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/Set/Intervals/Basic.lean | Set.Ico_eq_empty_of_le | [] | [
388,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/CategoryTheory/Limits/Preserves/Shapes/Biproducts.lean | CategoryTheory.Functor.inl_biprodComparison' | [] | [
347,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.subtype_map | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.130155\nγ : Type ?u.130158\np : α → Prop\ninst✝ : DecidablePred p\ns : Finset α\nx : α\n⊢ x ∈ map (Embedding.subtype p) (Finset.subtype p s) ↔ x ∈ filter p s",
"state_before": "α : Type u_1\nβ : Type ?u.130155\nγ : Type ?u.130158\np : α → Prop\ninst✝ : Dec... | [
684,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
681,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.prod_multiset_root_eq_finset_root | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np q : R[X]\n⊢ Multiset.prod (Multiset.map (fun a => X - ↑C a) (roots p)) =\n Finset.prod (Multiset.toFinset (roots p)) fun a => (X - ↑C a) ^ rootMultiplicity a p",
... | [
1073,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1070,
1
] |
Mathlib/Algebra/Group/Basic.lean | inv_eq_one_div | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.17881\nβ : Type ?u.17884\nG : Type u_1\ninst✝ : DivInvMonoid G\na b c x : G\n⊢ x⁻¹ = 1 / x",
"tactic": "rw [div_eq_mul_inv, one_mul]"
}
] | [
296,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Analysis/Complex/Liouville.lean | Differentiable.exists_eq_const_of_bounded | [] | [
135,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.liftPropOn_indep_chart | [
{
"state_after": "case h.e'_3\nH : Type u_1\nM : Type u_2\nH' : Type u_3\nM' : Type u_4\nX : Type ?u.31197\ninst✝⁸ : TopologicalSpace H\ninst✝⁷ : TopologicalSpace M\ninst✝⁶ : ChartedSpace H M\ninst✝⁵ : TopologicalSpace H'\ninst✝⁴ : TopologicalSpace M'\ninst✝³ : ChartedSpace H' M'\ninst✝² : TopologicalSpace X\nG... | [
360,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.lift_apply' | [] | [
1969,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1967,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.prod_singleton | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.11541\nα : Type u_1\nβ : Type ?u.11547\nγ : Type ?u.11550\ninst✝ : CommMonoid α\ns t : Multiset α\na✝ : α\nm : Multiset ι\nf g : ι → α\na : α\n⊢ prod {a} = a",
"tactic": "simp only [mul_one, prod_cons, ← cons_zero, eq_self_iff_true, prod_zero]"
... | [
107,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Analysis/InnerProductSpace/PiL2.lean | EuclideanSpace.inner_single_right | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nι' : Type ?u.652079\n𝕜 : Type u_2\ninst✝¹⁰ : IsROrC 𝕜\nE : Type ?u.652088\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : InnerProductSpace 𝕜 E\nE' : Type ?u.652108\ninst✝⁷ : NormedAddCommGroup E'\ninst✝⁶ : InnerProductSpace 𝕜 E'\nF : Type ?u.652126\n... | [
280,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Topology/ContinuousFunction/Algebra.lean | ContinuousMap.one_apply | [] | [
99,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.add_div_right | [
{
"state_after": "no goals",
"state_before": "x z : Nat\nH : 0 < z\n⊢ (x + z) / z = succ (x / z)",
"tactic": "rw [div_eq_sub_div H (Nat.le_add_left _ _), Nat.add_sub_cancel]"
}
] | [
565,
66
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
564,
9
] |
Mathlib/Computability/Primrec.lean | PrimrecPred.and | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.132958\nγ : Type ?u.132961\nδ : Type ?u.132964\nσ : Type ?u.132967\ninst✝⁶ : Primcodable α\ninst✝⁵ : Primcodable β\ninst✝⁴ : Primcodable γ\ninst✝³ : Primcodable δ\ninst✝² : Primcodable σ\np q : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ ... | [
734,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
732,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.curryLeft_compAlternatingMap | [] | [
1297,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1294,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.Path.insert_toList | [
{
"state_after": "α : Type u_1\nt : RBNode α\nv : α\np : Path α\n⊢ toList\n (match t with\n | nil => insertNew p v\n | node c a v_1 b => fill p (node c a v b)) =\n listL p ++ (toList (setRoot v t) ++ listR p)",
"state_before": "α : Type u_1\nt : RBNode α\nv : α\np : Path α\n⊢ toList (inser... | [
500,
42
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
498,
1
] |
Mathlib/RingTheory/Localization/Away/Basic.lean | selfZpow_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\ninst✝³ : CommRing R\nx : R\nB : Type u_1\ninst✝² : CommRing B\ninst✝¹ : Algebra R B\ninst✝ : IsLocalization.Away x B\n⊢ selfZpow x B 0 = 1",
"tactic": "simp [selfZpow_of_nonneg _ _ le_rfl]"
}
] | [
226,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.preimage_mul_preimage_subset | [
{
"state_after": "case intro.intro.intro.intro\nF : Type u_3\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.154622\ninst✝² : Mul α\ninst✝¹ : Mul β\ninst✝ : MulHomClass F α β\nm : F\ns✝ t✝ : Set α\ns t : Set β\nw✝¹ w✝ : α\nleft✝¹ : w✝¹ ∈ ↑m ⁻¹' s\nleft✝ : w✝ ∈ ↑m ⁻¹' t\n⊢ (fun x x_1 => x * x_1) w✝¹ w✝ ∈ ↑m ⁻¹' (s * t)... | [
1303,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1301,
1
] |
Mathlib/Data/PNat/Find.lean | PNat.find_lt_iff | [] | [
87,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.coe_smul | [] | [
1054,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1053,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.continuousAt_symm | [] | [
359,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/Algebra/Associated.lean | Associates.le_mul_right | [] | [
913,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
912,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.covby_succ_of_not_isMax | [] | [
250,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | Filter.EventuallyEq.hasFDerivAt_iff | [] | [
849,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
847,
1
] |
Mathlib/Data/Set/Prod.lean | Set.prod_eq_iff_eq | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.90755\nδ : Type ?u.90758\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\na : α\nb : β\nht : Set.Nonempty t\n⊢ s = ∅ ∧ s₁ = ∅ → s = s₁",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.90755\nδ : Type ?u.90758\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\na : α\nb :... | [
427,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/Algebra/DirectSum/Module.lean | DirectSum.sigmaLuncurry_apply | [] | [
277,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/Analysis/Asymptotics/AsymptoticEquivalent.lean | Asymptotics.IsEquivalent.isLittleO | [] | [
83,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.relabel_imp | [] | [
618,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
1
] |
Mathlib/Combinatorics/Catalan.lean | catalan_succ' | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ catalan (n + 1) = ∑ ij in Nat.antidiagonal n, catalan ij.fst * catalan ij.snd",
"tactic": "rw [catalan_succ, Nat.sum_antidiagonal_eq_sum_range_succ (fun x y => catalan x * catalan y) n,\n sum_range]"
}
] | [
78,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Std/Data/Fin/Lemmas.lean | USize.lt_def | [] | [
24,
73
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
24,
9
] |
Mathlib/Combinatorics/Additive/SalemSpencer.lean | rothNumberNat_isBigO_id | [] | [
523,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
522,
1
] |
Mathlib/Logic/Relation.lean | Relation.equivalence_join_reflTransGen | [] | [
647,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | LipschitzWith.norm_compLp_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nE : Type u_1\nF : Type u_2\nG : Type ?u.2588935\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : MeasureTheory.Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\ng : E → F\nc : ℝ≥0\nhg : Lipschit... | [
926,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
925,
1
] |
Mathlib/Data/Set/Pairwise/Basic.lean | Set.pairwise_empty | [] | [
88,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.mul_right | [
{
"state_after": "R : Type u\ninst✝ : CommSemiring R\nx y z : R\nH1 : IsCoprime y x\nH2 : IsCoprime z x\n⊢ IsCoprime (y * z) x",
"state_before": "R : Type u\ninst✝ : CommSemiring R\nx y z : R\nH1 : IsCoprime x y\nH2 : IsCoprime x z\n⊢ IsCoprime x (y * z)",
"tactic": "rw [isCoprime_comm] at H1 H2⊢"
},
... | [
116,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | MeasureTheory.locallyIntegrableOn_iff | [
{
"state_after": "X : Type u_1\nY : Type ?u.120325\nE : Type u_2\nR : Type ?u.120331\ninst✝⁶ : MeasurableSpace X\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : MeasurableSpace Y\ninst✝³ : TopologicalSpace Y\ninst✝² : NormedAddCommGroup E\nf : X → E\nμ : Measure X\ns : Set X\ninst✝¹ : LocallyCompactSpace X\ninst✝ : T2Sp... | [
116,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Order/Lattice.lean | ofDual_max | [] | [
982,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
981,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.tendsto_integral_approxOn_of_measurable | [
{
"state_after": "α : Type u_2\nE : Type u_1\nF : Type ?u.1273109\n𝕜 : Type ?u.1273112\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedSpace ℝ E\ninst✝¹¹ : CompleteSpace E\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : SMulCommClass ℝ 𝕜 E\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : N... | [
1389,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1381,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.bounded_range | [] | [
120,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Topology/MetricSpace/Contracting.lean | ContractingWith.restrict | [] | [
95,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_subset_Ioo_right | [] | [
501,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
500,
1
] |
Mathlib/Analysis/Normed/Field/Basic.lean | NormedField.exists_one_lt_norm | [] | [
726,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
725,
1
] |
Mathlib/Topology/Constructions.lean | isClosed_range_sigmaMk | [] | [
1484,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1483,
1
] |
Mathlib/LinearAlgebra/Finrank.lean | FiniteDimensional.rank_lt_of_finrank_lt | [
{
"state_after": "case hc\nK : Type u\nV : Type v\ninst✝⁴ : Ring K\ninst✝³ : AddCommGroup V\ninst✝² : Module K V\nV₂ : Type v'\ninst✝¹ : AddCommGroup V₂\ninst✝ : Module K V₂\nn : ℕ\nh : n < finrank K V\n⊢ ↑n < ℵ₀\n\ncase hd\nK : Type u\nV : Type v\ninst✝⁴ : Ring K\ninst✝³ : AddCommGroup V\ninst✝² : Module K V\n... | [
88,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Data/Polynomial/Module.lean | PolynomialModule.eval_lsingle | [] | [
288,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/CategoryTheory/Idempotents/Basic.lean | CategoryTheory.Idempotents.isIdempotentComplete_iff_idempotents_have_kernels | [
{
"state_after": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\n⊢ (∀ (X : C) (p : X ⟶ X), p ≫ p = p → HasEqualizer (𝟙 X) p) ↔ ∀ (X : C) (p : X ⟶ X), p ≫ p = p → HasKernel p",
"state_before": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\n⊢ IsIdempotentComplete C ↔ ∀ (X : C) (p : X ⟶... | [
120,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.coeff_zero_eq_constantCoeff_apply | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nφ : PowerSeries R\n⊢ ↑(coeff R 0) φ = ↑(constantCoeff R) φ",
"tactic": "rw [coeff_zero_eq_constantCoeff]"
}
] | [
1400,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1399,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.inv_mem | [] | [
583,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
582,
11
] |
Mathlib/Computability/Primrec.lean | Primrec.bind_decode_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_3\nγ : Type ?u.116843\nδ : Type ?u.116846\nσ : Type u_1\ninst✝⁴ : Primcodable α\ninst✝³ : Primcodable β\ninst✝² : Primcodable γ\ninst✝¹ : Primcodable δ\ninst✝ : Primcodable σ\nf : α → β → Option σ\nh : Primrec₂ fun a n => Option.bind (de... | [
658,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurableSet_lt | [] | [
545,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_pos | [] | [
398,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
11
] |
Mathlib/Topology/Sets/Order.lean | ClopenUpperSet.clopen | [] | [
52,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.FiniteAtFilter.inf_of_right | [] | [
4110,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4109,
1
] |
Mathlib/Order/Cover.lean | ofDual_wcovby_ofDual_iff | [] | [
144,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Algebra/Order/Monoid/ToMulBot.lean | WithZero.toMulBot_symm_bot | [] | [
48,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Analysis/Convex/Topology.lean | TopologicalAddGroup.pathConnectedSpace | [] | [
370,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
11
] |
Mathlib/CategoryTheory/Sites/CoverLifting.lean | CategoryTheory.RanIsSheafOfCoverLifting.helper | [
{
"state_after": "C D : Type u\ninst✝³ : Category C\ninst✝² : Category D\nA : Type w\ninst✝¹ : Category A\ninst✝ : HasLimits A\nJ : GrothendieckTopology C\nK : GrothendieckTopology D\nG : C ⥤ D\nhu : CoverLifting J K G\nℱ : Sheaf J A\nX : A\nU : D\nS : Sieve U\nhS : S ∈ GrothendieckTopology.sieves K U\nx : Fami... | [
253,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.min_le_right | [
{
"state_after": "a b : Nat\n⊢ (if a ≤ b then a else b) ≤ b",
"state_before": "a b : Nat\n⊢ min a b ≤ b",
"tactic": "rw [Nat.min_def]"
},
{
"state_after": "no goals",
"state_before": "a b : Nat\n⊢ (if a ≤ b then a else b) ≤ b",
"tactic": "split <;> simp [*]"
}
] | [
177,
100
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
177,
11
] |
Mathlib/Analysis/Calculus/Deriv/Mul.lean | HasStrictDerivAt.mul_const | [
{
"state_after": "case h.e'_7\n𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace 𝕜 F\nE : Type w\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL L₁ L₂ : Filter 𝕜\n𝕜' : Typ... | [
221,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.map_mk | [] | [
239,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Order/Monotone/Basic.lean | Subsingleton.monotone' | [] | [
491,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/Data/Int/Units.lean | Int.isUnit_iff_natAbs_eq | [
{
"state_after": "no goals",
"state_before": "n : ℤ\n⊢ IsUnit n ↔ natAbs n = 1",
"tactic": "simp [natAbs_eq_iff, isUnit_iff, Nat.cast_zero]"
}
] | [
91,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Analysis/InnerProductSpace/PiL2.lean | EuclideanSpace.dist_single_same | [] | [
298,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Topology/Bases.lean | TopologicalSpace.IsTopologicalBasis.insert_empty | [
{
"state_after": "case refine'_1\nα : Type u\nt : TopologicalSpace α\ns : Set (Set α)\nh : IsTopologicalBasis s\n⊢ ∀ (t₁ : Set α),\n t₁ ∈ insert ∅ s →\n ∀ (t₂ : Set α), t₂ ∈ insert ∅ s → ∀ (x : α), x ∈ t₁ ∩ t₂ → ∃ t₃, t₃ ∈ insert ∅ s ∧ x ∈ t₃ ∧ t₃ ⊆ t₁ ∩ t₂\n\ncase refine'_2\nα : Type u\nt : Topological... | [
94,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | HasFTaylorSeriesUpToOn.contDiffOn | [
{
"state_after": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nX : Type uX\ninst✝¹ : NormedAdd... | [
641,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.top_ne_nat | [] | [
692,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
9
] |
Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsLimit.OfNatIso.homOfCone_coneOfHom | [] | [
498,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.conj_neg_I | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nE : Type ?u.2812841\ninst✝ : IsROrC K\n⊢ ↑(starRingEnd K) (-I) = I",
"tactic": "rw [map_neg, conj_I, neg_neg]"
}
] | [
373,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.insert_inj_on | [] | [
1176,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1175,
1
] |
Mathlib/MeasureTheory/Group/Prod.lean | MeasureTheory.measure_eq_div_smul | [
{
"state_after": "case h\nG : Type u_1\ninst✝⁷ : MeasurableSpace G\ninst✝⁶ : Group G\ninst✝⁵ : MeasurableMul₂ G\nμ ν : Measure G\ninst✝⁴ : SigmaFinite ν\ninst✝³ : SigmaFinite μ\ns : Set G\ninst✝² : MeasurableInv G\ninst✝¹ : IsMulLeftInvariant μ\ninst✝ : IsMulLeftInvariant ν\nhs : MeasurableSet s\nh2s : ↑↑ν s ≠ ... | [
359,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.range_coprod | [] | [
1154,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1152,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.isUnit_of_isUnit_leadingCoeff_of_isUnit_map | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝² : Semiring R\ninst✝¹ : CommRing S\ninst✝ : IsDomain S\nφ : R →+* S\nf : R[X]\nhf : IsUnit (leadingCoeff f)\nH : IsUnit (map φ f)\ndz : degree (map φ f) = 0\n⊢ IsUnit f",
"state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\... | [
1237,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1222,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | PosMulReflectLT.toPosMulMono | [] | [
304,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/Data/List/Cycle.lean | List.next_get | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\nl : List α\nx : α\nx✝ : Nodup []\ni : Fin (length [])\n⊢ next [] (get [] i) (_ : get [] { val := ↑i, isLt := (_ : ↑i < length []) } ∈ []) =\n get [] { val := (↑i + 1) % length [], isLt := (_ : (↑i + 1) % length [] < length... | [
305,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Algebra/Order/Rearrangement.lean | MonovaryOn.sum_comp_perm_mul_le_sum_mul | [] | [
380,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.bliminf_sup_le_and | [] | [
907,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
906,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.single_mul_apply_of_not_exists_mul | [
{
"state_after": "k : Type u₁\nG : Type u₂\nR : Type ?u.524025\ninst✝¹ : Semiring k\ninst✝ : Mul G\nr : k\ng g' : G\nx : MonoidAlgebra k G\nh : ¬∃ d, g' = g * d\n⊢ (sum x fun a₂ b₂ => if g * a₂ = g' then r * b₂ else 0) = 0\n\nk : Type u₁\nG : Type u₂\nR : Type ?u.524025\ninst✝¹ : Semiring k\ninst✝ : Mul G\nr : ... | [
602,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.Perm.sigmaCongrRight_refl | [] | [
794,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
792,
9
] |
Mathlib/Algebra/Module/LinearMap.lean | Module.End.natCast_apply | [] | [
1074,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1073,
1
] |
Mathlib/Topology/Basic.lean | isClosed_of_closure_subset | [
{
"state_after": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns✝ s₁ s₂ t : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\ns : Set α\nh : closure s ⊆ s\n⊢ IsClosed (closure s)",
"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✝ : TopologicalSpace... | [
477,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
1
] |
Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean | MeasureTheory.FiniteMeasure.toMeasure_normalize_eq_of_nonzero | [
{
"state_after": "case h\nΩ : Type u_1\ninst✝ : Nonempty Ω\nm0 : MeasurableSpace Ω\nμ : FiniteMeasure Ω\nnonzero : μ ≠ 0\ns : Set Ω\n_s_mble : MeasurableSet s\n⊢ ↑↑↑(normalize μ) s = ↑↑↑((mass μ)⁻¹ • μ) s",
"state_before": "Ω : Type u_1\ninst✝ : Nonempty Ω\nm0 : MeasurableSpace Ω\nμ : FiniteMeasure Ω\nnonze... | [
374,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Std/Data/Nat/Gcd.lean | Nat.div_gcd_pos_of_pos_right | [] | [
101,
99
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
100,
1
] |
Mathlib/Analysis/Complex/Circle.lean | ne_zero_of_mem_circle | [] | [
73,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.BoundedFormula.realize_toPrenexImp | [
{
"state_after": "L : Language\nL' : Language\nM : Type w\nN : Type ?u.197102\nP : Type ?u.197105\ninst✝³ : Structure L M\ninst✝² : Structure L N\ninst✝¹ : Structure L P\nα : Type u'\nβ : Type v'\nn l : ℕ\nφ✝ ψ : BoundedFormula L α l\nθ : BoundedFormula L α (Nat.succ l)\nv✝ : α → M\nxs✝ : Fin l → M\ninst✝ : Non... | [
553,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.union_subset_right | [] | [
1420,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1419,
1
] |
Mathlib/Data/Nat/Lattice.lean | Nat.nonempty_of_sInf_eq_succ | [] | [
99,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Analysis/Calculus/Deriv/Inv.lean | deriv_div | [] | [
242,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/GroupTheory/SpecificGroups/Cyclic.lean | IsCyclic.iff_exponent_eq_card | [] | [
586,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
584,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.mem_toSubfield | [] | [
119,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelEmbedding.trans_apply | [] | [
314,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Algebra/Order/UpperLower.lean | lowerClosure_mul | [
{
"state_after": "α : Type u_1\ninst✝ : OrderedCommGroup α\ns t : Set α\na : α\n⊢ t * ↑(lowerClosure s) = ↑(lowerClosure (t * s))",
"state_before": "α : Type u_1\ninst✝ : OrderedCommGroup α\ns t : Set α\na : α\n⊢ ↑(lowerClosure s) * t = ↑(lowerClosure (s * t))",
"tactic": "simp_rw [mul_comm _ t]"
},
... | [
313,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/Analysis/Asymptotics/AsymptoticEquivalent.lean | Asymptotics.isEquivalent_zero_iff_isBigO_zero | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝ : NormedAddCommGroup β\nu v w : α → β\nl : Filter α\nh : u =O[l] 0\n⊢ u ~[l] 0",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝ : NormedAddCommGroup β\nu v w : α → β\nl : Filter α\n⊢ u ~[l] 0 ↔ u =O[l] 0",
"tactic": "refine' ⟨IsEquivalent.isBigO, f... | [
132,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Data/List/Chain.lean | List.chain'_isInfix | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nR r : α → α → Prop\nl✝ l₁ l₂ : List α\na✝ b✝ a b : α\nl : List α\n⊢ [] ++ [a, b] ++ l = a :: b :: l",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nR r : α → α → Prop\nl✝ l₁ l₂ :... | [
212,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Analysis/Normed/MulAction.lean | dist_smul_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\ninst✝³ : SeminormedAddGroup α\ninst✝² : SeminormedAddGroup β\ninst✝¹ : SMulZeroClass α β\ninst✝ : BoundedSMul α β\ns : α\nx y : β\n⊢ dist (s • x) (s • y) ≤ ‖s‖ * dist x y",
"tactic": "simpa only [dist_eq_norm, sub_zero] using dist... | [
42,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Logic/Unique.lean | Unique.subsingleton_unique' | [
{
"state_after": "case e_toInhabited.e_default\nα : Sort u_1\nx : α\nh : ∀ (a : α), a = default\ny : α\nuniq✝ : ∀ (a : α), a = default\n⊢ x = y",
"state_before": "α : Sort u_1\nx : α\nh : ∀ (a : α), a = default\ny : α\nuniq✝ : ∀ (a : α), a = default\n⊢ { toInhabited := { default := x }, uniq := h } = { toIn... | [
169,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
11
] |
Mathlib/Data/Nat/Prime.lean | Nat.prime_def_lt | [] | [
119,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | hasSum_single | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.38564\nδ : Type ?u.38567\ninst✝¹ : AddCommMonoid α\ninst✝ : TopologicalSpace α\nf✝ g : β → α\na b✝ : α\ns : Finset β\nf : β → α\nb : β\nhf : ∀ (b' : β), b' ≠ b → f b' = 0\nthis : HasSum f (∑ b' in {b}, f b')\n⊢ HasSum f (f... | [
205,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.monomial_neg | [
{
"state_after": "no goals",
"state_before": "R : Type u\na✝ b : R\nm n✝ : ℕ\ninst✝ : Ring R\nn : ℕ\na : R\n⊢ ↑(monomial n) (-a) = -↑(monomial n) a",
"tactic": "rw [eq_neg_iff_add_eq_zero, ← monomial_add, neg_add_self, monomial_zero_right]"
}
] | [
1173,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1172,
1
] |
Mathlib/LinearAlgebra/Matrix/Charpoly/LinearMap.lean | LinearMap.exists_monic_and_aeval_eq_zero | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.205232\ninst✝⁴ : Fintype ι\nM : Type u_2\ninst✝³ : AddCommGroup M\nR : Type u_1\ninst✝² : CommRing R\ninst✝¹ : Module R M\nI : Ideal R\nb : ι → M\nhb : Submodule.span R (Set.range b) = ⊤\ninst✝ : Module.Finite R M\nf : Module.End R M\n⊢ range f ≤ ⊤ •... | [
253,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Algebra/Category/ModuleCat/Monoidal/Closed.lean | ModuleCat.ihom_coev_app | [] | [
101,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Topology/Bornology/Constructions.lean | Bornology.isBounded_image_subtype_val | [] | [
141,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.