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/Order/SuccPred/Basic.lean | exists_pred_iterate_or | [] | [
1458,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1457,
1
] |
Mathlib/Data/Subtype.lean | Subtype.coind_bijective | [] | [
198,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.sub_mem_ball | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.882649\nR' : Type ?u.882652\n𝕜 : Type u_1\n𝕜₂ : Type ?u.882658\n𝕜₃ : Type ?u.882661\n𝕝 : Type ?u.882664\nE : Type u_2\nE₂ : Type ?u.882670\nE₃ : Type ?u.882673\nF : Type ?u.882676\nG : Type ?u.882679\nι : Type ?u.882682\ninst✝² : SeminormedRing �... | [
768,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
767,
1
] |
Mathlib/MeasureTheory/Measure/Regular.lean | Set.exists_isOpen_lt_add | [] | [
264,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Algebra/GCDMonoid/Multiset.lean | Multiset.lcm_dedup | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ninst✝¹ : NormalizedGCDMonoid α\ninst✝ : DecidableEq α\ns : Multiset α\n⊢ lcm (dedup 0) = lcm 0",
"tactic": "simp"
},
{
"state_after": "case pos\nα : Type u_1\ninst✝² : CancelCommMonoidWithZero α\nins... | [
103,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | IsLUB.ciSup_eq | [] | [
537,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
536,
1
] |
Mathlib/NumberTheory/Fermat4.lean | not_fermat_4 | [
{
"state_after": "a b c : ℤ\nha : a ≠ 0\nhb : b ≠ 0\nheq : a ^ 4 + b ^ 4 = c ^ 4\n⊢ False",
"state_before": "a b c : ℤ\nha : a ≠ 0\nhb : b ≠ 0\n⊢ a ^ 4 + b ^ 4 ≠ c ^ 4",
"tactic": "intro heq"
},
{
"state_after": "a b c : ℤ\nha : a ≠ 0\nhb : b ≠ 0\nheq : a ^ 4 + b ^ 4 = c ^ 4\n⊢ a ^ 4 + b ^ 4 = (... | [
316,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.le_functorPushforward_pullback | [] | [
681,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
679,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.mul_eq_mul | [] | [
934,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
933,
1
] |
Std/Data/List/Lemmas.lean | List.Fin.exists_iff | [] | [
537,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
536,
1
] |
Mathlib/GroupTheory/Submonoid/Inverses.lean | Submonoid.fromLeftInv_mul | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝ : CommMonoid M\nS : Submonoid M\nx : { x // x ∈ leftInv S }\n⊢ ↑(fromLeftInv S x) * ↑x = 1",
"tactic": "rw [mul_comm, mul_fromLeftInv]"
}
] | [
126,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Filter.lean | BoxIntegral.IntegrationParams.hasBasis_toFilteriUnion_top | [
{
"state_after": "no goals",
"state_before": "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\nI : Box ι\n⊢ HasBasis (toFilteriUnion l I ⊤) (fun r => ∀ (c : ℝ≥0), RCond l (r c)) fun r =>\n {π |... | [
497,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | ChainComplex.of_d_ne | [
{
"state_after": "ι : Type ?u.77771\nV : Type u\ninst✝⁴ : Category V\ninst✝³ : HasZeroMorphisms V\nα : Type u_1\ninst✝² : AddRightCancelSemigroup α\ninst✝¹ : One α\ninst✝ : DecidableEq α\nX : α → V\nd : (n : α) → X (n + 1) ⟶ X n\nsq : ∀ (n : α), d (n + 1) ≫ d n = 0\ni j : α\nh : i ≠ j + 1\n⊢ (if h : i = j + 1 t... | [
641,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
639,
1
] |
Mathlib/Init/Algebra/Order.lean | lt_trichotomy | [] | [
322,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.order_single | [] | [
249,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.lt_translationNumber_of_forall_add_lt | [
{
"state_after": "f g : CircleDeg1Lift\nhf : Continuous ↑f\nz : ℝ\nhz : ∀ (x : ℝ), x + z < ↑f x\n⊢ ∃ x, x ∈ Icc 0 1 ∧ ∀ (y : ℝ), y ∈ Icc 0 1 → ↑f x - x ≤ ↑f y - y\n\ncase intro.intro\nf g : CircleDeg1Lift\nhf : Continuous ↑f\nz : ℝ\nhz : ∀ (x : ℝ), x + z < ↑f x\nx : ℝ\nhx : ∀ (y : ℝ), y ∈ Icc 0 1 → ↑f x - x ≤ ↑... | [
926,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
918,
1
] |
Mathlib/Computability/Primrec.lean | Primrec₂.nat_iff | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nσ : Type u_3\ninst✝² : Primcodable α\ninst✝¹ : Primcodable β\ninst✝ : Primcodable σ\nf : α → β → σ\nthis :\n ∀ (a : Option α) (b : Option β),\n Option.map (fun p => f p.fst p.snd) (Option.bind a fun a => Option.map (Prod.mk a) b) =\n Option.bind a fun a => ... | [
541,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_of_empty' | [] | [
1503,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1502,
1
] |
Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.iIndepSet.indep_generateFrom_le | [
{
"state_after": "case h.e'_2.h.e'_2\nΩ : Type u_2\nι : Type u_1\nm0 : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\ninst✝¹ : LinearOrder ι\ninst✝ : IsProbabilityMeasure μ\ns : ι → Set Ω\nhsm : ∀ (n : ι), MeasurableSet (s n)\nhs : iIndepSet s\ni k : ι\nhk : i < k\n⊢ {s k} = {t | ∃ n, n ∈ {k} ∧ s n = t}",
... | [
494,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.tsum_eval | [] | [
682,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.translationNumber_eq_of_semiconj | [] | [
724,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
722,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | UniformCauchySeqOn.mono | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝ : UniformSpace β\nF : ι → α → β\nf : α → β\ns s'✝ : Set α\nx : α\np : Filter ι\np' : Filter α\ng : ι → α\ns' : Set α\nhf : UniformCauchySeqOnFilter F p (𝓟 s)\nhss' : s' ⊆ s\n⊢ UniformCauchySeqOnFilter F p (𝓟 s')",
"state_before": "α :... | [
493,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | lebesgue_number_lemma_sUnion | [
{
"state_after": "α✝ : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.183504\nα : Type u\ninst✝ : UniformSpace α\ns : Set α\nc : Set (Set α)\nhs : IsCompact s\nhc₁ : ∀ (t : Set α), t ∈ c → IsOpen t\nhc₂ : s ⊆ ⋃ (i : ↑c), ↑i\n⊢ ∃ n, n ∈ 𝓤 α ∧ ∀ (x : α), x ∈ s → ∃ t, t ∈ c ∧ ∀ (y : α), (x, y) ∈ n → ... | [
1865,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1862,
1
] |
Mathlib/Data/List/Basic.lean | List.zipLeft'_nil_left | [] | [
4045,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4044,
1
] |
Mathlib/Analysis/Normed/Field/UnitBall.lean | coe_mul_unitSphere | [] | [
167,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Rat.cast_finsupp_sum | [] | [
423,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Algebra/Module/LocalizedModule.lean | LocalizedModule.mul_smul' | [
{
"state_after": "case H\nR : Type u\ninst✝² : CommSemiring R\nS : Submonoid R\nM : Type v\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\ny : Localization S\nm : LocalizedModule S M\ndata : R × { x // x ∈ S }\n⊢ (Localization.mk data.fst data.snd * y) • m = Localization.mk data.fst data.snd • y • m",
"state... | [
351,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
9
] |
Mathlib/GroupTheory/Torsion.lean | Monoid.not_isTorsion_iff | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nH : Type ?u.104\ninst✝ : Monoid G\n⊢ ¬IsTorsion G ↔ ∃ g, ¬IsOfFinOrder g",
"tactic": "rw [IsTorsion, not_forall]"
}
] | [
67,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Data/Rat/NNRat.lean | NNRat.coe_natCast | [] | [
214,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.coe_eq_one | [
{
"state_after": "no goals",
"state_before": "r : ℝ≥0\n⊢ ↑r = 1 ↔ r = 1",
"tactic": "rw [← NNReal.coe_one, NNReal.coe_eq]"
}
] | [
221,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
11
] |
Mathlib/FieldTheory/Fixed.lean | FixedPoints.minpoly.monic | [
{
"state_after": "M : Type u\ninst✝⁵ : Monoid M\nG : Type u\ninst✝⁴ : Group G\nF : Type v\ninst✝³ : Field F\ninst✝² : MulSemiringAction M F\ninst✝¹ : MulSemiringAction G F\nm : M\ninst✝ : Fintype G\nx : F\n⊢ Polynomial.Monic (prodXSubSmul G F x)",
"state_before": "M : Type u\ninst✝⁵ : Monoid M\nG : Type u\n... | [
190,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/MeasureTheory/Constructions/Polish.lean | IsOpen.analyticSet_image | [
{
"state_after": "α : Type u_2\ninst✝² : TopologicalSpace α\nι : Type ?u.1515\nβ : Type u_1\ninst✝¹ : TopologicalSpace β\ninst✝ : PolishSpace β\ns : Set β\nhs : IsOpen s\nf : β → α\nf_cont : Continuous f\n⊢ AnalyticSet (range fun x => f ↑x)",
"state_before": "α : Type u_2\ninst✝² : TopologicalSpace α\nι : T... | [
106,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/LinearAlgebra/Matrix/IsDiag.lean | Matrix.IsDiag.sub | [
{
"state_after": "α : Type u_1\nβ : Type ?u.6998\nR : Type ?u.7001\nn : Type u_2\nm : Type ?u.7007\ninst✝ : AddGroup α\nA B : Matrix n n α\nha : IsDiag A\nhb : IsDiag B\ni j : n\nh : i ≠ j\n⊢ (A - B) i j = 0",
"state_before": "α : Type u_1\nβ : Type ?u.6998\nR : Type ?u.7001\nn : Type u_2\nm : Type ?u.7007\... | [
104,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.proj_bot_eq | [] | [
268,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.coe_sInf | [] | [
989,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
988,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasFDerivWithinAt.mono | [] | [
364,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
8
] |
Mathlib/Topology/Algebra/Group/Basic.lean | continuousOn_zpow | [] | [
516,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
1
] |
Mathlib/Data/FunLike/Equiv.lean | EquivLike.bijective | [] | [
174,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
11
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.inf_limZero | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedField α\nf g : CauSeq α abs\nhf : LimZero f\nhg : LimZero g\nε : α\nε0 : ε > 0\ni : ℕ\nH : ∀ (j : ℕ), j ≥ i → abs (↑f j) < ε ∧ abs (↑g j) < ε\nj : ℕ\nij : j ≥ i\nH₁ : abs (↑f j) < ε\nH₂ : abs (↑g j) < ε\n⊢ abs (↑(f ⊓ g) j) < ε",
"state_before": "α : Type ... | [
861,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
856,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Complex.lean | Complex.cpow_zero | [
{
"state_after": "no goals",
"state_before": "x : ℂ\n⊢ x ^ 0 = 1",
"tactic": "simp [cpow_def]"
}
] | [
48,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.conj_im | [] | [
513,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiff_id | [] | [
174,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.ne_neg_self_iff | [
{
"state_after": "no goals",
"state_before": "θ : Angle\n⊢ θ ≠ -θ ↔ θ ≠ 0 ∧ θ ≠ ↑π",
"tactic": "rw [← not_or, ← eq_neg_self_iff.not]"
}
] | [
219,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.list_tail | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.250075\nγ : Type ?u.250078\nσ : Type ?u.250081\ninst✝³ : Primcodable α\ninst✝² : Primcodable β\ninst✝¹ : Primcodable γ\ninst✝ : Primcodable σ\nl : List α\n⊢ (List.casesOn (id l) [] fun b l_1 => (l, b, l_1).snd.snd) = List.tail l",
"... | [
1051,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1050,
1
] |
Mathlib/Analysis/SpecialFunctions/Arsinh.lean | Differentiable.arsinh | [] | [
273,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Std/Data/Int/Lemmas.lean | Int.neg_of_neg_pos | [
{
"state_after": "no goals",
"state_before": "a : Int\nh : 0 < -a\n⊢ -0 < -a",
"tactic": "rwa [Int.neg_zero]"
}
] | [
896,
28
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
894,
11
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.equalizer.condition | [] | [
781,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
780,
1
] |
Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.bind₂_comp_bind₂ | [
{
"state_after": "no goals",
"state_before": "σ : Type u_3\nτ : Type ?u.435135\nR : Type u_1\nS : Type u_2\nT : Type u_4\ninst✝² : CommSemiring R\ninst✝¹ : CommSemiring S\ninst✝ : CommSemiring T\nf✝ : σ → MvPolynomial τ R\nf : R →+* MvPolynomial σ S\ng : S →+* MvPolynomial σ T\n⊢ RingHom.comp (bind₂ g) (bin... | [
239,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Analysis/Convex/Combination.lean | affineCombination_eq_centerMass | [
{
"state_after": "R : Type u_2\nE : Type u_3\nF : Type ?u.126038\nι✝ : Type ?u.126041\nι' : Type ?u.126044\nα : Type ?u.126047\ninst✝⁷ : LinearOrderedField R\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : LinearOrderedAddCommGroup α\ninst✝³ : Module R E\ninst✝² : Module R F\ninst✝¹ : Module R α\nin... | [
240,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Computability/Partrec.lean | Computable.cond | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.182461\nγ : Type ?u.182464\nσ : Type u_2\ninst✝³ : Primcodable α\ninst✝² : Primcodable β\ninst✝¹ : Primcodable γ\ninst✝ : Primcodable σ\nc : α → Bool\nf g : α → σ\nhc : Computable c\nhf : Computable f\nhg : Computable g\na : α\n⊢ (Nat.c... | [
681,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
679,
1
] |
Mathlib/Combinatorics/SetFamily/Intersecting.lean | Set.Intersecting.not_mem | [] | [
155,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
src/lean/Init/WF.lean | WellFounded.fix_eq | [] | [
77,
27
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
75,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.nth_interleave_left | [
{
"state_after": "α : Type u\nβ : Type v\nδ : Type w\nn : ℕ\ns₁ s₂ : Stream' α\n⊢ nth (s₁ ⋈ s₂) (succ (succ (2 * n))) = nth s₁ (succ n)",
"state_before": "α : Type u\nβ : Type v\nδ : Type w\nn : ℕ\ns₁ s₂ : Stream' α\n⊢ nth (s₁ ⋈ s₂) (2 * (n + 1)) = nth s₁ (n + 1)",
"tactic": "change nth (s₁ ⋈ s₂) (succ ... | [
439,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.disjoint_atBot_principal_Ici | [] | [
96,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Topology/CompactOpen.lean | ContinuousMap.gen_empty | [] | [
60,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Std/Classes/Order.lean | Std.TransCmp.gt_trans | [
{
"state_after": "cmp✝ : ?m.2531 → ?m.2531 → Ordering\ninst✝¹ : TransCmp cmp✝\nx✝ : Sort ?u.2529\ncmp : x✝ → x✝ → Ordering\ninst✝ : TransCmp cmp\nx y z : x✝\nh₁ : cmp y x = Ordering.lt\nh₂ : cmp z y = Ordering.lt\n⊢ cmp z x = Ordering.lt",
"state_before": "cmp✝ : ?m.2531 → ?m.2531 → Ordering\ninst✝¹ : Trans... | [
74,
50
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
73,
1
] |
Mathlib/Data/List/Dedup.lean | List.dedup_cons_of_mem | [] | [
56,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.toNat_lt_iff_lt_of_lt_aleph0 | [
{
"state_after": "no goals",
"state_before": "α β : Type u\nc d : Cardinal\nhc : c < ℵ₀\nhd : d < ℵ₀\n⊢ ↑toNat c < ↑toNat d ↔ c < d",
"tactic": "rw [← natCast_lt, cast_toNat_of_lt_aleph0 hc, cast_toNat_of_lt_aleph0 hd]"
}
] | [
1700,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1698,
1
] |
Mathlib/Algebra/Associated.lean | Associates.mk_le_mk_of_dvd | [
{
"state_after": "α : Type u_1\nβ : Type ?u.307911\nγ : Type ?u.307914\nδ : Type ?u.307917\ninst✝ : CommMonoid α\na b : α\nx✝ : a ∣ b\nc : α\nhc : b = a * c\n⊢ Associates.mk (a * c) = Associates.mk a * Associates.mk c",
"state_before": "α : Type u_1\nβ : Type ?u.307911\nγ : Type ?u.307914\nδ : Type ?u.30791... | [
940,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
939,
1
] |
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | isBoundedBilinearMap_compMultilinear | [] | [
486,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.equivProdDfinsupp_smul | [] | [
1693,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1691,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.insert | [
{
"state_after": "no goals",
"state_before": "α : Type uu\nβ : Type vv\nl₁✝ l₂✝ : List α\ninst✝ : DecidableEq α\na : α\nl₁ l₂ : List α\np : l₁ ~ l₂\nh : a ∈ l₁\n⊢ List.insert a l₁ ~ List.insert a l₂",
"tactic": "simpa [h, p.subset h] using p"
},
{
"state_after": "no goals",
"state_before": "... | [
965,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
963,
1
] |
Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.IndepSets.indep_aux | [
{
"state_after": "Ω : Type u_1\nι : Type ?u.1680679\nm2 m : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\ninst✝ : IsProbabilityMeasure μ\np1 p2 : Set (Set Ω)\nh2 : m2 ≤ m\nhp2 : IsPiSystem p2\nhpm2 : m2 = generateFrom p2\nhyp : IndepSets p1 p2\nt1 t2 : Set Ω\nht1 : t1 ∈ p1\nht2m : MeasurableSet t2\nμ_inter : ... | [
359,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
9
] |
Mathlib/InformationTheory/Hamming.lean | Hamming.ofHamming_zero | [] | [
355,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.basisFun_map | [] | [
992,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
990,
1
] |
Mathlib/Data/Option/NAry.lean | Option.map₂_none_left | [] | [
61,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Analysis/Convex/Extreme.lean | IsExtreme.convex_diff | [] | [
192,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/GroupTheory/Commutator.lean | commutator_mem_commutatorSet | [] | [
271,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Data/MvPolynomial/Division.lean | MvPolynomial.divMonomial_monomial | [] | [
98,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.neg_fuzzy_neg_iff | [
{
"state_after": "no goals",
"state_before": "x y : PGame\n⊢ -x ‖ -y ↔ x ‖ y",
"tactic": "rw [Fuzzy, Fuzzy, neg_lf_neg_iff, neg_lf_neg_iff, and_comm]"
}
] | [
1342,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1341,
1
] |
Mathlib/Data/Nat/Sqrt.lean | Nat.sqrt_add_eq' | [] | [
152,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.of_rat_sub | [
{
"state_after": "no goals",
"state_before": "q : ℚ\nx y : ℝ\nh : Irrational (↑q - x)\n⊢ Irrational (↑q + -x)",
"tactic": "simpa only [sub_eq_add_neg] using h"
}
] | [
292,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/Analysis/Convex/Between.lean | Sbtw.trans_left_right | [] | [
841,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
839,
1
] |
Mathlib/Algebra/Polynomial/BigOperators.lean | Polynomial.multiset_prod_X_sub_C_coeff_card_pred | [
{
"state_after": "R : Type u\nι : Type w\ns : Finset ι\ninst✝ : CommRing R\nt : Multiset R\nht : 0 < ↑Multiset.card t\n✝ : Nontrivial R\n⊢ coeff (prod (Multiset.map (fun x => X - ↑C x) t)) (↑Multiset.card t - 1) = -Multiset.sum t",
"state_before": "R : Type u\nι : Type w\ns : Finset ι\ninst✝ : CommRing R\nt... | [
277,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Analysis/Calculus/Deriv/Pow.lean | deriv_pow | [] | [
91,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/LinearAlgebra/Matrix/Charpoly/LinearMap.lean | Matrix.Represents.smul | [
{
"state_after": "ι : Type u_1\ninst✝⁴ : Fintype ι\nM : Type u_3\ninst✝³ : AddCommGroup M\nR : Type u_2\ninst✝² : CommRing R\ninst✝¹ : Module R M\nI : Ideal R\nb : ι → M\nhb : Submodule.span R (Set.range b) = ⊤\ninst✝ : DecidableEq ι\nA : Matrix ι ι R\nf : Module.End R M\nh : ↑(PiToModule.fromMatrix R b) A = ↑(... | [
149,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | Left.one_lt_mul_of_le_of_lt_of_pos | [] | [
787,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
785,
1
] |
Mathlib/CategoryTheory/Sites/Adjunction.lean | CategoryTheory.Sheaf.adjunctionToTypes_counit_app_val | [
{
"state_after": "case a\nC : Type u\ninst✝⁹ : Category C\nJ : GrothendieckTopology C\nD : Type w₁\ninst✝⁸ : Category D\nE : Type w₂\ninst✝⁷ : Category E\nF : D ⥤ E\nG✝ : E ⥤ D\ninst✝⁶ : (X : C) → (S : Cover J X) → (P : Cᵒᵖ ⥤ D) → PreservesLimit (MulticospanIndex.multicospan (Cover.index S P)) F\ninst✝⁵ : Concr... | [
153,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pullback.lift_fst | [] | [
1173,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1171,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.sInf_adj | [] | [
395,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.div_le_iff' | [] | [
813,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
812,
8
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.restrictScalars_ball | [] | [
1092,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1091,
1
] |
Mathlib/Analysis/Calculus/Taylor.lean | taylor_within_apply | [
{
"state_after": "case zero\n𝕜 : Type ?u.230356\nE : Type u_1\nF : Type ?u.230362\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : ℝ → E\ns : Set ℝ\nx₀ x : ℝ\n⊢ taylorWithinEval f Nat.zero s x₀ x =\n ∑ k in Finset.range (Nat.zero + 1), ((↑k !)⁻¹ * (x - x₀) ^ k) • iteratedDerivWithin k f s x₀\n\n... | [
123,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Order/GameAdd.lean | Sym2.GameAdd.induction | [] | [
250,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_bij | [] | [
553,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.lt_add_of_pos_left | [
{
"state_after": "n k : Nat\nh : 0 < k\n⊢ n < n + k",
"state_before": "n k : Nat\nh : 0 < k\n⊢ n < k + n",
"tactic": "rw [Nat.add_comm]"
},
{
"state_after": "no goals",
"state_before": "n k : Nat\nh : 0 < k\n⊢ n < n + k",
"tactic": "exact Nat.lt_add_of_pos_right h"
}
] | [
93,
53
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
92,
11
] |
Mathlib/Order/Filter/Extr.lean | IsMinOn.sup | [] | [
544,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
] |
Mathlib/Algebra/Hom/Units.lean | IsUnit.mul_liftRight_inv | [
{
"state_after": "F : Type ?u.42331\nG : Type ?u.42334\nα : Type ?u.42337\nM : Type u_1\nN : Type u_2\ninst✝¹ : Monoid M\ninst✝ : Monoid N\nf : M →* N\nh : ∀ (x : M), IsUnit (↑f x)\nx x✝ : M\n⊢ ↑(IsUnit.unit (_ : IsUnit (↑f x✝))) = ↑f x✝",
"state_before": "F : Type ?u.42331\nG : Type ?u.42334\nα : Type ?u.4... | [
260,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Std/Data/Int/Lemmas.lean | Int.sign_of_succ | [] | [
199,
62
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
199,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | zpow_one | [
{
"state_after": "case h.e'_2\nα : Type ?u.54010\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : DivInvMonoid G\na : G\n⊢ a ^ 1 = a ^ 1",
"state_before": "α : Type ?u.54010\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR :... | [
288,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.coe_bind | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.9950\nδ : Type ?u.9953\na : α\ns t : Multiset α\nf✝ g : α → Multiset β\nl : List α\nf : α → List β\n⊢ (bind ↑l fun a => ↑(f a)) = join ↑(List.map (ofList ∘ f) l)",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.9950\nδ : Type ?u.9953\na : α... | [
102,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Algebra/Algebra/Bilinear.lean | LinearMap.mulRight_one | [
{
"state_after": "case h\nR : Type u_2\nA : Type u_1\ninst✝² : CommSemiring R\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\nx✝ : A\n⊢ ↑(mulRight R 1) x✝ = ↑id x✝",
"state_before": "R : Type u_2\nA : Type u_1\ninst✝² : CommSemiring R\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\n⊢ mulRight R 1 = id",
"tactic":... | [
217,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | HasDerivWithinAt.cexp | [] | [
102,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.coe_trans_to_affineMap | [] | [
346,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.insert | [] | [
671,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
668,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.LpToLpRestrictCLM_coeFn | [] | [
929,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
927,
1
] |
Mathlib/Algebra/Order/Ring/WithTop.lean | WithTop.top_mul' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝² : DecidableEq α\ninst✝¹ : Zero α\ninst✝ : Mul α\na : WithTop α\n⊢ ⊤ * a = if a = 0 then 0 else ⊤",
"tactic": "induction a using recTopCoe <;> simp [mul_def] <;> rfl"
}
] | [
57,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/GroupTheory/Commutator.lean | commutatorElement_inv | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nG' : Type ?u.10728\nF : Type ?u.10731\ninst✝² : Group G\ninst✝¹ : Group G'\ninst✝ : MonoidHomClass F G G'\nf : F\ng₁ g₂ g₃ g : G\n⊢ ⁅g₁, g₂⁆⁻¹ = ⁅g₂, g₁⁆",
"tactic": "simp_rw [commutatorElement_def, mul_inv_rev, inv_inv, mul_assoc]"
}
] | [
63,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/CategoryTheory/Monad/Algebra.lean | CategoryTheory.Monad.leftAdjoint_forget | [] | [
243,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | LocalHomeomorph.map_extend_nhdsWithin_eq_image | [
{
"state_after": "𝕜 : Type u_4\nE : Type u_3\nM : Type u_1\nH : Type u_2\nE' : Type ?u.150056\nM' : Type ?u.150059\nH' : Type ?u.150062\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : TopologicalSpace H\ninst✝⁴ : TopologicalSpace M\nf f' : LocalHomeomorp... | [
896,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
886,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.