file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/Sum/Basic.lean | Sum.isRight_map | [
{
"state_after": "no goals",
"state_before": "α : Type u\nα' : Type w\nβ : Type v\nβ' : Type x\nγ : Type u_1\nδ : Type u_2\nf : α → β\ng : γ → δ\nx : α ⊕ γ\n⊢ isRight (Sum.map f g x) = isRight x",
"tactic": "cases x <;> rfl"
}
] | [
261,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSet.empty | [] | [
84,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Topology/Connected.lean | ConnectedComponents.quotientMap_coe | [] | [
1469,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1468,
1
] |
Mathlib/Algebra/Order/WithZero.lean | mul_le_mul_right₀ | [] | [
232,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.le_iff_sign | [
{
"state_after": "case mp\nx y : EReal\n⊢ x ≤ y →\n ↑sign x < ↑sign y ∨\n ↑sign x = SignType.neg ∧ ↑sign y = SignType.neg ∧ EReal.abs y ≤ EReal.abs x ∨\n ↑sign x = SignType.zero ∧ ↑sign y = SignType.zero ∨\n ↑sign x = SignType.pos ∧ ↑sign y = SignType.pos ∧ EReal.abs x ≤ EReal.abs y\n\nc... | [
1174,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1159,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.equivProdDfinsupp_add | [] | [
1688,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1686,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.rank_adjoin_simple_eq_one_iff | [
{
"state_after": "F : Type u_2\ninst✝² : Field F\nE : Type u_1\ninst✝¹ : Field E\ninst✝ : Algebra F E\nα : E\nS : Set E\nK L : IntermediateField F E\n⊢ Insert.insert ∅ α ⊆ ↑⊥ ↔ α ∈ ⊥",
"state_before": "F : Type u_2\ninst✝² : Field F\nE : Type u_1\ninst✝¹ : Field E\ninst✝ : Algebra F E\nα : E\nS : Set E\nK L... | [
736,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
1
] |
Mathlib/Topology/Instances/Irrational.lean | Irrational.eventually_forall_le_dist_cast_div | [
{
"state_after": "x : ℝ\nhx : Irrational x\nn : ℕ\nA : IsClosed (range fun m => (↑n)⁻¹ * ↑m)\n⊢ ∀ᶠ (ε : ℝ) in 𝓝 0, ∀ (m : ℤ), ε ≤ dist x (↑m / ↑n)",
"state_before": "x : ℝ\nhx : Irrational x\nn : ℕ\n⊢ ∀ᶠ (ε : ℝ) in 𝓝 0, ∀ (m : ℤ), ε ≤ dist x (↑m / ↑n)",
"tactic": "have A : IsClosed (range (fun m => (n... | [
90,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Topology/Constructions.lean | isOpen_sigma_fst_preimage | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type ?u.527967\nδ : Type ?u.527970\nε : Type ?u.527973\nζ : Type ?u.527976\nι : Type u_1\nκ : Type ?u.527982\nσ : ι → Type u_2\nτ : κ → Type ?u.527992\ninst✝² : (i : ι) → TopologicalSpace (σ i)\ninst✝¹ : (k : κ) → TopologicalSpace (τ k)\ninst✝ : TopologicalSpace α\n... | [
1517,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1514,
1
] |
Mathlib/Data/Bitvec/Lemmas.lean | Bitvec.toFin_val | [
{
"state_after": "n : ℕ\nv : Bitvec n\n⊢ Bitvec.toNat v < 2 ^ n",
"state_before": "n : ℕ\nv : Bitvec n\n⊢ ↑(toFin v) = Bitvec.toNat v",
"tactic": "rw [toFin, Fin.coe_ofNat_eq_mod, Nat.mod_eq_of_lt]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\nv : Bitvec n\n⊢ Bitvec.toNat v < 2 ^ ... | [
152,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.tendsto_snd | [] | [
144,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/GroupTheory/GroupAction/Embedding.lean | Function.Embedding.smul_apply | [] | [
43,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/Data/Setoid/Basic.lean | Setoid.mapOfSurjective_eq_map | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nr : Setoid α\nf : α → β\nh : ker f ≤ r\nhf : Surjective f\n⊢ map r f = EqvGen.Setoid Setoid.r",
"state_before": "α : Type u_1\nβ : Type u_2\nr : Setoid α\nf : α → β\nh : ker f ≤ r\nhf : Surjective f\n⊢ map r f = mapOfSurjective r f h hf",
"tactic": "rw [← eq... | [
385,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Geometry/Euclidean/Sphere/SecondInter.lean | EuclideanGeometry.Sphere.secondInter_eq_lineMap | [] | [
140,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.coe_zero | [] | [
293,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.mk'_toAddSubmonoid | [] | [
297,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.nat_casesOn' | [] | [
593,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
591,
1
] |
Mathlib/Algebra/Order/Sub/Defs.lean | AddLECancellable.le_tsub_of_add_le_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.24546\ninst✝³ : Preorder α\ninst✝² : AddCommSemigroup α\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\na b c d : α\nhb : AddLECancellable b\nh : a + b ≤ c\n⊢ b + a ≤ c",
"tactic": "rwa [add_comm]"
}
] | [
216,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
11
] |
Mathlib/Algebra/Tropical/Basic.lean | Tropical.trop_inf | [] | [
284,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/Algebra/Lie/Nilpotent.lean | Function.Surjective.lieModuleIsNilpotent | [
{
"state_after": "case mk.intro\nR : Type u\nL : Type v\nM : Type w\ninst✝¹³ : CommRing R\ninst✝¹² : LieRing L\ninst✝¹¹ : LieAlgebra R L\ninst✝¹⁰ : AddCommGroup M\ninst✝⁹ : Module R M\ninst✝⁸ : LieRingModule L M\ninst✝⁷ : LieModule R L M\nk✝ : ℕ\nN : LieSubmodule R L M\nL₂ : Type u_1\nM₂ : Type u_2\ninst✝⁶ : Li... | [
487,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.leadingCoeff_normalize | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizationMonoid R\np : R[X]\n⊢ leadingCoeff (↑normalize p) = ↑normalize (leadingCoeff p)",
"tactic": "simp"
}
] | [
101,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.MeasurableSet.nullMeasurableSet_subtype_coe | [
{
"state_after": "α : Type u_1\nβ : Type ?u.253013\nγ : Type ?u.253016\nδ : Type ?u.253019\nι : Type ?u.253022\nR : Type ?u.253025\nR' : Type ?u.253028\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t✝ : Set α\nt : Set ↑s\nhs : NullMeasura... | [
1407,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1391,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.mul_im | [] | [
273,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.spanExt_hom_app_left | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nX Y Z X' Y' Z' : C\niX : X ≅ X'\niY : Y ≅ Y'\niZ : Z ≅ Z'\nf : X ⟶ Y\ng : X ⟶ Z\nf' : X' ⟶ Y'\ng' : X' ⟶ Z'\nwf : iX.hom ≫ f' = f ≫ iY.hom\nwg : iX.hom ≫ g' = g ≫ iZ.hom\n⊢ (spanExt iX iY iZ wf wg... | [
476,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Filter.Tendsto.isBigO_one | [] | [
1351,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1349,
1
] |
Mathlib/Topology/MetricSpace/Antilipschitz.lean | AntilipschitzWith.mul_le_dist | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.3257\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\nK : ℝ≥0\nf : α → β\nhf : AntilipschitzWith K f\nx y : α\n⊢ ↑K⁻¹ * dist x y ≤ dist (f x) (f y)",
"tactic": "exact_mod_cast hf.mul_le_nndist x y"
}
] | [
84,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableEmbedding.measurable_comp_iff | [
{
"state_after": "α : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.382740\nδ' : Type ?u.382743\nι : Sort uι\ns t u : Set α\nmα : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nf : α → β\ng : β → γ\nhg : MeasurableEmbedding g\nH : Measurable (g ∘ f)\n⊢ Measurable f",
"state_be... | [
1140,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1136,
1
] |
Mathlib/Data/Set/NAry.lean | Set.image2_subset_right | [] | [
69,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Algebra/CharP/Basic.lean | CharP.neg_one_ne_one | [
{
"state_after": "R : Type u_1\ninst✝² : Ring R\np : ℕ\ninst✝¹ : CharP R p\ninst✝ : Fact (2 < p)\n⊢ 2 ≠ 0",
"state_before": "R : Type u_1\ninst✝² : Ring R\np : ℕ\ninst✝¹ : CharP R p\ninst✝ : Fact (2 < p)\n⊢ -1 ≠ 1",
"tactic": "suffices (2 : R) ≠ 0 by\n intro h\n symm at h\n rw [← sub_eq_zero, sub_neg... | [
308,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.reverse_reverse | [
{
"state_after": "case mk\nn : ℕ\nα : Type u_1\nval✝ : List α\nproperty✝ : List.length val✝ = n\n⊢ reverse (reverse { val := val✝, property := property✝ }) = { val := val✝, property := property✝ }",
"state_before": "n : ℕ\nα : Type u_1\nv : Vector α n\n⊢ reverse (reverse v) = v",
"tactic": "cases v"
}... | [
253,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Algebra/AddTorsor.lean | vadd_vsub_vadd_cancel_left | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nP : Type u_2\ninst✝¹ : AddCommGroup G\ninst✝ : AddTorsor G P\nv : G\np1 p2 : P\n⊢ v +ᵥ p1 -ᵥ (v +ᵥ p2) = p1 -ᵥ p2",
"tactic": "rw [vsub_vadd_eq_vsub_sub, vadd_vsub_assoc, add_sub_cancel']"
}
] | [
263,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Algebra/BigOperators/Ring.lean | Finset.prod_natCast | [] | [
220,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | Right.one_lt_mul_of_lt_of_lt | [] | [
905,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
903,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | CategoryTheory.Limits.IsTerminal.isSplitMono_from | [] | [
174,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Data/Polynomial/Lifts.lean | Polynomial.mem_lifts_and_degree_eq | [
{
"state_after": "R : Type u\ninst✝¹ : Semiring R\nS : Type v\ninst✝ : Semiring S\nf : R →+* S\np : S[X]\nhlifts : p ∈ lifts f\nd : ℕ\nhd : natDegree p = d\n⊢ ∃ q, map f q = p ∧ degree q = degree p",
"state_before": "R : Type u\ninst✝¹ : Semiring R\nS : Type v\ninst✝ : Semiring S\nf : R →+* S\np : S[X]\nhli... | [
205,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/CategoryTheory/Closed/Monoidal.lean | CategoryTheory.MonoidalClosed.coev_app_comp_pre_app | [] | [
271,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Data/Finset/MulAntidiagonal.lean | Finset.mulAntidiagonal_min_mul_min | [
{
"state_after": "case a.mk\nα✝ : Type ?u.14971\ninst✝¹ : OrderedCancelCommMonoid α✝\ns✝ t✝ : Set α✝\nhs✝ : Set.IsPwo s✝\nht✝ : Set.IsPwo t✝\na✝ : α✝\nu : Set α✝\nhu : Set.IsPwo u\nx : α✝ × α✝\nα : Type u_1\ninst✝ : LinearOrderedCancelCommMonoid α\ns t : Set α\nhs : Set.IsWf s\nht : Set.IsWf t\nhns : Set.Nonemp... | [
130,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.measurable | [] | [
146,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
11
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.some_eq_coe | [] | [
152,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
9
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Summable.even_add_odd | [] | [
387,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Std/Data/Array/Init/Lemmas.lean | Array.mkEmpty_eq | [] | [
22,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
22,
9
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.mem_Iio_iff | [] | [
1195,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1194,
1
] |
Mathlib/CategoryTheory/Filtered.lean | CategoryTheory.IsFiltered.sup_exists | [
{
"state_after": "case empty\nC : Type u\ninst✝¹ : Category C\ninst✝ : IsFiltered C\nO : Finset C\nH : Finset ((X : C) ×' (Y : C) ×' (_ : X ∈ O) ×' (_ : Y ∈ O) ×' (X ⟶ Y))\n⊢ ∃ S T,\n ∀ {X Y : C} (mX : X ∈ O) (mY : Y ∈ O) {f : X ⟶ Y},\n { fst := X, snd := { fst := Y, snd := { fst := mX, snd := { fst := ... | [
255,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.inter_congr_left | [] | [
1803,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1802,
1
] |
Mathlib/Data/Set/Function.lean | Set.mapsTo_empty | [] | [
404,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/Data/List/Pairwise.lean | List.Pairwise.filter | [] | [
230,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/LinearAlgebra/Finrank.lean | FiniteDimensional.finrank_zero_of_subsingleton | [
{
"state_after": "K : Type u\nV : Type v\ninst✝⁶ : Ring K\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module K V\nV₂ : Type v'\ninst✝³ : AddCommGroup V₂\ninst✝² : Module K V₂\ninst✝¹ : Nontrivial K\ninst✝ : NoZeroSMulDivisors K V\nh : Subsingleton V\nh0 : ¬finrank K V = 0\n⊢ False",
"state_before": "K : Type u\nV : ... | [
116,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/GroupTheory/Subsemigroup/Basic.lean | Subsemigroup.closure_eq | [] | [
416,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/Data/Multiset/Sum.lean | Multiset.disjSum_lt_disjSum_of_le_of_lt | [] | [
95,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/RingTheory/PrincipalIdealDomain.lean | Ideal.IsPrincipal.of_comap | [
{
"state_after": "no goals",
"state_before": "R : Type u\nM : Type v\nS : Type u_1\nN : Type ?u.185417\ninst✝⁵ : Ring R\ninst✝⁴ : AddCommGroup M\ninst✝³ : AddCommGroup N\ninst✝² : Ring S\ninst✝¹ : Module R M\ninst✝ : Module R N\nf : R →+* S\nhf : Surjective ↑f\nI : Ideal S\nhI : IsPrincipal (comap f I)\n⊢ I... | [
339,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/Topology/Sheaves/Sheafify.lean | TopCat.Presheaf.stalkToFiber_surjective | [
{
"state_after": "case w\nX : TopCat\nF : Presheaf (Type v) X\nx : ↑X\n⊢ ∀ (t : stalk F x), ∃ U f x_1, f { val := x, property := (_ : x ∈ U.obj) } = t",
"state_before": "X : TopCat\nF : Presheaf (Type v) X\nx : ↑X\n⊢ Function.Surjective (stalkToFiber F x)",
"tactic": "apply TopCat.stalkToFiber_surjectiv... | [
104,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | expSeries_div_hasSum_exp_of_mem_ball | [
{
"state_after": "𝕂 : Type u_2\n𝔸 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕂\ninst✝² : NormedDivisionRing 𝔸\ninst✝¹ : NormedAlgebra 𝕂 𝔸\ninst✝ : CompleteSpace 𝔸\nx : 𝔸\nhx : x ∈ EMetric.ball 0 (FormalMultilinearSeries.radius (expSeries 𝕂 𝔸))\n⊢ HasSum (fun n => ↑(expSeries 𝕂 𝔸 n) fun x_1 => x) (... | [
354,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.isLocalization_iff_of_ringEquiv | [] | [
775,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
772,
1
] |
Mathlib/Data/QPF/Univariate/Basic.lean | Qpf.Cofix.dest_corec | [
{
"state_after": "F : Type u → Type u\ninst✝ : Functor F\nq : Qpf F\nα : Type u\ng : α → F α\nx : α\n⊢ Quot.lift (fun x => Quot.mk Mcongr <$> abs (PFunctor.M.dest x))\n (_ :\n ∀ (x y : PFunctor.M (P F)),\n Mcongr x y →\n (fun x => Quot.mk Mcongr <$> abs (PFunctor.M.dest x)) x =\n... | [
431,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Data/Nat/Squarefree.lean | Nat.squarefree_iff_nodup_factors | [
{
"state_after": "n : ℕ\nh0 : n ≠ 0\n⊢ Multiset.Nodup ↑(factors n) ↔ List.Nodup (factors n)",
"state_before": "n : ℕ\nh0 : n ≠ 0\n⊢ Squarefree n ↔ List.Nodup (factors n)",
"tactic": "rw [UniqueFactorizationMonoid.squarefree_iff_nodup_normalizedFactors h0, Nat.factors_eq]"
},
{
"state_after": "no... | [
34,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/RepresentationTheory/Action.lean | Action.comp_hom | [] | [
160,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Algebra/Algebra/Basic.lean | Algebra.smul_def | [] | [
353,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.X_pow_order_dvd | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\nφ : PowerSeries R\nh : (order φ).Dom\n⊢ φ = X ^ Part.get (order φ) h * mk fun n => ↑(coeff R (n + Part.get (order φ) h)) φ",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nφ : PowerSeries R\nh : (order φ).Dom\n⊢ X ^ Part.get (order φ) h ∣ φ",
"tact... | [
2450,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2441,
1
] |
Mathlib/CategoryTheory/Subobject/MonoOver.lean | CategoryTheory.MonoOver.map_obj_left | [] | [
270,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Order/Cover.lean | Wcovby.rfl | [] | [
58,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/RingTheory/Localization/Submodule.lean | IsLocalization.coeSubmodule_injective | [] | [
127,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/MeasureTheory/Group/Integration.lean | MeasureTheory.integral_smul_eq_self | [
{
"state_after": "𝕜 : Type ?u.84709\nM : Type ?u.84712\nα : Type u_1\nG : Type u_2\nE : Type u_3\nF : Type ?u.84724\ninst✝⁹ : MeasurableSpace G\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : CompleteSpace E\ninst✝⁵ : NormedAddCommGroup F\nμ✝ : Measure G\nf✝ : G → E\ng✝ : G\ninst✝⁴ : Group G... | [
208,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Analysis/InnerProductSpace/LaxMilgram.lean | IsCoercive.unique_continuousLinearEquivOfBilin | [] | [
128,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Algebra/Algebra/Basic.lean | Algebra.algebraMap_ofSubring_apply | [] | [
547,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
1
] |
Mathlib/Analysis/NormedSpace/TrivSqZeroExt.lean | TrivSqZeroExt.fst_exp | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_3\nR : Type u_1\nM : Type u_2\ninst✝¹⁵ : IsROrC 𝕜\ninst✝¹⁴ : NormedCommRing R\ninst✝¹³ : AddCommGroup M\ninst✝¹² : NormedAlgebra 𝕜 R\ninst✝¹¹ : Module R M\ninst✝¹⁰ : Module Rᵐᵒᵖ M\ninst✝⁹ : IsCentralScalar R M\ninst✝⁸ : Module 𝕜 M\ninst✝⁷ : IsScal... | [
153,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Data/Finset/Fold.lean | Finset.fold_max_add | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.73169\nop : β → β → β\nhc : IsCommutative β op\nha : IsAssociative β op\nf : α → β\nb : β\ns✝ : Finset α\na : α\ninst✝² : LinearOrder β\nc : β\ninst✝¹ : Add β\ninst✝ : CovariantClass β β (Function.swap fun x x_1 => x + x_1... | [
269,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.affineCombination_subtype_eq_filter | [
{
"state_after": "no goals",
"state_before": "k : Type u_3\nV : Type u_4\nP : Type u_2\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\nS : AffineSpace V P\nι : Type u_1\ns : Finset ι\nι₂ : Type ?u.365709\ns₂ : Finset ι₂\nw : ι → k\np : ι → P\npred : ι → Prop\ninst✝ : DecidablePred pred\n⊢ (↑... | [
563,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | gcd_dvd_gcd_mul_left | [] | [
484,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/MeasureTheory/Function/UniformIntegrable.lean | MeasureTheory.unifIntegrable_const | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nι : Type u_3\nm : MeasurableSpace α\nμ : Measure α\ninst✝ : NormedAddCommGroup β\np : ℝ≥0∞\nf g : α → β\nhp : 1 ≤ p\nhp_ne_top : p ≠ ⊤\nhg : Memℒp g p\nε : ℝ\nhε : 0 < ε\n⊢ ∃ δ x,\n ∀ (i : ι) (s : Set α),\n MeasurableSet s → ↑↑μ s ≤ ENNReal.ofReal δ → snorm ... | [
409,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
1
] |
Mathlib/Combinatorics/Pigeonhole.lean | Fintype.exists_le_sum_fiber_of_nsmul_le_sum | [] | [
350,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/MeasureTheory/Function/SpecialFunctions/Basic.lean | Real.measurable_arcsin | [] | [
64,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_inv | [
{
"state_after": "no goals",
"state_before": "b x✝ y x : ℝ\n⊢ logb b x⁻¹ = -logb b x",
"tactic": "simp [logb, neg_div]"
}
] | [
77,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Algebra/Order/Field/Power.lean | zpow_two_nonneg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\na✝ b c d : α\nn : ℤ\na : α\n⊢ 0 ≤ a ^ 2",
"tactic": "convert zpow_bit0_nonneg a 1"
}
] | [
134,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.coe_zero | [] | [
270,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.trim_trim | [] | [
1667,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1666,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | FiniteDimensional.finrank_pos | [] | [
337,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/Order/Heyting/Basic.lean | IsCompl.compl_eq | [] | [
860,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
859,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | CauchySeq.comp_injective | [] | [
209,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Data/List/Basic.lean | List.mem_pure | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.23772\nα✝ : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α✝\nα : Type u_1\nx y : α\n⊢ x ∈ [y] ↔ x = y",
"tactic": "simp"
}
] | [
525,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
524,
1
] |
Mathlib/Data/Nat/Order/Lemmas.lean | Nat.mul_div_eq_iff_dvd | [
{
"state_after": "no goals",
"state_before": "a b m n✝ k n d : ℕ\n⊢ d * (n / d) = n ↔ d * (n / d) = d * (n / d) + n % d",
"tactic": "rw [div_add_mod]"
},
{
"state_after": "no goals",
"state_before": "a b m n✝ k n d : ℕ\n⊢ d * (n / d) = d * (n / d) + n % d ↔ d ∣ n",
"tactic": "rw [self_eq... | [
65,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/RingTheory/AlgebraicIndependent.lean | AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin | [
{
"state_after": "case refine'_1\nι : Type u_1\nι' : Type ?u.1231476\nR : Type u_2\nK : Type ?u.1231482\nA : Type u_3\nA' : Type ?u.1231488\nA'' : Type ?u.1231491\nV : Type u\nV' : Type ?u.1231496\nx : ι → A\ninst✝⁶ : CommRing R\ninst✝⁵ : CommRing A\ninst✝⁴ : CommRing A'\ninst✝³ : CommRing A''\ninst✝² : Algebra... | [
487,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Std/Data/Int/Lemmas.lean | Int.mul_le_mul_of_nonneg_left | [
{
"state_after": "no goals",
"state_before": "a b c : Int\nh₁ : a ≤ b\nh₂ : 0 ≤ c\n⊢ c * a ≤ c * b",
"tactic": "if hba : b ≤ a then rw [Int.le_antisymm hba h₁]; apply Int.le_refl else\nif hc0 : c ≤ 0 then simp [Int.le_antisymm hc0 h₂, Int.zero_mul] else\nexact Int.le_of_lt <| Int.mul_lt_mul_of_pos_left\... | [
1168,
74
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1163,
11
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.map_denom_ne_zero | [] | [
1342,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1340,
1
] |
Mathlib/NumberTheory/LucasLehmer.lean | lucas_lehmer_sufficiency | [
{
"state_after": "p : ℕ\nw : 1 < p\np' : ℕ := p - 2\n⊢ LucasLehmerTest p → Nat.Prime (mersenne p)",
"state_before": "p : ℕ\nw : 1 < p\n⊢ LucasLehmerTest p → Nat.Prime (mersenne p)",
"tactic": "let p' := p - 2"
},
{
"state_after": "p : ℕ\nw : 1 < p\np' : ℕ := p - 2\nz : p = p' + 2\n⊢ LucasLehmerT... | [
517,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Mathlib/Order/SupIndep.lean | CompleteLattice.Independent.comp' | [
{
"state_after": "α : Type u_3\nβ : Type ?u.52493\nι✝ : Type ?u.52496\nι'✝ : Type ?u.52499\ninst✝ : CompleteLattice α\ns : Set α\nhs : SetIndependent s\nt✝ : ι✝ → α\nht✝ : Independent t✝\nι : Sort u_1\nι' : Sort u_2\nt : ι → α\nf : ι' → ι\nht : Independent (t ∘ f)\nhf : Surjective f\ni : ι\n⊢ Disjoint (t i) (⨆ ... | [
303,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.aeval_eq_zero | [] | [
1550,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1548,
1
] |
Mathlib/Topology/Basic.lean | acc_iff_cluster | [
{
"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\nx : α\nF : Filter α\n⊢ AccPt x F ↔ ClusterPt x (𝓟 ({x}ᶜ) ⊓ F)",
"tactic": "rw [AccPt, nhdsWithin, ClusterPt, inf_assoc]"
}
] | [
1173,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1172,
1
] |
Mathlib/LinearAlgebra/Matrix/MvPolynomial.lean | Matrix.mvPolynomialX_apply | [] | [
44,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/Algebra/Module/Submodule/Pointwise.lean | Submodule.smul_mem_pointwise_smul | [] | [
231,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/Data/SetLike/Basic.lean | SetLike.coe_injective | [] | [
137,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Data/Set/Basic.lean | Set.inter_subset_inter_right | [] | [
1019,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1018,
1
] |
Mathlib/CategoryTheory/Sites/Subsheaf.lean | CategoryTheory.GrothendieckTopology.Subpresheaf.eq_sheafify | [
{
"state_after": "C : Type u\ninst✝ : Category C\nJ : GrothendieckTopology C\nF F' F'' : Cᵒᵖ ⥤ Type w\nG G' : Subpresheaf F\nh : Presieve.IsSheaf J F\nhG : Presieve.IsSheaf J (toPresheaf G)\n⊢ sheafify J G ≤ G",
"state_before": "C : Type u\ninst✝ : Category C\nJ : GrothendieckTopology C\nF F' F'' : Cᵒᵖ ⥤ Ty... | [
215,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Data/Real/Pointwise.lean | Real.smul_iInf_of_nonneg | [] | [
52,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | GroupSeminorm.coe_lt_coe | [] | [
243,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.withDensity_apply | [] | [
1551,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1549,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mk_finsupp_lift_of_infinite' | [
{
"state_after": "case inl\nα : Type u\nβ : Type v\ninst✝² : Nonempty α\ninst✝¹ : Zero β\ninst✝ : Infinite β\nval✝ : Fintype α\n⊢ (#α →₀ β) = max (lift (#α)) (lift (#β))\n\ncase inr\nα : Type u\nβ : Type v\ninst✝² : Nonempty α\ninst✝¹ : Zero β\ninst✝ : Infinite β\nval✝ : Infinite α\n⊢ (#α →₀ β) = max (lift (#α)... | [
1061,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1054,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.add_eq_sup | [] | [
468,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
1
] |
Mathlib/Topology/Constructions.lean | pi_generateFrom_eq | [
{
"state_after": "case refine_1\nα : Type u\nβ : Type v\nγ : Type ?u.341773\nδ : Type ?u.341776\nε : Type ?u.341779\nζ : Type ?u.341782\nι : Type u_2\nπ✝ : ι → Type ?u.341790\nκ : Type ?u.341793\ninst✝¹ : TopologicalSpace α\ninst✝ : (i : ι) → TopologicalSpace (π✝ i)\nf : α → (i : ι) → π✝ i\nπ : ι → Type u_1\ng ... | [
1379,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1368,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.coe_toFinset | [] | [
810,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
809,
1
] |
Mathlib/Combinatorics/Additive/SalemSpencer.lean | mulSalemSpencer_pi | [] | [
113,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.