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/Nat/Prime.lean | Nat.minFacAux_has_prop | [
{
"state_after": "n : ℕ\nn2 : 2 ≤ n\nx✝ : ℕ\nk : ℕ := x✝\ni : ℕ\ne : x✝ = 2 * i + 3\na : ∀ (m : ℕ), 2 ≤ m → m ∣ n → x✝ ≤ m\n⊢ Nat.minFacProp n\n (if h : n < x✝ * x✝ then n\n else\n if x✝ ∣ n then x✝\n else\n let_fun this := (_ : sqrt n - x✝ < sqrt n + 2 - x✝);\n minFacAux n (x✝ + 2... | [
312,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.dmuld | [
{
"state_after": "no goals",
"state_before": "d : ℤ\n⊢ sqrtd * sqrtd = ↑d",
"tactic": "simp [ext]"
}
] | [
330,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.toL1_smul | [] | [
1422,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1420,
1
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Std/Data/List/Lemmas.lean | List.get_cons_succ | [] | [
499,
71
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
498,
9
] |
Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | UniformOnFun.uniformContinuous_eval_of_mem | [] | [
722,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
719,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.HasAntitoneBasis.comp_strictMono | [] | [
1785,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1783,
1
] |
Mathlib/Order/LiminfLimsup.lean | Monotone.isBoundedUnder_ge_comp | [] | [
1190,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.StableUnderBaseChange.op | [] | [
286,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/RingTheory/Polynomial/Eisenstein/Basic.lean | Polynomial.dvd_pow_natDegree_of_eval₂_eq_zero | [
{
"state_after": "R : Type u\nA : Type u_1\ninst✝¹ : CommRing R\ninst✝ : CommRing A\nf : R →+* A\nhf : Function.Injective ↑f\np : R[X]\nhp : Monic p\nx y : R\nz : A\nh : eval₂ f z p = 0\nhz : ↑f x * z = ↑f y\n⊢ y ^ natDegree (scaleRoots p x) ∈ span {x}",
"state_before": "R : Type u\nA : Type u_1\ninst✝¹ : C... | [
183,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
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Mathlib/Topology/Constructions.lean | isOpenMap_sigmaMk | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type ?u.514883\nδ : Type ?u.514886\nε : Type ?u.514889\nζ : Type ?u.514892\nι : Type u_2\nκ : Type ?u.514898\nσ : ι → Type u_1\nτ : κ → Type ?u.514908\ninst✝² : (i : ι) → TopologicalSpace (σ i)\ninst✝¹ : (k : κ) → TopologicalSpace (τ k)\ninst✝ : TopologicalSpace α\n... | [
1466,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1459,
1
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Mathlib/Logic/Equiv/Basic.lean | Equiv.coe_prodUnique | [] | [
184,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
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Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | LinearMap.mul_toMatrix₂ | [
{
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"state_before": "R : Type u_1\nR₁ : Type ?u.1832104\nR₂ : Type ?u.1832107\nM✝ : Type ?u.1832110\nM₁ : Type u_2\nM₂ : Type u_3\nM₁' : Type u_7\nM₂' : Type ?u.1832122\nn : Type u_5\nm : Type u_6\nn' : Type u_4\nm' : Type ?u.1832134\nι : Type ?u.1832137\ninst✝¹⁶ : CommRing R\ninst✝... | [
498,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
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Mathlib/Algebra/Group/Ext.lean | CancelMonoid.toLeftCancelMonoid_injective | [
{
"state_after": "case mk.mk\nM : Type u\ntoLeftCancelMonoid✝¹ : LeftCancelMonoid M\nmul_right_cancel✝¹ : ∀ (a b c : M), a * b = c * b → a = c\ntoLeftCancelMonoid✝ : LeftCancelMonoid M\nmul_right_cancel✝ : ∀ (a b c : M), a * b = c * b → a = c\nh : toLeftCancelMonoid = toLeftCancelMonoid\n⊢ mk mul_right_cancel✝¹... | [
95,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
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Mathlib/Data/Setoid/Basic.lean | Setoid.top_def | [] | [
189,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.filter_apply | [
{
"state_after": "no goals",
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"tactic": "rw [filter, normalize_apply]"
}
] | [
276,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
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Mathlib/Data/Set/Sigma.lean | Set.sigma_singleton | [
{
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126,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Analysis/Convex/Segment.lean | Prod.openSegment_subset | [
{
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600,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
1
] |
Mathlib/Data/Int/GCD.lean | Nat.gcdA_zero_right | [
{
"state_after": "s : ℕ\nh : s ≠ 0\n⊢ (xgcdAux s 1 0 0 0 1).snd.fst = 1",
"state_before": "s : ℕ\nh : s ≠ 0\n⊢ gcdA s 0 = 1",
"tactic": "unfold gcdA xgcd"
},
{
"state_after": "case intro\ns : ℕ\nh : succ s ≠ 0\n⊢ (xgcdAux (succ s) 1 0 0 0 1).snd.fst = 1",
"state_before": "s : ℕ\nh : s ≠ 0\n⊢... | [
101,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.dropFun_subtypeVal | [] | [
696,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
694,
1
] |
Std/Data/List/Lemmas.lean | List.mem_of_ne_of_mem | [] | [
94,
45
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
93,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.functorPullback_pushforward_le | [] | [
686,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
684,
1
] |
Mathlib/Algebra/Order/Sub/Defs.lean | lt_tsub_of_add_lt_left | [] | [
378,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.comp_traverse | [
{
"state_after": "case h_nil\nn : ℕ\nF G : Type u → Type u\ninst✝³ : Applicative F\ninst✝² : Applicative G\ninst✝¹ : LawfulApplicative F\ninst✝ : LawfulApplicative G\nα β γ : Type u\nf : β → F γ\ng : α → G β\n⊢ Vector.traverse (Comp.mk ∘ Functor.map f ∘ g) nil = Comp.mk (Vector.traverse f <$> Vector.traverse g ... | [
687,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
11
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.card_support_cycleOf_pos_iff | [
{
"state_after": "ι : Type ?u.2442862\nα : Type u_1\nβ : Type ?u.2442868\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nx y : α\n⊢ Nat.succ 0 ≤ card (support (cycleOf f x)) ↔ 2 ≤ card (support (cycleOf f x))",
"state_before": "ι : Type ?u.2442862\nα : Type u_1\nβ : Type ?u.2442868\ninst✝¹ : Decid... | [
1106,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1104,
1
] |
Mathlib/Data/Polynomial/Monic.lean | Polynomial.monic_of_injective | [
{
"state_after": "case a\nR : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝¹ : Semiring R\ninst✝ : Semiring S\nf : R →+* S\nhf : Injective ↑f\np : R[X]\nhp : Monic (map f p)\n⊢ ↑f (leadingCoeff p) = ↑f 1",
"state_before": "R : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝¹ : Semiring R\n... | [
359,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.mul_def | [] | [
405,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.submatrix_add | [] | [
2414,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2412,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.map_add_add | [
{
"state_after": "𝕜 : Type u_1\n𝕜₂ : Type ?u.2511974\n𝕜₃ : Type ?u.2511977\nE : Type u_2\nEₗ : Type ?u.2511983\nF : Type ?u.2511986\nFₗ : Type u_4\nG : Type ?u.2511992\nGₗ : Type u_3\n𝓕 : Type ?u.2511998\ninst✝³¹ : SeminormedAddCommGroup E\ninst✝³⁰ : SeminormedAddCommGroup Eₗ\ninst✝²⁹ : SeminormedAddCommGro... | [
1384,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1381,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.toWithTop_le | [
{
"state_after": "case a\nx : PartENat\nhx : Decidable x.Dom\nhy : Decidable ⊤.Dom\n⊢ toWithTop x ≤ toWithTop ⊤ ↔ x ≤ ⊤\n\ncase a\nx : PartENat\nhx : Decidable x.Dom\nn✝ : ℕ\nhy : Decidable (↑n✝).Dom\n⊢ toWithTop x ≤ toWithTop ↑n✝ ↔ x ≤ ↑n✝",
"state_before": "x y : PartENat\nhx : Decidable x.Dom\nhy : Decid... | [
605,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
599,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.sub_lt_iff_lt_right | [] | [
1173,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1172,
11
] |
Mathlib/Topology/Separation.lean | TopologicalSpace.IsTopologicalBasis.nhds_basis_closure | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : TopologicalSpace α\ninst✝ : RegularSpace α\na✝ : α\ns : Set α\nB : Set (Set α)\nhB : IsTopologicalBasis B\na : α\n⊢ HasBasis (𝓝 a) (fun s => a ∈ s ∧ s ∈ B) closure",
"tactic": "simpa only [and_comm] using hB.nhds_hasBasis.nh... | [
1561,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1558,
1
] |
Mathlib/Topology/Basic.lean | interior_eq_nhds' | [
{
"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 : Set α\nx : α\n⊢ x ∈ interior s ↔ x ∈ {a | s ∈ 𝓝 a}",
"tactic": "simp only [mem_interior, mem_nhds_iff, mem_setOf_eq]"
}
] | [
1205,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1204,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | HasSum.hasSum_of_sum_eq | [] | [
119,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.le_rootMultiplicity_map | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\na✝ b : R\nn : ℕ\nA : Type u_1\nB : Type u_2\ninst✝¹ : CommRing A\ninst✝ : CommRing B\np : A[X]\nf : A →+* B\nhmap : map f p ≠ 0\na : A\n⊢ (X - ↑C (↑f a)) ^ rootMultiplicity a p ∣ map f p",
"state_before": "R : Type u\nS : Type v\nT : Type w\na✝ b : R\nn ... | [
1148,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1144,
1
] |
Mathlib/Order/LocallyFinite.lean | Finset.coe_Ioc | [] | [
358,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean | SimpleGraph.ComponentCompl.coe_inj | [] | [
112,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Midpoint.lean | left_sub_midpoint | [] | [
152,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.le_digits_len_le | [] | [
442,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
] |
Mathlib/RingTheory/WittVector/IsPoly.lean | WittVector.IsPoly₂.comp | [
{
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329,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
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Mathlib/Algebra/Parity.lean | Even.pow_of_ne_zero | [
{
"state_after": "F : Type ?u.74464\nα : Type u_1\nβ : Type ?u.74470\nR : Type ?u.74473\ninst✝¹ : Semiring α\ninst✝ : Semiring β\nm n : α\nhm : Even m\na : ℕ\nx✝ : a + 1 ≠ 0\n⊢ Even (m * m ^ a)",
"state_before": "F : Type ?u.74464\nα : Type u_1\nβ : Type ?u.74470\nR : Type ?u.74473\ninst✝¹ : Semiring α\nins... | [
298,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.firstDiff_lt_shortestPrefixDiff | [
{
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"state_before": "E ... | [
522,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
1
] |
Mathlib/Algebra/Order/Monoid/WithZero/Defs.lean | WithZero.zero_lt_coe | [] | [
57,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.prod_append | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.5270\nα : Type ?u.5273\nM : Type u_1\nN : Type ?u.5279\nP : Type ?u.5282\nM₀ : Type ?u.5285\nG : Type ?u.5288\nR : Type ?u.5291\ninst✝² : Monoid M\ninst✝¹ : Monoid N\ninst✝ : Monoid P\nl l₁ l₂ : List M\na : M\n⊢ prod (l₁ ++ l₂) = foldl (fun x x_1 => ... | [
56,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.gc_map_comap | [] | [
1504,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1503,
1
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Mathlib/Algebra/Order/Sub/Defs.lean | tsub_right_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.33907\ninst✝³ : PartialOrder α\ninst✝² : AddCommSemigroup α\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\na b c d : α\n⊢ a - b - c = a - c - b",
"tactic": "rw [←tsub_add_eq_tsub_tsub, tsub_add_eq_tsub_tsub_swap]"
}
] | [
279,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | IsConnected.Ioo_csInf_csSup_subset | [] | [
254,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Analysis/Asymptotics/Theta.lean | Asymptotics.IsTheta.smul | [] | [
224,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Algebra/Category/Ring/Colimits.lean | CommRingCat.Colimits.cocone_naturality | [
{
"state_after": "case w\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ CommRingCat\nj j' : J\nf : j ⟶ j'\nx✝ : (forget CommRingCat).obj (F.obj j)\n⊢ (forget CommRingCat).map (F.map f ≫ coconeMorphism F j') x✝ = (forget CommRingCat).map (coconeMorphism F j) x✝",
"state_before": "J : Type v\ninst✝ : SmallCate... | [
267,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/RingTheory/Congruence.lean | RingCon.coe_one | [] | [
230,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Algebra/QuaternionBasis.lean | QuaternionAlgebra.Basis.k_mul_i | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nA : Type u_1\nB : Type ?u.24590\ninst✝⁴ : CommRing R\ninst✝³ : Ring A\ninst✝² : Ring B\ninst✝¹ : Algebra R A\ninst✝ : Algebra R B\nc₁ c₂ : R\nq : Basis A c₁ c₂\n⊢ q.k * q.i = -c₁ • q.j",
"tactic": "rw [← i_mul_j, mul_assoc, j_mul_i, mul_neg, i_... | [
94,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Algebra/GCDMonoid/Multiset.lean | Multiset.lcm_add | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizedGCDMonoid α\ns₁ s₂ : Multiset α\n⊢ lcm (s₁ + s₂) = fold GCDMonoid.lcm (GCDMonoid.lcm 1 1) (s₁ + s₂)",
"tactic": "simp [lcm]"
}
] | [
63,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Filter.lean | BoxIntegral.IntegrationParams.tendsto_embedBox_toFilteriUnion_top | [
{
"state_after": "ι : Type u_1\ninst✝ : Fintype ι\nI J : Box ι\nc c₁ c₂ : ℝ≥0\nr r₁ r₂ : (ι → ℝ) → ↑(Set.Ioi 0)\nπ π₁ π₂ : TaggedPrepartition I\nl✝ l₁ l₂ l : IntegrationParams\nh : I ≤ J\n⊢ ∀ (i : ℝ≥0),\n Tendsto (↑(embedBox I J h)) (toFilterDistortioniUnion l I i ⊤)\n (⨆ (c : ℝ≥0), toFilterDistortioniU... | [
520,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Mathlib/CategoryTheory/Generator.lean | CategoryTheory.thin_of_isSeparating_empty | [] | [
224,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.le_iff | [] | [
968,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
967,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.edist_eq_sum | [] | [
155,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Algebra/Star/SelfAdjoint.lean | IsSelfAdjoint.add | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nA : Type ?u.6762\ninst✝¹ : AddMonoid R\ninst✝ : StarAddMonoid R\nx y : R\nhx : IsSelfAdjoint x\nhy : IsSelfAdjoint y\n⊢ IsSelfAdjoint (x + y)",
"tactic": "simp only [isSelfAdjoint_iff, star_add, hx.star_eq, hy.star_eq]"
}
] | [
116,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Data/Setoid/Partition.lean | Setoid.sUnion_classes | [] | [
200,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Order/Filter/Extr.lean | Filter.EventuallyEq.isExtrFilter_iff | [] | [
679,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
677,
1
] |
Mathlib/Order/Filter/Cofinite.lean | Function.Injective.tendsto_cofinite | [] | [
198,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/GroupTheory/Divisible.lean | AddCommGroup.smul_top_eq_top_of_divisibleBy_int | [] | [
175,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Data/Set/Sups.lean | Set.infs_inter_subset_right | [] | [
328,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Topology/Order/Basic.lean | Ioo_mem_nhdsWithin_Iio | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderClosedTopology α\na✝ b✝ : α\ninst✝ : TopologicalSpace γ\na b c : α\nH : b ∈ Ioc a c\n⊢ Ioo a c ∈ 𝓝[Iio b] b",
"tactic": "simpa only [dual_Ioo] using\n Io... | [
460,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/Data/Bundle.lean | Bundle.TotalSpace.mk_cast | [
{
"state_after": "B : Type u_1\nE : B → Type u_2\nx : B\nb : E x\n⊢ totalSpaceMk x (cast (_ : E x = E x) b) = totalSpaceMk x b",
"state_before": "B : Type u_1\nE : B → Type u_2\nx x' : B\nh : x = x'\nb : E x\n⊢ totalSpaceMk x' (cast (_ : E x = E x') b) = totalSpaceMk x b",
"tactic": "subst h"
},
{
... | [
80,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Order/WithBot.lean | WithTop.untop'_coe | [] | [
706,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
705,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.coeff_monomial_ne | [
{
"state_after": "σ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nm n : σ →₀ ℕ\nh : m ≠ n\na : R\n⊢ ↑(coeff R m) (↑(LinearMap.stdBasis R (fun x => R) n) a) = 0",
"state_before": "σ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nm n : σ →₀ ℕ\nh : m ≠ n\na : R\n⊢ ↑(coeff R m) (↑(monomial R n) a) = 0",
"tac... | [
168,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Data/Nat/Order/Lemmas.lean | Nat.dvd_right_iff_eq | [
{
"state_after": "no goals",
"state_before": "a b m✝ n✝¹ k m n✝ : ℕ\nh : m = n✝\nn : ℕ\n⊢ m ∣ n ↔ n✝ ∣ n",
"tactic": "rw [h]"
}
] | [
243,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Dynamics/Ergodic/Conservative.lean | MeasureTheory.Conservative.measure_mem_forall_ge_image_not_mem_eq_zero | [
{
"state_after": "ι : Type ?u.62235\nα : Type u_1\ninst✝ : MeasurableSpace α\nf : α → α\ns : Set α\nμ : Measure α\nhf : Conservative f μ\nhs : MeasurableSet s\nn : ℕ\nH : ¬↑↑μ {x | x ∈ s ∧ ∀ (m : ℕ), m ≥ n → ¬(f^[m]) x ∈ s} = 0\n⊢ False",
"state_before": "ι : Type ?u.62235\nα : Type u_1\ninst✝ : MeasurableS... | [
130,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.digits_lt_base' | [
{
"state_after": "n b m : ℕ\n⊢ ∀ (n : ℕ),\n (∀ (m : ℕ), m < n → ∀ {d : ℕ}, d ∈ digits (b + 2) m → d < b + 2) → ∀ {d : ℕ}, d ∈ digits (b + 2) n → d < b + 2",
"state_before": "n b m : ℕ\n⊢ ∀ {d : ℕ}, d ∈ digits (b + 2) m → d < b + 2",
"tactic": "apply Nat.strongInductionOn m"
},
{
"state_after"... | [
385,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/LinearAlgebra/Matrix/GeneralLinearGroup.lean | Matrix.SpecialLinearGroup.coe_to_GLPos_to_GL_det | [] | [
285,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/CategoryTheory/Preadditive/HomOrthogonal.lean | CategoryTheory.HomOrthogonal.matrixDecomposition_comp | [
{
"state_after": "case a.mk.refl.h.mk\nC : Type u\ninst✝⁵ : Category C\nι : Type u_1\ns : ι → C\ninst✝⁴ : Preadditive C\ninst✝³ : HasFiniteBiproducts C\no : HomOrthogonal s\nα β γ : Type\ninst✝² : Fintype α\ninst✝¹ : Fintype β\ninst✝ : Fintype γ\nf : α → ι\ng : β → ι\nh : γ → ι\nz : (⨁ fun a => s (f a)) ⟶ ⨁ fun... | [
174,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.coe_prod | [] | [
68,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Data/List/Infix.lean | List.infix_insert | [] | [
490,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/CategoryTheory/Abelian/FunctorCategory.lean | CategoryTheory.Abelian.FunctorCategory.coimageImageComparison_app' | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\nD : Type w\ninst✝¹ : Category D\ninst✝ : Abelian D\nF G : C ⥤ D\nα : F ⟶ G\nX : C\n⊢ (coimageImageComparison α).app X = (coimageObjIso α X).hom ≫ coimageImageComparison (α.app X) ≫ (imageObjIso α X).inv",
"tactic": "simp only... | [
87,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_pi_div_sixteen | [
{
"state_after": "x : ℝ\n⊢ sin (π / 16) = sin (π / 2 ^ 4)\n\nx : ℝ\n⊢ sin (π / 2 ^ 4) = sqrt (2 - sqrt (2 + sqrt 2)) / 2",
"state_before": "x : ℝ\n⊢ sin (π / 16) = sqrt (2 - sqrt (2 + sqrt 2)) / 2",
"tactic": "trans sin (π / 2 ^ 4)"
},
{
"state_after": "case e_x.e_a\nx : ℝ\n⊢ 16 = 2 ^ 4\n\nx : ℝ... | [
825,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
821,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_generateFrom | [] | [
238,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.mk_toGerm | [] | [
380,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.neg_le_iff | [
{
"state_after": "no goals",
"state_before": "x y : PGame\n⊢ -y ≤ x ↔ -x ≤ y",
"tactic": "rw [← neg_neg x, neg_le_neg_iff, neg_neg]"
}
] | [
1345,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1345,
1
] |
Mathlib/Algebra/GroupWithZero/Basic.lean | right_ne_zero_of_mul_eq_one | [] | [
155,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
src/lean/Init/Data/Nat/Div.lean | Nat.mod_lt | [
{
"state_after": "no goals",
"state_before": "x y : Nat\n⊢ y > 0 → x % y < y",
"tactic": "induction x, y using mod.inductionOn with\n| base x y h₁ =>\n intro h₂\n have h₁ : ¬ 0 < y ∨ ¬ y ≤ x := Iff.mp (Decidable.not_and_iff_or_not _ _) h₁\n match h₁ with\n | Or.inl h₁ => exact absurd h₂ h₁\n | Or.i... | [
138,
16
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
122,
1
] |
Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.isUnit_iff_degree_eq_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝ : Field R\np q : R[X]\nh : degree p = 0\n⊢ degree p ≤ 0",
"tactic": "simp [*, le_refl]"
},
{
"state_after": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝ :... | [
163,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Order/Basic.lean | Pi.compl_apply | [] | [
778,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
776,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.intDegree_polynomial | [
{
"state_after": "no goals",
"state_before": "K : Type u\ninst✝ : Field K\np : K[X]\n⊢ intDegree (↑(algebraMap K[X] (RatFunc K)) p) = ↑(natDegree p)",
"tactic": "rw [intDegree, RatFunc.num_algebraMap, RatFunc.denom_algebraMap, Polynomial.natDegree_one,\n Int.ofNat_zero, sub_zero]"
}
] | [
1597,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1594,
1
] |
Mathlib/Algebra/GroupPower/Ring.lean | sq_sub_sq | [] | [
277,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.eval_zero | [] | [
1525,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1524,
1
] |
Mathlib/Topology/UniformSpace/UniformEmbedding.lean | UniformInducing.inducing | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : UniformSpace β\ninst✝ : UniformSpace γ\nf : α → β\nh : UniformInducing f\n⊢ Inducing f",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : UniformSpace α\ninst✝¹ : UniformSpace β\ninst✝ : UniformSpace γ\nf : α → β\nh : UniformInducin... | [
106,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_empty | [] | [
1917,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1916,
1
] |
Mathlib/Analysis/Complex/Isometry.lean | rotation_ne_conjLie | [
{
"state_after": "a : { x // x ∈ circle }\nh : ↑rotation a = conjLie\n⊢ False",
"state_before": "a : { x // x ∈ circle }\n⊢ ↑rotation a ≠ conjLie",
"tactic": "intro h"
},
{
"state_after": "a : { x // x ∈ circle }\nh : ↑rotation a = conjLie\nh1 : ↑(↑rotation a) 1 = ↑(starRingEnd ℂ) 1\n⊢ False",
... | [
74,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/InformationTheory/Hamming.lean | hammingDist_eq_hammingNorm | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.32980\nι : Type u_2\nβ : ι → Type u_1\ninst✝³ : Fintype ι\ninst✝² : (i : ι) → DecidableEq (β i)\nγ : ι → Type ?u.33012\ninst✝¹ : (i : ι) → DecidableEq (γ i)\ninst✝ : (i : ι) → AddGroup (β i)\nx y : (i : ι) → β i\n⊢ hammingDist x y = hammingNorm (x - ... | [
240,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Algebra/Order/Monoid/WithZero/Defs.lean | WithZero.coe_le_coe | [] | [
71,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Order/OrdContinuous.lean | RightOrdContinuous.id | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : Preorder γ\ng : β → γ\nf : α → β\ns : Set α\nx : α\nh : IsGLB s x\n⊢ IsGLB (id '' s) (id x)",
"tactic": "simpa only [image_id] using h"
}
] | [
171,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
11
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integral_Icc_eq_integral_Ioo' | [] | [
632,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.map_comp | [
{
"state_after": "case a\nα : Type u\nβ : Type v\nγ : Type w\nf : α → β\ng : β → γ\ns : Stream' (Option α)\nal : IsSeq s\n⊢ ↑(map (g ∘ f) { val := s, property := al }) = ↑(map g (map f { val := s, property := al }))",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nf : α → β\ng : β → γ\ns : Stream' (Op... | [
719,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
715,
1
] |
Mathlib/Algebra/Group/Opposite.lean | Commute.op | [] | [
247,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.inv_single | [
{
"state_after": "no goals",
"state_before": "u : Lean.Level\nR✝ : Type ?u.356885\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝¹ : CommSemiring R✝\nR : Type u_1\ninst✝ : DivisionRing R\na b : R\nx✝ : a⁻¹ = b\n⊢ (a + 0)⁻¹ = b + 0",
"tactic": "simp [*]"
}
] | [
891,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
890,
1
] |
Mathlib/Analysis/NormedSpace/ENorm.lean | ENorm.finite_edist_eq | [] | [
226,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.ofWithBot_le | [
{
"state_after": "ι : Type u_1\nI J J₁ J₂ : Box ι\nπ π₁ π₂ : Prepartition I\nx : ι → ℝ\nπi πi₁ πi₂ : (J : Box ι) → Prepartition J\nboxes : Finset (WithBot (Box ι))\nle_of_mem : ∀ (J : WithBot (Box ι)), J ∈ boxes → J ≤ ↑I\npairwise_disjoint : Set.Pairwise (↑boxes) Disjoint\nH : ∀ (J : WithBot (Box ι)), J ∈ boxes... | [
441,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.le_count_apply | [] | [
2192,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2188,
1
] |
Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.map_tmul | [] | [
869,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
868,
1
] |
Mathlib/Algebra/Algebra/Tower.lean | Algebra.lsmul_injective | [] | [
366,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/Topology/Basic.lean | Filter.Eventually.self_of_nhds | [] | [
912,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
1
] |
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