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/Set/Intervals/Monotone.lean | strictMonoOn_Ici_of_pred_lt | [] | [
266,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/CategoryTheory/Functor/FullyFaithful.lean | CategoryTheory.Faithful.of_comp_eq | [] | [
321,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/GroupTheory/SpecificGroups/Dihedral.lean | DihedralGroup.sr_mul_r | [] | [
93,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Data/Nat/Sqrt.lean | Nat.sqrt_eq | [] | [
156,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/LogDeriv.lean | DifferentiableAt.clog | [] | [
115,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Order/MinMax.lean | min_lt_min_right_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : LinearOrder α\ninst✝ : LinearOrder β\nf : α → β\ns : Set α\na b c d : α\n⊢ min a b < min a c ↔ b < c ∧ b < a",
"tactic": "simp_rw [min_comm a, min_lt_min_left_iff]"
}
] | [
190,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Data/List/Nodup.lean | List.nodup_attach | [] | [
278,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.toReal_coe_eq_self_sub_two_pi_iff | [
{
"state_after": "no goals",
"state_before": "θ : ℝ\n⊢ toReal ↑θ = θ - 2 * π ↔ θ ∈ Set.Ioc π (3 * π)",
"tactic": "convert @toReal_coe_eq_self_sub_two_mul_int_mul_pi_iff θ 1 <;> norm_num"
}
] | [
690,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
688,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | pow_le_one_iff | [] | [
244,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Submodule.annihilator_eq_top_iff | [] | [
92,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.mul_ne_top | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.91147\nβ : Type ?u.91150\na b c d : ℝ≥0∞\nr p q : ℝ≥0\n⊢ a ≠ ⊤ → b ≠ ⊤ → a * b ≠ ⊤",
"tactic": "simpa only [lt_top_iff_ne_top] using mul_lt_top"
}
] | [
587,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
587,
1
] |
Std/Data/Array/Lemmas.lean | Array.pop_empty | [] | [
135,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
135,
9
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.aeval_C | [] | [
1450,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1449,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.ToPartrec.Code.tail_eval | [
{
"state_after": "no goals",
"state_before": "⊢ eval tail = fun v => pure (List.tail v)",
"tactic": "simp [eval]"
}
] | [
149,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/CategoryTheory/Monoidal/OfHasFiniteProducts.lean | CategoryTheory.monoidalOfHasFiniteCoproducts.rightUnitor_hom | [] | [
196,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.floor_le_of_le | [] | [
227,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Topology/Homotopy/Path.lean | ContinuousMap.homotopic_const_iff | [
{
"state_after": "X : Type u\nY : Type v\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\nx₀ x₁ x₂ x₃ : X\ninst✝ : Nonempty Y\ninhabited_h : Inhabited Y\n⊢ Homotopic (const Y x₀) (const Y x₁) ↔ Joined x₀ x₁",
"state_before": "X : Type u\nY : Type v\ninst✝² : TopologicalSpace X\ninst✝¹ : Topologica... | [
366,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Analysis/Normed/Field/Basic.lean | norm_map_one_of_pow_eq_one | [
{
"state_after": "case Hxpos\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.289026\nι : Type ?u.289029\ninst✝¹ : NormedDivisionRing α\ninst✝ : Monoid β\nφ : β →* α\nx : β\nk : ℕ+\nh : x ^ ↑k = 1\n⊢ 0 ≤ ‖↑φ x‖\n\ncase Hypos\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.289026\nι : Type ?u.289029\ninst✝¹ : NormedDivisionRin... | [
651,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Embedding.measurableEmbedding | [] | [
1024,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1020,
11
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.subset_adjoin_of_subset_right | [] | [
341,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Data/Finset/Option.lean | Finset.insertNone_eraseNone | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.15322\ninst✝ : DecidableEq (Option α)\ns : Finset (Option α)\n⊢ ↑insertNone (↑eraseNone s) = insert none s",
"tactic": "ext (_ | x) <;> simp"
}
] | [
158,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.index_iInf_le | [
{
"state_after": "no goals",
"state_before": "G : Type u_2\ninst✝¹ : Group G\nH K L : Subgroup G\nι : Type u_1\ninst✝ : Fintype ι\nf : ι → Subgroup G\n⊢ index (⨅ (i : ι), f i) ≤ ∏ i : ι, index (f i)",
"tactic": "simp_rw [← relindex_top_right, relindex_iInf_le]"
}
] | [
483,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
] |
Mathlib/Analysis/NormedSpace/Units.lean | NormedRing.inverse_one_sub_nth_order | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹ : NormedRing R\ninst✝ : CompleteSpace R\nn : ℕ\nt : R\nht : dist t 0 < 1\n⊢ ‖t‖ < 1",
"tactic": "rwa [← dist_zero_right]"
}
] | [
143,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | symm_le_uniformity | [] | [
447,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.edist_of_re_eq | [
{
"state_after": "no goals",
"state_before": "E : Type ?u.13430\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nz w : ℂ\nh : z.re = w.re\n⊢ edist z w = edist z.im w.im",
"tactic": "rw [edist_nndist, edist_nndist, nndist_of_re_eq h]"
}
] | [
115,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_norm_left | [
{
"state_after": "α : Type u_1\nβ : Type ?u.125138\nE : Type ?u.125141\nF : Type u_2\nG : Type ?u.125147\nE' : Type u_3\nF' : Type ?u.125153\nG' : Type ?u.125156\nE'' : Type ?u.125159\nF'' : Type ?u.125162\nG'' : Type ?u.125165\nR : Type ?u.125168\nR' : Type ?u.125171\n𝕜 : Type ?u.125174\n𝕜' : Type ?u.125177\... | [
791,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
789,
1
] |
Mathlib/Topology/Constructions.lean | nhdsWithin_prod_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.33531\nδ : Type ?u.33534\nε : Type ?u.33537\nζ : Type ?u.33540\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : TopologicalSpace β\ninst✝³ : TopologicalSpace γ\ninst✝² : TopologicalSpace δ\ninst✝¹ : TopologicalSpace ε\ninst✝ : Topologic... | [
520,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_mul_right | [
{
"state_after": "α : Type u_2\nE : Type ?u.936450\nF : Type ?u.936453\n𝕜 : Type ?u.936456\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace ℝ E\ninst✝⁷ : CompleteSpace E\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedSpace 𝕜 E\ninst✝⁴ : SMulCommClass ℝ 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : N... | [
910,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
908,
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] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.mem_lp_const | [] | [
245,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Topology/Separation.lean | Finset.isClosed | [] | [
455,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
11
] |
Mathlib/CategoryTheory/Subobject/MonoOver.lean | CategoryTheory.MonoOver.imageMonoOver_arrow | [] | [
352,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/Topology/Order/Basic.lean | Antitone.map_iInf_of_continuousAt | [] | [
2765,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2762,
1
] |
Std/Data/Int/Lemmas.lean | Int.eq_negSucc_of_lt_zero | [] | [
748,
27
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
746,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.succ_castSucc | [
{
"state_after": "no goals",
"state_before": "n✝ m n : ℕ\ni : Fin n\n⊢ ↑(succ (↑castSucc i)) = ↑(↑castSucc (succ i))",
"tactic": "simp"
}
] | [
1337,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1336,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.IsNormal.self_le | [] | [
444,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
1
] |
Mathlib/Order/Filter/IndicatorFunction.lean | Filter.EventuallyEq.indicator | [] | [
110,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Data/Set/Intervals/Disjoint.lean | IsGLB.biUnion_Ici_eq_Ici | [
{
"state_after": "case refine'_1\nι : Sort u\nα : Type v\nβ : Type w\ninst✝ : LinearOrder α\ns : Set α\na : α\nf : ι → α\na_glb : IsGLB s a\na_mem : a ∈ s\nx : α\nhx : x ∈ s\n⊢ Ici x ⊆ Ici a\n\ncase refine'_2\nι : Sort u\nα : Type v\nβ : Type w\ninst✝ : LinearOrder α\ns : Set α\na : α\nf : ι → α\na_glb : IsGLB ... | [
218,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Data/List/Perm.lean | List.Pairwise.perm | [] | [
1059,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1057,
1
] |
Mathlib/CategoryTheory/Functor/Basic.lean | CategoryTheory.Functor.id_comp | [
{
"state_after": "case mk\nC : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nE : Type u₃\ninst✝ : Category E\ntoPrefunctor✝ : C ⥤q D\nmap_id✝ : ∀ (X : C), toPrefunctor✝.map (𝟙 X) = 𝟙 (toPrefunctor✝.obj X)\nmap_comp✝ : ∀ {X Y Z : C} (f : X ⟶ Y) (g : Y ⟶ Z), toPrefunctor✝.map (f ≫ g) = toPrefu... | [
136,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
11
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.trans_self_symm | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.58218\nδ : Type ?u.58221\ne : LocalEquiv α β\ne' : LocalEquiv β γ\nA : (LocalEquiv.trans e (LocalEquiv.symm e)).source = e.source\n⊢ LocalEquiv.trans e (LocalEquiv.symm e) ≈ ofSet e.source",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.58... | [
895,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
891,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.destruct_map | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nf : α → β\ns : Computation α\n⊢ destruct (map f s) = lmap f (rmap (map f) (destruct s))",
"tactic": "apply s.recOn <;> intro <;> simp"
}
] | [
707,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
706,
1
] |
Mathlib/Data/Polynomial/HasseDeriv.lean | Polynomial.hasseDeriv_zero | [] | [
95,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.single_apply_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nE : α → Type u_1\np✝ q : ℝ≥0∞\ninst✝⁴ : (i : α) → NormedAddCommGroup (E i)\n𝕜 : Type ?u.858705\ninst✝³ : NormedRing 𝕜\ninst✝² : (i : α) → Module 𝕜 (E i)\ninst✝¹ : ∀ (i : α), BoundedSMul 𝕜 (E i)\ninst✝ : DecidableEq α\np : ℝ≥0∞\ni : α\na : E i\n... | [
1007,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1006,
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] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.mul_pf_right | [
{
"state_after": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na b₃ b₁ : R\nb₂ : ℕ\n⊢ a * (b₁ ^ b₂ * b₃) = b₁ ^ b₂ * (a * b₃)",
"state_before": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na b₃ c b₁ : R\nb... | [
362,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.periodicOrbit_def | [] | [
491,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_congr_Prop | [
{
"state_after": "G : Type ?u.40546\nM : Type u_1\nN : Type ?u.40552\nα : Sort ?u.40555\nβ : Sort ?u.40558\nι : Sort ?u.40561\ninst✝¹ : CommMonoid M\ninst✝ : CommMonoid N\np : Prop\nf g : p → M\nhfg : ∀ (h : p), f (_ : p) = g h\n⊢ finprod f = finprod g",
"state_before": "G : Type ?u.40546\nM : Type u_1\nN :... | [
267,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/LinearAlgebra/BilinearMap.lean | LinearMap.flip_apply | [] | [
142,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Tactic/PushNeg.lean | Mathlib.Tactic.PushNeg.not_lt_eq | [] | [
30,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.ext | [] | [
139,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/GroupTheory/EckmannHilton.lean | EckmannHilton.MulOneClass.isUnital | [] | [
45,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.range_mkQ | [
{
"state_after": "case mk\nR : Type u_2\nM : Type u_1\nr : R\nx✝¹ y : M\ninst✝⁵ : Ring R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\np p' : Submodule R M\nR₂ : Type ?u.216815\nM₂ : Type ?u.216818\ninst✝² : Ring R₂\ninst✝¹ : AddCommGroup M₂\ninst✝ : Module R₂ M₂\nτ₁₂ : R →+* R₂\nx✝ : M ⧸ p\nx : M\n⊢ Quot.mk S... | [
377,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | Submodule.coe_norm | [] | [
2719,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2717,
1
] |
Mathlib/Data/Rat/Order.lean | Rat.le_total | [
{
"state_after": "a b c : ℚ\nthis : Rat.Nonneg (b - a) ∨ Rat.Nonneg (-(b - a))\n⊢ a ≤ b ∨ b ≤ a",
"state_before": "a b c : ℚ\n⊢ a ≤ b ∨ b ≤ a",
"tactic": "have := Rat.nonneg_total (b - a)"
},
{
"state_after": "a b c : ℚ\nthis : Rat.Nonneg (b - a) ∨ Rat.Nonneg (-(b - a))\n⊢ Rat.Nonneg (b - a) ∨ R... | [
171,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
11
] |
Std/Data/List/Lemmas.lean | List.get?_set_of_lt' | [
{
"state_after": "α : Type u_1\na : α\nm n : Nat\nl : List α\nh : m < length l\n⊢ (if m = n then Option.map (fun x => a) (get? l n) else get? l n) = if m = n then some a else get? l n",
"state_before": "α : Type u_1\na : α\nm n : Nat\nl : List α\nh : m < length l\n⊢ get? (set l m a) n = if m = n then some a... | [
815,
68
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
813,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.exists_nat_pos_inv_mul_lt | [
{
"state_after": "case intro.intro\nα : Type ?u.341859\nβ : Type ?u.341862\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nha : a ≠ ⊤\nhb : b ≠ 0\nn : ℕ\nnpos : n > 0\nhn : a < ↑n * b\n⊢ ∃ n, n > 0 ∧ (↑n)⁻¹ * a < b",
"state_before": "α : Type ?u.341859\nβ : Type ?u.341862\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nha : a ≠ ⊤\nhb : b ≠ 0\... | [
1837,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1832,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | PSet.mem_image | [] | [
511,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Lemmas.lean | eq_div_iff_mul_eq | [] | [
104,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image₂_image₂_image₂_comm | [
{
"state_after": "α : Type u_7\nα' : Type ?u.76425\nβ : Type u_8\nβ' : Type ?u.76431\nγ✝ : Type ?u.76434\nγ' : Type ?u.76437\nδ✝ : Type ?u.76440\nδ' : Type ?u.76443\nε : Type u_6\nε' : Type u_9\nζ : Type u_3\nζ' : Type u_4\nν : Type u_5\ninst✝¹⁰ : DecidableEq α'\ninst✝⁹ : DecidableEq β'\ninst✝⁸ : DecidableEq γ✝... | [
406,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | rootsOfUnity.coe_mkOfPowEq | [] | [
119,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.HasZeroObject.zeroIsoTerminal_hom | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁴ : Category C\nD : Type u'\ninst✝³ : Category D\ninst✝² : HasZeroObject C\ninst✝¹ : HasZeroMorphisms C\ninst✝ : HasTerminal C\n⊢ zeroIsoTerminal.hom = 0",
"tactic": "ext"
}
] | [
328,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.integrable_of_continuousOn | [
{
"state_after": "ι : Type u\nE : Type v\nF : Type w\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\nI✝ J : Box ι\nπ : TaggedPrepartition I✝\ninst✝² : Fintype ι\nl : IntegrationParams\nf✝ g : (ι → ℝ) → E\nvol : ι →ᵇᵃ[⊤] E →L[ℝ] F\ny y' : F\ninst... | [
713,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
684,
1
] |
Mathlib/LinearAlgebra/TensorProductBasis.lean | Basis.tensorProduct_apply | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nM : Type u_3\nN : Type u_5\nι : Type u_1\nκ : Type u_4\ninst✝⁴ : CommRing R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : AddCommGroup N\ninst✝ : Module R N\nb : Basis ι R M\nc : Basis κ R N\ni : ι\nj : κ\n⊢ ↑(tensorProduct b c) (i, j) = ... | [
44,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/Data/Set/Function.lean | Set.univ_pi_piecewise | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.98315\nβ : Type ?u.98318\nγ : Type ?u.98321\nι✝ : Sort ?u.98324\nπ : α✝ → Type ?u.98329\nδ : α✝ → Sort ?u.98334\ns✝ : Set α✝\nf g : (i : α✝) → δ i\ninst✝¹ : (j : α✝) → Decidable (j ∈ s✝)\nι : Type u_1\nα : ι → Type u_2\ns : Set ι\nt t' : (i : ι) → S... | [
1533,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1531,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.zero_mem | [] | [
172,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
11
] |
Mathlib/Topology/Category/TopCat/Basic.lean | TopCat.coe_of | [] | [
93,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/GroupTheory/Torsion.lean | AddMonoid.IsTorsion.module_of_finite | [] | [
177,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.one_lt_prod_of_one_lt | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.131727\nα : Type ?u.131730\nM : Type u_1\nN : Type ?u.131736\nP : Type ?u.131739\nM₀ : Type ?u.131742\nG : Type ?u.131745\nR : Type ?u.131748\ninst✝ : OrderedCommMonoid M\nb : M\nh : ∀ (x : M), x ∈ [b] → 1 < x\nx✝ : [b] ≠ []\n⊢ 1 < prod [b]",
"ta... | [
502,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.prod_eq_prod_of_nonempty' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ne : LocalHomeomorph α β\ne' : LocalHomeomorph β γ\ne₁ e₁' : LocalHomeomorph α β\ne₂ e₂' : L... | [
1055,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1053,
1
] |
Mathlib/Data/Real/GoldenRatio.lean | fibRec_charPoly_eq | [
{
"state_after": "α : Type ?u.41184\ninst✝¹ : CommSemiring α\nβ : Type u_1\ninst✝ : CommRing β\n⊢ (↑(monomial { order := 2, coeffs := ![1, 1] }.order) 1 -\n Finset.sum Finset.univ fun i => ↑(monomial ↑i) (LinearRecurrence.coeffs { order := 2, coeffs := ![1, 1] } i)) =\n X ^ 2 - (X + 1)",
"state_befo... | [
183,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | Differentiable.differentiableAt | [] | [
600,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
599,
1
] |
Mathlib/Algebra/Hom/GroupInstances.lean | MonoidHom.map_mul₂ | [] | [
161,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.ext | [] | [
459,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | differentiableOn_neg_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.421118\ninst✝³ : NormedAddCommGroup G\ninst✝² : Normed... | [
443,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | Pretrivialization.linear | [] | [
87,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.zero_caratheodory | [] | [
1099,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1098,
1
] |
Mathlib/Order/Bounded.lean | Set.bounded_lt_Icc | [] | [
226,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Topology/Instances/EReal.lean | EReal.continuousAt_add_bot_bot | [
{
"state_after": "α : Type ?u.27248\ninst✝ : TopologicalSpace α\n⊢ ∀ (x : ℝ), ∀ᶠ (a : EReal × EReal) in 𝓝 (⊥, ⊥), a.fst + a.snd < ↑x",
"state_before": "α : Type ?u.27248\ninst✝ : TopologicalSpace α\n⊢ ContinuousAt (fun p => p.fst + p.snd) (⊥, ⊥)",
"tactic": "simp only [ContinuousAt, tendsto_nhds_bot_if... | [
223,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.constantCoeff_zero | [] | [
1551,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1550,
1
] |
Mathlib/Topology/Separation.lean | specializes_iff_inseparable | [] | [
1582,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1581,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | mul_le_of_mul_le_right | [] | [
252,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion₂_mono' | [] | [
403,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | Filter.EventuallyEq.differentiableWithinAt_iff | [] | [
869,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
867,
1
] |
Mathlib/Data/Quot.lean | Quot.lift₂_mk | [] | [
128,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Data/Countable/Defs.lean | Function.Injective.countable | [] | [
54,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
11
] |
Mathlib/Data/Nat/Sqrt.lean | Nat.le_three_of_sqrt_eq_one | [
{
"state_after": "n : ℕ\nh : sqrt n = 1\n⊢ 1 < 2",
"state_before": "n : ℕ\nh : sqrt n = 1\n⊢ sqrt n < 2",
"tactic": "rw [h]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\nh : sqrt n = 1\n⊢ 1 < 2",
"tactic": "decide"
}
] | [
131,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Data/List/Sort.lean | List.sorted_nil | [] | [
58,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.domCoprod_coe | [] | [
1090,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1087,
1
] |
Mathlib/NumberTheory/Multiplicity.lean | multiplicity.geom_sum₂_eq_one | [
{
"state_after": "R : Type u_1\nn : ℕ\ninst✝² : CommRing R\na b x y : R\np : ℕ\ninst✝¹ : IsDomain R\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\nhp : Prime ↑p\nhp1 : Odd p\nhxy : ↑p ∣ x - y\nhx : ¬↑p ∣ x\n⊢ multiplicity (↑p) (∑ i in range p, x ^ i * y ^ (p - ↑1 - i)) = 1",
"state_before": "R : Type u_1\nn : ... | [
179,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Data/UnionFind.lean | UFModel.Agrees.get_eq | [
{
"state_after": "case mk\nα : Type u_1\nβ : Sort u_2\nf : α → β\narr : Array α\n⊢ ∀ (i : ℕ) (h₁ h₂ : i < Array.size arr),\n f (Array.get arr { val := i, isLt := h₁ }) = (fun i => f (Array.get arr i)) { val := i, isLt := h₂ }",
"state_before": "α : Type u_1\nβ : Sort u_2\nf : α → β\narr : Array α\nn : ℕ\... | [
85,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Data/Fin/Tuple/Sort.lean | Tuple.antitone_pair_of_not_sorted' | [
{
"state_after": "n : ℕ\nα : Type u_1\ninst✝ : LinearOrder α\nf : Fin n → α\nσ : Equiv.Perm (Fin n)\nh : ∀ (i j : Fin n), i < j → (f ∘ ↑σ) i ≤ (f ∘ ↑σ) j\n⊢ f ∘ ↑σ = f ∘ ↑(sort f)",
"state_before": "n : ℕ\nα : Type u_1\ninst✝ : LinearOrder α\nf : Fin n → α\nσ : Equiv.Perm (Fin n)\nh : f ∘ ↑σ ≠ f ∘ ↑(sort f)... | [
177,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.continuous_negPart | [
{
"state_after": "α : Type u_1\nE : Type ?u.8098806\nF : Type ?u.8098809\nG : Type ?u.8098812\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedAddCommGroup G\ng : E → F\nc : ℝ≥0\ninst✝ : Fact (1 ≤ p)\neq : (fun f => negPart... | [
1139,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1136,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.tail_empty | [] | [
186,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Ring.lean | Commute.tsum_right | [] | [
68,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Order/MinMax.lean | min_lt_min_left_iff | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝¹ : LinearOrder α\ninst✝ : LinearOrder β\nf : α → β\ns : Set α\na b c d : α\n⊢ (a < b ∨ c < b) ∧ a < c ↔ a < b ∧ a < c",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : LinearOrder α\ninst✝ : LinearOrder β\nf : α → β\ns : Set α\na b c d : α\n⊢ min a c < min b... | [
186,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Combinatorics/SetFamily/Compression/Down.lean | Finset.nonMemberSubfamily_nonMemberSubfamily | [
{
"state_after": "case a\nα : Type u_1\ninst✝ : DecidableEq α\n𝒜 ℬ : Finset (Finset α)\ns : Finset α\na : α\na✝ : Finset α\n⊢ a✝ ∈ nonMemberSubfamily a (nonMemberSubfamily a 𝒜) ↔ a✝ ∈ nonMemberSubfamily a 𝒜",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\n𝒜 ℬ : Finset (Finset α)\ns : Finset α\na ... | [
139,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.subset_set_smul_iff₀ | [] | [
1043,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1042,
1
] |
Mathlib/Topology/Order.lean | forall_open_iff_discrete | [] | [
320,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/Data/List/Count.lean | List.count_pos | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl✝ : List α\ninst✝ : DecidableEq α\na : α\nl : List α\n⊢ 0 < count a l ↔ a ∈ l",
"tactic": "simp only [count, countp_pos, beq_iff_eq, exists_eq_right]"
}
] | [
245,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Topology/Algebra/Module/FiniteDimension.lean | Basis.constrL_apply | [] | [
468,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/Algebra/Group/Conj.lean | IsConj.trans | [] | [
51,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
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