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/Topology/LocalHomeomorph.lean | LocalHomeomorph.continuousAt_iff_continuousAt_comp_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type u_3\nδ : Type ?u.99038\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ne : LocalHomeomorph α β\ne' : LocalHomeomorph β γ\nf : β → γ\nx : β\nh : x ∈ e.target\... | [
1151,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1148,
1
] |
Mathlib/Data/Int/ModEq.lean | Int.ModEq.add | [
{
"state_after": "case h.e'_4\nm n a b c d : ℤ\nh₁ : a ≡ b [ZMOD n]\nh₂ : c ≡ d [ZMOD n]\n⊢ b + d - (a + c) = b - a + (d - c)",
"state_before": "m n a b c d : ℤ\nh₁ : a ≡ b [ZMOD n]\nh₂ : c ≡ d [ZMOD n]\n⊢ n ∣ b + d - (a + c)",
"tactic": "convert dvd_add h₁.dvd h₂.dvd using 1"
},
{
"state_after"... | [
147,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
11
] |
Mathlib/Data/List/Rotate.lean | List.isRotated_reverse_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nl l' : List α\n⊢ reverse l ~r reverse l' ↔ l ~r l'",
"tactic": "simp [isRotated_reverse_comm_iff]"
}
] | [
531,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
1
] |
Mathlib/Data/Set/Sigma.lean | Set.sigma_insert | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nι' : Type ?u.10187\nα : ι → Type u_2\nβ : ι → Type ?u.10197\ns s₁ s₂ : Set ι\nt t₁ t₂ : (i : ι) → Set (α i)\nu : Set ((i : ι) × α i)\nx : (i : ι) × α i\ni j : ι\na✝ : α i\na : (i : ι) → α i\n⊢ (Set.Sigma s fun i => insert (a i) (t i)) = (fun i => {... | [
156,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.le_def | [] | [
141,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.comp_lineMap | [] | [
609,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
1
] |
Mathlib/Topology/UniformSpace/AbstractCompletion.lean | AbstractCompletion.uniformContinuous_compare | [] | [
254,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_smul_le_snorm_mul_snorm_top | [] | [
1509,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1506,
1
] |
Mathlib/NumberTheory/LegendreSymbol/ZModChar.lean | ZMod.χ₄_int_one_mod_four | [
{
"state_after": "n : ℤ\nhn : n % 4 = 1\n⊢ ↑χ₄ ↑1 = 1",
"state_before": "n : ℤ\nhn : n % 4 = 1\n⊢ ↑χ₄ ↑n = 1",
"tactic": "rw [χ₄_int_mod_four, hn]"
},
{
"state_after": "no goals",
"state_before": "n : ℤ\nhn : n % 4 = 1\n⊢ ↑χ₄ ↑1 = 1",
"tactic": "rfl"
}
] | [
112,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/AlgebraicTopology/DoldKan/FunctorGamma.lean | AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_comp | [
{
"state_after": "case pos\nC : Type u_2\ninst✝³ : Category C\ninst✝² : Preadditive C\nK K' : ChainComplex C ℕ\nf : K ⟶ K'\nΔ Δ' Δ'' : SimplexCategory\ni' : Δ'' ⟶ Δ'\ni : Δ' ⟶ Δ\ninst✝¹ : Mono i'\ninst✝ : Mono i\nh₁ : Δ = Δ'\n⊢ mapMono K i ≫ mapMono K i' = mapMono K (i' ≫ i)\n\ncase neg\nC : Type u_2\ninst✝³ : ... | [
173,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgHom.coe_copy | [] | [
398,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/GroupTheory/Commutator.lean | Subgroup.commutator_le_right | [] | [
151,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Logic/Hydra.lean | Relation.acc_of_singleton | [
{
"state_after": "case empty\nα : Type u_1\nr : α → α → Prop\ninst✝ : IsIrrefl α r\nhs : ∀ (a : α), a ∈ 0 → Acc (CutExpand r) {a}\n⊢ Acc (CutExpand r) 0\n\ncase cons\nα : Type u_1\nr : α → α → Prop\ninst✝ : IsIrrefl α r\na✝¹ : α\ns✝ : Multiset α\na✝ : (∀ (a : α), a ∈ s✝ → Acc (CutExpand r) {a}) → Acc (CutExpand... | [
139,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiffOn_top_iff_derivWithin | [
{
"state_after": "case mp\n𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝⁹ : NormedAddCommGroup D\ninst✝⁸ : NormedSpace 𝕜 D\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... | [
2110,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2099,
1
] |
Mathlib/Order/Lattice.lean | Antitone.sup | [] | [
1165,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1163,
11
] |
Mathlib/CategoryTheory/Generator.lean | CategoryTheory.Subobject.eq_of_le_of_isDetecting | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\n𝒢 : Set C\nh𝒢 : IsDetecting 𝒢\nX : C\nP Q : Subobject X\nh₁ : P ≤ Q\nh₂ : ∀ (G : C), G ∈ 𝒢 → ∀ {f : G ⟶ X}, Factors Q f → Factors P f\n⊢ IsIso (ofLE P Q h₁)",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type ... | [
330,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.iInf_sets_eq | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.94306\nι : Sort x\nf✝ g : Filter α\ns t : Set α\nf : ι → Filter α\nh : Directed (fun x x_1 => x ≥ x_1) f\nne : Nonempty ι\ni : ι\n⊢ ∀ {x y : Set α} (x_1 : ι), x ∈ (f x_1).sets → x ⊆ y → ∃ i, y ∈ (f i).sets",
"state_before": "α : Type u\nβ : T... | [
817,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
801,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.SimpleFunc.memℒp_iff_finMeasSupp | [] | [
374,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_eq_nhds_of_re_pos | [] | [
512,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
1
] |
Mathlib/Algebra/Order/Interval.lean | NonemptyInterval.coe_inv_interval | [] | [
501,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
500,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.hausdorffDist_self_closure | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.86240\nα : Type u\nβ : Type v\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\ns t u : Set α\nx y : α\nΦ : α → β\n⊢ hausdorffDist s (closure s) = 0",
"tactic": "simp [hausdorffDist]"
}
] | [
857,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
857,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.tsum_measure_preimage_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.18843\nδ : Type ?u.18846\nι : Type ?u.18849\nR : Type ?u.18852\nR' : Type ?u.18855\nm : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns✝ s₁ s₂ t : Set α\ns : Set β\nhs : Set.Countable s\nf : α → β\nhf : ∀ (y : β), y ∈ s → Measur... | [
212,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Logic/Equiv/TransferInstance.lean | Equiv.one_def | [] | [
57,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.disjSups_union_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝³ : DecidableEq α\ninst✝² : SemilatticeSup α\ninst✝¹ : OrderBot α\ninst✝ : DecidableRel Disjoint\ns s₁ s₂ t t₁ t₂ u : Finset α\na b c : α\n⊢ (s₁ ∪ s₂) ○ t = s₁ ○ t ∪ s₂ ○ t",
"tactic": "simp [disjSups, filter_union, image_union]"
}
] | [
502,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | Measurable.comp_aemeasurable' | [] | [
734,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
732,
1
] |
Mathlib/Algebra/Algebra/Basic.lean | NeZero.of_noZeroSMulDivisors | [] | [
824,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
820,
1
] |
Mathlib/Data/Subtype.lean | Subtype.symm | [] | [
243,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
11
] |
Mathlib/Algebra/Algebra/Spectrum.lean | spectrum.smul_eq_smul | [
{
"state_after": "case inl\n𝕜 : Type u\nA : Type v\ninst✝³ : Field 𝕜\ninst✝² : Ring A\ninst✝¹ : Algebra 𝕜 A\ninst✝ : Nontrivial A\na : A\nha : Set.Nonempty (σ a)\n⊢ σ (0 • a) = 0 • σ a\n\ncase inr\n𝕜 : Type u\nA : Type v\ninst✝³ : Field 𝕜\ninst✝² : Ring A\ninst✝¹ : Algebra 𝕜 A\ninst✝ : Nontrivial A\nk : �... | [
364,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/Analysis/SpecialFunctions/Arsinh.lean | Real.arsinh_le_arsinh | [] | [
151,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Topology/NoetherianSpace.lean | TopologicalSpace.noetherianSpace_of_surjective | [] | [
128,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.some_eq_natCast | [] | [
111,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.xn_ge_a_pow | [
{
"state_after": "a : ℕ\na1 : 1 < a\nn : ℕ\n⊢ a ^ n * a ≤ xn a1 n * a + Pell.d a1 * yn a1 n",
"state_before": "a : ℕ\na1 : 1 < a\nn : ℕ\n⊢ a ^ (n + 1) ≤ xn a1 (n + 1)",
"tactic": "simp [_root_.pow_succ']"
},
{
"state_after": "no goals",
"state_before": "a : ℕ\na1 : 1 < a\nn : ℕ\n⊢ a ^ n * a ... | [
267,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_subset_Iio_self | [] | [
524,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
524,
1
] |
Mathlib/Data/Finset/Fold.lean | Finset.fold_congr | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.8657\nop : β → β → β\nhc : IsCommutative β op\nha : IsAssociative β op\nf : α → β\nb : β\ns : Finset α\na : α\ng : α → β\nH : ∀ (x : α), x ∈ s → f x = g x\n⊢ fold op b f s = fold op b g s",
"tactic": "rw [fold, fold, m... | [
79,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.Ioi_mem_atTop | [] | [
64,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.map_comp | [
{
"state_after": "case a\nα : Type u\nβ : Type v\nγ : Type w\nf : α → β\ng : β → γ\ns : Stream' (Option α)\nal : ∀ ⦃n : ℕ⦄ ⦃a : α⦄, s n = some a → s (n + 1) = some a\n⊢ ↑(map (g ∘ f) { val := s, property := al }) = ↑(map g (map f { val := s, property := al }))",
"state_before": "α : Type u\nβ : Type v\nγ : ... | [
723,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
719,
1
] |
Mathlib/Topology/Order.lean | continuous_iSup_dom | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.39838\nf : α → β\nι : Sort u_1\nt₁ : ι → TopologicalSpace α\nt₂ : TopologicalSpace β\n⊢ Continuous f ↔ ∀ (i : ι), Continuous f",
"tactic": "simp only [continuous_iff_le_induced, iSup_le_iff]"
}
] | [
764,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
762,
1
] |
Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.IsFundamentalDomain.measure_eq_card_smul_of_smul_ae_eq_self | [
{
"state_after": "G : Type u_1\nH : Type ?u.251442\nα : Type u_2\nβ : Type ?u.251448\nE : Type ?u.251451\ninst✝¹¹ : Group G\ninst✝¹⁰ : Group H\ninst✝⁹ : MulAction G α\ninst✝⁸ : MeasurableSpace α\ninst✝⁷ : MulAction H β\ninst✝⁶ : MeasurableSpace β\ninst✝⁵ : NormedAddCommGroup E\ns t✝ : Set α\nμ : Measure α\ninst... | [
324,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/GroupTheory/Nilpotent.lean | derived_le_lower_central | [
{
"state_after": "case zero\nG : Type u_1\ninst✝¹ : Group G\nH : Subgroup G\ninst✝ : Normal H\n⊢ derivedSeries G Nat.zero ≤ lowerCentralSeries G Nat.zero\n\ncase succ\nG : Type u_1\ninst✝¹ : Group G\nH : Subgroup G\ninst✝ : Normal H\ni : ℕ\nih : derivedSeries G i ≤ lowerCentralSeries G i\n⊢ derivedSeries G (Nat... | [
682,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
678,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.equivFun_self | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nι' : Type ?u.670971\nR : Type u_2\nR₂ : Type ?u.670977\nK : Type ?u.670980\nM : Type u_3\nM' : Type ?u.670986\nM'' : Type ?u.670989\nV : Type u\nV' : Type ?u.670994\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\ninst✝³ : AddCo... | [
938,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
937,
1
] |
Mathlib/ModelTheory/LanguageMap.lean | FirstOrder.Language.LHom.comp_sumElim | [] | [
198,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Data/List/Perm.lean | List.Sublist.exists_perm_append | [] | [
469,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.norm_le_of_tendsto | [
{
"state_after": "case intro\nα : Type u_1\nE : α → Type u_2\np q : ℝ≥0∞\ninst✝¹ : (i : α) → NormedAddCommGroup (E i)\nι : Type u_3\nl : Filter ι\ninst✝ : NeBot l\n_i : Fact (1 ≤ p)\nC : ℝ\nF : ι → { x // x ∈ lp E p }\nhCF : ∀ᶠ (k : ι) in l, ‖F k‖ ≤ C\nf : { x // x ∈ lp E p }\nhf : Tendsto (id fun i => ↑(F i)) ... | [
1171,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1161,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.LiftRel.refl | [] | [
1066,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1065,
1
] |
Mathlib/RingTheory/Localization/Away/AdjoinRoot.lean | IsLocalization.Away.finitePresentation | [] | [
52,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Data/Polynomial/Reverse.lean | Polynomial.reflect_C_mul_X_pow | [
{
"state_after": "case a\nR : Type u_1\ninst✝ : Semiring R\nf : R[X]\nN n : ℕ\nc : R\nn✝ : ℕ\n⊢ coeff (reflect N (↑C c * X ^ n)) n✝ = coeff (↑C c * X ^ ↑(revAt N) n) n✝",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nf : R[X]\nN n : ℕ\nc : R\n⊢ reflect N (↑C c * X ^ n) = ↑C c * X ^ ↑(revAt N) n",
"... | [
157,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Init/Data/Bool/Lemmas.lean | Bool.eq_false_of_not_eq_true | [] | [
79,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Data/Int/ModEq.lean | Int.ModEq.of_div | [
{
"state_after": "no goals",
"state_before": "m n a b c d : ℤ\nh : a / c ≡ b / c [ZMOD m / c]\nha✝¹ : c ∣ a\nha✝ : c ∣ b\nha : c ∣ m\n⊢ a ≡ b [ZMOD m]",
"tactic": "convert h.mul_left' <;> rwa [Int.mul_ediv_cancel']"
}
] | [
245,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | factorization_eq_count | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝³ : CancelCommMonoidWithZero α\ninst✝² : UniqueFactorizationMonoid α\ninst✝¹ : NormalizationMonoid α\ninst✝ : DecidableEq α\nn p : α\n⊢ ↑(factorization n) p = Multiset.count p (normalizedFactors n)",
"tactic": "simp [factorization]"
}
] | [
2012,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2011,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.cyclotomic_eq_prod_X_sub_primitiveRoots | [
{
"state_after": "K : Type u_1\ninst✝¹ : CommRing K\ninst✝ : IsDomain K\nζ : K\nn : ℕ\nhz : IsPrimitiveRoot ζ n\n⊢ cyclotomic n K = cyclotomic' n K",
"state_before": "K : Type u_1\ninst✝¹ : CommRing K\ninst✝ : IsDomain K\nζ : K\nn : ℕ\nhz : IsPrimitiveRoot ζ n\n⊢ cyclotomic n K = ∏ μ in primitiveRoots n K, ... | [
537,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
] |
Mathlib/Control/Functor.lean | Functor.Comp.id_map | [
{
"state_after": "F : Type u → Type w\nG : Type v → Type u\ninst✝³ : Functor F\ninst✝² : Functor G\ninst✝¹ : LawfulFunctor F\ninst✝ : LawfulFunctor G\nα β γ : Type v\nx : F (G α)\n⊢ mk (mk x) = mk x",
"state_before": "F : Type u → Type w\nG : Type v → Type u\ninst✝³ : Functor F\ninst✝² : Functor G\ninst✝¹ :... | [
211,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
11
] |
Mathlib/Data/Finset/Fin.lean | Finset.card_attachFin | [] | [
46,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/Order/Heyting/Basic.lean | sdiff_sdiff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.134830\nα : Type u_1\nβ : Type ?u.134836\ninst✝ : GeneralizedCoheytingAlgebra α\na✝ b✝ c✝ d✝ a b c d : α\n⊢ (a \\ b) \\ c ≤ d ↔ a \\ (b ⊔ c) ≤ d",
"tactic": "simp_rw [sdiff_le_iff, sup_assoc]"
}
] | [
620,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
619,
1
] |
Mathlib/LinearAlgebra/Orientation.lean | Basis.orientation_neg_single | [
{
"state_after": "R : Type u_1\ninst✝⁵ : LinearOrderedCommRing R\nM : Type u_3\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\nι : Type u_2\ninst✝² : Fintype ι\ninst✝¹ : DecidableEq ι\ninst✝ : Nontrivial R\ne : Basis ι R M\ni : ι\n⊢ (-1 * ∏ x in Finset.univ \\ {i}, OfNat.ofNat 1 x)⁻¹ • Basis.orientation e = -Bas... | [
269,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Analysis/Calculus/Dslope.lean | eqOn_dslope_sub_smul | [] | [
81,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Data/Multiset/Nodup.lean | Multiset.Nodup.pmap | [] | [
164,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Std/Data/Int/Lemmas.lean | Int.neg_lt_neg | [
{
"state_after": "a b : Int\nh : a < b\nthis : 0 < -a + b\n⊢ -b < -a",
"state_before": "a b : Int\nh : a < b\n⊢ -b < -a",
"tactic": "have : 0 < -a + b := Int.add_left_neg a ▸ Int.add_lt_add_left h (-a)"
},
{
"state_after": "a b : Int\nh : a < b\nthis✝ : 0 < -a + b\nthis : 0 + -b < -a + b + -b\n⊢... | [
882,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
879,
11
] |
Mathlib/CategoryTheory/Sites/Closed.lean | CategoryTheory.GrothendieckTopology.isClosed_iff_close_eq_self | [
{
"state_after": "case mp\nC : Type u\ninst✝ : Category C\nJ₁ J₂ : GrothendieckTopology C\nX : C\nS : Sieve X\n⊢ IsClosed J₁ S → close J₁ S = S\n\ncase mpr\nC : Type u\ninst✝ : Category C\nJ₁ J₂ : GrothendieckTopology C\nX : C\nS : Sieve X\n⊢ close J₁ S = S → IsClosed J₁ S",
"state_before": "C : Type u\nins... | [
121,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPullback.of_isLimit | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝ : Category C\nP X Y Z : C\nfst : P ⟶ X\nsnd : P ⟶ Y\nf : X ⟶ Z\ng : Y ⟶ Z\nc : PullbackCone f g\nh : IsLimit c\n⊢ PullbackCone.fst c =\n (Iso.refl c.pt).hom ≫\n PullbackCone.fst\n (PullbackCone.mk (PullbackCone.fst c) (PullbackC... | [
229,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/GroupTheory/GroupAction/SubMulAction.lean | SubMulAction.ext | [] | [
135,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Data/Semiquot.lean | Semiquot.mem_pure' | [] | [
80,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Order/SuccPred/Limit.lean | Order.mem_range_pred_of_not_isPredLimit | [
{
"state_after": "case intro\nα : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : PredOrder α\na b✝ : α\nC : α → Sort ?u.17064\nh : ¬IsPredLimit a\nb : α\nhb : ¬IsMin b ∧ pred b = a\n⊢ a ∈ range pred",
"state_before": "α : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : PredOrder α\na b : α\nC : α → Sort ?u.17064\nh ... | [
352,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/Topology/Algebra/ConstMulAction.lean | IsClosed.smul_of_ne_zero | [] | [
361,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_eq_bot | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.188056\nβ₂ : Type ?u.188059\nγ : Type ?u.188062\nι : Sort u_2\nι' : Sort ?u.188068\nκ : ι → Sort ?u.188073\nκ' : ι' → Sort ?u.188078\ninst✝ : CompleteLinearOrder α\nf : ι → α\n⊢ iInf f = ⊥ ↔ ∀ (b : α), b > ⊥ → ∃ i, f i < b",
"tactic... | [
1696,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1695,
1
] |
Mathlib/Order/CompleteLattice.lean | le_sSup_of_le | [] | [
156,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.ssubset_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.114504\nγ : Type ?u.114507\ninst✝ : DecidableEq α\ns t u v : Finset α\na b : α\n⊢ s ⊂ t ↔ ∃ a x, insert a s ⊆ t",
"tactic": "exact_mod_cast @Set.ssubset_iff_insert α s t"
}
] | [
1180,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1179,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.vaddConst_toAffineEquiv | [] | [
717,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
715,
1
] |
Mathlib/Topology/Sets/Closeds.lean | TopologicalSpace.Opens.compl_compl | [] | [
214,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
8
] |
Mathlib/LinearAlgebra/Dimension.lean | rank_eq_of_surjective | [
{
"state_after": "no goals",
"state_before": "K : Type u\nV V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.586525\ninst✝⁶ : DivisionRing K\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module K V\ninst✝³ : AddCommGroup V'\ninst✝² : Module K V'\ninst✝¹ : Add... | [
1098,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1096,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasStrictDerivAt.ccosh | [] | [
238,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Tactic/Ring/RingNF.lean | Mathlib.Tactic.RingNF.int_rawCast_1 | [
{
"state_after": "no goals",
"state_before": "R✝ : Type ?u.76784\ninst✝¹ : CommSemiring R✝\nR : Type u_1\ninst✝ : Ring R\n⊢ Int.rawCast (Int.negOfNat 1) = -1",
"tactic": "simp [Int.negOfNat_eq]"
}
] | [
118,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_self_eq_norm_mul_norm | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.2233904\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx : E\n⊢ ↑re (inner x x) = ‖x‖ * ‖x‖",
... | [
1010,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1008,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | intervalIntegral.inv_mul_integral_comp_div_add | [] | [
279,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Order/CompleteBooleanAlgebra.lean | compl_sSup | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nκ : ι → Sort ?u.27525\ninst✝ : CompleteBooleanAlgebra α\na b : α\ns : Set α\nf : ι → α\n⊢ sSup sᶜ = ⨅ (i : α) (_ : i ∈ s), iᶜ",
"tactic": "simp only [sSup_eq_iSup, compl_iSup]"
}
] | [
310,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Algebra/Lie/Nilpotent.lean | LieSubmodule.lcs_le_self | [
{
"state_after": "case zero\nR : Type u\nL : Type v\nM : Type w\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : LieRingModule L M\ninst✝ : LieModule R L M\nk : ℕ\nN : LieSubmodule R L M\n⊢ lcs Nat.zero N ≤ N\n\ncase succ\nR : Type u\nL : ... | [
106,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | nonpos_of_mul_nonneg_right | [] | [
943,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
942,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.mem_image_const | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.63472\ninst✝ : DecidableEq β\nf g : α → β\ns : Finset α\nt : Finset β\na : α\nb c : β\n⊢ (∃ a, a ∈ s ∧ const α b a = c) ↔ Finset.Nonempty s ∧ b = c",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.63472\ninst✝ : DecidableEq β\nf g : α → β\n... | [
343,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Algebra/Regular/SMul.lean | IsSMulRegular.mul_iff_right | [] | [
114,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.support_mapRange | [
{
"state_after": "no goals",
"state_before": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝⁵ : (i : ι) → Zero (β i)\ninst✝⁴ : (i : ι) → (x : β i) → Decidable (x ≠ 0)\ninst✝³ : (i : ι) → Zero (β₁ i)\ninst✝² : (i : ι) → Zero (β₂ i)\ninst✝¹ : (i : ι) → (... | [
1196,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1195,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.diam_subsingleton | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.528785\nι : Type ?u.528788\ninst✝ : PseudoMetricSpace α\ns : Set α\nx y z : α\nhs : Set.Subsingleton s\n⊢ diam s = 0",
"tactic": "simp only [diam, EMetric.diam_subsingleton hs, ENNReal.zero_toReal]"
}
] | [
2586,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2585,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | lt_mul_of_lt_of_one_lt | [] | [
694,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
688,
1
] |
Mathlib/Order/Hom/Basic.lean | WithBot.toDualTopEquiv_bot | [] | [
1259,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1258,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.filter_eq_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.321633\nγ : Type ?u.321636\np q : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred q\ns : Finset α\n⊢ filter p s = s ↔ ∀ (x : α), x ∈ s → p x",
"tactic": "simp [Finset.ext_iff]"
}
] | [
2692,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2692,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.isNoetherianRing | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type ?u.642876\nσ : Type v\nM : Type w\ninst✝³ : CommRing R\ninst✝² : CommRing S\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\ninst : IsNoetherianRing R\nI : Ideal R[X]\n⊢ IsNoetherian R R",
"tactic": "infer_instance"
},
{
"state_afte... | [
961,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
886,
11
] |
Mathlib/Algebra/Category/ModuleCat/Adjunctions.lean | ModuleCat.Free.μ_natural | [
{
"state_after": "R : Type u\ninst✝ : CommRing R\nX Y X' Y' : Type u\nf : X ⟶ Y\ng : X' ⟶ Y'\n⊢ ((free R).map f ⊗ (free R).map g) ≫ (μ R Y Y').hom = (μ R X X').hom ≫ (free R).map (f ⊗ g)",
"state_before": "R : Type u\ninst✝ : CommRing R\nX Y X' Y' : Type u\nf : X ⟶ Y\ng : X' ⟶ Y'\n⊢ ((free R).map f ⊗ (free ... | [
110,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Order/Lattice.lean | le_sup_inf | [] | [
757,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
756,
1
] |
Mathlib/Topology/Basic.lean | isOpen_singleton_iff_punctured_nhds | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u\nβ : Type v\nι : Sort w\na✝ : α✝\ns s₁ s₂ t : Set α✝\np p₁ p₂ : α✝ → Prop\ninst✝¹ : TopologicalSpace α✝\nα : Type u_1\ninst✝ : TopologicalSpace α\na : α\n⊢ IsOpen {a} ↔ 𝓝[{a}ᶜ] a = ⊥",
"tactic": "rw [isOpen_singleton_iff_nhds_eq_pure, nhdsWithin... | [
1263,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1260,
1
] |
Mathlib/Data/Option/Basic.lean | Option.some_bind' | [] | [
86,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Algebra/Category/ModuleCat/Basic.lean | ModuleCat.comp_def | [] | [
246,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Data/Nat/Pairing.lean | Nat.unpair_zero | [
{
"state_after": "⊢ (let s := sqrt 0;\n if 0 - s * s < s then (0 - s * s, s) else (s, 0 - s * s - s)) =\n 0",
"state_before": "⊢ unpair 0 = 0",
"tactic": "rw [unpair]"
},
{
"state_after": "no goals",
"state_before": "⊢ (let s := sqrt 0;\n if 0 - s * s < s then (0 - s * s, s) else (s... | [
110,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsLUB.mono | [] | [
250,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | AffineIndependent.affineSpan_eq_top_iff_card_eq_finrank_add_one | [
{
"state_after": "case mp\nk : Type u_1\nV : Type u_2\nP : Type u_4\nι : Type u_3\ninst✝⁵ : DivisionRing k\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module k V\ninst✝² : AffineSpace V P\ninst✝¹ : FiniteDimensional k V\ninst✝ : Fintype ι\np : ι → P\nhi : AffineIndependent k p\n⊢ affineSpan k (Set.range p) = ⊤ → Fintype... | [
274,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.ofInt_im | [] | [
62,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Data/Finsupp/WellFounded.lean | Finsupp.Lex.wellFounded' | [] | [
55,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.sum.map_mul | [] | [
960,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
959,
1
] |
Mathlib/Order/MinMax.lean | AntitoneOn.map_min | [] | [
253,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Data/List/Basic.lean | List.map_fst_add_enum_eq_enumFrom | [] | [
3918,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3916,
1
] |
Mathlib/CategoryTheory/Linear/Basic.lean | CategoryTheory.Linear.homCongr_symm_apply | [] | [
180,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
src/lean/Init/Data/List/Basic.lean | List.length_set | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nas : List α\ni : Nat\na : α\n⊢ length (set as i a) = length as",
"tactic": "induction as generalizing i with\n| nil => rfl\n| cons x xs ih =>\n cases i with\n | zero => rfl\n | succ i => simp [set, ih]"
},
{
"st... | [
781,
31
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
775,
9
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.sum_apply | [
{
"state_after": "no goals",
"state_before": "V : Type ?u.446095\nV₁ : Type u_2\nV₂ : Type u_3\nV₃ : Type ?u.446104\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : SeminormedAddCommGroup V₁\ninst✝¹ : SeminormedAddCommGroup V₂\ninst✝ : SeminormedAddCommGroup V₃\nf✝ g : NormedAddGroupHom V₁ V₂\nι : Type u_1\ns :... | [
629,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
1
] |
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