file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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values | start list |
|---|---|---|---|---|---|---|
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.continuousAt | [] | [
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28
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1892,
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Mathlib/Data/Finset/Lattice.lean | Finset.sup_union | [
{
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"ta... | [
82,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Logic/Basic.lean | xor_comm | [
{
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"tactic": "simp [Xor', and_comm, or_comm]"
}
] | [
290,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
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Mathlib/Order/Filter/Extr.lean | IsExtrFilter.filter_inf | [] | [
281,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
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Mathlib/Data/Set/Pointwise/Basic.lean | Set.union_div_inter_subset_union | [] | [
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34
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737,
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Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffOn.div_const | [] | [
1478,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1477,
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Mathlib/RingTheory/Valuation/ValuationRing.lean | ValuationRing.isInteger_or_isInteger | [] | [
345,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
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Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | Matrix.toLinearMapₛₗ₂'_apply | [] | [
200,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.mem_ofLe | [
{
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630,
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Mathlib/Topology/MetricSpace/Baire.lean | dense_biInter_of_open | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.13508\nι : Type ?u.13511\ninst✝¹ : TopologicalSpace α\ninst✝ : BaireSpace α\nS : Set β\nf : β → Set α\nho : ∀ (s : β), s ∈ S → IsOpen (f s)\nhS : Set.Countable S\nhd : ∀ (s : β), s ∈ S → Dense (f s)\n⊢ Dense (⋂₀ ((fun s => f s) '' S))",
"state_before... | [
217,
25
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211,
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.nhds_basis_eball | [] | [
632,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
631,
1
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Mathlib/Order/Filter/SmallSets.lean | Filter.Tendsto.of_smallSets | [] | [
151,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
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Mathlib/Algebra/PUnitInstances.lean | PUnit.inv_eq | [] | [
68,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
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Mathlib/Algebra/Ring/BooleanRing.lean | ofBoolAlg_sup | [] | [
294,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
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Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_sub_const_Iio | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\n⊢ (fun x => x - a) ⁻¹' Iio b = Iio (b + a)",
"tactic": "simp [sub_eq_add_neg]"
}
] | [
192,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
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Mathlib/Data/Quot.lean | Quotient.lift_comp_mk | [] | [
317,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
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Mathlib/Data/Analysis/Topology.lean | LocallyFinite.Realizer.to_locallyFinite | [] | [
253,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
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Mathlib/FieldTheory/Minpoly/Field.lean | minpoly.dvd_map_of_isScalarTower | [
{
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90,
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86,
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Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.mem_toSubmonoid | [] | [
207,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
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Mathlib/Data/Fintype/BigOperators.lean | Equiv.prod_comp' | [] | [
224,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
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] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.map_le_iff_le_comap | [] | [
271,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
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Mathlib/Order/RelIso/Basic.lean | RelIso.injective | [] | [
807,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
806,
11
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Mathlib/Topology/Connected.lean | isPreconnected_singleton | [] | [
93,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
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Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.zero_app | [] | [
172,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_congr_nnnorm_ae | [] | [
462,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
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Mathlib/Order/Bounds/Basic.lean | isGreatest_univ_iff | [
{
"state_after": "no goals",
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"tactic": "simp [IsGreatest, mem_upperBounds, IsTop]"
}
] | [
803,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
802,
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Mathlib/Order/Circular.lean | not_btw_of_sbtw | [] | [
198,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Real/NNReal.lean | NNReal.coe_mk | [] | [
140,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
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Mathlib/Algebra/Ring/BooleanRing.lean | mul_one_add_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.8793\nγ : Type ?u.8796\ninst✝ : BooleanRing α\na b : α\n⊢ a * (1 + a) = 0",
"tactic": "rw [mul_add, mul_one, mul_self, add_self]"
}
] | [
112,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
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Mathlib/Algebra/Lie/Basic.lean | LieModuleEquiv.one_apply | [] | [
1044,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1043,
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Mathlib/CategoryTheory/StructuredArrow.lean | CategoryTheory.StructuredArrow.mk_hom_eq_self | [] | [
80,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
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Mathlib/Topology/SubsetProperties.lean | Filter.mem_cocompact | [] | [
530,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.comap_surjective | [] | [
1285,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1284,
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Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.totalDegree_list_prod | [
{
"state_after": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.469070\nr : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝ : CommSemiring R\np q : MvPolynomial σ R\n⊢ 0 ≤ List.sum (List.map totalDegree [])",
"state_before": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.469070\nr : R\ne : ℕ\nn m : σ\ns : σ →₀... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Fin/VecNotation.lean | Matrix.sub_cons | [
{
"state_after": "case h\nα : Type u\nm n o : ℕ\nm' : Type ?u.70038\nn' : Type ?u.70041\no' : Type ?u.70044\ninst✝ : Sub α\nv : Fin (Nat.succ n) → α\ny : α\nw : Fin n → α\ni : Fin (Nat.succ n)\n⊢ (v - vecCons y w) i = vecCons (vecHead v - y) (vecTail v - w) i",
"state_before": "α : Type u\nm n o : ℕ\nm' : T... | [
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54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_mono_ae | [
{
"state_after": "case intro.intro.intro\nα : Type u_1\nβ : Type ?u.290555\nγ : Type ?u.290558\nδ : Type ?u.290561\nm : MeasurableSpace α\nμ ν : Measure α\nf g : α → ℝ≥0∞\nh : ∀ᵐ (a : α) ∂μ, f a ≤ g a\nt : Set α\nhts : {x | (fun a => f a ≤ g a) x}ᶜ ⊆ t\nht : MeasurableSet t\nht0 : ↑↑μ t = 0\n⊢ (∫⁻ (a : α), f a ... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.closedBall_top | [] | [
550,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
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] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.trStmts₁_supports' | [
{
"state_after": "S : Finset Λ'\nq : Λ'\nK : Finset Λ'\nH₁ : Λ'.Supports S q\nH₃ : K ⊆ S → Supports K S\nH₂ : trStmts₁ q ⊆ S ∧ K ⊆ S\n⊢ Supports (trStmts₁ q ∪ K) S",
"state_before": "S : Finset Λ'\nq : Λ'\nK : Finset Λ'\nH₁ : Λ'.Supports S q\nH₂ : trStmts₁ q ∪ K ⊆ S\nH₃ : K ⊆ S → Supports K S\n⊢ Supports (t... | [
1981,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1978,
1
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Mathlib/Algebra/Algebra/Hom.lean | AlgHom.comp_assoc | [] | [
359,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/Data/Int/GCD.lean | Int.gcd_dvd_left | [] | [
247,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Algebra/Module/BigOperators.lean | Finset.sum_smul | [] | [
42,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_of_countable | [] | [
292,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/MeasureTheory/Function/ConvergenceInMeasure.lean | MeasureTheory.tendstoInMeasure_of_tendsto_ae | [
{
"state_after": "α : Type u_1\nι : Type ?u.7016\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), AEStronglyMeasurable (f n) μ\nhfg : ∀ᵐ (x : α) ∂μ, Tendsto (fun n => f n x) atTop (𝓝 (g x))\nhg : AEStronglyMeasurab... | [
142,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.derivative_nodal | [
{
"state_after": "case refine'_1\nF : Type u_1\ninst✝¹ : Field F\nι : Type u_2\ns : Finset ι\nv : ι → F\ni : ι\nr : ι → F\nx : F\ninst✝ : DecidableEq ι\n⊢ ↑derivative (nodal ∅ v) = ∑ i in ∅, nodal (Finset.erase ∅ i) v\n\ncase refine'_2\nF : Type u_1\ninst✝¹ : Field F\nι : Type u_2\ns : Finset ι\nv : ι → F\ni : ... | [
547,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
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] |
Mathlib/Analysis/SpecialFunctions/Complex/Circle.lean | Real.Angle.expMapCircle_zero | [
{
"state_after": "no goals",
"state_before": "⊢ expMapCircle 0 = 1",
"tactic": "rw [← Real.Angle.coe_zero, Real.Angle.expMapCircle_coe, _root_.expMapCircle_zero]"
}
] | [
131,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.empty.nonempty_equiv_iff | [] | [
958,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
955,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.mkOfClosure_sets | [] | [
392,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.Eventually.choice | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.174506\nι : Sort x\nr : α → β → Prop\nl : Filter α\ninst✝ : NeBot l\nh : ∀ᶠ (x : α) in l, ∃ y, r x y\nthis : Nonempty β\n⊢ ∃ f, ∀ᶠ (x : α) in l, r x (f x)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.174506\nι : Sort x\n... | [
1419,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1415,
1
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Mathlib/Analysis/Calculus/FDeriv/Prod.lean | differentiableAt_pi | [] | [
441,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_const_mul_pow_atBot_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.252223\nι' : Type ?u.252226\nα : Type u_1\nβ : Type ?u.252232\nγ : Type ?u.252235\ninst✝ : LinearOrderedField α\nl : Filter β\nf : β → α\nr c : α\nn : ℕ\n⊢ Tendsto (fun x => c * x ^ n) atTop atBot ↔ n ≠ 0 ∧ c < 0",
"tactic": "simp only [← tendsto... | [
1246,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1244,
1
] |
Mathlib/Analysis/SpecialFunctions/Arsinh.lean | Real.sinh_surjective | [] | [
92,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Std/Data/Int/Lemmas.lean | Int.add_right_comm | [
{
"state_after": "no goals",
"state_before": "a b c : Int\n⊢ a + b + c = a + c + b",
"tactic": "rw [Int.add_assoc, Int.add_comm b, ← Int.add_assoc]"
}
] | [
287,
54
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
286,
11
] |
Mathlib/LinearAlgebra/Matrix/Transvection.lean | Matrix.diagonal_transvection_induction_of_det_ne_zero | [
{
"state_after": "n : Type u_1\np : Type ?u.340683\nR : Type u₂\n𝕜 : Type u_2\ninst✝⁴ : Field 𝕜\ninst✝³ : DecidableEq n\ninst✝² : DecidableEq p\ninst✝¹ : CommRing R\ninst✝ : Fintype n\nP : Matrix n n 𝕜 → Prop\nM : Matrix n n 𝕜\nhMdet : det M ≠ 0\nhdiag : ∀ (D : n → 𝕜), det (diagonal D) ≠ 0 → P (diagonal D)... | [
752,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
736,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mul_le_max_of_aleph0_le_left | [
{
"state_after": "case h.e'_4\na b : Cardinal\nh : ℵ₀ ≤ a\n⊢ max a b = max a b * max a b",
"state_before": "a b : Cardinal\nh : ℵ₀ ≤ a\n⊢ a * b ≤ max a b",
"tactic": "convert mul_le_mul' (le_max_left a b) (le_max_right a b) using 1"
},
{
"state_after": "case h.e'_4\na b : Cardinal\nh : ℵ₀ ≤ a\n⊢... | [
609,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
606,
1
] |
Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.adjugate_reindex | [] | [
266,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Combinatorics/SimpleGraph/Matching.lean | SimpleGraph.Subgraph.isPerfectMatching_iff | [
{
"state_after": "case refine'_1\nV : Type u\nG : SimpleGraph V\nM : Subgraph G\n⊢ IsPerfectMatching M → ∀ (v : V), ∃! w, Adj M v w\n\ncase refine'_2\nV : Type u\nG : SimpleGraph V\nM : Subgraph G\nhm : ∀ (v : V), ∃! w, Adj M v w\nv : V\n⊢ v ∈ M.verts",
"state_before": "V : Type u\nG : SimpleGraph V\nM : Su... | [
122,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Algebra/Order/Sub/Basic.lean | AddMonoidHom.le_map_tsub | [] | [
68,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Data/Rat/Cast.lean | Rat.preimage_cast_Ioc | [
{
"state_after": "case h\nF : Type ?u.72759\nι : Type ?u.72762\nα : Type ?u.72765\nβ : Type ?u.72768\nK : Type u_1\ninst✝ : LinearOrderedField K\na b x : ℚ\n⊢ x ∈ Rat.cast ⁻¹' Ioc ↑a ↑b ↔ x ∈ Ioc a b",
"state_before": "F : Type ?u.72759\nι : Type ?u.72762\nα : Type ?u.72765\nβ : Type ?u.72768\nK : Type u_1\... | [
383,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/Analysis/Normed/Field/UnitBall.lean | unitSphereToUnits_injective | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝ : NormedDivisionRing 𝕜\nx y : ↑(sphere 0 1)\nh : ↑(unitSphereToUnits 𝕜) x = ↑(unitSphereToUnits 𝕜) y\n⊢ ↑x = ↑y",
"tactic": "convert congr_arg Units.val h"
}
] | [
190,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/GroupTheory/Congruence.lean | Con.sup_eq_conGen | [
{
"state_after": "M : Type u_1\nN : Type ?u.28395\nP : Type ?u.28398\ninst✝² : Mul M\ninst✝¹ : Mul N\ninst✝ : Mul P\nc✝ c d : Con M\n⊢ c ⊔ d = sInf {s | ∀ (x y : M), ↑c x y ∨ ↑d x y → ↑s x y}",
"state_before": "M : Type u_1\nN : Type ?u.28395\nP : Type ?u.28398\ninst✝² : Mul M\ninst✝¹ : Mul N\ninst✝ : Mul P... | [
570,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
1
] |
Mathlib/Data/Set/Basic.lean | set_coe_cast | [] | [
209,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.powerlt_max | [] | [
2311,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2310,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | DifferentiableOn.ccosh | [] | [
467,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.restrict_zero | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.474705\nm inst✝³ : MeasurableSpace α\ninst✝² : MeasurableSpace β\nM : Type u_2\ninst✝¹ : AddCommMonoid M\ninst✝ : TopologicalSpace M\nv : VectorMeasure α M\ni : Set α\nhi : MeasurableSet i\n⊢ restrict 0 i = 0\n\ncase neg\nα : Type u_1\nβ : Type ?u.474705\nm ... | [
728,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
722,
1
] |
Mathlib/GroupTheory/Subgroup/ZPowers.lean | AddSubgroup.int_cast_mul_mem_zmultiples | [
{
"state_after": "no goals",
"state_before": "G : Type ?u.29474\ninst✝³ : Group G\nA : Type ?u.29480\ninst✝² : AddGroup A\nN : Type ?u.29486\ninst✝¹ : Group N\nR : Type u_1\ninst✝ : Ring R\nr : R\nk : ℤ\n⊢ ↑k * r ∈ zmultiples r",
"tactic": "simpa only [← zsmul_eq_mul] using zsmul_mem_zmultiples r k"
}... | [
142,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Data/Nat/Choose/Factorization.lean | Nat.factorization_choose_of_lt_three_mul | [
{
"state_after": "case inl\np n k : ℕ\nhp' : p ≠ 2\nhk : p ≤ k\nhk' : p ≤ n - k\nhn : n < 3 * p\nhp : ¬Prime p\n⊢ ↑(factorization (choose n k)) p = 0\n\ncase inr\np n k : ℕ\nhp' : p ≠ 2\nhk : p ≤ k\nhk' : p ≤ n - k\nhn : n < 3 * p\nhp : Prime p\n⊢ ↑(factorization (choose n k)) p = 0",
"state_before": "p n k... | [
93,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Data/List/Rotate.lean | List.IsRotated.trans | [
{
"state_after": "no goals",
"state_before": "α : Type u\nl l' l✝ : List α\nn m : ℕ\n⊢ rotate l✝ (n + m) = rotate (rotate l✝ n) m",
"tactic": "rw [rotate_rotate]"
}
] | [
465,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/Order/Closure.lean | LowerAdjoint.closure_iSup₂_closure | [] | [
470,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
] |
Std/Data/List/Lemmas.lean | List.get?_reverse' | [
{
"state_after": "α : Type u_1\na : α\nl : List α\ni : Nat\nh : i = length l\n⊢ get? (reverse (a :: l)) i = get? (a :: l) 0",
"state_before": "α : Type u_1\na : α\nl : List α\ni : Nat\nh : i + 0 + 1 = length (a :: l)\n⊢ get? (reverse (a :: l)) i = get? (a :: l) 0",
"tactic": "simp at h"
},
{
"st... | [
673,
80
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
666,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.norm_indicatorConstLp_top | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type u_2\nF : Type ?u.689528\nG : Type ?u.689531\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\ns : Set α\nhs : MeasurableSet s\nhμs : ↑↑μ... | [
759,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
755,
1
] |
Std/Data/String/Lemmas.lean | String.data_drop | [
{
"state_after": "no goals",
"state_before": "s : String\nn : Nat\n⊢ (drop s n).data = List.drop n s.data",
"tactic": "rw [drop_eq]"
}
] | [
1092,
96
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1092,
9
] |
Mathlib/Analysis/Calculus/ContDiff.lean | norm_iteratedFDeriv_comp_le | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nD✝ : Type uD\ninst✝⁹ : NormedAddCommGroup D✝\ninst✝⁸ : NormedSpace 𝕜 D✝\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 : Nor... | [
2709,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2702,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.restr_eq_of_source_subset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.40108\nδ : Type ?u.40111\ne✝ : LocalEquiv α β\ne' : LocalEquiv β γ\ne : LocalEquiv α β\ns : Set α\nh : e.source ⊆ s\n⊢ (LocalEquiv.restr e s).source = e.source",
"tactic": "simp [inter_eq_self_of_subset_left h]"
}
] | [
594,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Std/Data/List/Lemmas.lean | List.get?_set_eq_of_lt | [
{
"state_after": "α : Type u_1\na : α\nn : Nat\nl : List α\nh : n < length l\n⊢ (fun x => a) <$> some (get l { val := n, isLt := h }) = some a",
"state_before": "α : Type u_1\na : α\nn : Nat\nl : List α\nh : n < length l\n⊢ get? (set l n a) n = some a",
"tactic": "rw [get?_set_eq, get?_eq_get h]"
},
... | [
800,
73
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
799,
1
] |
Mathlib/RingTheory/FreeRing.lean | FreeRing.map_of | [] | [
112,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/CategoryTheory/Preadditive/Biproducts.lean | CategoryTheory.Limits.biproduct.matrix_map | [
{
"state_after": "case w.w\nC : Type u\ninst✝⁵ : Category C\ninst✝⁴ : Preadditive C\nJ : Type\ninst✝³ : Fintype J\nf✝ : J → C\ninst✝² : HasBiproduct f✝\nK : Type\ninst✝¹ : Fintype K\ninst✝ : HasFiniteBiproducts C\nf : J → C\ng h : K → C\nm : (j : J) → (k : K) → f j ⟶ g k\nn : (k : K) → g k ⟶ h k\nj✝¹ : J\nj✝ : ... | [
262,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.succAbove_ne_zero | [] | [
2049,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2047,
1
] |
Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | LinearMap.toMatrixₛₗ₂'_symm | [] | [
235,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.nontrivial_iff | [] | [
1072,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1069,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.add_mul_left_right_iff | [] | [
332,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.set_lintegral_dirac | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1692646\nγ : Type ?u.1692649\nδ : Type ?u.1692652\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝² : MeasurableSpace α\na : α\nf : α → ℝ≥0∞\ns : Set α\ninst✝¹ : MeasurableSingletonClass α\ninst✝ : Decidable (a ∈ s)\n⊢ (∫⁻ (x : α), f x ∂if a ∈ s then dirac a else 0) = i... | [
1392,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1387,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinitePos_mul_infinitePos | [] | [
864,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
862,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.SOppSide.exists_sbtw | [
{
"state_after": "case intro.intro\nR : Type u_1\nV : Type u_2\nV' : Type ?u.353300\nP : Type u_3\nP' : Type ?u.353306\ninst✝⁶ : LinearOrderedField R\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddTorsor V P\ninst✝² : AddCommGroup V'\ninst✝¹ : Module R V'\ninst✝ : AddTorsor V' P'\ns : AffineSubspace... | [
707,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/Logic/Relation.lean | Relation.ReflTransGen.mono | [] | [
534,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
1
] |
Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.IsOrtho.map_iff | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace 𝕜 F\nf : E ≃ₗᵢ[𝕜] F\nU V : Submodule 𝕜 E\nh : Submodule.map f U ⟂ Submodule.map f V\nhf : ∀ (p : Submodule ... | [
405,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/FieldTheory/PerfectClosure.lean | pthRoot_frobenius | [] | [
77,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.trans_left | [] | [
1037,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1035,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Concrete.lean | List.formPerm_apply_mem_eq_next | [
{
"state_after": "case intro.intro\nα : Type u_1\ninst✝ : DecidableEq α\nl l' : List α\nhl : Nodup l\nk : ℕ\nhk : k < length l\nhx : nthLe l k hk ∈ l\n⊢ ↑(formPerm l) (nthLe l k hk) = next l (nthLe l k hk) hx",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\nl l' : List α\nhl : Nodup l\nx : α\nhx : x ... | [
127,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.fromEdgeSet_inf | [
{
"state_after": "case Adj.h.h.a\nι : Sort ?u.83783\n𝕜 : Type ?u.83786\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v✝ w✝ : V\ne : Sym2 V\ns✝ s t : Set (Sym2 V)\nv w : V\n⊢ Adj (fromEdgeSet s ⊓ fromEdgeSet t) v w ↔ Adj (fromEdgeSet (s ∩ t)) v w",
"state_before": "ι : ... | [
653,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | ne_one_of_norm_ne_zero | [
{
"state_after": "𝓕 : Type ?u.73640\n𝕜 : Type ?u.73643\nα : Type ?u.73646\nι : Type ?u.73649\nκ : Type ?u.73652\nE : Type u_1\nF : Type ?u.73658\nG : Type ?u.73661\ninst✝² : SeminormedGroup E\ninst✝¹ : SeminormedGroup F\ninst✝ : SeminormedGroup G\ns : Set E\na₁ a₂ b b₁ b₂ : E\nr r₁ r₂ : ℝ\n⊢ ‖1‖ = 0",
"st... | [
523,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
] |
Mathlib/Topology/Semicontinuous.lean | Continuous.comp_lowerSemicontinuousOn | [] | [
336,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.sigma_apply | [] | [
785,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
1
] |
Mathlib/CategoryTheory/Limits/Constructions/Pullbacks.lean | CategoryTheory.Limits.hasLimit_cospan_of_hasLimit_pair_of_hasLimit_parallelPair | [
{
"state_after": "C : Type u\n𝒞 : Category C\nX Y Z : C\nf : X ⟶ Z\ng : Y ⟶ Z\ninst✝¹ : HasLimit (pair X Y)\ninst✝ : HasLimit (parallelPair (prod.fst ≫ f) (prod.snd ≫ g))\nπ₁ : X ⨯ Y ⟶ X := prod.fst\nπ₂ : X ⨯ Y ⟶ Y := prod.snd\ne : equalizer (π₁ ≫ f) (π₂ ≫ g) ⟶ X ⨯ Y := equalizer.ι (π₁ ≫ f) (π₂ ≫ g)\n⊢ equaliz... | [
49,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
31,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroObjects.lean | CategoryTheory.Limits.hasZeroObject_unop | [] | [
218,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.X_mul_C | [] | [
591,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
590,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.cancel_of_lt' | [] | [
1075,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1074,
1
] |
Mathlib/Algebra/BigOperators/Associated.lean | exists_associated_mem_of_dvd_prod | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.13323\nγ : Type ?u.13326\nδ : Type ?u.13329\ninst✝ : CancelCommMonoidWithZero α\np : α\nhp : Prime p\ns : Multiset α\n⊢ (∀ (r : α), r ∈ 0 → Prime r) → p ∣ Multiset.prod 0 → ∃ q, q ∈ 0 ∧ p ~ᵤ q",
"tactic": "simp [mt isUnit_iff_dvd_on... | [
64,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Algebra/Lie/OfAssociative.lean | lie_eq_smul | [] | [
115,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Algebra/Algebra/RestrictScalars.lean | RestrictScalars.lsmul_apply_apply | [] | [
188,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Data/PFun.lean | PFun.get_prodMap | [] | [
675,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
673,
1
] |
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