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/NormedSpace/lpSpace.lean | memℓp_infty_iff | [
{
"state_after": "α : Type u_1\nE : α → Type u_2\np q : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : (i : α) → E i\n⊢ (if ⊤ = 0 then Set.Finite {i | ¬f i = 0}\n else if ⊤ = ⊤ then BddAbove (Set.range fun i => ‖f i‖) else Summable fun i => ‖f i‖ ^ 0) ↔\n BddAbove (Set.range fun i => ‖f i‖)",
"... | [
97,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | affineSpan_induction' | [
{
"state_after": "k : Type u_2\nV : Type u_3\nP : Type u_1\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type ?u.343274\ns : Set P\np : (x : P) → x ∈ affineSpan k s → Prop\nHs : ∀ (y : P) (hys : y ∈ s), p y (_ : y ∈ ↑(affineSpan k s))\nHc :\n ∀ (c : k) (u : P) (hu... | [
1203,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1188,
1
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Mathlib/Computability/Partrec.lean | Nat.rfindOpt_spec | [] | [
133,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
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Mathlib/Analysis/InnerProductSpace/Basic.lean | OrthogonalFamily.summable_iff_norm_sq_summable | [
{
"state_after": "𝕜 : Type u_4\nE : Type u_1\nF : Type ?u.3720833\ninst✝⁷ : IsROrC 𝕜\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : InnerProductSpace 𝕜 E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nι : Type u_2\nG : ι → Type u_3\ninst✝² : (i : ι) → NormedAddCommGroup (G i... | [
2151,
15
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2111,
1
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Mathlib/Data/PFunctor/Univariate/M.lean | PFunctor.M.default_consistent | [] | [
204,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
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Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | Collinear.finiteDimensional_vectorSpan | [] | [
351,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/Order/Circular.lean | sbtw_cyclic_left | [] | [
218,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
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Mathlib/Order/FixedPoints.lean | OrderHom.isFixedPt_lfp | [] | [
86,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
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Mathlib/Data/Nat/Periodic.lean | Nat.periodic_gcd | [
{
"state_after": "no goals",
"state_before": "a : ℕ\n⊢ Periodic (gcd a) a",
"tactic": "simp only [forall_const, gcd_add_self_right, eq_self_iff_true, Periodic]"
}
] | [
28,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
27,
1
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Mathlib/Data/Set/Basic.lean | Set.inter_eq_self_of_subset_left | [] | [
977,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
976,
1
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Mathlib/Topology/UniformSpace/Cauchy.lean | cauchy_map_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : UniformSpace α\nl : Filter β\nf : β → α\n⊢ Cauchy (map f l) ↔ NeBot l ∧ Tendsto (fun p => (f p.fst, f p.snd)) (l ×ˢ l) (𝓤 α)",
"tactic": "rw [Cauchy, map_neBot_iff, prod_map_map_eq, Tendsto]"
}
] | [
69,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
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Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.sub_mem_orthogonal_of_inner_right | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.34324\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace 𝕜 F\nK : Submodule 𝕜 E\nx y : E\nh : ∀ (v : { x // x ∈ K }), inner (↑v) x = inner (↑v) y\nu : E\nhu : u... | [
103,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
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Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.tr_copy | [] | [
1119,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1118,
1
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Mathlib/Analysis/LocallyConvex/Basic.lean | Balanced.interior | [
{
"state_after": "𝕜 : Type u_1\n𝕝 : Type ?u.185016\nE : Type u_2\nι : Sort ?u.185022\nκ : ι → Sort ?u.185027\ninst✝⁸ : NormedField 𝕜\ninst✝⁷ : NormedRing 𝕝\ninst✝⁶ : NormedSpace 𝕜 𝕝\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : SMulWithZero 𝕝 E\ninst✝² : IsScalarTower 𝕜 𝕝 E\ns t u v A B : Se... | [
378,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
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Mathlib/Data/Set/Intervals/Disjoint.lean | Set.iUnion_Ioo_right | [
{
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"tactic": "simp only [← Ioi_inter_Iio, ← inter_iUnion, iUnion_Iio, inter_univ]"
}
] | [
113,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.set_lintegral_one | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.75773\nγ : Type ?u.75776\nδ : Type ?u.75779\nm : MeasurableSpace α\nμ ν : Measure α\ns : Set α\n⊢ (∫⁻ (x : α) in s, 1 ∂μ) = ↑↑μ s",
"tactic": "rw [set_lintegral_const, one_mul]"
}
] | [
186,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
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Mathlib/LinearAlgebra/Matrix/Trace.lean | Matrix.trace_sum | [] | [
111,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
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Mathlib/NumberTheory/VonMangoldt.lean | Nat.ArithmeticFunction.sum_moebius_mul_log_eq | [
{
"state_after": "n : ℕ\n⊢ ∑ x in divisors n, ↑(↑μ x) * Real.log ↑x = ∑ x in divisorsAntidiagonal n, ↑(↑μ x.fst) * -Real.log ↑x.snd",
"state_before": "n : ℕ\n⊢ ∑ d in divisors n, ↑(↑μ d) * ↑log d = -↑Λ n",
"tactic": "simp only [← log_mul_moebius_eq_vonMangoldt, mul_comm log, mul_apply, log_apply, intCoe... | [
161,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
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Mathlib/Analysis/Normed/Field/Basic.lean | dist_inv_inv₀ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.269625\nγ : Type ?u.269628\nι : Type ?u.269631\ninst✝ : NormedDivisionRing α\nz w : α\nhz : z ≠ 0\nhw : w ≠ 0\n⊢ dist z⁻¹ w⁻¹ = dist z w / (‖z‖ * ‖w‖)",
"tactic": "rw [dist_eq_norm, inv_sub_inv' hz hw, norm_mul, norm_mul, norm_inv, ... | [
597,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
594,
1
] |
Mathlib/Data/Set/Intervals/OrdConnected.lean | Set.Icc_subset | [] | [
81,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
11
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Mathlib/Algebra/Order/Floor.lean | round_sub_nat | [
{
"state_after": "F : Type ?u.257064\nα : Type u_1\nβ : Type ?u.257070\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nx : α\ny : ℕ\n⊢ round (x + -↑↑y) = round x - ↑y",
"state_before": "F : Type ?u.257064\nα : Type u_1\nβ : Type ?u.257070\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nx : α\ny : ℕ\... | [
1387,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1384,
1
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Mathlib/Analysis/Convex/Function.lean | StrictConcaveOn.sub | [] | [
902,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
900,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasStrictFDerivAt.csin | [] | [
374,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean | ModularGroup.coe_S | [] | [
357,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasStrictDerivAt.sin | [] | [
828,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
826,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.trans_tendsto_nhds | [] | [
1356,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1354,
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Mathlib/LinearAlgebra/Determinant.lean | Basis.det_smul_mk_coord_eq_det_update | [
{
"state_after": "R : Type u_2\ninst✝⁸ : CommRing R\nM : Type u_3\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\nM' : Type ?u.2746027\ninst✝⁵ : AddCommGroup M'\ninst✝⁴ : Module R M'\nι : Type u_1\ninst✝³ : DecidableEq ι\ninst✝² : Fintype ι\ne : Basis ι R M\nA : Type ?u.2747047\ninst✝¹ : CommRing A\ninst✝ : Modu... | [
657,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
646,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.of_const_mul_right | [] | [
1508,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1506,
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] |
Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.MulticospanIndex.multicospan_map_snd | [] | [
213,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
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Mathlib/Data/List/Basic.lean | List.getLast?_eq_getLast_of_ne_nil | [] | [
804,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
801,
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] |
Std/Data/String/Lemmas.lean | Substring.ValidFor.front | [] | [
880,
29
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
879,
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] |
Mathlib/Data/Finset/NoncommProd.lean | Multiset.noncommFold_cons | [
{
"state_after": "case h\nF : Type ?u.4278\nι : Type ?u.4281\nα : Type u_1\nβ : Type ?u.4287\nγ : Type ?u.4290\nf : α → β → β\nop : α → α → α\nassoc : IsAssociative α op\na x : α\na✝ : List α\nh : Set.Pairwise {x | x ∈ a ::ₘ Quotient.mk (List.isSetoid α) a✝} fun x y => op x y = op y x\nh' : Set.Pairwise {x | x ... | [
103,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Order/OrderIsoNat.lean | WellFounded.monotone_chain_condition | [
{
"state_after": "case a.h.h.e'_2.h.h.a\nα : Type u_1\ninst✝ : PartialOrder α\na✝¹ : ℕ →o α\nx✝ a✝ : ℕ\n⊢ x✝ ≤ a✝ → ¬↑a✝¹ x✝ < ↑a✝¹ a✝ ↔ x✝ ≤ a✝ → ↑a✝¹ x✝ = ↑a✝¹ a✝",
"state_before": "α : Type u_1\ninst✝ : PartialOrder α\n⊢ (∀ (a : ℕ →o α), ∃ n, ∀ (m : ℕ), n ≤ m → ¬↑a n < ↑a m) ↔ ∀ (a : ℕ →o α), ∃ n, ∀ (m :... | [
237,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Analysis/Convex/Segment.lean | vadd_openSegment | [] | [
259,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Algebra/Star/CHSH.lean | tsirelson_inequality | [
{
"state_after": "R : Type u\ninst✝⁴ : OrderedRing R\ninst✝³ : StarOrderedRing R\ninst✝² : Algebra ℝ R\ninst✝¹ : OrderedSMul ℝ R\ninst✝ : StarModule ℝ R\nA₀ A₁ B₀ B₁ : R\nT : IsCHSHTuple A₀ A₁ B₀ B₁\nM : ∀ (m : ℤ) (a : ℝ) (x : R), m • a • x = (↑m * a) • x\n⊢ A₀ * B₀ + A₀ * B₁ + A₁ * B₀ - A₁ * B₁ ≤ Real.sqrt 2 ^... | [
252,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
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Mathlib/Topology/Support.lean | isClosed_mulTSupport | [] | [
59,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
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Mathlib/ModelTheory/Skolem.lean | FirstOrder.Language.Substructure.coeSort_elementarySkolem₁Reduct | [] | [
109,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.isImage_source_target | [] | [
619,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Additive.lean | BoxIntegral.BoxAdditiveMap.toSMul_apply | [] | [
186,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | derivWithin_cexp | [] | [
107,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.IsBoundedUnder.mono_le | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.9288\nι : Type ?u.9291\nr : α → α → Prop\nf g : Filter α\ninst✝ : Preorder β\nl : Filter α\nu v : α → β\nhu : IsBoundedUnder (fun x x_1 => x ≤ x_1) l u\nhv : v ≤ᶠ[l] u\n⊢ ∀ (a : β), (∀ᶠ (x : β) in map u l, (fun x x_1 => x ≤ x_1) x a) → ∀ᶠ (x : β) in map ... | [
109,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.tendsto_integral_of_L1 | [
{
"state_after": "α : Type u_3\nE : Type u_2\nF✝ : Type ?u.983342\n𝕜 : Type ?u.983345\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : CompleteSpace E\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : SMulCommClass ℝ 𝕜 E\ninst✝² : NormedAddCommGroup F✝\ninst✝¹ : Norme... | [
983,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
978,
1
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Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.sMod_succ | [
{
"state_after": "p i : ℕ\n⊢ sMod p (i + 1) = (sMod p i * sMod p i - 2) % (2 ^ p - 1)",
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"tactic": "substs a b c"
},
{
"state_after": "p i : ℕ\n⊢ sMod p (i + 1) =... | [
533,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.TM1to1.trTape'_move_right | [
{
"state_after": "Γ : Type u_1\ninst✝² : Inhabited Γ\nΛ : Type ?u.373349\ninst✝¹ : Inhabited Λ\nσ : Type ?u.373355\ninst✝ : Inhabited σ\nn : ℕ\nenc : Γ → Vector Bool n\ndec : Vector Bool n → Γ\nenc0 : enc default = Vector.replicate n false\nM : Λ → Stmt₁\nL R : ListBlank Γ\n⊢ ∀ (i : ℕ) (L : Tape Bool), (Tape.mo... | [
1798,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1789,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | MonoidHom.coe_mrangeRestrict | [] | [
1144,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1142,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.norm_setToL1_le' | [] | [
1247,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1246,
1
] |
Mathlib/Logic/Encodable/Basic.lean | Encodable.encode_some | [] | [
174,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsLeast.isGLB | [] | [
279,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Order/Bounds/Basic.lean | MonotoneOn.mem_upperBounds_image | [] | [
1156,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1154,
1
] |
Mathlib/Data/Nat/Log.lean | Nat.log_zero_left | [] | [
72,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.support_trinomial' | [] | [
882,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
872,
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Mathlib/Data/List/Indexes.lean | List.mapIdxM'_eq_mapIdxM | [] | [
362,
36
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360,
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Mathlib/Analysis/Normed/Group/Pointwise.lean | inv_thickening | [
{
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Mathlib/Data/MvPolynomial/Equiv.lean | MvPolynomial.sumToIter_Xl | [] | [
178,
26
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177,
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Mathlib/Analysis/NormedSpace/Basic.lean | frontier_ball | [
{
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129,
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Mathlib/Analysis/Calculus/Deriv/Mul.lean | deriv_smul_const | [] | [
116,
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114,
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | MeasurableSet.nhdsWithin_isMeasurablyGenerated | [] | [
370,
39
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367,
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Mathlib/Analysis/Calculus/Deriv/Basic.lean | derivWithin_of_mem | [] | [
494,
78
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492,
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Mathlib/CategoryTheory/Limits/Shapes/Images.lean | CategoryTheory.Limits.image.isImage_lift | [] | [
363,
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362,
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Mathlib/Data/Finset/Pi.lean | Finset.Pi.cons_injective | [
{
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86,
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Mathlib/Algebra/Group/Prod.lean | Prod.fst_div | [] | [
170,
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Mathlib/Analysis/LocallyConvex/WeakDual.lean | LinearMap.toSeminorm_comp | [
{
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Mathlib/LinearAlgebra/Dual.lean | Subspace.dualAnnihilator_dualCoannihilator_eq | [
{
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953,
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Mathlib/Data/Sum/Order.lean | WithBot.orderIsoPUnitSumLex_bot | [] | [
750,
6
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749,
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Mathlib/Data/List/Perm.lean | List.Perm.mem_iff | [
{
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95,
27
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Mathlib/CategoryTheory/Limits/Preserves/Shapes/Biproducts.lean | CategoryTheory.Functor.mapBiproduct_inv | [] | [
312,
84
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310,
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.map_injective_of_ker_le | [
{
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_map | [
{
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935,
56
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Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.coeff_index_single_X | [
{
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] | [
407,
67
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405,
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Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.compMeasurable_eq_mk | [
{
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257,
70
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255,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.of_bound | [] | [
124,
22
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123,
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Mathlib/Data/Subtype.lean | Subtype.surjective_restrict | [
{
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177,
19
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172,
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Mathlib/Data/Set/Basic.lean | Set.ne_insert_of_not_mem | [] | [
1143,
38
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1142,
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Mathlib/Data/TypeVec.lean | TypeVec.lastFun_toSubtype | [
{
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... | [
716,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
713,
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Std/Data/Nat/Lemmas.lean | Nat.succ_pred_eq_of_pos | [] | [
146,
21
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145,
1
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Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.lt_blsub₂ | [
{
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108,
30
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101,
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Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.Homotopic.hcomp | [] | [
376,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.Dart.toProd_injective | [] | [
713,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
712,
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | OrderIso.map_ciSup | [] | [
1336,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1334,
1
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Mathlib/Data/Polynomial/Derivative.lean | Polynomial.derivative_bit0 | [
{
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}
] | [
147,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
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src/lean/Init/Core.lean | not_not_intro | [] | [
522,
23
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521,
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Mathlib/Data/Polynomial/Div.lean | Polynomial.rootMultiplicity_eq_nat_find_of_nonzero | [
{
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"state_before": "R : Type u\nS : Typ... | [
548,
14
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544,
1
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.normSq_add | [
{
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513,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
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Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.HomotopyWith.trans_apply | [] | [
531,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
524,
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Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.coe_bot | [] | [
187,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
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Mathlib/Data/Finset/Basic.lean | Finset.coe_empty | [
{
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}
] | [
622,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
1
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Mathlib/Order/Disjoint.lean | IsCompl.left_le_iff | [] | [
547,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
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Mathlib/CategoryTheory/Types.lean | CategoryTheory.injective_of_mono | [] | [
253,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
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Std/Data/RBMap/Lemmas.lean | Std.RBNode.Path.insertNew_toList | [
{
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}
] | [
496,
19
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495,
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Mathlib/Topology/Sheaves/SheafCondition/PairwiseIntersections.lean | TopCat.Sheaf.interUnionPullbackConeLift_right | [
{
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403,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
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Mathlib/Order/LiminfLimsup.lean | Filter.liminf_nat_add | [
{
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808,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
805,
1
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.aefinStronglyMeasurable_iff_aemeasurable | [
{
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1974,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1972,
1
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Mathlib/Order/Zorn.lean | zorn_nonempty_partialOrder | [] | [
170,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
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Mathlib/Order/GaloisConnection.lean | GaloisInsertion.l_biSup_u | [
{
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549,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
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Mathlib/Data/List/Basic.lean | List.cons_eq_cons | [] | [
66,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
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Mathlib/Order/UpperLower/Basic.lean | LowerSet.compl_inf | [] | [
897,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
896,
11
] |
Mathlib/Order/Bounds/Basic.lean | BddBelow.union | [] | [
431,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.ofMulEquivOfLocalizations_eq | [] | [
1414,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1413,
1
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Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.LHom.mem_onTheory | [] | [
938,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
936,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Associates.mk_ne_zero' | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : CommSemiring R\nr : R\n⊢ Associates.mk (Ideal.span {r}) ≠ 0 ↔ r ≠ 0",
"tactic": "rw [Associates.mk_ne_zero, Ideal.zero_eq_bot, Ne.def, Ideal.span_singleton_eq_bot]"
}
] | [
1967,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1965,
1
] |
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