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/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.lift_of_comp | [
{
"state_after": "case h\nM : Type u_3\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type u_1\ninst✝¹ : CommMonoid N\nP : Type u_2\ninst✝ : CommMonoid P\nf : LocalizationMap S N\ng : M →* P\nhg : ∀ (y : { x // x ∈ S }), IsUnit (↑g ↑y)\nj : N →* P\nx✝ : N\n⊢ ↑(lift f (_ : ∀ (y : { x // x ∈ S }), IsUnit (↑(MonoidH... | [
1032,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1028,
1
] |
Mathlib/Topology/NhdsSet.lean | nhdsSet_eq_principal_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.11427\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t s₁ s₂ t₁ t₂ : Set α\nx : α\n⊢ 𝓝ˢ s = 𝓟 s ↔ IsOpen s",
"tactic": "rw [← principal_le_nhdsSet.le_iff_eq, le_principal_iff, mem_nhdsSet_iff_forall,\n isOpen_iff_mem... | [
89,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffOn.pow | [] | [
1464,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1463,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_ne_coe_iff | [] | [
117,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
11
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | AddGroupSeminorm.smul_sup | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.123700\nR : Type u_2\nR' : Type ?u.123706\nE : Type u_1\nF : Type ?u.123712\nG : Type ?u.123715\ninst✝³ : AddGroup E\ninst✝² : SMul R ℝ\ninst✝¹ : SMul R ℝ≥0\ninst✝ : IsScalarTower R ℝ≥0 ℝ\np✝ : AddGroupSeminorm E\nr : R\np q : AddGroupSeminorm E\nx y... | [
499,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
495,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.restrictScalars_self | [] | [
451,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Data/Real/Sqrt.lean | Real.sqrt_inv | [
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ sqrt x⁻¹ = (sqrt x)⁻¹",
"tactic": "rw [sqrt, Real.toNNReal_inv, NNReal.sqrt_inv, NNReal.coe_inv, sqrt]"
}
] | [
406,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieModuleHom.map_top | [
{
"state_after": "case h\nR : Type u\nL : Type v\nM : Type w\nN : Type w₁\ninst✝¹⁰ : CommRing R\ninst✝⁹ : LieRing L\ninst✝⁸ : LieAlgebra R L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\ninst✝¹ : LieRingModule L... | [
1225,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1225,
1
] |
Mathlib/LinearAlgebra/PiTensorProduct.lean | PiTensorProduct.subsingletonEquiv_apply_tprod | [] | [
592,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
590,
1
] |
Mathlib/Order/Filter/Extr.lean | IsMinFilter.isExtr | [] | [
162,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.image_projection_prod | [
{
"state_after": "case h₁\nα✝ : Type ?u.77979\nβ : Type ?u.77982\nγ : Type ?u.77985\nι✝ : Sort ?u.77988\nι' : Sort ?u.77991\nι₂ : Sort ?u.77994\nκ : ι✝ → Sort ?u.77999\nκ₁ : ι✝ → Sort ?u.78004\nκ₂ : ι✝ → Sort ?u.78009\nκ' : ι' → Sort ?u.78014\nι : Type u_1\nα : ι → Type u_2\nv : (i : ι) → Set (α i)\nhv : Set.No... | [
659,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
1
] |
Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.colLen_eq_card | [
{
"state_after": "no goals",
"state_before": "μ : YoungDiagram\nj : ℕ\n⊢ colLen μ j = Finset.card (col μ j)",
"tactic": "simp [col_eq_prod]"
}
] | [
392,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
] |
Mathlib/Analysis/Calculus/FDerivMeasurable.lean | aemeasurable_derivWithin_Ici | [] | [
796,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
1
] |
Mathlib/Analysis/Calculus/Inverse.lean | HasStrictFDerivAt.image_mem_toLocalHomeomorph_target | [] | [
607,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
605,
1
] |
Mathlib/Order/Compare.lean | Ordering.Compares.le_antisymm | [] | [
120,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/LinearAlgebra/SModEq.lean | SModEq.symm | [] | [
80,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
8
] |
Mathlib/Algebra/Group/Basic.lean | div_right_injective | [
{
"state_after": "α : Type ?u.56480\nβ : Type ?u.56483\nG : Type u_1\ninst✝ : Group G\na b c d : G\n⊢ Injective fun a => b * a⁻¹",
"state_before": "α : Type ?u.56480\nβ : Type ?u.56483\nG : Type u_1\ninst✝ : Group G\na b c d : G\n⊢ Injective fun a => b / a",
"tactic": "simp only [div_eq_mul_inv]"
},
... | [
737,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
734,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid.dual | [] | [
1088,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1087,
1
] |
Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.universalMulHom_apply | [] | [
420,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.iInter_vsub_subset | [] | [
735,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
734,
1
] |
Mathlib/Data/Fin/VecNotation.lean | Matrix.empty_add_empty | [] | [
453,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.norm_def | [] | [
556,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/Data/List/Dedup.lean | List.dedup_nil | [] | [
34,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.single_neg | [] | [
1147,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1146,
1
] |
Mathlib/Topology/PathConnected.lean | Path.ofLine_mem | [] | [
313,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.colimit.cocone_x | [] | [
723,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
722,
1
] |
Mathlib/Data/List/Perm.lean | List.Subperm.diff_right | [
{
"state_after": "no goals",
"state_before": "α : Type uu\nβ : Type vv\nl₁✝ l₂✝ : List α\ninst✝ : DecidableEq α\nl₁ l₂ : List α\nh : l₁ <+~ l₂\nt : List α\n⊢ List.diff l₁ t <+~ List.diff l₂ t",
"tactic": "induction t generalizing l₁ l₂ h <;> simp [*, Subperm.erase]"
}
] | [
810,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
809,
1
] |
Mathlib/Analysis/InnerProductSpace/l2Space.lean | exists_hilbertBasis | [] | [
607,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
605,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iio_subset_Iic_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.74390\ninst✝¹ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\ninst✝ : DenselyOrdered α\n⊢ Iio a ⊆ Iic b ↔ a ≤ b",
"tactic": "rw [← diff_eq_empty, Iio_diff_Iic, Ioo_eq_empty_iff, not_lt]"
}
] | [
1193,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1192,
1
] |
Mathlib/Algebra/Tropical/Basic.lean | Tropical.min_eq_add | [] | [
312,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.BoundedFormula.realize_liftAt_one | [
{
"state_after": "no goals",
"state_before": "L : Language\nL' : Language\nM : Type w\nN : Type ?u.118977\nP : Type ?u.118980\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : 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 →... | [
442,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | ContinuousLinearEquiv.isOpen | [
{
"state_after": "𝕜 : Type u_3\ninst✝⁷ : NontriviallyNormedField 𝕜\nE : Type u_1\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\nF : Type u_2\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace 𝕜 F\nG : Type ?u.451582\ninst✝² : NormedAddCommGroup G\ninst✝¹ : NormedSpace 𝕜 G\ninst✝ : CompleteSpac... | [
567,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
11
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.measure_inter_eq_of_measure_eq | [
{
"state_after": "α : Type u_1\nβ : Type ?u.86486\nγ : Type ?u.86489\nδ : Type ?u.86492\nι : Type ?u.86495\nR : Type ?u.86498\nR' : Type ?u.86501\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t✝ s t u : Set α\nhs : MeasurableSet s\nh : ↑... | [
728,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
715,
1
] |
Mathlib/Topology/MetricSpace/Metrizable.lean | TopologicalSpace.exists_embedding_l_infty | [
{
"state_after": "ι : Type ?u.4814\nX : Type u_1\nY : Type ?u.4820\nπ : ι → Type ?u.4825\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : TopologicalSpace Y\ninst✝³ : Finite ι\ninst✝² : (i : ι) → TopologicalSpace (π i)\ninst✝¹ : T3Space X\ninst✝ : SecondCountableTopology X\nthis : NormalSpace X\n⊢ ∃ f, Embedding f",
... | [
229,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/RingTheory/Derivation/Basic.lean | Derivation.map_coe_int | [
{
"state_after": "no goals",
"state_before": "R : Type u_3\ninst✝⁵ : CommRing R\nA : Type u_2\ninst✝⁴ : CommRing A\ninst✝³ : Algebra R A\nM : Type u_1\ninst✝² : AddCommGroup M\ninst✝¹ : Module A M\ninst✝ : Module R M\nD D1 D2 : Derivation R A M\nr : R\na b : A\nn : ℤ\n⊢ ↑D ↑n = 0",
"tactic": "rw [← zsmu... | [
396,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.set_integral_deterministic | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_3\nι : Type ?u.403779\nmα : MeasurableSpace α\nmβ : MeasurableSpace β\nκ : { x // x ∈ kernel α β }\nE : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : CompleteSpace E\nf : β → E\ng : α → β\na : α\nhg : Measur... | [
420,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/Algebra/Group/Commute.lean | Commute.mul_left | [] | [
111,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Std/Logic.lean | iff_true_intro | [] | [
71,
62
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
71,
1
] |
Mathlib/Data/Set/Image.lean | Set.preimage_univ | [] | [
81,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.int_cast_imI | [] | [
445,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.biSup_add_biSup_le' | [
{
"state_after": "α : Type ?u.140110\nβ : Type ?u.140113\nγ : Type ?u.140116\na✝ b c d : ℝ≥0∞\nr p✝ q✝ : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\nι : Sort u_1\nι' : Sort u_2\np : ι → Prop\nq : ι' → Prop\nhp : ∃ i, p i\nhq : ∃ j, q j\nf : ι → ℝ≥0∞\ng : ι' → ℝ≥0∞\na : ℝ≥0∞\nh : ∀ (i : ι), p i → ∀ (j : ι'), q j → ... | [
606,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
] |
Mathlib/Data/Set/Basic.lean | Set.inter_inter_inter_comm | [] | [
1094,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1093,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.Multiequalizer.multifork_ι | [] | [
774,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
773,
1
] |
Mathlib/RingTheory/PrincipalIdealDomain.lean | Irreducible.coprime_pow_of_not_dvd | [] | [
453,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_mul_left_Icc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\na✝ a b c : α\nha : 0 ≤ a\nhbc : b ≤ c\n⊢ (fun x x_1 => x * x_1) a '' Icc b c = Icc (a * b) (a * c)",
"tactic": "convert image_mul_right_Icc hbc ha using 1 <;> simp only [mul_comm _ a]"
}
] | [
749,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
747,
1
] |
Mathlib/Order/Interval.lean | NonemptyInterval.dual_map | [] | [
199,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Topology/Connected.lean | isTotallySeparated_empty | [] | [
1368,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1368,
1
] |
Mathlib/Order/Filter/Pi.lean | Filter.coprodᵢ_neBot | [] | [
249,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Algebra/Parity.lean | Odd.mul | [
{
"state_after": "case intro.intro\nF : Type ?u.88859\nα : Type u_1\nβ : Type ?u.88865\nR : Type ?u.88868\ninst✝¹ : Semiring α\ninst✝ : Semiring β\nm n : α\n⊢ Odd ((2 * m + 1) * (2 * n + 1))",
"state_before": "F : Type ?u.88859\nα : Type u_1\nβ : Type ?u.88865\nR : Type ?u.88868\ninst✝¹ : Semiring α\ninst✝ ... | [
367,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/MeasureTheory/Measure/Stieltjes.lean | StieltjesFunction.rightLim_eq | [
{
"state_after": "f✝ f : StieltjesFunction\nx : ℝ\n⊢ ContinuousWithinAt (↑f) (Ici x) x",
"state_before": "f✝ f : StieltjesFunction\nx : ℝ\n⊢ rightLim (↑f) x = ↑f x",
"tactic": "rw [← f.mono.continuousWithinAt_Ioi_iff_rightLim_eq, continuousWithinAt_Ioi_iff_Ici]"
},
{
"state_after": "no goals",
... | [
235,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.inv_le_iff_le_mul | [
{
"state_after": "case hb0\nα : Type ?u.294363\nβ : Type ?u.294366\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nh₁ : b = ⊤ → a ≠ 0\nh₂ : a = ⊤ → b ≠ 0\n⊢ a ≠ 0 ∨ b ≠ ⊤\n\ncase hbt\nα : Type ?u.294363\nβ : Type ?u.294366\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nh₁ : b = ⊤ → a ≠ 0\nh₂ : a = ⊤ → b ≠ 0\n⊢ a ≠ ⊤ ∨ b ≠ 0",
"state_before":... | [
1627,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1625,
1
] |
Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Functor.inv_inv | [] | [
561,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
560,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | InnerProductGeometry.angle_add_eq_arccos_of_inner_eq_zero | [
{
"state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : inner x y = 0\n⊢ Real.arccos (‖x‖ * ‖x‖ / (‖x‖ * ‖x + y‖)) = Real.arccos (‖x‖ / ‖x + y‖)",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : inne... | [
80,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.coe_one | [] | [
397,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
11
] |
Mathlib/Topology/Order/Basic.lean | Filter.Tendsto.add_atTop | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : TopologicalSpace α\ninst✝¹ : LinearOrderedAddCommGroup α\ninst✝ : OrderTopology α\nl : Filter β\nf g : β → α\nC : α\nhf : Tendsto f l (𝓝 C)\nhg : Tendsto g l atTop\n✝ : Nontrivial α\n⊢ Tendsto (fun x => f x + g x) l atTop",
"state_before": "α :... | [
1884,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1879,
1
] |
Mathlib/Algebra/Group/WithOne/Defs.lean | WithZero.coe_inv | [] | [
293,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Topology/Algebra/Module/Multilinear.lean | ContinuousMultilinearMap.smul_apply | [] | [
169,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Analysis/Convex/Function.lean | convexOn_iff_forall_pos | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.138089\nα : Type ?u.138092\nβ : Type u_3\nι : Type ?u.138098\ninst✝⁶ : OrderedSemiring 𝕜\ninst✝⁵ : AddCommMonoid E\ninst✝⁴ : AddCommMonoid F\ninst✝³ : OrderedAddCommMonoid α\ninst✝² : OrderedAddCommMonoid β\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 β\ns... | [
327,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.ceil_sub_int | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.214227\nα : Type u_1\nβ : Type ?u.214233\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz✝ : ℤ\na✝ a : α\nz : ℤ\n⊢ ⌈a - ↑z⌉ = ⌈a + ↑(-z)⌉",
"tactic": "rw [Int.cast_neg, sub_eq_add_neg]"
}
] | [
1160,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1159,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.ElementarilyEquivalent.nonempty_iff | [] | [
1130,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1129,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.castPred_monotone | [] | [
2361,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2360,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.isPath_reverse_iff | [
{
"state_after": "case h.e'_5\nV : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V\np : Walk G u v\nh : IsPath (reverse p)\n⊢ p = reverse (reverse p)",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'... | [
989,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
988,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.singleton_disjiUnion | [] | [
3475,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3474,
1
] |
Mathlib/Data/QPF/Univariate/Basic.lean | Qpf.liftr_iff | [
{
"state_after": "case mp\nF : Type u → Type u\ninst✝ : Functor F\nq : Qpf F\nα : Type u\nr : α → α → Prop\nx y : F α\n⊢ Liftr r x y →\n ∃ a f₀ f₁,\n x = abs { fst := a, snd := f₀ } ∧ y = abs { fst := a, snd := f₁ } ∧ ∀ (i : PFunctor.B (P F) a), r (f₀ i) (f₁ i)\n\ncase mpr\nF : Type u → Type u\ninst✝ : ... | [
156,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.comap_bot | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.251865\nι : Sort x\nf f₁ f₂ : Filter α\ng g₁ g₂ : Filter β\nm : α → β\nm' : β → γ\ns✝ : Set α\nt : Set β\ns : Set α\nx✝ : s ∈ ⊥\n⊢ m ⁻¹' ∅ ⊆ s",
"tactic": "simp only [empty_subset, preimage_empty]"
}
] | [
2207,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2206,
1
] |
Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.adjoin_toSubmodule_le | [
{
"state_after": "no goals",
"state_before": "R : Type u\nA : Type v\nB : Type w\ninst✝⁴ : CommSemiring R\ninst✝³ : Semiring A\ninst✝² : Semiring B\ninst✝¹ : Algebra R A\ninst✝ : Algebra R B\ns✝ t✝ s : Set A\nt : Submodule R A\n⊢ ↑Subalgebra.toSubmodule (adjoin R s) ≤ t ↔ ↑(Submonoid.closure s) ⊆ ↑t",
"... | [
202,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.le_lintegral_add | [
{
"state_after": "α : Type u_1\nβ : Type ?u.797130\nγ : Type ?u.797133\nδ : Type ?u.797136\nm : MeasurableSpace α\nμ ν : Measure α\nf g : α → ℝ≥0∞\n⊢ ((⨆ (g : α →ₛ ℝ≥0∞) (_ : ↑g ≤ fun a => f a), SimpleFunc.lintegral g μ) +\n ⨆ (g_1 : α →ₛ ℝ≥0∞) (_ : ↑g_1 ≤ fun a => g a), SimpleFunc.lintegral g_1 μ) ≤\n ... | [
532,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.curryLeft_add | [] | [
1266,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1264,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.neg_re | [] | [
907,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
907,
9
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.hasSum_im | [] | [
611,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
610,
1
] |
Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.degree_gcd_le_right | [
{
"state_after": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\np q : R[X]\nhq : q ≠ 0\n⊢ degree (gcd q p) ≤ degree q",
"state_before": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\np q : R[X]\nhq : q ≠ 0\n⊢ degree (gcd p q) ... | [
514,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | LinearMap.compMultilinearMap_codRestrict | [] | [
812,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
808,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.append_nil | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V\np : Walk G u v\n⊢ append p nil = p",
"tactic": "induction p with\n| nil => rfl\n| cons _ _ ih => rw [cons_append, ih]"
},
{
"state_after": ... | [
259,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Analysis/SpecificLimits/Normed.lean | NormedField.tendsto_norm_zpow_nhdsWithin_0_atTop | [
{
"state_after": "case intro\nα : Type ?u.55104\nβ : Type ?u.55107\nι : Type ?u.55110\n𝕜 : Type u_1\ninst✝ : NormedField 𝕜\nm : ℤ\nhm : -m < 0\n⊢ Tendsto (fun x => ‖x ^ (-m)‖) (𝓝[{0}ᶜ] 0) atTop",
"state_before": "α : Type ?u.55104\nβ : Type ?u.55107\nι : Type ?u.55110\n𝕜 : Type u_1\ninst✝ : NormedField ... | [
66,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Algebra/RingQuot.lean | RingQuot.mkAlgHom_surjective | [
{
"state_after": "R : Type u₁\ninst✝⁴ : Semiring R\nS : Type u₂\ninst✝³ : CommSemiring S\nA : Type u₃\ninst✝² : Semiring A\ninst✝¹ : Algebra S A\nr : R → R → Prop\nT : Type u₄\ninst✝ : Semiring T\ns : A → A → Prop\nthis : Function.Surjective fun x => { toQuot := Quot.mk (Rel s) x }\n⊢ Function.Surjective ↑(mkAl... | [
611,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.mod_add_mod | [
{
"state_after": "m n k : Nat\nthis : (m % n + k) % n = (m % n + k + n * (m / n)) % n\n⊢ (m % n + k) % n = (m + k) % n",
"state_before": "m n k : Nat\n⊢ (m % n + k) % n = (m + k) % n",
"tactic": "have := (add_mul_mod_self_left (m % n + k) n (m / n)).symm"
},
{
"state_after": "no goals",
"sta... | [
786,
48
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
784,
9
] |
Mathlib/Topology/Constructions.lean | Continuous.codRestrict | [] | [
1110,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1108,
1
] |
Mathlib/Control/LawfulFix.lean | Part.to_unit_cont | [
{
"state_after": "case h.unit\nα : Type u_1\nβ : α → Type ?u.16900\nf : Part α →o Part α\nhc : Continuous f\nx✝ : Chain (Unit → Part α)\n⊢ ↑(toUnitMono f) (ωSup x✝) PUnit.unit = ωSup (Chain.map x✝ (toUnitMono f)) PUnit.unit",
"state_before": "α : Type u_1\nβ : α → Type ?u.16900\nf : Part α →o Part α\nhc : C... | [
207,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.Ordered.lowerBound?_lt | [
{
"state_after": "case refine_1\nα : Type u_1\ncmp : α → α → Ordering\ncut : α → Ordering\nt : RBNode α\nx y : α\ninst✝¹ : TransCmp cmp\ninst✝ : IsStrictCut cmp cut\nht : Ordered cmp t\nH : x ∈ lowerBound? cut t none\nhy : y ∈ t\nh : cmp x y = Ordering.lt\n⊢ cut y = Ordering.lt\n\ncase refine_2\nα : Type u_1\nc... | [
323,
93
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
316,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.blsub_comp | [
{
"state_after": "α : Type ?u.365393\nβ : Type ?u.365396\nγ : Type ?u.365399\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no o' : Ordinal\nf : (a : Ordinal) → a < o → Ordinal\nhf : ∀ {i j : Ordinal} (hi : i < o) (hj : j < o), i ≤ j → f i hi ≤ f j hj\ng : (a : Ordinal) → a < o' → Ordinal\nhg : blsub o' ... | [
1959,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1954,
1
] |
Mathlib/GroupTheory/Nilpotent.lean | lowerCentralSeries_map_subtype_le | [
{
"state_after": "case zero\nG : Type u_1\ninst✝¹ : Group G\nH✝ : Subgroup G\ninst✝ : Normal H✝\nH : Subgroup G\n⊢ Subgroup.map (Subgroup.subtype H) (lowerCentralSeries { x // x ∈ H } Nat.zero) ≤ lowerCentralSeries G Nat.zero\n\ncase succ\nG : Type u_1\ninst✝¹ : Group G\nH✝ : Subgroup G\ninst✝ : Normal H✝\nH : ... | [
458,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
Mathlib/Topology/ContinuousFunction/Algebra.lean | ContinuousMap.inv_comp | [] | [
193,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | nhds_eq_comap_uniformity | [
{
"state_after": "case a\nα : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.58422\ninst✝ : UniformSpace α\nx : α\ns : Set α\n⊢ s ∈ 𝓝 x ↔ s ∈ comap (Prod.mk x) (𝓤 α)",
"state_before": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.58422\ninst✝ : UniformSpace α\nx : α\n⊢ 𝓝 x... | [
714,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
712,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Uniform.lean | Pmf.mem_support_ofMultiset_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.182816\nγ : Type ?u.182819\ns : Multiset α\nhs : s ≠ 0\na : α\n⊢ a ∈ support (ofMultiset s hs) ↔ a ∈ Multiset.toFinset s",
"tactic": "simp"
}
] | [
190,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.Ico_pred_right_eq_insert | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝² : PartialOrder α\ninst✝¹ : PredOrder α\na b : α\ninst✝ : NoMinOrder α\nh : a ≤ b\n⊢ Ioc (pred a) b = insert a (Ioc a b)",
"tactic": "simp_rw [← Ioi_inter_Iic, Ioi_pred_eq_insert, insert_inter_of_mem (mem_Iic.2 h)]"
}
] | [
855,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
854,
1
] |
Mathlib/Algebra/Module/Submodule/Lattice.lean | Submodule.toAddSubgroup_toIntSubmodule | [] | [
418,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.liftRingHom_apply_ofFractionRing_mk | [] | [
781,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
779,
1
] |
Std/Data/Int/Lemmas.lean | Int.lt_add_one_iff | [] | [
848,
85
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
848,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | add_one_le_two_mul | [] | [
129,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Order/Disjoint.lean | disjoint_bot_right | [] | [
65,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Analysis/Complex/CauchyIntegral.lean | Complex.circleIntegral_div_sub_of_differentiable_on_off_countable | [
{
"state_after": "no goals",
"state_before": "E : Type u\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nR : ℝ\nc w : ℂ\ns : Set ℂ\nhs : Set.Countable s\nhw : w ∈ ball c R\nf : ℂ → ℂ\nhc : ContinuousOn f (closedBall c R)\nhd : ∀ (z : ℂ), z ∈ ball c R \\ s → DifferentiableA... | [
552,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
1
] |
Mathlib/Order/LocallyFinite.lean | Finset.mem_Ici | [] | [
384,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Order/Bounds/Basic.lean | AntitoneOn.image_upperBounds_subset_lowerBounds_image | [] | [
1235,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1233,
1
] |
Mathlib/Data/Set/Basic.lean | Set.inter_distrib_left | [] | [
1042,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1041,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.top_prod | [
{
"state_after": "no goals",
"state_before": "M : Type u_2\nN : Type u_1\nP : Type ?u.99119\ninst✝³ : MulOneClass M\ninst✝² : MulOneClass N\ninst✝¹ : MulOneClass P\nS : Submonoid M\nA : Type ?u.99140\ninst✝ : SetLike A M\nhA : SubmonoidClass A M\nS' : A\ns : Submonoid N\nx : M × N\n⊢ x ∈ prod ⊤ s ↔ x ∈ coma... | [
879,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
878,
1
] |
Mathlib/Data/Finset/Option.lean | Finset.coe_eraseNone | [] | [
116,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Algebra/ContinuedFractions/Translations.lean | GeneralizedContinuedFraction.first_denominator_eq | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\ng : GeneralizedContinuedFraction K\nn : ℕ\ninst✝ : DivisionRing K\ngp : Pair K\nzeroth_s_eq : Stream'.Seq.get? g.s 0 = some gp\n⊢ denominators g 1 = gp.b",
"tactic": "simp [denom_eq_conts_b, first_continuant_eq zeroth_s_eq]"
}
] | [
168,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Analysis/InnerProductSpace/Adjoint.lean | orthogonalProjection_isSelfAdjoint | [] | [
322,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | posMulMono_iff_mulPosMono | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na b c d : α\ninst✝² : CommSemigroup α\ninst✝¹ : Zero α\ninst✝ : Preorder α\n⊢ PosMulMono α ↔ MulPosMono α",
"tactic": "simp only [PosMulMono, MulPosMono, mul_comm]"
}
] | [
1039,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1038,
1
] |
Mathlib/Data/Polynomial/DenomsClearable.lean | one_le_pow_mul_abs_eval_div | [
{
"state_after": "case intro.intro.intro\nK : Type u_1\ninst✝ : LinearOrderedField K\nf : ℤ[X]\na b : ℤ\nb0 : 0 < b\nfab : eval (↑a / ↑b) (Polynomial.map (algebraMap ℤ K) f) ≠ 0\nev : ℤ\nbi : K\nbu : bi * ↑(algebraMap ℤ K) b = 1\nhF :\n ↑(algebraMap ℤ K) ev =\n ↑(algebraMap ℤ K) b ^ natDegree f * eval (↑(al... | [
111,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.