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/SetTheory/ZFC/Basic.lean | Class.mem_asymm | [] | [
1553,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1552,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.cos_add_cos | [
{
"state_after": "x y : ℂ\nh2 : 2 ≠ 0\n⊢ cos x + cos y = 2 * cos ((x + y) / 2) * cos ((x - y) / 2)",
"state_before": "x y : ℂ\n⊢ cos x + cos y = 2 * cos ((x + y) / 2) * cos ((x - y) / 2)",
"tactic": "have h2 : (2 : ℂ) ≠ 0 := by norm_num"
},
{
"state_after": "case calc_1\nx y : ℂ\nh2 : 2 ≠ 0\n⊢ c... | [
924,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
912,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.Frequently.mono | [] | [
1278,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1276,
1
] |
Mathlib/Topology/StoneCech.lean | continuous_stoneCechUnit | [
{
"state_after": "α : Type u\ninst✝ : TopologicalSpace α\nx : α\ng : Ultrafilter α\ngx : ↑g ≤ 𝓝 x\nthis : ↑(Ultrafilter.map pure g) ≤ 𝓝 g\n⊢ Tendsto stoneCechUnit (↑g) (𝓝 (stoneCechUnit x))",
"state_before": "α : Type u\ninst✝ : TopologicalSpace α\nx : α\ng : Ultrafilter α\ngx : ↑g ≤ 𝓝 x\n⊢ Tendsto ston... | [
312,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/Data/Prod/Basic.lean | Function.Injective.Prod_map | [] | [
315,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/RingTheory/DedekindDomain/Dvr.lean | IsDedekindDomain.isDedekindDomainDvr | [] | [
155,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ico_self | [] | [
283,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Data/List/Range.lean | List.finRange_map_get | [
{
"state_after": "no goals",
"state_before": "α : Type u\nl : List α\n⊢ length (map (get l) (finRange (length l))) = length l",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nl : List α\n⊢ ∀ (n : ℕ) (h₁ : n < length (map (get l) (finRange (length l)))) (h₂ : n ... | [
215,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Data/Polynomial/EraseLead.lean | Polynomial.eraseLead_add_monomial_natDegree_leadingCoeff | [] | [
68,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Topology/PathConnected.lean | locPathConnected_of_bases | [
{
"state_after": "case path_connected_basis\nX : Type u_1\nY : Type ?u.702092\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx y z : X\nι : Type u_2\nF : Set X\np : ι → Prop\ns : X → ι → Set X\nh : ∀ (x : X), HasBasis (𝓝 x) p (s x)\nh' : ∀ (x : X) (i : ι), p i → IsPathConnected (s x i)\n⊢ ∀ (x : X),... | [
1210,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1200,
1
] |
Mathlib/Data/Int/GCD.lean | Nat.xgcd_val | [
{
"state_after": "x y : ℕ\n⊢ xgcd x y = ((xgcd x y).fst, (xgcd x y).snd)",
"state_before": "x y : ℕ\n⊢ xgcd x y = (gcdA x y, gcdB x y)",
"tactic": "unfold gcdA gcdB"
},
{
"state_after": "case mk\nx y : ℕ\nfst✝ snd✝ : ℤ\n⊢ (fst✝, snd✝) = ((fst✝, snd✝).fst, (fst✝, snd✝).snd)",
"state_before": ... | [
125,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Topology/Constructions.lean | exists_nhds_square | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.50921\nδ : Type ?u.50924\nε : Type ?u.50927\nζ : Type ?u.50930\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : TopologicalSpace β\ninst✝³ : TopologicalSpace γ\ninst✝² : TopologicalSpace δ\ninst✝¹ : TopologicalSpace ε\ninst✝ : Topologic... | [
688,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
686,
1
] |
Mathlib/CategoryTheory/Monoidal/Free/Basic.lean | CategoryTheory.FreeMonoidalCategory.mk_α_inv | [] | [
211,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Algebra/Group/Commute.lean | Commute.pow_self | [] | [
202,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | Filter.HasBasis.cauchy_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : UniformSpace α\nι : Sort u_1\np : ι → Prop\ns : ι → Set (α × α)\nh : HasBasis (𝓤 α) p s\nf : Filter α\n⊢ (∀ (i' : ι), p i' → ∃ i, i ∈ f ∧ id i ×ˢ id i ⊆ s i') ↔\n ∀ (i : ι), p i → ∃ t, t ∈ f ∧ ∀ (x : α), x ∈ t → ∀ (y : α), y ∈... | [
47,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Std/Logic.lean | iff_congr | [] | [
78,
79
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
77,
1
] |
Mathlib/Data/Set/Image.lean | Function.Surjective.preimage_subset_preimage_iff | [
{
"state_after": "case hs\nι : Sort ?u.104761\nα : Type u_2\nβ : Type u_1\nf : α → β\ns t : Set β\nhf : Surjective f\n⊢ s ⊆ range f",
"state_before": "ι : Sort ?u.104761\nα : Type u_2\nβ : Type u_1\nf : α → β\ns t : Set β\nhf : Surjective f\n⊢ f ⁻¹' s ⊆ f ⁻¹' t ↔ s ⊆ t",
"tactic": "apply Set.preimage_su... | [
1324,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1320,
1
] |
Mathlib/Analysis/Convex/Gauge.lean | gauge_mono | [] | [
90,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Analysis/LocallyConvex/Basic.lean | balanced_iff_neg_mem | [
{
"state_after": "𝕜 : Type ?u.232896\n𝕝 : Type ?u.232899\nE : Type u_1\nι : Sort ?u.232905\nκ : ι → Sort ?u.232910\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\ns : Set E\nhs : Convex ℝ s\nh : ∀ ⦃x : E⦄, x ∈ s → -x ∈ s\na : ℝ\nha : ‖a‖ ≤ 1\nx : E\nhx : x ∈ s\n⊢ a • x ∈ s",
"state_before": "𝕜 : Type ?u.23... | [
429,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | InnerProductSpace.Core.inner_sub_right | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type ?u.603708\nF : Type u_2\ninst✝² : IsROrC 𝕜\ninst✝¹ : AddCommGroup F\ninst✝ : Module 𝕜 F\nc : Core 𝕜 F\nx y z : F\n⊢ inner x (y - z) = inner x y - inner x z",
"tactic": "simp [sub_eq_add_neg, inner_add_right, inner_neg_right]"
}
] | [
297,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_C_mul_X_pow_le | [] | [
687,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
686,
1
] |
Std/Logic.lean | not_forall_of_exists_not | [] | [
445,
27
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
444,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_bit1 | [] | [
394,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
Mathlib/Data/Nat/Bits.lean | Nat.boddDiv2_eq | [
{
"state_after": "n✝ n : ℕ\n⊢ boddDiv2 n = ((boddDiv2 n).fst, (boddDiv2 n).snd)",
"state_before": "n✝ n : ℕ\n⊢ boddDiv2 n = (bodd n, div2 n)",
"tactic": "unfold bodd div2"
},
{
"state_after": "case mk\nn✝ n : ℕ\nfst✝ : Bool\nsnd✝ : ℕ\n⊢ (fst✝, snd✝) = ((fst✝, snd✝).fst, (fst✝, snd✝).snd)",
"... | [
42,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.map_id' | [] | [
234,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | Measurable.of_uncurry_right | [] | [
701,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
699,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.opow_dvd_opow_iff | [] | [
223,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.eq_of_eq | [
{
"state_after": "case intro\nM : Type u_1\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type u_3\ninst✝¹ : CommMonoid N\nP : Type u_2\ninst✝ : CommMonoid P\nf : LocalizationMap S N\ng : M →* P\nhg : ∀ (y : { x // x ∈ S }), IsUnit (↑g ↑y)\nx y : M\nh : ↑(toMap f) x = ↑(toMap f) y\nc : { x // x ∈ S }\nhc : ↑c * x... | [
898,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
894,
1
] |
Std/Data/Int/Lemmas.lean | Int.negSucc_eq' | [
{
"state_after": "m : Nat\n⊢ -↑m + -1 = -↑m - 1",
"state_before": "m : Nat\n⊢ -[m+1] = -↑m - 1",
"tactic": "simp only [negSucc_eq, Int.neg_add]"
},
{
"state_after": "no goals",
"state_before": "m : Nat\n⊢ -↑m + -1 = -↑m - 1",
"tactic": "rfl"
}
] | [
1354,
95
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1354,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.map_le_of_le_comap | [] | [
1423,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1422,
1
] |
Mathlib/LinearAlgebra/Eigenspace/Basic.lean | Module.End.hasGeneralizedEigenvalue_of_hasGeneralizedEigenvalue_of_le | [
{
"state_after": "K R : Type v\nV M : Type w\ninst✝⁵ : CommRing R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\ninst✝² : Field K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nf : End R M\nμ : R\nk m : ℕ\nhm : k ≤ m\nhk : ↑(generalizedEigenspace f μ) k ≠ ⊥\n⊢ ↑(generalizedEigenspace f μ) m ≠ ⊥",
"state_befo... | [
339,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/MeasureTheory/Group/Prod.lean | MeasureTheory.measure_mul_right_null | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝⁶ : MeasurableSpace G\ninst✝⁵ : Group G\ninst✝⁴ : MeasurableMul₂ G\nμ ν : Measure G\ninst✝³ : SigmaFinite ν\ninst✝² : SigmaFinite μ\ns : Set G\ninst✝¹ : MeasurableInv G\ninst✝ : IsMulLeftInvariant μ\ny : G\n⊢ ↑↑μ ((fun x => x * y) ⁻¹' s) = 0 ↔... | [
219,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Filter.lean | BoxIntegral.IntegrationParams.hasBasis_toFilter | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\ninst✝ : Fintype ι\nI✝ J : Box ι\nc c₁ c₂ : ℝ≥0\nr r₁ r₂ : (ι → ℝ) → ↑(Set.Ioi 0)\nπ π₁ π₂ : TaggedPrepartition I✝\nl✝ l₁ l₂ l : IntegrationParams\nI : Box ι\n⊢ HasBasis (toFilter l I) (fun r => ∀ (c : ℝ≥0), RCond l (r c)) fun r => {π | ∃ c, MemBase... | [
503,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
500,
1
] |
Mathlib/CategoryTheory/Types.lean | CategoryTheory.Iso.toEquiv_id | [] | [
366,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Topology/UniformSpace/UniformEmbedding.lean | UniformInducing.uniformContinuous | [] | [
95,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.dvd_iff_multiplicity_pos | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : Monoid α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\na b : α\nhdvd : a ∣ b\nheq : 0 = multiplicity a b\n⊢ multiplicity a b < 1",
"tactic": "simpa only [heq, Nat.cast_zero] using PartENat.coe_lt_coe.mpr zero_lt_one"
},
{
"state_... | [
280,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/LinearAlgebra/SymplecticGroup.lean | SymplecticGroup.neg_mem | [
{
"state_after": "l : Type u_1\nR : Type u_2\ninst✝² : DecidableEq l\ninst✝¹ : Fintype l\ninst✝ : CommRing R\nA : Matrix (l ⊕ l) (l ⊕ l) R\nh : A ⬝ J l R ⬝ Aᵀ = J l R\n⊢ (-A) ⬝ J l R ⬝ (-A)ᵀ = J l R",
"state_before": "l : Type u_1\nR : Type u_2\ninst✝² : DecidableEq l\ninst✝¹ : Fintype l\ninst✝ : CommRing R... | [
142,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.Lp.simpleFunc.coeFn_zero | [] | [
836,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
835,
1
] |
Mathlib/Topology/Bases.lean | TopologicalSpace.IsTopologicalBasis.secondCountableTopology | [] | [
604,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
11
] |
Mathlib/Data/Sum/Basic.lean | Function.Injective.sum_map | [] | [
569,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
566,
1
] |
Mathlib/Algebra/Category/ModuleCat/EpiMono.lean | ModuleCat.mono_iff_ker_eq_bot | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝² : Ring R\nX Y : ModuleCat R\nf : X ⟶ Y\nM : Type v\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nhf : LinearMap.ker f = ⊥\n⊢ Function.Injective ((forget (ModuleCat R)).map f)",
"tactic": "convert LinearMap.ker_eq_bot.1 hf"
}
] | [
44,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/GroupTheory/CommutingProbability.lean | inv_card_commutator_le_commProb | [] | [
126,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Topology/Separation.lean | Set.Subsingleton.closure | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : TopologicalSpace α\ninst✝ : T1Space α\ns : Set α\nhs : Set.Subsingleton s\n⊢ Set.Subsingleton (_root_.closure s)",
"tactic": "rcases hs.eq_empty_or_singleton with (rfl | ⟨x, rfl⟩) <;> simp"
}
] | [
633,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
631,
1
] |
Mathlib/Analysis/Calculus/Deriv/Linear.lean | LinearMap.hasDerivAtFilter | [] | [
87,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
11
] |
Mathlib/Algebra/Associated.lean | Associates.exists_non_zero_rep | [] | [
979,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
978,
1
] |
Mathlib/CategoryTheory/StructuredArrow.lean | CategoryTheory.CostructuredArrow.comp_left | [] | [
322,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/Algebra/Ring/BooleanRing.lean | toBoolAlg_add | [] | [
353,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.biUnion_self | [] | [
926,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
925,
1
] |
Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.nontrivial | [
{
"state_after": "R : Type u\nS : Type v\nK : Type w\ninst✝¹ : CommRing R\nf : R[X]\ninst✝ : IsDomain R\nh : degree f ≠ 0\n⊢ ∀ (x : R), IsUnit x → ¬↑C x = f",
"state_before": "R : Type u\nS : Type v\nK : Type w\ninst✝¹ : CommRing R\nf : R[X]\ninst✝ : IsDomain R\nh : degree f ≠ 0\n⊢ span {f} ≠ ⊤",
"tacti... | [
92,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
11
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.parallelPair_obj_zero | [] | [
227,
85
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227,
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Mathlib/ModelTheory/Definability.lean | Set.Definable.map_expansion | [
{
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src/lean/Init/SizeOf.lean | sizeOf_nat | [] | [
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Mathlib/Data/Polynomial/EraseLead.lean | Polynomial.natDegree_not_mem_eraseLead_support | [] | [
109,
46
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Mathlib/Geometry/Manifold/ChartedSpace.lean | coe_achart | [] | [
568,
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567,
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Mathlib/Analysis/Normed/Group/InfiniteSum.lean | summable_of_summable_nnnorm | [] | [
181,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
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Mathlib/CategoryTheory/Limits/Shapes/Types.lean | CategoryTheory.Limits.Types.binaryProductIso_inv_comp_fst | [] | [
169,
75
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167,
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Mathlib/Data/Multiset/FinsetOps.lean | Multiset.ndunion_eq_union | [] | [
204,
94
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203,
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Mathlib/RingTheory/WittVector/Basic.lean | WittVector.ghostFun_zsmul | [
{
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Mathlib/Data/List/Basic.lean | List.enum_map_snd | [] | [
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.toFinsupp_neg | [
{
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Mathlib/SetTheory/ZFC/Basic.lean | Class.coe_sUnion | [
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.L1.ofReal_norm_eq_lintegral | [
{
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1327,
45
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Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoUniformlyOn.tendstoLocallyUniformlyOn | [
{
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639,
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Mathlib/RingTheory/Ideal/Operations.lean | Submodule.top_smul | [] | [
200,
82
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Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.prod.symmetry' | [] | [
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1005,
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Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.inv_adjugate | [
{
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514,
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Mathlib/Topology/Algebra/Order/LeftRightLim.lean | Antitone.leftLim_le_rightLim | [] | [
332,
38
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331,
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Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.ofSubtype_apply_coe | [] | [
455,
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454,
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Mathlib/Combinatorics/Additive/SalemSpencer.lean | AddSalemSpencer.le_rothNumberNat | [] | [
486,
74
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Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.add_lt_top | [
{
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}
] | [
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50
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Mathlib/RingTheory/PowerSeries/Basic.lean | Polynomial.coe_pow | [] | [
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Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Equivalence.unitInv_app_inverse | [
{
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225,
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221,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_const_mul_left_iff | [] | [
1489,
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1487,
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Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.IsPrenex.induction_on_all_not | [] | [
772,
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Mathlib/Algebra/Order/AbsoluteValue.lean | AbsoluteValue.map_neg | [
{
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Mathlib/Data/Multiset/Fintype.lean | Multiset.forall_coe | [] | [
98,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
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Mathlib/MeasureTheory/Measure/Regular.lean | MeasureTheory.Measure.WeaklyRegular.innerRegular_measurable | [] | [
578,
31
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575,
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Mathlib/CategoryTheory/EssentialImage.lean | CategoryTheory.Functor.essImage.ofIso | [] | [
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40
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Mathlib/Data/Dfinsupp/Lex.lean | Dfinsupp.lex_lt_of_lt | [
{
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39
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63,
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Mathlib/Algebra/Associated.lean | Associates.isUnit_mk | [
{
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] | [
897,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
893,
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Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_const_sub_Iio | [
{
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341,
40
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339,
1
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Std/Data/List/Lemmas.lean | List.get_set_ne | [
{
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},
{
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... | [
842,
72
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839,
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Mathlib/Data/Num/Lemmas.lean | Num.toZNumNeg_succ | [] | [
1245,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Computability/Ackermann.lean | not_primrec₂_ack | [] | [
395,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.all_one_of_le_one_le_of_prod_eq_one | [
{
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391,
61
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387,
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Mathlib/GroupTheory/FreeAbelianGroupFinsupp.lean | FreeAbelianGroup.support_nsmul | [
{
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"tactic": "apply support_zsmul k _ a"
},
{
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193,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
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Mathlib/FieldTheory/ChevalleyWarning.lean | MvPolynomial.sum_eval_eq_zero | [
{
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102,
50
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Mathlib/Data/MvPolynomial/Derivation.lean | MvPolynomial.derivation_C_mul | [
{
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"tactic": ... | [
71,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
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Mathlib/RingTheory/Subring/Basic.lean | Subring.map_equiv_eq_comap_symm | [] | [
1178,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1176,
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Mathlib/CategoryTheory/Monad/Basic.lean | CategoryTheory.Comonad.coassoc | [] | [
163,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
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Mathlib/Topology/Sets/Closeds.lean | TopologicalSpace.Clopens.coe_inf | [] | [
329,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
9
] |
Mathlib/Algebra/Order/Ring/Defs.lean | mul_lt_of_one_lt_right | [
{
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"tactic": "simpa only [mul_one] using mul_lt_mul_of_neg_left h ha"
}
] | [
719,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
718,
1
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Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.finitePresentation | [] | [
168,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Computability/PartrecCode.lean | Nat.Partrec.Code.encode_lt_prec | [
{
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"state_before": "cf cg : Code\n⊢ encode cf < encode (prec cf cg) ∧ encode cg < encode (prec cf cg)",
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},
{
"state_af... | [
223,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
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Mathlib/Topology/Instances/Int.lean | Int.uniformEmbedding_coe_real | [] | [
47,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
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Mathlib/Order/UpperLower/Basic.lean | lowerClosure_univ | [] | [
1419,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1418,
1
] |
Std/Data/Nat/Gcd.lean | Nat.coprime.gcd_mul_left_cancel_right | [
{
"state_after": "no goals",
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"tactic": "rw [gcd_comm m n, gcd_comm m (k * n), H.gcd_mul_left_cancel n]"
}
] | [
267,
65
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
265,
1
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Mathlib/Data/Set/Prod.lean | Set.mk_mem_prod | [] | [
69,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
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Mathlib/Algebra/Order/Floor.lean | Int.ceil_add_ceil_le | [
{
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1188,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1184,
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Mathlib/MeasureTheory/Measure/Haar/InnerProductSpace.lean | Orientation.measure_eq_volume | [
{
"state_after": "ι : Type ?u.6740\nF : Type u_1\ninst✝⁵ : Fintype ι\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace ℝ F\ninst✝² : FiniteDimensional ℝ F\ninst✝¹ : MeasurableSpace F\ninst✝ : BorelSpace F\nm n : ℕ\n_i : Fact (finrank ℝ F = n)\no : Orientation ℝ F (Fin n)\nA :\n ↑↑(AlternatingMap.measu... | [
59,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
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