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/NormedSpace/AddTorsor.lean | dist_midpoint_midpoint_le | [
{
"state_after": "α : Type ?u.99524\nV : Type u_1\nP : Type ?u.99530\nW : Type ?u.99533\nQ : Type ?u.99536\ninst✝⁷ : SeminormedAddCommGroup V\ninst✝⁶ : PseudoMetricSpace P\ninst✝⁵ : NormedAddTorsor V P\ninst✝⁴ : NormedAddCommGroup W\ninst✝³ : MetricSpace Q\ninst✝² : NormedAddTorsor W Q\ninst✝¹ : NormedSpace ℝ V... | [
271,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Data/List/Basic.lean | List.reverse_inj | [] | [
629,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
1
] |
Mathlib/Data/Num/Lemmas.lean | PosNum.to_nat_pos | [] | [
139,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.ext | [] | [
325,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
11
] |
Mathlib/MeasureTheory/Covering/LiminfLimsup.lean | blimsup_thickening_mul_ae_eq_aux | [
{
"state_after": "α : Type u_1\ninst✝⁵ : MetricSpace α\ninst✝⁴ : SecondCountableTopology α\ninst✝³ : MeasurableSpace α\ninst✝² : BorelSpace α\nμ : MeasureTheory.Measure α\ninst✝¹ : IsLocallyFiniteMeasure μ\ninst✝ : IsUnifLocDoublingMeasure μ\np : ℕ → Prop\ns : ℕ → Set α\nM : ℝ\nhM : 0 < M\nr : ℕ → ℝ\nhr : Tends... | [
257,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_div | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nE : Type ?u.940098\nF : Type ?u.940101\n𝕜 : Type ?u.940104\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace ℝ E\ninst✝⁷ : CompleteSpace E\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedSpace 𝕜 E\ninst✝⁴ : SMulCommClass ℝ 𝕜 E\ninst✝³ : ... | [
915,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
913,
1
] |
Mathlib/Data/Polynomial/Expand.lean | Polynomial.expand_eq_C | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹ : CommSemiring R\nS : Type v\ninst✝ : CommSemiring S\np✝ q p : ℕ\nhp : 0 < p\nf : R[X]\nr : R\n⊢ ↑(expand R p) f = ↑C r ↔ f = ↑C r",
"tactic": "rw [← expand_C, expand_inj hp, expand_C]"
}
] | [
150,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Algebra/Algebra/Tower.lean | IsScalarTower.of_algebraMap_eq | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nA : Type w\nB : Type u₁\nM : Type v₁\ninst✝⁷ : CommSemiring R\ninst✝⁶ : CommSemiring S\ninst✝⁵ : Semiring A\ninst✝⁴ : Semiring B\ninst✝³ : Algebra R S\ninst✝² : Algebra S A\ninst✝¹ : Algebra S B\ninst✝ : Algebra R A\nh : ∀ (x : R), ↑(alge... | [
88,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/LinearAlgebra/TensorPower.lean | TensorPower.galgebra_toFun_def | [] | [
298,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/CategoryTheory/Preadditive/Biproducts.lean | CategoryTheory.Limits.biproduct.lift_desc | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝³ : Category C\ninst✝² : Preadditive C\nJ : Type\ninst✝¹ : Fintype J\nf : J → C\ninst✝ : HasBiproduct f\nT U : C\ng : (j : J) → T ⟶ f j\nh : (j : J) → f j ⟶ U\n⊢ lift g ≫ desc h = ∑ j : J, g j ≫ h j",
"tactic": "simp [biproduct.lift_eq, bipr... | [
232,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.coprod.hom_ext | [] | [
599,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
1
] |
Mathlib/CategoryTheory/Idempotents/Biproducts.lean | CategoryTheory.Idempotents.Karoubi.karoubi_hasFiniteBiproducts | [
{
"state_after": "C : Type u_1\ninst✝² : Category C\ninst✝¹ : Preadditive C\ninst✝ : HasFiniteBiproducts C\nn : ℕ\nF : Fin n → Karoubi C\n⊢ (Finset.sum Finset.univ fun j => Bicone.π (Biproducts.bicone F) j ≫ Bicone.ι (Biproducts.bicone F) j) =\n 𝟙 (Biproducts.bicone F).pt",
"state_before": "C : Type u_1... | [
91,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Analysis/Convex/SpecificFunctions/Deriv.lean | deriv2_sqrt_mul_log | [
{
"state_after": "x : ℝ\n⊢ deriv (fun x => (2 + log x) / (2 * sqrt x)) x = -log x / (↑4 * sqrt x ^ 3)",
"state_before": "x : ℝ\n⊢ (deriv^[2]) (fun x => sqrt x * log x) x = -log x / (↑4 * sqrt x ^ 3)",
"tactic": "simp only [Nat.iterate, deriv_sqrt_mul_log']"
},
{
"state_after": "case inl\nx : ℝ\n... | [
153,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Algebra/Free.lean | Magma.AssocQuotient.lift_of | [] | [
415,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.Measure.pi_noAtoms | [] | [
549,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.min'_erase_ne_self | [] | [
1548,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1547,
1
] |
Mathlib/Topology/SubsetProperties.lean | isClopen_iff_frontier_eq_empty | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.171474\nπ : ι → Type ?u.171479\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns✝ t s : Set α\n⊢ interior s = s ∧ closure s = s ↔ closure s ⊆ interior s",
"state_before": "α : Type u\nβ : Type v\nι : Type ?u.171474\nπ : ι → Type ?u.171479\ninst... | [
1547,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1543,
1
] |
Mathlib/Data/List/Sigma.lean | List.keys_nil | [] | [
51,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Order/Disjoint.lean | symmetric_disjoint | [] | [
57,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.piecewise_idem_left | [] | [
2517,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2515,
1
] |
Std/Data/Range/Lemmas.lean | Std.Range.mem_range'_elems | [
{
"state_after": "case intro.intro\nr : Range\ni : Nat\nh' : i < numElems r\nh : r.start + r.step * i ∈ List.range' r.start (numElems r) r.step\n⊢ r.start + r.step * i ∈ r",
"state_before": "x : Nat\nr : Range\nh : x ∈ List.range' r.start (numElems r) r.step\n⊢ x ∈ r",
"tactic": "obtain ⟨i, h', rfl⟩ := ... | [
41,
74
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
34,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.reindex_trans | [] | [
2572,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2569,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.right_vsub_lineMap | [
{
"state_after": "no goals",
"state_before": "k : Type u_3\nV1 : Type u_1\nP1 : Type u_2\nV2 : Type ?u.565275\nP2 : Type ?u.565278\nV3 : Type ?u.565281\nP3 : Type ?u.565284\nV4 : Type ?u.565287\nP4 : Type ?u.565290\ninst✝¹² : Ring k\ninst✝¹¹ : AddCommGroup V1\ninst✝¹⁰ : Module k V1\ninst✝⁹ : AffineSpace V1 ... | [
651,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
650,
1
] |
Mathlib/Order/Heyting/Basic.lean | compl_le_compl | [] | [
907,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
906,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasurableEquiv.map_symm_map | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.2129036\nδ : Type ?u.2129039\nι : Type ?u.2129042\nR : Type ?u.2129045\nR' : Type ?u.2129048\ninst✝¹ : MeasurableSpace α\ninst✝ : MeasurableSpace β\nμ : MeasureTheory.Measure α\nν : MeasureTheory.Measure β\ne : α ≃ᵐ β\n⊢ M... | [
4298,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4297,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.eventually_all_finset | [] | [
1176,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1174,
9
] |
Mathlib/Data/Nat/WithBot.lean | Nat.WithBot.lt_one_iff_le_zero | [
{
"state_after": "no goals",
"state_before": "x : WithBot ℕ\n⊢ ¬x < 1 ↔ ¬x ≤ 0",
"tactic": "simpa using one_le_iff_zero_lt"
}
] | [
83,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Data/Fintype/BigOperators.lean | Fin.prod_univ_eq_prod_range | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.51670\nγ : Type ?u.51673\ninst✝ : CommMonoid α\nf : ℕ → α\nn : ℕ\n⊢ ∀ (x : ℕ), x < n ↔ x ∈ range n",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.51670\nγ : Type ?u.51673\ni... | [
235,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.nondegenerate_congr_iff | [
{
"state_after": "case h.e'_6\nR : Type ?u.1410438\nM : Type ?u.1410441\ninst✝¹⁶ : Semiring R\ninst✝¹⁵ : AddCommMonoid M\ninst✝¹⁴ : Module R M\nR₁ : Type ?u.1410477\nM₁ : Type ?u.1410480\ninst✝¹³ : Ring R₁\ninst✝¹² : AddCommGroup M₁\ninst✝¹¹ : Module R₁ M₁\nR₂ : Type u_1\nM₂ : Type u_2\ninst✝¹⁰ : CommSemiring R... | [
1309,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1305,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.setRed_toList | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nt : RBNode α\n⊢ toList (setRed t) = toList t",
"tactic": "cases t <;> simp [setRed]"
}
] | [
417,
28
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
416,
9
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.isBigOWith_sub | [] | [
681,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
679,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.coe_of_injective_castLE_symm | [
{
"state_after": "n✝ m n k : ℕ\nh : n ≤ k\ni : Fin k\nhi : i ∈ Set.range ↑(castLE h)\n⊢ ↑(↑(castLE ?h) (↑(Equiv.ofInjective ↑(castLE h) (_ : Injective ↑(castLE h))).symm { val := i, property := hi })) = ↑i\n\ncase h\nn✝ m n k : ℕ\nh : n ≤ k\ni : Fin k\nhi : i ∈ Set.range ↑(castLE h)\n⊢ n ≤ ?m.75230\n\nn✝ m n k ... | [
1040,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1037,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.union_zeroLocus | [
{
"state_after": "R : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\ns s' : Set R\n⊢ zeroLocus s ∪ zeroLocus s' = zeroLocus ↑(Ideal.span s) ∪ zeroLocus ↑(Ideal.span s')",
"state_before": "R : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\ns s' : Set R\n⊢ zeroLocus s ∪ zeroLocus s... | [
365,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.sumElim_inl | [] | [
1324,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1322,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsGLB.exists_between | [] | [
1134,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1132,
1
] |
Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.mk'_eq_mk' | [
{
"state_after": "no goals",
"state_before": "G : Type u\ninst✝¹ : Group G\nN : Subgroup G\nnN : Subgroup.Normal N\nH : Type v\ninst✝ : Group H\nx y : G\n⊢ x⁻¹ * y ∈ N ↔ ∃ z, z ∈ N ∧ x * z = y",
"tactic": "simp only [← _root_.eq_inv_mul_iff_mul_eq, exists_prop, exists_eq_right]"
}
] | [
104,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Order/RelClasses.lean | antisymm_of | [] | [
53,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Data/MvPolynomial/Derivation.lean | MvPolynomial.derivation_ext | [] | [
102,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.floor_eq_on_Ico' | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.41083\nα : Type u_1\nβ : Type ?u.41089\ninst✝¹ : LinearOrderedSemiring α\ninst✝ : FloorSemiring α\na : α\nn✝ n : ℕ\nx : α\nhx : x ∈ Ico (↑n) (↑n + 1)\n⊢ ↑⌊x⌋₊ = ↑n",
"tactic": "exact_mod_cast floor_eq_on_Ico n x hx"
}
] | [
256,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Analysis/Complex/OperatorNorm.lean | Complex.ofRealClm_norm | [] | [
78,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Algebra/Algebra/Operations.lean | SubMulAction.algebraMap_mem | [] | [
61,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.dirac_caratheodory | [
{
"state_after": "case pos\nα : Type u_1\na : α\ns : Set α\nx✝ : MeasurableSet s\nt : Set α\nht : a ∈ t\n⊢ ↑(dirac a) t = ↑(dirac a) (t ∩ s) + ↑(dirac a) (t \\ s)\n\ncase neg\nα : Type u_1\na : α\ns : Set α\nx✝ : MeasurableSet s\nt : Set α\nht : ¬a ∈ t\n⊢ ↑(dirac a) t = ↑(dirac a) (t ∩ s) + ↑(dirac a) (t \\ s)"... | [
1130,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1127,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toNNReal_iInf | [
{
"state_after": "case inl\nα : Type ?u.838531\nβ : Type ?u.838534\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nι : Sort u_1\nf g : ι → ℝ≥0∞\nhf : ∀ (i : ι), f i ≠ ⊤\nh✝ : IsEmpty ι\n⊢ ENNReal.toNNReal (iInf f) = ⨅ (i : ι), ENNReal.toNNReal (f i)\n\ncase inr\nα : Type ?u.838531\nβ : Type ?u.838534\na b c d : ℝ≥0∞\nr p q : ℝ≥0... | [
2352,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2348,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_inter_add_diff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1027905\nγ : Type ?u.1027908\nδ : Type ?u.1027911\nm : MeasurableSpace α\nμ ν : Measure α\nB : Set α\nf : α → ℝ≥0∞\nA : Set α\nhB : MeasurableSet B\n⊢ ((∫⁻ (x : α) in A ∩ B, f x ∂μ) + ∫⁻ (x : α) in A \\ B, f x ∂μ) = ∫⁻ (x : α) in A, f x... | [
1234,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1232,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.mem_map_equiv | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\ninst✝² : NonUnitalNonAssocSemiring R\nM : Subsemigroup R\ninst✝¹ : NonUnitalNonAssocSemiring S\ninst✝ : NonUnitalNonAssocSemiring T\nf : R ≃+* S\nK : NonUnitalSubsemiring R\nx : S\n⊢ x ∈ map (↑f) K ↔ ↑(RingEquiv.symm f) x ∈ K"... | [
595,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/CategoryTheory/GlueData.lean | CategoryTheory.GlueData.t_inv | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nC' : Type u₂\ninst✝ : Category C'\nD : GlueData C\ni j : D.J\neq : (pullbackSymmetry (f D i i) (f D i j)).hom = pullback.snd ≫ inv pullback.fst\n⊢ t D i j ≫ t D j i = 𝟙 (V D (i, j))",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nC' : Type u₂\ninst✝ ... | [
108,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Order/Bounds/Basic.lean | image2_lowerBounds_lowerBounds_subset | [
{
"state_after": "case intro.intro.intro.intro\nα : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : Preorder γ\nf : α → β → γ\ns : Set α\nt : Set β\na✝ : α\nb✝ : β\nh₀ : ∀ (b : β), Monotone (swap f b)\nh₁ : ∀ (a : α), Monotone (f a)\na : α\nb : β\nha : a ∈ lowerBoun... | [
1375,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1372,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.mem_closedBall' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.32147\nι : Type ?u.32150\ninst✝ : PseudoMetricSpace α\nx y z : α\nδ ε ε₁ ε₂ : ℝ\ns : Set α\n⊢ y ∈ closedBall x ε ↔ dist x y ≤ ε",
"tactic": "rw [dist_comm, mem_closedBall]"
}
] | [
484,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.OpenNhdsOf.toOpens_injective | [] | [
431,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/Data/Nat/Count.lean | Nat.count_eq_card_filter_range | [
{
"state_after": "p : ℕ → Prop\ninst✝ : DecidablePred p\nn : ℕ\n⊢ List.length (List.filter (fun b => decide (p b)) (List.range n)) = card (filter p (range n))",
"state_before": "p : ℕ → Prop\ninst✝ : DecidablePred p\nn : ℕ\n⊢ count p n = card (filter p (range n))",
"tactic": "rw [count, List.countp_eq_l... | [
59,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Algebra/Ring/Idempotents.lean | IsIdempotentElem.of_isIdempotent | [] | [
48,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | integrableOn_Icc_iff_integrableOn_Ioc | [
{
"state_after": "α : Type u_1\nβ : Type ?u.3994641\nE : Type u_2\nF : Type ?u.3994647\ninst✝⁴ : MeasurableSpace α\ninst✝³ : NormedAddCommGroup E\ninst✝² : PartialOrder α\ninst✝¹ : MeasurableSingletonClass α\nf : α → E\nμ : MeasureTheory.Measure α\na b : α\ninst✝ : NoAtoms μ\n⊢ 0 ≠ ⊤",
"state_before": "α : ... | [
679,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
677,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | Memℓp.finset_sum | [
{
"state_after": "α : Type u_2\nE : α → Type u_3\np q : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nι : Type u_1\ns : Finset ι\nf : ι → (i : α) → E i\nhf : ∀ (i : ι), i ∈ s → Memℓp (f i) p\nthis : DecidableEq ι\n⊢ Memℓp (fun a => ∑ i in s, f i a) p",
"state_before": "α : Type u_2\nE : α → Type u_3\np ... | [
261,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.Compacts.coe_inf | [] | [
113,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Data/Rat/Lemmas.lean | Rat.exists_eq_mul_div_num_and_eq_mul_div_den | [
{
"state_after": "no goals",
"state_before": "n d : ℤ\nd_ne_zero : d ≠ 0\n⊢ ↑n / ↑d = n /. d",
"tactic": "rw [← Rat.divInt_eq_div]"
}
] | [
123,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | sq_eq_sq_iff_abs_eq_abs | [
{
"state_after": "no goals",
"state_before": "β : Type ?u.267249\nA : Type ?u.267252\nG : Type ?u.267255\nM : Type ?u.267258\nR : Type u_1\ninst✝ : LinearOrderedRing R\nx✝ y✝ x y : R\n⊢ x ^ 2 = y ^ 2 ↔ abs x = abs y",
"tactic": "simp only [le_antisymm_iff, sq_le_sq]"
}
] | [
726,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
725,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.balance'_lemma | [
{
"state_after": "case inl.intro.inl\nα✝ : Type ?u.331855\ninst✝ : Preorder α✝\nα : Type u_1\nl : Ordnode α\nl' : ℕ\nr : Ordnode α\nhl : Nat.dist (size l) l' ≤ 1\nh : l' + size r ≤ 1\n⊢ size r ≤ 3 * (size l + 1)\n\ncase inl.intro.inr.intro\nα✝ : Type ?u.331855\ninst✝ : Preorder α✝\nα : Type u_1\nl : Ordnode α\n... | [
1332,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1316,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.SimpleFunc.setToL1S_congr_measure | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type ?u.490028\nG : Type ?u.490031\n𝕜 : Type ?u.490034\np : ℝ≥0∞\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace ℝ F\ninst✝⁴ : NormedAddCommGroup F'\ninst✝³ : NormedSpace ℝ F'\ninst✝² ... | [
731,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
723,
1
] |
Mathlib/Logic/Basic.lean | exists_exists_eq_and | [] | [
787,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
785,
9
] |
Mathlib/Algebra/Homology/ImageToKernel.lean | homology.map_desc | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.113120\nV : Type u\ninst✝¹⁹ : Category V\ninst✝¹⁸ : HasZeroMorphisms V\nA B C : V\nf : A ⟶ B\ninst✝¹⁷ : HasImage f\ng : B ⟶ C\ninst✝¹⁶ : HasKernel g\nw : f ≫ g = 0\nA' B' C' : V\nf' : A' ⟶ B'\ninst✝¹⁵ : HasImage f'\ng' : B' ⟶ C'\ninst✝¹⁴ : HasKernel ... | [
298,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.range_prod_eq | [
{
"state_after": "R : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nM₅ : Type ?u.481077\nM₆ : Type ?u.481080\ninst✝⁶ : Ring R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : AddCommGroup M₂\ninst✝³ : AddCommGroup M₃\ninst✝² : Module R M\ninst✝¹ :... | [
853,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
842,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | isConnected_Iio | [] | [
478,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/Topology/ContinuousFunction/Ordered.lean | ContinuousMap.coe_IccExtend | [] | [
166,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Topology/MetricSpace/Antilipschitz.lean | AntilipschitzWith.subsingleton | [] | [
215,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
11
] |
Mathlib/Computability/TuringMachine.lean | Turing.TM1to0.tr_respects | [
{
"state_after": "case none\nΓ : Type u_3\ninst✝² : Inhabited Γ\nΛ : Type u_2\ninst✝¹ : Inhabited Λ\nσ : Type u_1\ninst✝ : Inhabited σ\nM : Λ → Stmt₁\nx✝ : Cfg₁\nv : σ\nT : Tape Γ\n⊢ FRespects (TM0.step (tr M)) (fun c₁ => trCfg M c₁) (trCfg M { l := none, var := v, Tape := T })\n (TM1.step M { l := none, var... | [
1516,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1502,
1
] |
Mathlib/ModelTheory/Basic.lean | Equiv.toEquiv_inducedStructureEquiv | [] | [
1043,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1041,
1
] |
Mathlib/Analysis/Calculus/Deriv/Comp.lean | HasDerivWithinAt.scomp_hasDerivAt | [] | [
87,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Data/Finset/Lattice.lean | map_finset_sup | [
{
"state_after": "no goals",
"state_before": "F : Type u_2\nα : Type u_3\nβ : Type u_1\nγ : Type ?u.18510\nι : Type u_4\nκ : Type ?u.18516\ninst✝⁴ : SemilatticeSup α\ninst✝³ : OrderBot α\ns✝¹ s₁ s₂ : Finset β\nf✝ g✝ : β → α\na : α\ninst✝² : SemilatticeSup β\ninst✝¹ : OrderBot β\ninst✝ : SupBotHomClass F α β... | [
102,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Combinatorics/SetFamily/Compression/Down.lean | Down.erase_mem_compression | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\n𝒜 ℬ : Finset (Finset α)\ns : Finset α\na : α\nhs : s ∈ 𝒜\n⊢ erase s a ∈ 𝒜 ∨ ¬erase s a ∈ 𝒜 ∧ insert a (erase s a) ∈ 𝒜",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\n𝒜 ℬ : Finset (Finset α)\ns : Finset α\na : α\nhs : s ∈ 𝒜\n⊢ erase s a ∈ ... | [
180,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Algebra/Homology/Opposite.lean | imageToKernel_unop | [
{
"state_after": "no goals",
"state_before": "V : Type ?u.7533\ninst✝¹ : Category V\ninst✝ : Abelian V\nX Y Z : Vᵒᵖ\nf : X ⟶ Y\ng : Y ⟶ Z\nw : f ≫ g = 0\n⊢ g.unop ≫ f.unop = 0",
"tactic": "rw [← unop_comp, w, unop_zero]"
},
{
"state_after": "no goals",
"state_before": "V : Type ?u.7533\ninst... | [
65,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean | SimpleGraph.ComponentCompl.hom_eq_iff_le | [] | [
194,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Submodule.dualAnnihilator_bot | [] | [
853,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
852,
1
] |
Mathlib/CategoryTheory/Subobject/FactorThru.lean | CategoryTheory.Subobject.factorThru_add_sub_factorThru_right | [
{
"state_after": "case h\nC : Type u₁\ninst✝² : Category C\nX✝ Y✝ Z : C\nD : Type u₂\ninst✝¹ : Category D\ninst✝ : Preadditive C\nX Y : C\nP : Subobject Y\nf g : X ⟶ Y\nw : Factors P (f + g)\nwg : Factors P g\n⊢ (factorThru P (f + g) w - factorThru P g wg) ≫ arrow P = factorThru P f (_ : Factors P f) ≫ arrow P"... | [
210,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.add_one_eq | [] | [
816,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
815,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.smul_univ | [
{
"state_after": "F : Type ?u.857977\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.857986\ninst✝³ : DecidableEq β\ninst✝² : Group α\ninst✝¹ : MulAction α β\ns✝ t : Finset β\na : α\nb : β\ninst✝ : Fintype β\ns : Finset α\nhs : Finset.Nonempty s\n⊢ ↑s • Set.univ = Set.univ",
"state_before": "F : Type ?u.857977\nα ... | [
2018,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2015,
1
] |
Mathlib/Computability/Primrec.lean | Nat.Primrec'.idv | [] | [
1428,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1427,
1
] |
Mathlib/Data/ENat/Basic.lean | ENat.recTopCoe_coe | [] | [
134,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.ncard_univ | [
{
"state_after": "case inl\nα✝ : Type ?u.4996\nβ : Type ?u.4999\ns t : Set α✝\na b x y : α✝\nf : α✝ → β\nα : Type u_1\nh : Finite α\n⊢ ncard univ = Nat.card α\n\ncase inr\nα✝ : Type ?u.4996\nβ : Type ?u.4999\ns t : Set α✝\na b x y : α✝\nf : α✝ → β\nα : Type u_1\nh : Infinite α\n⊢ ncard univ = Nat.card α",
"... | [
105,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.blunt_strictlyPositive | [] | [
631,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.piecewise_le_of_le_of_le | [] | [
2559,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2557,
1
] |
Std/Data/List/Lemmas.lean | List.getLast?_nil | [] | [
475,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
475,
9
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | vectorSpan_eq_span_vsub_set_right | [
{
"state_after": "k : Type u_3\nV : Type u_2\nP : Type u_1\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type ?u.254707\ns : Set P\np : P\nhp : p ∈ s\n⊢ Submodule.span k (s -ᵥ s) = Submodule.span k ((fun x => x -ᵥ p) '' s)",
"state_before": "k : Type u_3\nV : T... | [
1049,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1039,
1
] |
Mathlib/Order/Filter/Extr.lean | IsMaxFilter.filter_mono | [] | [
265,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.NullMeasurableSet.measurable_of_complete | [] | [
472,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup₂_eq_bot | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.88303\nβ₂ : Type ?u.88306\nγ : Type ?u.88309\nι : Sort u_2\nι' : Sort ?u.88315\nκ : ι → Sort u_3\nκ' : ι' → Sort ?u.88325\ninst✝ : CompleteLattice α\nf✝ g s t : ι → α\na b : α\nf : (i : ι) → κ i → α\n⊢ (⨆ (i : ι) (j : κ i), f i j) = ⊥ ↔... | [
1072,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1071,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.cos_eq_iff_eq_or_eq_neg | [
{
"state_after": "case h\nθ : Angle\nx✝ : ℝ\n⊢ cos θ = cos ↑x✝ ↔ θ = ↑x✝ ∨ θ = -↑x✝",
"state_before": "θ ψ : Angle\n⊢ cos θ = cos ψ ↔ θ = ψ ∨ θ = -ψ",
"tactic": "induction ψ using Real.Angle.induction_on"
},
{
"state_after": "no goals",
"state_before": "case h\nθ : Angle\nx✝ : ℝ\n⊢ cos θ = c... | [
343,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.coe_toEquiv | [] | [
212,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.rat_cast_re | [] | [
1351,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1350,
1
] |
Mathlib/CategoryTheory/Monoidal/Rigid/Basic.lean | CategoryTheory.leftDualIso_id | [
{
"state_after": "case w\nC : Type u₁\ninst✝¹ : Category C\ninst✝ : MonoidalCategory C\nX Y : C\np : ExactPairing X Y\n⊢ (leftDualIso p p).hom = (Iso.refl X).hom",
"state_before": "C : Type u₁\ninst✝¹ : Category C\ninst✝ : MonoidalCategory C\nX Y : C\np : ExactPairing X Y\n⊢ leftDualIso p p = Iso.refl X",
... | [
663,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
661,
1
] |
Mathlib/GroupTheory/GroupAction/ConjAct.lean | ConjAct.forall | [] | [
94,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.mem_toList | [
{
"state_after": "no goals",
"state_before": "X : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\ns : CompositionSeries X\nx : X\n⊢ x ∈ toList s ↔ x ∈ s",
"tactic": "rw [toList, List.mem_ofFn, mem_def]"
}
] | [
270,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Logic/Equiv/Set.lean | Equiv.Set.insert_apply_right | [] | [
308,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | DoubleQuot.quotQuotEquivComm_comp_quotQuotMkₐ | [] | [
812,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
810,
1
] |
Mathlib/Analysis/SpecialFunctions/ImproperIntegrals.lean | integrableOn_exp_Iic | [
{
"state_after": "c y : ℝ\nx✝ : y ∈ Iic 0\n⊢ (∫ (x : ℝ) in id y..c, ‖exp x‖) ≤ exp c",
"state_before": "c : ℝ\n⊢ IntegrableOn exp (Iic c)",
"tactic": "refine'\n integrableOn_Iic_of_intervalIntegral_norm_bounded (exp c) c\n (fun y => intervalIntegrable_exp.1) tendsto_id\n (eventually_of_mem (Iic_m... | [
41,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Integral.lean | integral_comp_neg_Ioi | [
{
"state_after": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nc : ℝ\nf : ℝ → E\n⊢ (∫ (x : ℝ) in Iic (-c), f (- -x)) = ∫ (x : ℝ) in Iic (- - -c), f x",
"state_before": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteS... | [
108,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Types.lean | CategoryTheory.Limits.Types.binaryProductIso_inv_comp_snd | [] | [
175,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubalgebra.exists_nested_lieIdeal_coe_eq_iff | [
{
"state_after": "R : 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 K' : LieSubalgebra R L\nh : K ≤ K'\n⊢ (∀ (x y : { x // x ∈ K' }), ↑y ∈ K → ⁅↑x, ↑y⁆ ∈ K) ↔ ... | [
335,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | DifferentiableWithinAt.rpow | [] | [
435,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | cmp_mul_left' | [] | [
1556,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1553,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.einfsep_le_edist_of_mem | [] | [
117,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.