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/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.iUnion_eq_empty | [
{
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"tactic": "simp [← injective_boxes.eq_iff, Finset.ext_iff, Prepartition.iUnion, imp_false]"
}
] | [
239,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
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Mathlib/Data/Finset/Image.lean | Finset.image_val_of_injOn | [] | [
408,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Finset/Pointwise.lean | Finset.smul_finset_neg | [
{
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"tactic": "simp only [← image_smul, ← i... | [
2145,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2144,
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Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_mulSupport | [] | [
178,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
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Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.nfpBFamily_eq_self | [] | [
340,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
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Mathlib/LinearAlgebra/Matrix/Basis.lean | Basis.toMatrix_reindex' | [
{
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.comp_smulₛₗ | [
{
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1525,
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Mathlib/Data/Nat/Fib.lean | Nat.fib_two_mul | [
{
"state_after": "case zero\n\n⊢ fib (2 * zero) = fib zero * (2 * fib (zero + 1) - fib zero)\n\ncase succ\nn✝ : ℕ\n⊢ fib (2 * succ n✝) = fib (succ n✝) * (2 * fib (succ n✝ + 1) - fib (succ n✝))",
"state_before": "n : ℕ\n⊢ fib (2 * n) = fib n * (2 * fib (n + 1) - fib n)",
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},
{
... | [
165,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
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Mathlib/GroupTheory/Complement.lean | Subgroup.isComplement'_iff_card_mul_and_disjoint | [] | [
544,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
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Mathlib/Order/Lattice.lean | Antitone.max | [] | [
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12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1175,
11
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Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.Monic.geom_sum | [
{
"state_after": "R : Type u\nS : Type ?u.54680\ninst✝ : Semiring R\nP : R[X]\nhP : Monic P\nhdeg : 0 < natDegree P\nn : ℕ\nhn : n ≠ 0\n✝ : Nontrivial R\n⊢ Monic (∑ i in range n, P ^ i)",
"state_before": "R : Type u\nS : Type ?u.54680\ninst✝ : Semiring R\nP : R[X]\nhP : Monic P\nhdeg : 0 < natDegree P\nn : ... | [
244,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
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Mathlib/Data/Real/Basic.lean | Real.cauchy_add | [
{
"state_after": "no goals",
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"tactic": "rw [add_def]"
}
] | [
153,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
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Mathlib/Order/Filter/Pointwise.lean | Filter.map₂_div | [] | [
435,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
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Mathlib/Algebra/BigOperators/Finsupp.lean | Finset.sum_apply' | [] | [
626,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
1
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Mathlib/Order/SupIndep.lean | CompleteLattice.Independent.injective | [
{
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"state_before": "α : Type u_2\nβ : Type ?u.53351\nι : Type u_1... | [
322,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
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Mathlib/SetTheory/ZFC/Basic.lean | Class.sUnion_empty | [
{
"state_after": "case a\nz✝ : ZFSet\n⊢ (⋃₀ ∅) z✝ ↔ ∅ z✝",
"state_before": "⊢ ⋃₀ ∅ = ∅",
"tactic": "ext"
},
{
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}
] | [
1728,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1726,
1
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Mathlib/Topology/UniformSpace/Cauchy.lean | Filter.Tendsto.cauchySeq | [] | [
190,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.natTrailingDegree_monomial_le | [
{
"state_after": "no goals",
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"tactic": "simp [ha]"
}
] | [
213,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
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Mathlib/Order/CompleteLattice.lean | Prod.iSup_mk | [] | [
1888,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1886,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sqrtTwoAddSeries_lt_two | [
{
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"tactic": "norm_num"
},
{
"state_after": "x : ℝ\nn : ℕ\n⊢ sqrtTwoAddSeries 0 (n + 1) < sqrt (2 ^ 2)",
"state_before": "x : ℝ\nn : ℕ\n⊢ sqrtTwoAddSeries 0 (n + 1) < 2",
"tactic": "refine' lt_of_lt_of_le _ (s... | [
708,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
701,
1
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.coeff_map | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n✝ : ℕ\ninst✝¹ : Semiring R\np q r : R[X]\ninst✝ : Semiring S\nf : R →+* S\nn : ℕ\n⊢ ∑ n_1 in support p, coeff (↑(RingHom.comp C f) (coeff p n_1) * X ^ n_1) n = ↑f (coeff p n)",
"state_before": "R : Type u\nS : Type v\nT : Type w\n... | [
793,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Normed/Group/Basic.lean | Int.norm_eq_abs | [
{
"state_after": "no goals",
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1791,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/GroupPower/Basic.lean | nsmul_zero | [
{
"state_after": "case zero\nα : Type ?u.8662\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✝¹ : Monoid M\ninst✝ : AddMonoid A\n⊢ Nat.zero • 0 = 0\n\ncase succ\nα : Type ?u.8662\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : ... | [
78,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Classes/LawfulMonad.lean | SatisfiesM.pure | [
{
"state_after": "no goals",
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"tactic": "simp"
}
] | [
121,
73
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
120,
11
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_smul_le_snorm_top_mul_snorm | [] | [
1503,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1500,
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Mathlib/Control/Traversable/Equiv.lean | Equiv.comp_traverse | [
{
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150,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
11
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pullbackConeOfLeftIso_x | [] | [
1617,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1617,
1
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Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.NeWord.inv_head | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nM : ι → Type ?u.649174\ninst✝² : (i : ι) → Monoid (M i)\nN : Type ?u.649185\ninst✝¹ : Monoid N\nG : ι → Type u_2\ninst✝ : (i : ι) → Group (G i)\ni j : ι\nw : NeWord G i j\n⊢ head (inv w) = (last w)⁻¹",
"tactic": "induction w <;> simp [inv, *]"
... | [
685,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
684,
1
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Mathlib/CategoryTheory/Endofunctor/Algebra.lean | CategoryTheory.Endofunctor.Coalgebra.iso_of_iso | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\nF : C ⥤ C\nV V₀ V₁ V₂ : Coalgebra F\nf✝ : V₀ ⟶ V₁\ng : V₁ ⟶ V₂\nf : V₀ ⟶ V₁\ninst✝ : IsIso f.f\n⊢ V₀.str ≫ F.map f.f ≫ F.map (inv f.f) = V₀.str",
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378,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Topology/Algebra/Nonarchimedean/AdicTopology.lean | Ideal.hasBasis_nhds_zero_adic | [
{
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"state_before": "R : Type u_1\ninst✝ : CommRing R\nI : Ideal R\n⊢ ∀ (t : Set R), t ∈ 𝓝 0 ↔ ∃ i, True ∧ ↑(I ^ i) ⊆ t",
"tactic": "intro U"
},
{
"state_after": "R : Type u_1\ninst✝ ... | [
107,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | norm_le_mul_norm_add | [
{
"state_after": "no goals",
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601,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
1
] |
Mathlib/Logic/Encodable/Basic.lean | Encodable.decode₂_ne_none_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.7543\ninst✝ : Encodable α\nn : ℕ\n⊢ decode₂ α n ≠ none ↔ n ∈ Set.range encode",
"tactic": "simp_rw [Set.range, Set.mem_setOf_eq, Ne.def, Option.eq_none_iff_forall_not_mem,\n Encodable.mem_decode₂, not_forall, not_not]"
}
] | [
217,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
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Mathlib/MeasureTheory/Function/ConvergenceInMeasure.lean | MeasureTheory.tendstoInMeasure_of_tendsto_ae_of_stronglyMeasurable | [
{
"state_after": "α : Type u_1\nι : Type ?u.3660\nE : Type u_2\nm : MeasurableSpace α\nμ : Measure α\ninst✝¹ : MetricSpace E\nf : ℕ → α → E\ng : α → E\ninst✝ : IsFiniteMeasure μ\nhf : ∀ (n : ℕ), StronglyMeasurable (f n)\nhg : StronglyMeasurable g\nhfg : ∀ᵐ (x : α) ∂μ, Tendsto (fun n => f n x) atTop (𝓝 (g x))\n... | [
128,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.ext_iff | [] | [
487,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.nat_lt_lift_iff | [
{
"state_after": "no goals",
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"tactic": "rw [← lift_natCast.{v,u}, lift_lt]"
}
] | [
1313,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1312,
1
] |
Mathlib/Data/Polynomial/Module.lean | PolynomialModule.eval_map' | [] | [
318,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/Data/Set/Image.lean | Set.prod_quotient_preimage_eq_image | [] | [
576,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.sign_swap | [] | [
579,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
578,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.isMultiplicative_sigma | [
{
"state_after": "R : Type ?u.546111\nk : ℕ\n⊢ IsMultiplicative (ζ * pow k)",
"state_before": "R : Type ?u.546111\nk : ℕ\n⊢ IsMultiplicative (σ k)",
"tactic": "rw [← zeta_mul_pow_eq_sigma]"
},
{
"state_after": "no goals",
"state_before": "R : Type ?u.546111\nk : ℕ\n⊢ IsMultiplicative (ζ * po... | [
841,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
839,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_eq_prod_of_mulSupport_toFinset_subset | [] | [
399,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | UniformContinuous.inf_dom_left | [] | [
1386,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1384,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.AECover.superset | [] | [
119,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Order/Bounds/Basic.lean | upperBounds_Icc | [] | [
696,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
695,
1
] |
Mathlib/Order/Disjoint.lean | eq_bot_of_isCompl_top | [] | [
638,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
637,
1
] |
Mathlib/Topology/FiberBundle/Constructions.lean | Trivialization.Prod.left_inv | [
{
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205,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.exists_factorization_lt_of_lt | [
{
"state_after": "a b : ℕ\nha : a ≠ 0\nhab : a < b\nhb : b ≠ 0\n⊢ ∃ p, ↑(factorization a) p < ↑(factorization b) p",
"state_before": "a b : ℕ\nha : a ≠ 0\nhab : a < b\n⊢ ∃ p, ↑(factorization a) p < ↑(factorization b) p",
"tactic": "have hb : b ≠ 0 := (ha.bot_lt.trans hab).ne'"
},
{
"state_after"... | [
512,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | IsUnit.stronglyMeasurable_const_smul_iff | [] | [
501,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
8
] |
Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.norm_restrict_mono_set | [] | [
264,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Std/Data/List/Basic.lean | List.splitOnP_eq_splitOnPTR | [
{
"state_after": "case h.h.h\nα : Type u_1\nP : α → Bool\nl : List α\n⊢ splitOnP P l = splitOnPTR P l",
"state_before": "⊢ @splitOnP = @splitOnPTR",
"tactic": "funext α P l"
},
{
"state_after": "case h.h.h\nα : Type u_1\nP : α → Bool\nl : List α\n⊢ splitOnP P l = splitOnPTR.go P l #[] #[]",
... | [
499,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
494,
10
] |
Mathlib/Topology/Algebra/Ring/Basic.lean | TopologicalRing.of_addGroup_of_nhds_zero | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.17126\nR : Type u_1\ninst✝² : NonUnitalNonAssocRing R\ninst✝¹ : TopologicalSpace R\ninst✝ : TopologicalAddGroup R\nhmul : Tendsto (uncurry fun x x_1 => x * x_1) (𝓝 0 ×ˢ 𝓝 0) (𝓝 0)\nhmul_left : ∀ (x₀ : R), Tendsto (fun x => x₀ * x) (𝓝 0) (𝓝 0)\nh... | [
208,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | TopologicalGroup.ext | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nG✝ : Type w\nH : Type x\ninst✝⁴ : TopologicalSpace G✝\ninst✝³ : Group G✝\ninst✝² : TopologicalGroup G✝\ninst✝¹ : TopologicalSpace α\nf : α → G✝\ns : Set α\nx✝ : α\nG : Type u_1\ninst✝ : Group G\nt t' : TopologicalSpace G\ntg : Topological... | [
894,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
890,
1
] |
Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.Ioo_cons_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : LocallyFiniteOrder α\na b : α\nh : a < b\n⊢ a ::ₘ Ioo a b = Ico a b",
"tactic": "classical\n rw [Ioo, ← Finset.insert_val_of_not_mem left_not_mem_Ioo, Finset.Ioo_insert_left h]\n rfl"
},
{
"state_after... | [
206,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.multiplicity_eq_zero | [
{
"state_after": "α : Type u_1\ninst✝¹ : Monoid α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\na b : α\n⊢ a ^ 0 ∣ b ∧ ¬a ^ (0 + 1) ∣ b ↔ ¬a ∣ b",
"state_before": "α : Type u_1\ninst✝¹ : Monoid α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\na b : α\n⊢ multiplicity a b = 0 ↔ ¬a ∣ b",
"tactic": "rw [← Nat.ca... | [
206,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.nadd_lt_nadd_iff_right | [] | [
423,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/Topology/Instances/TrivSqZeroExt.lean | TrivSqZeroExt.hasSum_snd | [] | [
166,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Analysis/Asymptotics/Theta.lean | Asymptotics.IsTheta.trans_isBigO | [] | [
102,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Topology/UniformSpace/CompactConvergence.lean | ContinuousMap.hasBasis_compactConvergenceUniformity_aux | [
{
"state_after": "α : Type u₁\nβ : Type u₂\ninst✝¹ : TopologicalSpace α\ninst✝ : UniformSpace β\nK : Set α\nV : Set (β × β)\nf : C(α, β)\n⊢ DirectedOn ((fun KV => {fg | ∀ (x : α), x ∈ KV.fst → (↑fg.fst x, ↑fg.snd x) ∈ KV.snd}) ⁻¹'o fun x x_1 => x ≥ x_1)\n {KV | IsCompact KV.fst ∧ KV.snd ∈ 𝓤 β}",
"state_... | [
307,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/Topology/Basic.lean | DenseRange.nonempty | [] | [
1858,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1857,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Ideal.is_fg_degreeLE | [] | [
736,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
732,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.num_div_dvd | [
{
"state_after": "K : Type u\ninst✝ : Field K\np q : K[X]\nhq : q ≠ 0\n⊢ p / gcd p q ∣ p\n\nK : Type u\ninst✝ : Field K\np q : K[X]\nhq : q ≠ 0\n⊢ (leadingCoeff (q / gcd p q))⁻¹ ≠ 0",
"state_before": "K : Type u\ninst✝ : Field K\np q : K[X]\nhq : q ≠ 0\n⊢ num (↑(algebraMap K[X] (RatFunc K)) p / ↑(algebraMap... | [
1177,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1173,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.isClosed_image_coe_closedBall | [] | [
1662,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1660,
1
] |
Mathlib/CategoryTheory/Preadditive/Basic.lean | CategoryTheory.Preadditive.hasCoequalizers_of_hasCokernels | [] | [
444,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.bot_prod_bot | [] | [
1572,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1571,
1
] |
Mathlib/GroupTheory/Subsemigroup/Center.lean | Set.center_eq_univ | [] | [
134,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Topology/Order.lean | continuous_sInf_dom | [] | [
790,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
787,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.pow_mem | [] | [
137,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
11
] |
Mathlib/Order/Filter/Basic.lean | Filter.mem_sSup | [] | [
568,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
1
] |
Mathlib/Data/PNat/Prime.lean | Nat.Primes.coe_pnat_nat | [] | [
35,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/Data/Polynomial/EraseLead.lean | Polynomial.eraseLead_card_support' | [] | [
126,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Data/Int/Lemmas.lean | Int.le_coe_nat_sub | [
{
"state_after": "case pos\nm n : ℕ\nh : m ≥ n\n⊢ ↑m - ↑n ≤ ↑(m - n)\n\ncase neg\nm n : ℕ\nh : ¬m ≥ n\n⊢ ↑m - ↑n ≤ ↑(m - n)",
"state_before": "m n : ℕ\n⊢ ↑m - ↑n ≤ ↑(m - n)",
"tactic": "by_cases h : m ≥ n"
},
{
"state_after": "no goals",
"state_before": "case pos\nm n : ℕ\nh : m ≥ n\n⊢ ↑m - ... | [
33,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Mathlib/Data/Int/Order/Basic.lean | Int.le_ediv_iff_mul_le | [] | [
443,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
11
] |
Mathlib/LinearAlgebra/Matrix/Trace.lean | Matrix.trace_fin_two | [] | [
195,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | HomologicalComplex.Hom.comm | [
{
"state_after": "case pos\nι : Type u_1\nV : Type u\ninst✝¹ : Category V\ninst✝ : HasZeroMorphisms V\nc : ComplexShape ι\nC A B : HomologicalComplex V c\nf : Hom A B\ni j : ι\nhij : ComplexShape.Rel c i j\n⊢ HomologicalComplex.Hom.f f i ≫ d B i j = d A i j ≫ HomologicalComplex.Hom.f f j\n\ncase neg\nι : Type u... | [
191,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/CategoryTheory/Balanced.lean | CategoryTheory.isIso_iff_mono_and_epi | [] | [
47,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/Algebra/Hom/GroupAction.lean | MulActionHom.comp_id | [
{
"state_after": "no goals",
"state_before": "M' : Type u_1\nX : Type u_2\ninst✝²³ : SMul M' X\nY : Type u_3\ninst✝²² : SMul M' Y\nZ : Type ?u.48568\ninst✝²¹ : SMul M' Z\nM : Type ?u.48575\ninst✝²⁰ : Monoid M\nA : Type ?u.48581\ninst✝¹⁹ : AddMonoid A\ninst✝¹⁸ : DistribMulAction M A\nA' : Type ?u.48609\ninst... | [
171,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Independent.lean | affineCombination_mem_affineSpan_pair | [
{
"state_after": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type u_4\np : ι → P\nh : AffineIndependent k p\nw w₁ w₂ : ι → k\ns : Finset ι\nx✝ : ∑ i in s, w i = 1\nhw₁ : ∑ i in s, w₁ i = 1\nhw₂ : ∑ i in s, w₂ i = 1\n⊢ (∃ ... | [
539,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | LinearMap.toMatrixAlgEquiv_apply | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁹ : CommSemiring R\nl : Type ?u.2330336\nm : Type ?u.2330339\nn : Type u_3\ninst✝⁸ : Fintype n\ninst✝⁷ : Fintype m\ninst✝⁶ : DecidableEq n\nM₁ : Type u_2\nM₂ : Type ?u.2330363\ninst✝⁵ : AddCommMonoid M₁\ninst✝⁴ : AddCommMonoid M₂\ninst✝³ : Mod... | [
748,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
746,
1
] |
Mathlib/Computability/Primrec.lean | Nat.Primrec'.cons | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\nf : Vector ℕ n → ℕ\ng : Vector ℕ n → Vector ℕ m\nhf : Primrec' f\nhg : Vec g\ni : Fin (Nat.succ m)\n⊢ Primrec' fun v => Vector.get ((fun v => f v ::ᵥ g v) v) 0",
"tactic": "simp [*]"
},
{
"state_after": "no goals",
"state_before": "n m :... | [
1424,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1423,
11
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.IsImage.leftInvOn_piecewise | [] | [
570,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.cthickening_eq_iInter_cthickening' | [
{
"state_after": "case h₁\nι : Sort ?u.139615\nα : Type u\nβ : Type v\ninst✝ : PseudoEMetricSpace α\nδ✝ ε : ℝ\ns✝ t : Set α\nx : α\nδ : ℝ\ns : Set ℝ\nhsδ : s ⊆ Ioi δ\nhs : ∀ (ε : ℝ), δ < ε → Set.Nonempty (s ∩ Ioc δ ε)\nE : Set α\n⊢ cthickening δ E ⊆ ⋂ (ε : ℝ) (_ : ε ∈ s), cthickening ε E\n\ncase h₂\nι : Sort ?u... | [
1310,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1297,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_of_finite | [] | [
296,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_le_rpow_left_iff | [
{
"state_after": "x y z : ℝ\nhx : 1 < x\nx_pos : 0 < x\n⊢ x ^ y ≤ x ^ z ↔ y ≤ z",
"state_before": "x y z : ℝ\nhx : 1 < x\n⊢ x ^ y ≤ x ^ z ↔ y ≤ z",
"tactic": "have x_pos : 0 < x := lt_trans zero_lt_one hx"
},
{
"state_after": "no goals",
"state_before": "x y z : ℝ\nhx : 1 < x\nx_pos : 0 < x\... | [
484,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/RingTheory/RootsOfUnity/Complex.lean | IsPrimitiveRoot.arg_eq_pi_iff | [] | [
132,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_iUnion_apply | [
{
"state_after": "case pos\nα : Type u_3\nβ : Type ?u.157531\nι✝ : Type ?u.157534\nM✝ : Type ?u.157537\nN : Type ?u.157540\ninst✝³ : One M✝\ns✝ t : Set α\nf✝ g : α → M✝\na : α\ny : M✝\ninst✝² : Preorder M✝\nι : Sort u_1\nM : Type u_2\ninst✝¹ : CompleteLattice M\ninst✝ : One M\nh1 : ⊥ = 1\ns : ι → Set α\nf : α →... | [
849,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
838,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.aleph'_cof | [] | [
726,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
725,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.rpow_inv_rpow_self | [
{
"state_after": "no goals",
"state_before": "y : ℝ\nhy : y ≠ 0\nx : ℝ≥0\n⊢ (x ^ y) ^ (1 / y) = x",
"tactic": "field_simp [← rpow_mul]"
}
] | [
108,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.exists_closedBall_inter_eq_singleton_of_discrete | [] | [
1129,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1127,
1
] |
Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.rootSet_prod | [
{
"state_after": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝³ : Field R\np q : R[X]\ninst✝² : CommRing S\ninst✝¹ : IsDomain S\ninst✝ : Algebra R S\nι : Type u_1\nf : ι → R[X]\ns : Finset ι\nh : Finset.prod s f ≠ 0\n⊢ ↑(Multiset.toFinset (roots (map (algebraMap R S) (Finset.prod s f)))... | [
391,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.attach_cons | [
{
"state_after": "α : Type u_1\nβ : Type ?u.143075\nγ : Type ?u.143078\na : α\nm : Multiset α\nl : List α\n⊢ List.pmap mk l (_ : ∀ (x : α), x ∈ l → (fun a_2 => a_2 ∈ a ::ₘ Quotient.mk (isSetoid α) l) x) =\n List.pmap\n (fun a_1 h =>\n { val := ↑{ val := a_1, property := h },\n property :... | [
1577,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1571,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.ofFinsupp_pow | [
{
"state_after": "R : Type u\na✝ b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q : R[X]\na : AddMonoidAlgebra R ℕ\nn : ℕ\n⊢ { toFinsupp := a ^ n } = npowRec n { toFinsupp := a }",
"state_before": "R : Type u\na✝ b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q : R[X]\na : AddMonoidAlgebra R ℕ\nn : ℕ\n⊢ { toFinsupp := a ^ ... | [
198,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.left_inv' | [] | [
171,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Order/Antichain.lean | isAntichain_insert_of_symmetric | [] | [
115,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Analysis/Convex/Basic.lean | convex_singleton | [] | [
175,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Algebra/Support.lean | Function.mulSupport_comp_eq_preimage | [] | [
223,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.mem_cycleType_iff | [
{
"state_after": "case mp\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nn : ℕ\nσ : Perm α\n⊢ n ∈ cycleType σ → ∃ c τ, σ = c * τ ∧ Disjoint c τ ∧ IsCycle c ∧ Finset.card (support c) = n\n\ncase mpr\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nn : ℕ\nσ : Perm α\n⊢ (∃ c τ, σ = c * τ ∧ Disj... | [
304,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Combinatorics/Colex.lean | Colex.le_def | [] | [
101,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/MeasureTheory/Measure/Haar/NormedSpace.lean | MeasureTheory.Measure.integral_comp_mul_left | [
{
"state_after": "no goals",
"state_before": "E : Type ?u.85697\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : MeasurableSpace E\ninst✝⁵ : BorelSpace E\ninst✝⁴ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝³ : IsAddHaarMeasure μ\nF : Type u_1\ninst✝² : NormedAddCommGroup F\ninst✝¹ : Norme... | [
113,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.minpoly_gen | [
{
"state_after": "F : Type u_1\ninst✝⁴ : Field F\nE : Type u_2\ninst✝³ : Field E\ninst✝² : Algebra F E\nα✝ : E\nK : Type ?u.813260\ninst✝¹ : Field K\ninst✝ : Algebra F K\nα : E\nh : IsIntegral F (↑(algebraMap { x // x ∈ F⟮α⟯ } E) (AdjoinSimple.gen F α))\n⊢ minpoly F (AdjoinSimple.gen F α) = minpoly F α",
"s... | [
802,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
] |
Mathlib/Order/Heyting/Hom.lean | HeytingHom.ext | [] | [
273,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Complex.lean | Complex.cpow_one | [
{
"state_after": "no goals",
"state_before": "x : ℂ\nhx : x = 0\n⊢ x ^ 1 = x",
"tactic": "simp [hx, cpow_def]"
},
{
"state_after": "no goals",
"state_before": "x : ℂ\nhx : ¬x = 0\n⊢ x ^ 1 = x",
"tactic": "rw [cpow_def, if_neg (one_ne_zero : (1 : ℂ) ≠ 0), if_neg hx, mul_one, exp_log hx]"
... | [
85,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
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