file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/GroupTheory/Subsemigroup/Operations.lean | MulHom.coe_srange | [] | [
760,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | iteratedFDeriv_succ_apply_right | [
{
"state_after": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nX : Type uX\ninst✝¹ : NormedAdd... | [
1609,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1605,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.coe_trans | [] | [
804,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
803,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.curryRight_apply | [] | [
1386,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1384,
1
] |
Mathlib/Analysis/Convex/Basic.lean | convex_univ | [] | [
94,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Data/Set/Function.lean | Function.invFunOn_eq | [] | [
1223,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1222,
1
] |
Mathlib/Data/Set/Basic.lean | Set.union_subset_iff | [] | [
830,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
829,
1
] |
Mathlib/MeasureTheory/Function/Egorov.lean | MeasureTheory.Egorov.iUnionNotConvergentSeq_subset | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nι : Type u_3\nm : MeasurableSpace α\ninst✝³ : MetricSpace β\nμ : Measure α\nn : ℕ\ni j : ι\ns : Set α\nε : ℝ\nf : ι → α → β\ng : α → β\ninst✝² : SemilatticeSup ι\ninst✝¹ : Nonempty ι\ninst✝ : Countable ι\nhε : 0 < ε\nhf : ∀ (n : ι), StronglyMeasurable (f n)\nhg : St... | [
169,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.X_dvd_iff | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\nφ : PowerSeries R\n⊢ (∀ (m : ℕ), m < 1 → ↑(coeff R m) φ = 0) ↔ ↑(coeff R 0) φ = 0",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nφ : PowerSeries R\n⊢ X ∣ φ ↔ ↑(constantCoeff R) φ = 0",
"tactic": "rw [← pow_one (X : PowerSeries R), X_pow_dvd_iff, ... | [
1724,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1719,
1
] |
Mathlib/LinearAlgebra/Span.lean | LinearMap.eqOn_span' | [] | [
959,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
957,
1
] |
Mathlib/Topology/SubsetProperties.lean | countable_cover_nhdsWithin_of_sigma_compact | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.164016\nπ : ι → Type ?u.164021\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ns✝ t : Set α\ninst✝ : SigmaCompactSpace α\nf : α → Set α\ns : Set α\nhs : IsClosed s\nhf : ∀ (x : α), x ∈ s → {x_1 | x_1 ∈ s → x_1 ∈ f x} ∈ 𝓝 x\n⊢ ∃ t x, Set.Countable... | [
1403,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1393,
1
] |
Mathlib/Topology/Order/Basic.lean | nhdsWithin_Ioc_eq_nhdsWithin_Iic | [
{
"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 : α\nh : a < b\n⊢ 𝓝[Ioc a b] b = 𝓝[Iic b] b",
"tactic": "simpa only [dual_Ico] using nhdsWit... | [
599,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
1
] |
Mathlib/GroupTheory/Solvable.lean | solvable_of_solvable_injective | [] | [
155,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoUniformlyOnFilter.prod | [] | [
306,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.mem_inf | [] | [
718,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
717,
1
] |
Mathlib/Computability/Halting.lean | Nat.Partrec'.vec_iff | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\nf : Vector ℕ m → Vector ℕ n\nh : Vec f\n⊢ Computable f",
"tactic": "simpa only [ofFn_get] using vector_ofFn fun i => to_part (h i)"
}
] | [
437,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsGLB.dual | [] | [
167,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.comap_le_comap_iff_of_surjective | [] | [
505,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
1
] |
Mathlib/CategoryTheory/StructuredArrow.lean | CategoryTheory.CostructuredArrow.eqToHom_left | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nT T' T'' : D\nY✝ Y' : C\nS : C ⥤ D\nX Y : CostructuredArrow S T\nh : X = Y\n⊢ X.left = Y.left",
"tactic": "rw [h]"
},
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\n... | [
331,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/Data/ENat/Basic.lean | ENat.one_le_iff_pos | [] | [
197,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Data/Set/Sups.lean | Set.Nonempty.sups | [] | [
120,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
11
] |
Mathlib/Analysis/Calculus/LocalExtr.lean | IsLocalMin.fderiv_eq_zero | [] | [
199,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Order/Filter/Pi.lean | Filter.map_eval_pi | [
{
"state_after": "ι : Type u_2\nα : ι → Type u_1\nf✝ f₁ f₂ : (i : ι) → Filter (α i)\ns✝ : (i : ι) → Set (α i)\nf : (i : ι) → Filter (α i)\ninst✝ : ∀ (i : ι), NeBot (f i)\ni : ι\ns : Set (α i)\nhs : s ∈ map (eval i) (pi f)\n⊢ s ∈ f i",
"state_before": "ι : Type u_2\nα : ι → Type u_1\nf✝ f₁ f₂ : (i : ι) → Fil... | [
174,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.repr_apply_eq | [
{
"state_after": "ι : Type u_1\nι' : Type ?u.220743\nR : Type u_2\nR₂ : Type ?u.220749\nK : Type ?u.220752\nM : Type u_3\nM' : Type ?u.220758\nM'' : Type ?u.220761\nV : Type u\nV' : Type ?u.220766\ninst✝⁹ : Semiring R\ninst✝⁸ : AddCommMonoid M\ninst✝⁷ : Module R M\ninst✝⁶ : AddCommMonoid M'\ninst✝⁵ : Module R M... | [
330,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.countp_congr | [
{
"state_after": "α : Type uu\nβ : Type vv\nl₁ l₂ : List α\ns : l₁ ~ l₂\np p' : α → Bool\nhp : ∀ (x : α), x ∈ l₁ → p x = p' x\n⊢ countp p l₁ = countp p' l₁",
"state_before": "α : Type uu\nβ : Type vv\nl₁ l₂ : List α\ns : l₁ ~ l₂\np p' : α → Bool\nhp : ∀ (x : α), x ∈ l₁ → p x = p' x\n⊢ countp p l₁ = countp p... | [
489,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.approx_apply | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.821186\nδ : Type ?u.821189\ninst✝⁷ : MeasurableSpace α\nK : Type ?u.821195\ninst✝⁶ : SemilatticeSup β\ninst✝⁵ : OrderBot β\ninst✝⁴ : Zero β\ninst✝³ : TopologicalSpace β\ninst✝² : OrderClosedTopology β\ninst✝¹ : MeasurableSpace β\ninst✝ : OpensMeasurableS... | [
842,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
833,
1
] |
Mathlib/Deprecated/Group.lean | RingHom.to_isMonoidHom | [] | [
376,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Order/Bounds/Basic.lean | bddAbove_Ico | [] | [
664,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
663,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_apply₀ | [
{
"state_after": "α : Type u_1\nβ : Type ?u.278939\nγ : Type ?u.278942\nδ : Type ?u.278945\nι : Type ?u.278948\nR : Type ?u.278951\nR' : Type ?u.278954\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\nht : NullMeasurableSet t✝\n... | [
1519,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1514,
1
] |
Mathlib/Order/Filter/Partial.lean | Filter.tendsto_iff_rtendsto | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nl₁ : Filter α\nl₂ : Filter β\nf : α → β\n⊢ Tendsto f l₁ l₂ ↔ RTendsto (Function.graph f) l₁ l₂",
"tactic": "simp [tendsto_def, Function.graph, rtendsto_def, Rel.core, Set.preimage]"
}
] | [
200,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Algebra/ContinuedFractions/Translations.lean | GeneralizedContinuedFraction.num_eq_conts_a | [] | [
97,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | Right.mul_le_one | [] | [
823,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
820,
1
] |
Mathlib/Algebra/CharP/Basic.lean | sub_pow_char | [] | [
287,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/MeasureTheory/Function/Floor.lean | Int.measurable_floor | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.120\nR : Type u_1\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : LinearOrderedRing R\ninst✝⁴ : FloorRing R\ninst✝³ : TopologicalSpace R\ninst✝² : OrderTopology R\ninst✝¹ : MeasurableSpace R\ninst✝ : OpensMeasurableSpace R\nx : R\n⊢ MeasurableSet (floor ⁻¹' {⌊... | [
30,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
28,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.IsImage.symm | [] | [
371,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
11
] |
Mathlib/Data/Nat/GCD/Basic.lean | Nat.coprime_one_right_iff | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ coprime n 1 ↔ True",
"tactic": "simp [coprime]"
}
] | [
212,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | WfDvdMonoid.induction_on_irreducible | [] | [
109,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Algebra/Order/Sub/Canonical.lean | tsub_tsub_cancel_of_le | [] | [
299,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.toReal_coe_eq_self_sub_two_mul_int_mul_pi_iff | [
{
"state_after": "θ : ℝ\nk : ℤ\n⊢ -π < θ - 2 * ↑k * π ∧ θ - 2 * ↑k * π ≤ π ↔ (2 * ↑k - 1) * π < θ ∧ θ ≤ (2 * ↑k + 1) * π",
"state_before": "θ : ℝ\nk : ℤ\n⊢ toReal ↑θ = θ - 2 * ↑k * π ↔ θ ∈ Set.Ioc ((2 * ↑k - 1) * π) ((2 * ↑k + 1) * π)",
"tactic": "rw [← sub_zero (θ : Angle), ← zsmul_zero k, ← coe_two_pi... | [
685,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
681,
1
] |
Mathlib/Topology/Order.lean | gc_nhds | [
{
"state_after": "α : Type u\nβ : Type v\na : α\nf : Filter α\nt : TopologicalSpace α\n⊢ nhdsAdjoint a f ≤ t ↔ ∀ (s : Set α), a ∈ s → IsOpen s → s ∈ f",
"state_before": "α : Type u\nβ : Type v\na : α\nf : Filter α\nt : TopologicalSpace α\n⊢ nhdsAdjoint a f ≤ t ↔ f ≤ (fun t => 𝓝 a) t",
"tactic": "rw [le... | [
589,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
587,
1
] |
Mathlib/Data/PFunctor/Multivariate/Basic.lean | MvPFunctor.liftP_iff | [
{
"state_after": "case mp\nn m : ℕ\nP : MvPFunctor n\nQ : Fin2 n → MvPFunctor m\nα✝ β : TypeVec m\nα : TypeVec n\np : ⦃i : Fin2 n⦄ → α i → Prop\nx : Obj P α\n⊢ LiftP p x → ∃ a f, x = { fst := a, snd := f } ∧ ∀ (i : Fin2 n) (j : B P a i), p (f i j)\n\ncase mpr\nn m : ℕ\nP : MvPFunctor n\nQ : Fin2 n → MvPFunctor ... | [
169,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/CategoryTheory/Adjunction/Limits.lean | CategoryTheory.Adjunction.hasColimit_comp_equivalence | [] | [
142,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.SSameSide.trans_sOppSide | [] | [
574,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
572,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | Padic.exi_rat_seq_conv | [
{
"state_after": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nf : CauSeq ℚ_[p] ↑padicNormE\nε : ℚ\nhε : 0 < ε\nN : ℕ\nhN : 1 / ε < ↑N\ni : ℕ\nhi : i ≥ N\n⊢ ↑padicNormE (↑f i - ↑(limSeq f i)) < ε",
"state_before": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nf : CauSeq ℚ_[p] ↑padicNormE\nε : ℚ\nhε : 0 < ε\n⊢ ∃ N, ∀ (i : ℕ), i... | [
700,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.sum_add_sum | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.347212\nγ : Type ?u.347215\nδ : Type ?u.347218\nι : Type ?u.347221\nR : Type ?u.347224\nR' : Type ?u.347227\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\nμ ν : ℕ → Measure ... | [
2129,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2126,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.limsup_eq_sInf_sSup | [
{
"state_after": "case refine'_1\nα : Type ?u.120102\nβ : Type ?u.120105\nγ : Type ?u.120108\nι✝ : Type ?u.120111\ninst✝¹ : CompleteLattice α\nι : Type u_1\nR : Type u_2\nF : Filter ι\ninst✝ : CompleteLattice R\na : ι → R\n⊢ limsup a F ≤ sInf ((fun I => sSup (a '' I)) '' F.sets)\n\ncase refine'_2\nα : Type ?u.1... | [
793,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
781,
1
] |
Mathlib/LinearAlgebra/SModEq.lean | SModEq.mono | [] | [
63,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Data/Int/Order/Basic.lean | Int.le_induction | [
{
"state_after": "case refine_1\nP : ℤ → Prop\nm : ℤ\nh0 : P m\nh1 : ∀ (n : ℤ), m ≤ n → P n → P (n + 1)\nn : ℤ\n⊢ m ≤ m → P m\n\ncase refine_2\nP : ℤ → Prop\nm : ℤ\nh0 : P m\nh1 : ∀ (n : ℤ), m ≤ n → P n → P (n + 1)\nn : ℤ\n⊢ ∀ (k : ℤ), m ≤ k → (m ≤ k → P k) → m ≤ k + 1 → P (k + 1)\n\ncase refine_3\nP : ℤ → Prop... | [
175,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
11
] |
Mathlib/Data/Set/Finite.lean | Set.iInf_iSup_of_monotone | [] | [
1513,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1510,
1
] |
Mathlib/Algebra/Lie/Normalizer.lean | LieSubmodule.gc_top_lie_normalizer | [] | [
95,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/LinearAlgebra/Matrix/Symmetric.lean | Matrix.IsSymm.apply | [] | [
55,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.coe_mul | [] | [
382,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.x_sub_y_dvd_pow_lem | [
{
"state_after": "no goals",
"state_before": "a : ℕ\na1 : 1 < a\ny2 y1 y0 yn1 yn0 xn1 xn0 ay a2 : ℤ\n⊢ (a2 * yn1 - yn0) * ay + y2 - (a2 * xn1 - xn0) = y2 - a2 * y1 + y0 + a2 * (yn1 * ay + y1 - xn1) - (yn0 * ay + y0 - xn0)",
"tactic": "ring"
}
] | [
570,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
1
] |
Mathlib/Data/Prod/TProd.lean | List.TProd.elim_mk | [
{
"state_after": "case pos\nι : Type u\nα : ι → Type v\ni✝ j✝ : ι\nl : List ι\nf✝ : (i : ι) → α i\ninst✝ : DecidableEq ι\ni : ι\nis : List ι\nf : (i : ι) → α i\nj : ι\nhj : j ∈ i :: is\nhji : j = i\n⊢ TProd.elim (TProd.mk (i :: is) f) hj = f j\n\ncase neg\nι : Type u\nα : ι → Type v\ni✝ j✝ : ι\nl : List ι\nf✝ :... | [
115,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | differentiableWithinAt_const_sub_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.545914\ninst✝³ : NormedAddCommGroup G\ninst✝² : Normed... | [
626,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
624,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.hasFiniteIntegral_zero_measure | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.721423\nδ : Type ?u.721426\nm✝ : MeasurableSpace α\nμ ν : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\nm : MeasurableSpace α\nf : α → β\n⊢ HasFiniteIntegral f",
"t... | [
226,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Data/Finset/Prod.lean | Finset.map_swap_product | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.17685\ns✝ s' : Finset α\nt✝ t' : Finset β\na : α\nb : β\ns : Finset α\nt : Finset β\n⊢ (fun a => ↑{ toFun := Prod.swap, inj' := (_ : Function.Injective Prod.swap) } a) '' ↑t ×ˢ ↑s = ↑s ×ˢ ↑t",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.... | [
109,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Data/LazyList/Basic.lean | LazyList.mem_cons | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nx y : α\nys : Thunk (LazyList α)\n⊢ x ∈ cons y ys ↔ x = y ∨ x ∈ Thunk.get ys",
"tactic": "simp [Membership.mem, LazyList.Mem]"
}
] | [
258,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/GroupTheory/Complement.lean | Subgroup.smul_apply_eq_smul_apply_inv_smul | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝³ : Group G\nH K : Subgroup G\nS T✝ : Set G\nF : Type u_2\ninst✝² : Group F\ninst✝¹ : MulAction F G\ninst✝ : QuotientAction F H\nf : F\nT : ↑(leftTransversals ↑H)\nq : G ⧸ H\n⊢ ↑(↑(toEquiv (_ : ↑(f • T) ∈ leftTransversals ↑H)) q) = f • ↑(↑(toE... | [
480,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.prod_eq_bot | [
{
"state_after": "R✝ : Type u\nι : Type ?u.301378\ninst✝² : CommSemiring R✝\nI J K L : Ideal R✝\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\ns : Multiset (Ideal R)\n⊢ (∃ r x, r = 0) ↔ ∃ I, I ∈ s ∧ I = 0",
"state_before": "R✝ : Type u\nι : Type ?u.301378\ninst✝² : CommSemiring R✝\nI J K L : Ideal ... | [
823,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
820,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.iSup_comap_le | [] | [
1531,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1529,
1
] |
Mathlib/Algebra/Order/Group/Abs.lean | abs_eq_zero | [] | [
184,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.vanishingIdeal_iUnion | [] | [
354,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Data/Set/Basic.lean | Set.eq_singleton_iff_unique_mem | [] | [
1363,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1362,
1
] |
Mathlib/GroupTheory/Finiteness.lean | AddGroup.fg_def | [] | [
301,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Algebra/Module/LocalizedModule.lean | IsLocalizedModule.smul_injective | [] | [
910,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
909,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.coe_zpow | [] | [
1342,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1341,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.of_apply | [] | [
124,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.EqOnSource.eqOn | [] | [
962,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
961,
1
] |
Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.lift_ofList | [] | [
243,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Topology/Sheaves/Stalks.lean | TopCat.Presheaf.isIso_iff_stalkFunctor_map_iso | [] | [
637,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
633,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.eq_symm_apply | [] | [
168,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.mk'_toSubmonoid | [] | [
318,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.coe_zero | [] | [
268,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
11
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.coe_iInf | [
{
"state_after": "no goals",
"state_before": "F : Type u_2\ninst✝² : Field F\nE : Type u_3\ninst✝¹ : Field E\ninst✝ : Algebra F E\nι : Sort u_1\nS : ι → IntermediateField F E\n⊢ ↑(iInf S) = ⋂ (i : ι), ↑(S i)",
"tactic": "simp [iInf]"
}
] | [
164,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.collinear_of_angle_eq_zero | [] | [
447,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
Mathlib/Analysis/Normed/Order/Lattice.lean | continuous_pos | [] | [
209,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | measure_Ico_lt_top | [] | [
4594,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4593,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.sum_lt_lift_of_isRegular | [] | [
1115,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1113,
1
] |
Std/Logic.lean | Decidable.imp_iff_not_or | [] | [
556,
39
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
555,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.drop.aux_none | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nn : ℕ\n⊢ Computation.bind (Computation.pure none) (aux n) = Computation.pure none",
"tactic": "rw [ret_bind, drop.aux_none n]"
}
] | [
821,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
817,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.castSucc_pred_eq_pred_castSucc | [
{
"state_after": "case mk\nn m val✝ : ℕ\nisLt✝ : val✝ < n + 1\nha : { val := val✝, isLt := isLt✝ } ≠ 0\nha' : optParam (↑castSucc { val := val✝, isLt := isLt✝ } ≠ 0) (_ : ↑castSucc { val := val✝, isLt := isLt✝ } ≠ 0)\n⊢ ↑castSucc (pred { val := val✝, isLt := isLt✝ } ha) = pred (↑castSucc { val := val✝, isLt := ... | [
2408,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2405,
1
] |
Mathlib/Order/Cover.lean | Prod.mk_wcovby_mk_iff | [
{
"state_after": "case refine'_1\nα : Type u_2\nβ : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : PartialOrder β\na a₁ a₂ : α\nb b₁ b₂ : β\nx y : α × β\nh : (a₁, b₁) ⩿ (a₂, b₂)\n⊢ a₁ ⩿ a₂ ∧ b₁ = b₂ ∨ b₁ ⩿ b₂ ∧ a₁ = a₂\n\ncase refine'_2\nα : Type u_2\nβ : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : PartialOrder β\na... | [
543,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
536,
1
] |
Mathlib/Data/Set/Prod.lean | Set.fst_image_prod_subset | [] | [
353,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.tan_nat_mul_pi | [] | [
1319,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1318,
1
] |
Mathlib/Logic/Basic.lean | eq_true_eq_id | [
{
"state_after": "case h\nx✝ : Prop\n⊢ (True = x✝) = id x✝",
"state_before": "⊢ Eq True = id",
"tactic": "funext _"
},
{
"state_after": "no goals",
"state_before": "case h\nx✝ : Prop\n⊢ (True = x✝) = id x✝",
"tactic": "simp only [true_iff, id.def, eq_iff_iff]"
}
] | [
170,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
9
] |
Mathlib/GroupTheory/OrderOfElement.lean | zpowersEquivZpowers_apply | [
{
"state_after": "G : Type u\nA : Type v\nx y : G\na b : A\nn✝ m : ℕ\ninst✝² : Group G\ninst✝¹ : AddGroup A\ninst✝ : Finite G\nh : orderOf x = orderOf y\nn : ℕ\n⊢ ↑(Fin.cast h).toEquiv { val := n % orderOf x, isLt := (_ : n % orderOf x < orderOf x) } =\n { val := n % orderOf y, isLt := (_ : n % orderOf y < o... | [
884,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
880,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | orderOf_eq_iff | [
{
"state_after": "G : Type u\nA : Type v\nx y : G\na b : A\nn✝ m : ℕ\ninst✝¹ : Monoid G\ninst✝ : AddMonoid A\nn : ℕ\nh : 0 < n\n⊢ (if h : 1 ∈ periodicPts fun x_1 => x * x_1 then Nat.find h else 0) = n ↔\n IsPeriodicPt (fun x_1 => x * x_1) n 1 ∧ ∀ (m : ℕ), m < n → 0 < m → ¬IsPeriodicPt (fun x_1 => x * x_1) m ... | [
195,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_restrict_iff'₀ | [
{
"state_after": "α : Type u_1\nβ : Type ?u.576111\nγ : Type ?u.576114\nδ : Type ?u.576117\nι : Type ?u.576120\nR : Type ?u.576123\nR' : Type ?u.576126\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\np : α → Prop\nhs : NullMeasur... | [
2840,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2837,
1
] |
Mathlib/Analysis/Asymptotics/AsymptoticEquivalent.lean | Asymptotics.IsEquivalent.add_isLittleO | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝ : NormedAddCommGroup β\nu v w : α → β\nl : Filter α\nhuv : u ~[l] v\nhwv : w =o[l] v\n⊢ u + w ~[l] v",
"tactic": "simpa only [IsEquivalent, add_sub_right_comm] using huv.add hwv"
}
] | [
169,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/NumberTheory/LegendreSymbol/MulCharacter.lean | MulChar.inv_apply' | [] | [
373,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Std/Data/List/Lemmas.lean | List.filter_nil | [] | [
1106,
68
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1106,
9
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.single_mem_supported | [] | [
215,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.choose_mul_factorial_mul_factorial | [
{
"state_after": "no goals",
"state_before": "x✝ : ℕ\nhk : x✝ ≤ 0\n⊢ choose 0 x✝ * x✝! * (0 - x✝)! = 0!",
"tactic": "simp [Nat.eq_zero_of_le_zero hk]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\nx✝ : 0 ≤ n + 1\n⊢ choose (n + 1) 0 * 0! * (n + 1 - 0)! = (n + 1)!",
"tactic": "si... | [
146,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | rel_sup_add | [
{
"state_after": "case h.e'_1.h.e'_1\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.378311\nδ : Type ?u.378314\ninst✝⁴ : AddCommMonoid α\ninst✝³ : TopologicalSpace α\ninst✝² : T2Space α\nf g : β → α\na a₁ a₂ : α\ninst✝¹ : Countable γ\ninst✝ : CompleteLattice β\nm : β → α\nm0 : m ⊥ = 0\nR : α → α → Prop\nm_iSup : ∀ (s... | [
765,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
760,
1
] |
Mathlib/Topology/LocallyConstant/Basic.lean | IsLocallyConstant.isClosed_fiber | [] | [
79,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/CategoryTheory/Preadditive/Basic.lean | CategoryTheory.Preadditive.zsmul_comp | [] | [
178,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Data/Nat/Bits.lean | Nat.pos_of_bit0_pos | [
{
"state_after": "case zero\nn : ℕ\nh : 0 < bit0 zero\n⊢ 0 < zero\n\ncase succ\nn n✝ : ℕ\nh : 0 < bit0 (succ n✝)\n⊢ 0 < succ n✝",
"state_before": "n✝ n : ℕ\nh : 0 < bit0 n\n⊢ 0 < n",
"tactic": "cases n"
},
{
"state_after": "no goals",
"state_before": "case zero\nn : ℕ\nh : 0 < bit0 zero\n⊢ 0... | [
119,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iic_subset_Iio | [] | [
432,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iio_subset_Iic | [] | [
619,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.