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/Analytic/Basic.lean | HasFPowerSeriesAt.eventually_eq_zero | [] | [
515,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
1
] |
Mathlib/Order/WithBot.lean | WithTop.untop'_eq_self_iff | [] | [
719,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
718,
9
] |
Mathlib/Logic/Encodable/Basic.lean | Encodable.decode_nat | [] | [
134,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Basic.lean | Pmf.apply_ne_top | [] | [
141,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Data/Option/Basic.lean | Option.map_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_3\nγ : Type u_4\nδ : Type u_2\nf₁ : α → β\nf₂ : α → γ\ng₁ : β → δ\ng₂ : γ → δ\nh : g₁ ∘ f₁ = g₂ ∘ f₂\na : α\n⊢ Option.map g₁ (Option.map f₁ (some a)) = Option.map g₂ (Option.map f₂ (some a))",
"tactic": "rw [map_map, h, ← map_map]"
... | [
135,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Topology/Basic.lean | closure_diff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns✝ s₁ s₂ t✝ : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\ns t : Set α\n⊢ closure s \\ closure t = closure tᶜ ∩ closure s",
"tactic": "simp only [diff_eq, inter_comm]"
},
{
"state_after": "no goals... | [
1439,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1434,
1
] |
Mathlib/GroupTheory/Abelianization.lean | Abelianization.lift_of | [] | [
159,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Algebra/DualQuaternion.lean | Quaternion.imI_fst_dualNumberEquiv | [] | [
73,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.mul_def | [] | [
442,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.addCases_right | [
{
"state_after": "n✝ m✝ m n : ℕ\nC : Fin (m + n) → Sort u_1\nhleft : (i : Fin m) → C (↑(castAdd n) i)\nhright : (i : Fin n) → C (↑(natAdd m) i)\ni : Fin n\nthis : ¬↑(↑(natAdd m) i) < m\n⊢ addCases hleft hright (↑(natAdd m) i) = hright i",
"state_before": "n✝ m✝ m n : ℕ\nC : Fin (m + n) → Sort u_1\nhleft : (... | [
1863,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1857,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | Cauchy.map | [] | [
146,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
8
] |
Mathlib/Data/Fintype/Basic.lean | Finset.coe_eq_univ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1379\nγ : Type ?u.1382\ninst✝ : Fintype α\ns t : Finset α\n⊢ ↑s = Set.univ ↔ s = univ",
"tactic": "rw [← coe_univ, coe_inj]"
}
] | [
96,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.symm_apply_eq | [
{
"state_after": "no goals",
"state_before": "α✝ : Sort u\nβ✝ : Sort v\nγ : Sort w\nα : Sort u_1\nβ : Sort u_2\ne : α ≃ β\nx : β\ny : (fun x => α) x\nH : ↑e.symm x = y\n⊢ x = ↑e y",
"tactic": "simp [H.symm]"
},
{
"state_after": "no goals",
"state_before": "α✝ : Sort u\nβ✝ : Sort v\nγ : Sort ... | [
331,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.principal_add_iff_add_left_eq_self | [
{
"state_after": "case refine'_1\no : Ordinal\nho : Principal (fun x x_1 => x + x_1) o\na : Ordinal\nhao : a < o\n⊢ a + o = o\n\ncase refine'_2\no : Ordinal\nh : ∀ (a : Ordinal), a < o → a + o = o\na b : Ordinal\nhao : a < o\nhbo : b < o\n⊢ (fun x x_1 => x + x_1) a b < o",
"state_before": "o : Ordinal\n⊢ Pr... | [
165,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Products.lean | CategoryTheory.Limits.hasProducts_of_limit_fans | [] | [
313,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Algebra/Tropical/Basic.lean | Tropical.untrop_mul | [] | [
393,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_norm_ext | [
{
"state_after": "𝕜 : Type u_1\n𝕜₂ : Type u_3\n𝕜₃ : Type u_2\nE : Type u_4\nEₗ : Type ?u.840908\nF : Type u_5\nFₗ : Type ?u.840914\nG : Type u_6\nGₗ : Type ?u.840920\n𝓕 : Type ?u.840923\ninst✝¹⁶ : SeminormedAddCommGroup E\ninst✝¹⁵ : SeminormedAddCommGroup Eₗ\ninst✝¹⁴ : SeminormedAddCommGroup F\ninst✝¹³ : Se... | [
599,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
590,
1
] |
Mathlib/Data/List/Basic.lean | List.foldlM_eq_foldl | [
{
"state_after": "ι : Type ?u.281379\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nm : Type v → Type w\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nf : β → α → m β\nb : β\nl : List α\nh :\n ∀ (mb : m β),\n (do\n let b ← mb\n List.foldlM f b l) =\n foldl\n (fun mb a ... | [
2822,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2815,
1
] |
Mathlib/RingTheory/Localization/Submodule.lean | IsLocalization.coeSubmodule_mono | [] | [
48,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Data/Setoid/Partition.lean | Setoid.classes_mkClasses | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nc : Set (Set α)\nhc : IsPartition c\ns : Set α\nx✝ : s ∈ classes (mkClasses c (_ : ∀ (a : α), ∃! b x, a ∈ b))\ny : α\nhs : s = {x | Rel (mkClasses c (_ : ∀ (a : α), ∃! b x, a ∈ b)) x y}\nb : Set α\nhm : b ∈ c\nhb : y ∈ b\n_hy : ∀ (y_1 : Set α), y_1... | [
251,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Topology/ContinuousOn.lean | continuousOn_pi | [] | [
578,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
576,
1
] |
Mathlib/Analysis/Calculus/IteratedDeriv.lean | iteratedDeriv_one | [
{
"state_after": "case h\n𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type ?u.117629\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nn : ℕ\nf : 𝕜 → F\ns : Set 𝕜\nx✝ x : 𝕜\n⊢ iteratedDeriv 1 f x = deriv f x",
"st... | [
256,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Algebra/DirectSum/Internal.lean | Submodule.iSup_eq_toSubmodule_range | [] | [
331,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.add_le_add_iff_of_lt_aleph0 | [
{
"state_after": "α β γ : Cardinal\nγ₀ : γ < ℵ₀\nh : α + γ ≤ β + γ\n⊢ α ≤ β",
"state_before": "α β γ : Cardinal\nγ₀ : γ < ℵ₀\n⊢ α + γ ≤ β + γ ↔ α ≤ β",
"tactic": "refine' ⟨fun h => _, fun h => add_le_add_right h γ⟩"
},
{
"state_after": "α β γ : Cardinal\nγ₀ : γ < ℵ₀\nh : ¬α ≤ β\n⊢ ¬α + γ ≤ β + γ... | [
885,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
880,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.ofReal | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1130946\nγ : Type ?u.1130949\nδ : Type ?u.1130952\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝³ : MeasurableSpace δ\ninst✝² : NormedAddCommGroup β\ninst✝¹ : NormedAddCommGroup γ\n𝕜 : Type u_2\ninst✝ : IsROrC 𝕜\nf✝ : α → 𝕜\nf : α → ℝ\nhf : Memℒp f 1\n⊢ Memℒp (fun ... | [
1135,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1132,
1
] |
Mathlib/Combinatorics/SimpleGraph/AdjMatrix.lean | SimpleGraph.adjMatrix_mul_apply | [
{
"state_after": "no goals",
"state_before": "V : Type u_2\nα : Type u_1\nβ : Type ?u.46167\nG : SimpleGraph V\ninst✝² : DecidableRel G.Adj\ninst✝¹ : Fintype V\ninst✝ : NonAssocSemiring α\nM : Matrix V V α\nv w : V\n⊢ (adjMatrix α G ⬝ M) v w = ∑ u in neighborFinset G v, M u w",
"tactic": "simp [mul_appl... | [
230,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.copy_eq | [] | [
166,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.preimage_mul_right_singleton | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.128850\nα : Type u_1\nβ : Type ?u.128856\nγ : Type ?u.128859\ninst✝ : Group α\ns t : Set α\na b : α\n⊢ (fun x => x * a) ⁻¹' {b} = {b * a⁻¹}",
"tactic": "rw [← image_mul_right', image_singleton]"
}
] | [
1228,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1227,
1
] |
Mathlib/Topology/Algebra/Order/MonotoneConvergence.lean | tendsto_atBot_iSup | [] | [
164,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.map_nat_add | [] | [
383,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/Topology/Algebra/Module/Determinant.lean | ContinuousLinearEquiv.det_coe_symm | [] | [
37,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.cond_decide | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\np : Prop\ninst✝ : Decidable p\nt e : α\n⊢ (bif decide p then t else e) = if p then t else e",
"tactic": "by_cases p <;> simp [*]"
}
] | [
132,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/CategoryTheory/Monoidal/Braided.lean | CategoryTheory.tensor_μ_def₂ | [
{
"state_after": "C : Type u₁\ninst✝⁸ : Category C\ninst✝⁷ : MonoidalCategory C\ninst✝⁶ : BraidedCategory C\nD : Type u₂\ninst✝⁵ : Category D\ninst✝⁴ : MonoidalCategory D\ninst✝³ : BraidedCategory D\nE : Type u₃\ninst✝² : Category E\ninst✝¹ : MonoidalCategory E\ninst✝ : BraidedCategory E\nX₁ X₂ Y₁ Y₂ : C\n⊢ (𝟙... | [
399,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.strictMonoOn_logb | [] | [
221,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.ext | [] | [
117,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.Surjective.right_cancellable | [] | [
232,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
11
] |
Mathlib/Order/Atoms.lean | isCoatomistic_dual_iff_isAtomistic | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.17844\ninst✝ : CompleteLattice α\nh : IsCoatomistic αᵒᵈ\nb : α\n⊢ ∃ s, b = sSup s ∧ ∀ (a : α), a ∈ s → IsAtom a",
"tactic": "apply h.eq_sInf_coatoms"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Typ... | [
358,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/RingTheory/PowerBasis.lean | PowerBasis.algHom_ext | [
{
"state_after": "case H\nR : Type u_2\nS : Type u_3\nT : Type ?u.54281\ninst✝⁹ : CommRing R\ninst✝⁸ : Ring S\ninst✝⁷ : Algebra R S\nA : Type ?u.54584\nB : Type ?u.54587\ninst✝⁶ : CommRing A\ninst✝⁵ : CommRing B\ninst✝⁴ : IsDomain B\ninst✝³ : Algebra A B\nK : Type ?u.55009\ninst✝² : Field K\nS' : Type u_1\ninst... | [
145,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Analysis/NormedSpace/Pointwise.lean | disjoint_closedBall_ball_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.218373\nE : Type u_1\ninst✝³ : NormedField 𝕜\ninst✝² : SeminormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : NormedSpace ℝ E\nx y z : E\nδ ε : ℝ\nhδ : 0 ≤ δ\nhε : 0 < ε\n⊢ Disjoint (closedBall x δ) (ball y ε) ↔ δ + ε ≤ dist x y",
"tactic... | [
233,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/LinearAlgebra/Matrix/Hermitian.lean | Matrix.IsHermitian.map | [] | [
71,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.sum_const_nat | [] | [
573,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
572,
1
] |
Mathlib/GroupTheory/GroupAction/Basic.lean | MulAction.fixed_eq_iInter_fixedBy | [] | [
129,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Algebra/Tropical/Basic.lean | Tropical.add_eq_right_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : LinearOrder R\nx y : Tropical R\n⊢ x + y = y ↔ y ≤ x",
"tactic": "rw [trop_add_def, trop_eq_iff_eq_untrop, ← untrop_le_iff, min_eq_right_iff]"
}
] | [
343,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.Tendsto.eventually_ne_atTop | [] | [
213,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
11
] |
Mathlib/Data/List/Nodup.lean | List.Nodup.not_mem | [] | [
72,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/RepresentationTheory/Action.lean | Action.tensor_rho | [] | [
500,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/Topology/Algebra/Order/MonotoneConvergence.lean | Monotone.le_of_tendsto | [] | [
262,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | Real.smoothTransition.zero_of_nonpos | [] | [
192,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Data/Set/Intervals/Instances.lean | Set.Ioo.one_minus_lt_one | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.66971\ninst✝¹ : StrictOrderedSemiring α\nβ : Type u_1\ninst✝ : OrderedRing β\nx : ↑(Ioo 0 1)\n⊢ 1 - ↑x < 1",
"tactic": "simpa using x.2.1"
}
] | [
386,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Std/Data/String/Lemmas.lean | String.utf8Len_reverse | [] | [
58,
96
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
58,
9
] |
Mathlib/CategoryTheory/Monad/Limits.lean | CategoryTheory.hasColimitsOfShape_of_reflective | [
{
"state_after": "C : Type u₁\ninst✝⁴ : Category C\nD : Type u₂\ninst✝³ : Category D\nJ : Type u\ninst✝² : Category J\nR : D ⥤ C\ninst✝¹ : Reflective R\ninst✝ : HasColimitsOfShape J C\nF : J ⥤ D\nc : Cocone ((F ⋙ R) ⋙ leftAdjoint R) := (leftAdjoint R).mapCocone (colimit.cocone (F ⋙ R))\n⊢ HasColimit F",
"st... | [
384,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.reverse_get_zero | [
{
"state_after": "n : ℕ\nα : Type u_1\nv : Vector α (n + 1)\n⊢ List.get (toList (reverse v)) (↑(Fin.cast (_ : Nat.succ n = List.length (toList (reverse v)))) 0) =\n List.get (toList v) (↑(Fin.cast (_ : n + 1 = List.length (toList v))) (Fin.last n))",
"state_before": "n : ℕ\nα : Type u_1\nv : Vector α (n ... | [
299,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csSup_Iic | [] | [
760,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
1
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | expNegInvGlue.contDiff_polynomial_eval_inv_mul | [
{
"state_after": "n : ℕ∞\np : ℝ[X]\nm : ℕ\n⊢ ContDiff ℝ ↑m fun x => Polynomial.eval x⁻¹ p * expNegInvGlue x",
"state_before": "n : ℕ∞\np : ℝ[X]\n⊢ ContDiff ℝ n fun x => Polynomial.eval x⁻¹ p * expNegInvGlue x",
"tactic": "apply contDiff_all_iff_nat.2 (fun m => ?_) n"
},
{
"state_after": "no goal... | [
156,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Init/CcLemmas.lean | and_eq_of_eq_true_left | [] | [
22,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
21,
1
] |
Mathlib/RingTheory/FinitePresentation.lean | Algebra.FinitePresentation.iff | [
{
"state_after": "case mp\nR : Type w₁\nA : Type w₂\nB : Type w₃\ninst✝⁴ : CommRing R\ninst✝³ : CommRing A\ninst✝² : Algebra R A\ninst✝¹ : CommRing B\ninst✝ : Algebra R B\n⊢ FinitePresentation R A → ∃ n I x, Ideal.FG I\n\ncase mpr\nR : Type w₁\nA : Type w₂\nB : Type w₃\ninst✝⁴ : CommRing R\ninst✝³ : CommRing A\... | [
154,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.mem_support_swap_mul_imp_mem_support_ne | [
{
"state_after": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nx y : α\nhy : (if ↑f y = x then ↑f x else if y = x then x else ↑f y) ≠ y\n⊢ ↑f y ≠ y ∧ y ≠ x",
"state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nx y : α\nhy : y ∈ support (swap x (↑... | [
506,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | CauchySeq.tendsto_uniformity | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : UniformSpace α\ninst✝ : SemilatticeSup β\nu : β → α\nh : CauchySeq u\n⊢ Tendsto (Prod.map u u) atTop (𝓤 α)",
"tactic": "simpa only [Tendsto, prod_map_map_eq', prod_atTop_atTop_eq] using h.right"
}
] | [
174,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Data/List/Indexes.lean | List.list_reverse_induction | [
{
"state_after": "α : Type u\nβ : Type v\np : List α → Prop\nbase : p []\nind : ∀ (l : List α) (e : α), p l → p (l ++ [e])\nq : List α → Prop := fun l => p (reverse l)\n⊢ ∀ (l : List α), p l",
"state_before": "α : Type u\nβ : Type v\np : List α → Prop\nbase : p []\nind : ∀ (l : List α) (e : α), p l → p (l +... | [
73,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Data/Finset/Sum.lean | Finset.mem_disjSum | [] | [
72,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/RingTheory/PowerBasis.lean | PowerBasis.constr_pow_mul | [
{
"state_after": "case intro\nR : Type ?u.455322\nS : Type u_2\nT : Type ?u.455328\ninst✝¹⁰ : CommRing R\ninst✝⁹ : Ring S\ninst✝⁸ : Algebra R S\nA : Type u_1\nB : Type ?u.455634\ninst✝⁷ : CommRing A\ninst✝⁶ : CommRing B\ninst✝⁵ : IsDomain B\ninst✝⁴ : Algebra A B\nK : Type ?u.456056\ninst✝³ : Field K\ninst✝² : A... | [
286,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Algebra/Group/Basic.lean | eq_div_iff_mul_eq' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.62263\nβ : Type ?u.62266\nG : Type u_1\ninst✝ : Group G\na b c d : G\n⊢ a = b / c ↔ a * c = b",
"tactic": "rw [div_eq_mul_inv, eq_mul_inv_iff_mul_eq]"
}
] | [
838,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
838,
1
] |
Mathlib/Order/Filter/Germ.lean | Filter.Germ.coe_coeRingHom | [] | [
551,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
550,
1
] |
Mathlib/MeasureTheory/Measure/Stieltjes.lean | StieltjesFunction.length_mono | [] | [
334,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/RingTheory/Artinian.lean | IsArtinian.disjoint_partial_infs_eventually_top | [
{
"state_after": "case intro\nR : Type u_1\nM : Type u_2\ninst✝³ : Ring R\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\ninst✝ : IsArtinian R M\nf : ℕ → Submodule R M\nh : ∀ (n : ℕ), Disjoint (↑(partialSups (↑OrderDual.toDual ∘ f)) n) (↑OrderDual.toDual (f (n + 1)))\nn : ℕ\nw : ∀ (m : ℕ), n ≤ m → ↑OrderDual.toD... | [
270,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.coe_sub | [] | [
1251,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1250,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.lineMap_same | [] | [
555,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
] |
Mathlib/CategoryTheory/Subobject/Comma.lean | CategoryTheory.CostructuredArrow.projectQuotient_mk | [] | [
148,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Init/Algebra/Order.lean | le_iff_lt_or_eq | [] | [
237,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.factorSetMem_eq_mem | [] | [
1331,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1330,
1
] |
Mathlib/Data/Set/Intervals/Group.lean | Set.pairwise_disjoint_Ico_zpow | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedCommGroup α\na b : α\n⊢ Pairwise (Disjoint on fun n => Ico (b ^ n) (b ^ (n + 1)))",
"tactic": "simpa only [one_mul] using pairwise_disjoint_Ico_mul_zpow 1 b"
}
] | [
220,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiffOn_inv | [] | [
1692,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1691,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Memℒp.toLp_eq_toLp_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nE : Type u_1\nF : Type ?u.350511\nG : Type ?u.350514\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf g : α → E\nhf : Memℒp f p\nhg : Memℒp g ... | [
131,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.frontier_preimage | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.62554\nB : Type u_1\nF : Type u_2\nE : B → Type ?u.62565\nZ : Type u_3\ninst✝⁴ : TopologicalSpace B\ninst✝³ : TopologicalSpace F\nproj : Z → B\ninst✝² : TopologicalSpace Z\ninst✝¹ : TopologicalSpace (TotalSpace E)\ne✝ : Trivialization F proj\nx : Z\n... | [
749,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
746,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.inter_mul_singleton | [] | [
1918,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1917,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.mem_bind | [] | [
2745,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2740,
1
] |
Mathlib/Algebra/Category/ModuleCat/Monoidal/Closed.lean | ModuleCat.ihom_ev_app | [
{
"state_after": "case H\nR : Type u\ninst✝ : CommRing R\nM N : ModuleCat R\n⊢ ∀ (x : ↑M) (y : ↑((ihom M).obj N)),\n ↑((ihom.ev M).app N) (x ⊗ₜ[R] y) =\n ↑(↑(TensorProduct.uncurry R (↑M) (↑M →ₗ[R] ↑N) ↑N) (LinearMap.flip LinearMap.id)) (x ⊗ₜ[R] y)",
"state_before": "R : Type u\ninst✝ : CommRing R\nM... | [
92,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Data/List/Nodup.lean | List.Nodup.diff | [] | [
321,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mem_sSup_of_directedOn | [
{
"state_after": "G : Type u_1\nG' : Type ?u.229139\ninst✝² : Group G\ninst✝¹ : Group G'\nA : Type ?u.229148\ninst✝ : AddGroup A\nH K✝ : Subgroup G\nk : Set G\nK : Set (Subgroup G)\nKne : Set.Nonempty K\nhK : DirectedOn (fun x x_1 => x ≤ x_1) K\nx : G\nthis : Nonempty ↑K\n⊢ x ∈ sSup K ↔ ∃ s, s ∈ K ∧ x ∈ s",
... | [
1344,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1340,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.cyclotomic_eq_X_pow_sub_one_div | [
{
"state_after": "R : Type u_1\ninst✝ : CommRing R\nn : ℕ\nhpos : 0 < n\n✝ : Nontrivial R\n⊢ cyclotomic n R = (X ^ n - 1) /ₘ ∏ i in Nat.properDivisors n, cyclotomic i R",
"state_before": "R : Type u_1\ninst✝ : CommRing R\nn : ℕ\nhpos : 0 < n\n⊢ cyclotomic n R = (X ^ n - 1) /ₘ ∏ i in Nat.properDivisors n, cy... | [
504,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/Algebra/Group/Defs.lean | mul_right_inv | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝ : Group G\na✝ b c a : G\n⊢ a * a⁻¹ = 1",
"tactic": "rw [← mul_left_inv a⁻¹, inv_eq_of_mul (mul_left_inv a)]"
}
] | [
1095,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1094,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | PSet.mem_toSet | [] | [
351,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | Localization.algEquiv_symm_mk | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁴ : CommSemiring R\nM : Submonoid R\nS : Type u_2\ninst✝³ : CommSemiring S\ninst✝² : Algebra R S\nP : Type ?u.2944703\ninst✝¹ : CommSemiring P\ninst✝ : IsLocalization M S\nx : R\ny : { x // x ∈ M }\n⊢ ↑(AlgEquiv.symm (algEquiv M S)) (mk' S x y... | [
1083,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1082,
1
] |
Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.aeval_primPart_eq_zero | [
{
"state_after": "R : Type u_2\ninst✝⁶ : CommRing R\ninst✝⁵ : IsDomain R\ninst✝⁴ : NormalizedGCDMonoid R\nS : Type u_1\ninst✝³ : Ring S\ninst✝² : IsDomain S\ninst✝¹ : Algebra R S\ninst✝ : NoZeroSMulDivisors R S\np : R[X]\ns : S\nhpzero : p ≠ 0\nhp : ↑(algebraMap R S) (content p) * ↑(aeval s) (primPart p) = 0\n⊢... | [
323,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/Data/Int/Range.lean | Int.mem_range_iff | [
{
"state_after": "m n r : ℤ\n⊢ (∃ a, m + ↑a < n ∧ m + ↑a = r) ↔ m ≤ r ∧ r < n",
"state_before": "m n r : ℤ\n⊢ r ∈ range m n ↔ m ≤ r ∧ r < n",
"tactic": "simp only [range, List.mem_map, List.mem_range, lt_toNat, lt_sub_iff_add_lt, add_comm]"
},
{
"state_after": "no goals",
"state_before": "m ... | [
36,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.toSubsemigroup_strictMono | [] | [
153,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Analysis/MeanInequalities.lean | ENNReal.inner_le_Lp_mul_Lq | [
{
"state_after": "case pos\nι : Type u\ns : Finset ι\nf g : ι → ℝ≥0∞\np q : ℝ\nhpq : Real.IsConjugateExponent p q\nH : (∑ i in s, f i ^ p) ^ (1 / p) = 0 ∨ (∑ i in s, g i ^ q) ^ (1 / q) = 0\n⊢ ∑ i in s, f i * g i ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q)\n\ncase neg\nι : Type u\ns : Finset ... | [
747,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
724,
1
] |
Mathlib/RingTheory/Localization/AsSubring.lean | Localization.map_isUnit_of_le | [
{
"state_after": "no goals",
"state_before": "A : Type u_1\nK : Type u_2\ninst✝³ : CommRing A\nS : Submonoid A\nhS✝ : S ≤ A⁰\ninst✝² : CommRing K\ninst✝¹ : Algebra A K\ninst✝ : IsFractionRing A K\nhS : S ≤ A⁰\ns : { x // x ∈ S }\n⊢ IsUnit (↑(algebraMap A K) ↑s)",
"tactic": "apply IsLocalization.map_unit... | [
35,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/Data/Nat/Periodic.lean | Nat.filter_Ico_card_eq_of_periodic | [] | [
69,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.one_def | [] | [
1318,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1317,
1
] |
Mathlib/Data/Nat/Squarefree.lean | Nat.Squarefree.factorization_le_one | [
{
"state_after": "case inl\np : ℕ\nhn : Squarefree 0\n⊢ ↑(factorization 0) p ≤ 1\n\ncase inr\nn p : ℕ\nhn : Squarefree n\nhn' : n ≠ 0\n⊢ ↑(factorization n) p ≤ 1",
"state_before": "n p : ℕ\nhn : Squarefree n\n⊢ ↑(factorization n) p ≤ 1",
"tactic": "rcases eq_or_ne n 0 with (rfl | hn')"
},
{
"sta... | [
52,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Algebra/AddTorsor.lean | Equiv.constVAdd_zero | [] | [
419,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.ofReal_exp | [] | [
581,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderHom.curry_apply | [] | [
345,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/Data/Analysis/Topology.lean | locallyFinite_iff_exists_realizer | [] | [
269,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.prod_mono_right | [] | [
1113,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1112,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.comap_id | [
{
"state_after": "no goals",
"state_before": "M : Type ?u.7514\nN : Type ?u.7517\nP : Type u_1\nσ : Type ?u.7523\ninst✝² : Mul M\ninst✝¹ : Mul N\ninst✝ : Mul P\nS✝ : Subsemigroup M\nS : Subsemigroup P\n⊢ ∀ (x : P), x ∈ comap (MulHom.id P) S ↔ x ∈ S",
"tactic": "simp"
}
] | [
214,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.ext | [] | [
89,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
11
] |
Mathlib/CategoryTheory/Groupoid.lean | CategoryTheory.Groupoid.inv_eq_inv | [] | [
80,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.filter_subset | [] | [
1949,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1948,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.