninst✝ : DecidableEq α✝\ns t u v : Finset α✝\na b : α✝\nα : Type u_1\np : Finset α → Prop\nempty : p ∅\ncons : ∀ ⦃a : α⦄ {s : Finset α} (h : ¬a ∈ s), p s → p (Finset.cons a s h)\nnd : Nodup ... | [
1197,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1188,
1
] |
Mathlib/Topology/MetricSpace/GromovHausdorffRealized.lean | GromovHausdorff.isometry_optimalGHInjr | [] | [
485,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/Data/MvPolynomial/Derivation.lean | MvPolynomial.mkDerivationₗ_monomial | [] | [
50,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Data/Finset/Sigma.lean | Finset.sigmaLift_mono | [
{
"state_after": "ι : Type u_2\nα : ι → Type u_3\nβ : ι → Type u_4\nγ : ι → Type u_1\ninst✝ : DecidableEq ι\nf g : ⦃i : ι⦄ → α i → β i → Finset (γ i)\na✝ : (i : ι) × α i\nb✝ : (i : ι) × β i\nh : ∀ ⦃i : ι⦄ ⦃a : α i⦄ ⦃b : β i⦄, f a b ⊆ g a b\na : (i : ι) × α i\nb : (i : ι) × β i\nx : (i : ι) × γ i\nhx : x ∈ sigma... | [
187,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Icc_eq_cons_Ioc | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.108081\nα : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : LocallyFiniteOrder α\na b c : α\nh : a ≤ b\n⊢ Icc a b = cons a (Ioc a b) (_ : ¬a ∈ Ioc a b)",
"tactic": "classical rw [cons_eq_insert, Ioc_insert_left h]"
},
{
"state_after": "no goal... | [
620,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
619,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | ModelWithCorners.symm_continuousWithinAt_comp_right_iff | [
{
"state_after": "case refine'_1\n𝕜 : Type u_4\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nH : Type u_2\ninst✝¹ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nX : Type u_1\ninst✝ : TopologicalSpace X\nf : H → X\ns : Set H\nx : H\nh : Continu... | [
348,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Logic/Function/Iterate.lean | Function.iterate_succ | [] | [
55,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.posDefOfNonneg | [] | [
946,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
945,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | HasFDerivWithinAt.sub | [] | [
488,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
8
] |
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