file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/Complex/Exponential.lean | Real.exp_list_sum | [] | [
1148,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1147,
1
] |
Mathlib/RingTheory/NonZeroDivisors.lean | mem_nonZeroDivisors_iff_ne_zero | [] | [
127,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | Continuous.edist | [] | [
1459,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1457,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | MulOpposite.nnnorm_unop | [] | [
2622,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2621,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.updateRow_eq_self | [] | [
2843,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2842,
1
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Mathlib/Algebra/Module/LinearMap.lean | LinearMap.add_comp | [] | [
891,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
889,
1
] |
Mathlib/Data/Polynomial/EraseLead.lean | Polynomial.eraseLead_natDegree_lt_or_eraseLead_eq_zero | [
{
"state_after": "case pos\nR : Type u_1\ninst✝ : Semiring R\nf✝ f : R[X]\nh : card (support f) ≤ 1\n⊢ natDegree (eraseLead f) < natDegree f ∨ eraseLead f = 0\n\ncase neg\nR : Type u_1\ninst✝ : Semiring R\nf✝ f : R[X]\nh : ¬card (support f) ≤ 1\n⊢ natDegree (eraseLead f) < natDegree f ∨ eraseLead f = 0",
"s... | [
204,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.alternatingProd_nil | [] | [
624,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.zeroLocus_empty_iff_eq_top | [
{
"state_after": "case mp\nR : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nI : Ideal R\n⊢ zeroLocus ↑I = ∅ → I = ⊤\n\ncase mpr\nR : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nI : Ideal R\n⊢ I = ⊤ → zeroLocus ↑I = ∅",
"state_before": "R : Type u\nS : Type v\ninst✝¹ : CommRi... | [
311,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/Data/MvPolynomial/Division.lean | MvPolynomial.coeff_modMonomial_of_le | [] | [
120,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Topology/Order/Basic.lean | map_coe_atBot_of_Ioo_subset | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na b : α\ns : Set α\nha : s ⊆ Ioi a\nhs : ∀ (b' : α), b' > a → ∃ b, b > a ∧ Ioo a b ⊆ s\nb' : αᵒᵈ\nhb' : b' < ↑toDual a\n⊢ ∃ a_1, a_1 < ↑toDual a ∧ Ioo a_... | [
2484,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2479,
1
] |
Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.SignedMeasure.rnDeriv_def | [] | [
907,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
904,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.one_mem | [] | [
569,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
11
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.map_comap_le | [] | [
876,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
874,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | Continuous.zpow | [] | [
510,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_mul_const_atBot_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.238911\nι' : Type ?u.238914\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.238923\ninst✝¹ : LinearOrderedField α\nl : Filter β\nf : β → α\nr : α\ninst✝ : NeBot l\n⊢ Tendsto (fun x => f x * r) l atBot ↔ 0 < r ∧ Tendsto f l atBot ∨ r < 0 ∧ Tendsto f l atTop"... | [
1145,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1143,
1
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Mathlib/CategoryTheory/Limits/Shapes/Images.lean | CategoryTheory.Limits.image.preComp_comp | [
{
"state_after": "C : Type u\ninst✝⁴ : Category C\nX Y : C\nf : X ⟶ Y\nZ : C\ng : Y ⟶ Z\nW : C\nh : Z ⟶ W\ninst✝³ : HasImage (g ≫ h)\ninst✝² : HasImage (f ≫ g ≫ h)\ninst✝¹ : HasImage h\ninst✝ : HasImage ((f ≫ g) ≫ h)\n⊢ (preComp f (g ≫ h) ≫ preComp g h) ≫ ι h = (eqToHom (_ : f ≫ g ≫ h = (f ≫ g) ≫ h) ≫ preComp (... | [
581,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
574,
1
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Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.ext | [] | [
126,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Analysis/NormedSpace/FiniteDimension.lean | exists_mem_frontier_infDist_compl_eq_dist | [
{
"state_after": "case intro.intro\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : FiniteDimensional ℝ E\nx : E\ns : Set E\nhx : x ∈ s\nhs : s ≠ univ\ny : E\nhys : y ∈ closure (sᶜ)\nhyd : Metric.infDist x (sᶜ) = dist x y\n⊢ ∃ y, y ∈ frontier s ∧ Metric.infDist x (sᶜ) = dist x y",... | [
632,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.mem_sUnion_of_mem | [] | [
1031,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1029,
1
] |
Mathlib/Order/Basic.lean | update_le_self_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : Type u\nβ : Type v\nγ : Type w\nπ : ι → Type u_2\nr : α → α → Prop\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → Preorder (π i)\nx y : (i : ι) → π i\ni : ι\na b : π i\n⊢ update x i a ≤ x ↔ a ≤ x i",
"tactic": "simp [update_le_iff]"
}
] | [
890,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
890,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | FractionalIdeal.inv_anti_mono | [
{
"state_after": "R : Type ?u.15693\nA : Type ?u.15696\nK : Type u_1\ninst✝⁷ : CommRing R\ninst✝⁶ : CommRing A\ninst✝⁵ : Field K\ninst✝⁴ : IsDomain A\nR₁ : Type u_2\ninst✝³ : CommRing R₁\ninst✝² : IsDomain R₁\ninst✝¹ : Algebra R₁ K\ninst✝ : IsFractionRing R₁ K\nI J : FractionalIdeal R₁⁰ K\nhI : I ≠ 0\nhJ : J ≠ ... | [
100,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Data/Multiset/FinsetOps.lean | Multiset.Nodup.ndunion | [] | [
199,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Order/Hom/Bounded.lean | TopHom.coe_sup | [] | [
359,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_equiv | [] | [
257,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.lowerBound?_mem | [] | [
251,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
250,
1
] |
Mathlib/MeasureTheory/Lattice.lean | Measurable.inf' | [] | [
210,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Data/Vector3.lean | vectorAllP_singleton | [] | [
272,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.nonempty_iInter | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.135153\nγ : Type ?u.135156\nι : Sort u_2\nι' : Sort ?u.135162\nι₂ : Sort ?u.135165\nκ : ι → Sort ?u.135170\nκ₁ : ι → Sort ?u.135175\nκ₂ : ι → Sort ?u.135180\nκ' : ι' → Sort ?u.135185\nf : ι → Set α\n⊢ Set.Nonempty (⋂ (i : ι), f i) ↔ ∃ x... | [
1220,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1219,
1
] |
Mathlib/GroupTheory/Congruence.lean | Con.inf_def | [] | [
494,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/MeasureTheory/Decomposition/Jordan.lean | MeasureTheory.SignedMeasure.totalVariation_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.86752\ninst✝ : MeasurableSpace α\n⊢ totalVariation 0 = 0",
"tactic": "simp [totalVariation, toJordanDecomposition_zero]"
}
] | [
504,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/Data/List/Basic.lean | List.Sublist.cons_cons | [] | [
1042,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1041,
1
] |
Mathlib/Data/List/Dedup.lean | List.dedup_idempotent | [] | [
89,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.of_apply | [] | [
124,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Logic/Relation.lean | Symmetric.swap_eq | [] | [
89,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | convexOn_of_deriv2_nonneg | [
{
"state_after": "no goals",
"state_before": "E : Type ?u.455453\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type ?u.455549\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nD : Set ℝ\nhD : Convex ℝ D\nf : ℝ → ℝ\nhf : ContinuousOn f D\nhf' : DifferentiableOn ℝ f (interior D)\nhf'' :... | [
1173,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1168,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf_mono | [] | [
418,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Units.coe_prod | [] | [
2264,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2262,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.comap_boundedBy | [
{
"state_after": "case refine'_1\nα : Type u_2\nm : Set α → ℝ≥0∞\nβ : Type u_1\nf : β → α\nh : (Monotone fun s => m ↑s) ∨ Surjective f\n⊢ (Monotone fun s => ⨆ (_ : Set.Nonempty s), m s) ∨ Surjective f\n\ncase refine'_2\nα : Type u_2\nm : Set α → ℝ≥0∞\nβ : Type u_1\nf : β → α\nh : (Monotone fun s => m ↑s) ∨ Surj... | [
914,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
905,
1
] |
Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.mul_eq_opow_log_succ | [
{
"state_after": "case a\na b : Ordinal\nha : a ≠ 0\nhb : Principal (fun x x_1 => x * x_1) b\nhb₂ : 2 < b\n⊢ a * b ≤ b ^ succ (log b a)\n\ncase a\na b : Ordinal\nha : a ≠ 0\nhb : Principal (fun x x_1 => x * x_1) b\nhb₂ : 2 < b\n⊢ b ^ succ (log b a) ≤ a * b",
"state_before": "a b : Ordinal\nha : a ≠ 0\nhb : ... | [
429,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Order/SupIndep.lean | CompleteLattice.setIndependent_iff | [
{
"state_after": "α✝ : Type ?u.27201\nβ : Type ?u.27204\nι : Type ?u.27207\nι' : Type ?u.27210\ninst✝¹ : CompleteLattice α✝\ns✝ : Set α✝\nhs : SetIndependent s✝\nα : Type u_1\ninst✝ : CompleteLattice α\ns : Set α\n⊢ (∀ ⦃a : α⦄, a ∈ s → Disjoint a (⨆ (a_2 : α) (_ : a_2 ∈ s \\ {a}), a_2)) ↔\n ∀ (x : α) (h : x ... | [
250,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.nonzero_iff_exists | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.17001\nγ : Type ?u.17004\nι : Type ?u.17007\nM : Type u_2\nM' : Type ?u.17013\nN : Type ?u.17016\nP : Type ?u.17019\nG : Type ?u.17022\nH : Type ?u.17025\nR : Type ?u.17028\nS : Type ?u.17031\ninst✝ : Zero M\nf : α →₀ M\n⊢ f ≠ 0 ↔ ∃ a, ... | [
226,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.boundedBy_caratheodory | [
{
"state_after": "case hs\nα : Type u_1\nm : Set α → ℝ≥0∞\ns : Set α\nhs : ∀ (t : Set α), m (t ∩ s) + m (t \\ s) ≤ m t\n⊢ ∀ (t : Set α),\n ((⨆ (_ : Set.Nonempty (t ∩ s)), m (t ∩ s)) + ⨆ (_ : Set.Nonempty (t \\ s)), m (t \\ s)) ≤ ⨆ (_ : Set.Nonempty t), m t",
"state_before": "α : Type u_1\nm : Set α → ℝ≥0... | [
1094,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1087,
1
] |
Mathlib/CategoryTheory/Adjunction/Basic.lean | CategoryTheory.Equivalence.asEquivalence_toAdjunction_unit | [] | [
632,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_eq_of_eq_det_one_mul | [
{
"state_after": "no goals",
"state_before": "m : Type ?u.1669131\nn : Type u_1\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\nR : Type v\ninst✝ : CommRing R\nA B C : Matrix n n R\nhC : det C = 1\nhA : A = C ⬝ B\n⊢ det C * det B = det B",
"tactic": "rw [hC, one_... | [
445,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.lift_mk | [] | [
154,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
11
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_comp_sub_left | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.14958229\n𝕜 : Type ?u.14958232\nE : Type u_1\nF : Type ?u.14958238\nA : Type ?u.14958241\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na b c d✝ : ℝ\nf : ℝ → E\nd : ℝ\n⊢ (∫ (x : ℝ) in a..b, f (d - x)) = ∫ (x : ℝ) ... | [
857,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
856,
1
] |
Mathlib/CategoryTheory/Over.lean | CategoryTheory.Under.isoMk_hom_right | [] | [
380,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/CategoryTheory/Comma.lean | CategoryTheory.Comma.id_left | [] | [
121,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Data/Polynomial/Reverse.lean | Polynomial.reflect_zero | [] | [
126,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.eval₂Hom_comp_bind₂ | [
{
"state_after": "no goals",
"state_before": "σ : Type u_4\nτ : Type ?u.1084014\nR : Type u_3\nS : Type u_1\nT : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : CommSemiring S\ninst✝ : CommSemiring T\nf✝ : σ → MvPolynomial τ R\nf : S →+* T\ng : σ → T\nh : R →+* MvPolynomial σ S\n⊢ RingHom.comp (eval₂Hom f g) (b... | [
323,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_mul_const_Ioc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\na✝ a b c : α\nh : 0 < c\n⊢ (fun x => x * c) ⁻¹' Ioc a b = Ioc (a / c) (b / c)",
"tactic": "simp [← Ioi_inter_Iic, h]"
}
] | [
541,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.ext_iff | [
{
"state_after": "case e_a\nR : Type u_1\ninst✝⁶ : Ring R\nE : Type u_2\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module R E\nF : Type u_3\ninst✝³ : AddCommGroup F\ninst✝² : Module R F\nG : Type ?u.27327\ninst✝¹ : AddCommGroup G\ninst✝ : Module R G\nf g : E →ₗ.[R] F\nEQ : f = g\nx y : { x // x ∈ f.domain }\nh : ↑x = ↑... | [
93,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.ext_iff_natDegree_le | [
{
"state_after": "R : Type u\nS : Type v\na b c d : R\nn✝ m : ℕ\ninst✝ : Semiring R\np✝ q✝ r p q : R[X]\nn : ℕ\nhp : natDegree p ≤ n\nhq : natDegree q ≤ n\n⊢ (∀ (n : ℕ), coeff p n = coeff q n) ↔ ∀ (i : ℕ), i ≤ n → coeff p i = coeff q i",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn✝ m : ℕ\ninst✝ ... | [
365,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/Order/Chain.lean | IsChain.total | [] | [
115,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.inv_smul' | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.293786\nm : Type u\nn : Type u'\nα : Type v\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing α\nA B : Matrix n n α\nk : αˣ\nh : IsUnit (det A)\n⊢ (k⁻¹ • A⁻¹) ⬝ (k • A) = 1",
"tactic": "simp [h, smul_smul]"
}
] | [
509,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.sum_apply | [] | [
230,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Analysis/Convex/Slope.lean | strictConvexOn_of_slope_strict_mono_adjacent | [
{
"state_after": "𝕜 : Type u_1\ninst✝ : LinearOrderedField 𝕜\ns : Set 𝕜\nf : 𝕜 → 𝕜\nhs : Convex 𝕜 s\nhf : ∀ {x y z : 𝕜}, x ∈ s → z ∈ s → x < y → y < z → (f y - f x) / (y - x) < (f z - f y) / (z - y)\nx : 𝕜\nhx : x ∈ s\nz : 𝕜\nhz : z ∈ s\nhxz : x < z\na b : 𝕜\nha : 0 < a\nhb : 0 < b\nhab : a + b = 1\ny... | [
177,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Std/Data/Array/Lemmas.lean | getElem!_fin | [] | [
21,
68
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
20,
9
] |
Mathlib/Topology/Algebra/GroupWithZero.lean | continuousOn_inv₀ | [] | [
111,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.le_of_add_le_add_left | [] | [
758,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
757,
11
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Preconnected.map | [] | [
1934,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1932,
1
] |
Mathlib/Topology/Algebra/FilterBasis.lean | RingFilterBasis.mul_left | [] | [
295,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.EqOnSource.trans' | [
{
"state_after": "case left\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type ?u.56904\ne✝ : LocalEquiv α β\ne'✝ : LocalEquiv β γ\ne e' : LocalEquiv α β\nf f' : LocalEquiv β γ\nhe : e ≈ e'\nhf : f ≈ f'\n⊢ (LocalEquiv.trans e f).source = (LocalEquiv.trans e' f').source\n\ncase right\nα : Type u_1\nβ : Type u_2... | [
871,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
864,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.mem_support_append_iff | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nt u v w : V\np : Walk G u v\np' : Walk G v w\n⊢ t = u ∨ t ∈ List.tail (support p) ∨ t ∈ List.tail (support p') ↔\n (t = u ∨ t ∈ List.tail (support p)) ∨ t = v ∨ t ∈ List.tail (support p')",... | [
612,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
1
] |
Mathlib/Deprecated/Subgroup.lean | isNormalSubgroup_of_commGroup | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nH : Type ?u.18673\nA : Type ?u.18676\na a₁ a₂ b c : G\ninst✝ : CommGroup G\ns : Set G\nhs : IsSubgroup s\nn : G\nhn : n ∈ s\ng : G\n⊢ g * n * g⁻¹ ∈ s",
"tactic": "rwa [mul_right_comm, mul_right_inv, one_mul]"
}
] | [
183,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infiniteNeg_mul_of_not_infinitesimal_neg_infinitePos | [] | [
848,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
846,
1
] |
Mathlib/Algebra/Order/Field/Power.lean | zpow_bit0_pos | [] | [
142,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | uniformity_additive | [] | [
1463,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1463,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.appendFun_inj | [] | [
240,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.rpow_lt_one | [] | [
201,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Logic/Nonempty.lean | exists_true_iff_nonempty | [] | [
36,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | add_thirds | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.104315\nα : Type u_1\nβ : Type ?u.104321\ninst✝ : LinearOrderedSemifield α\na✝ b c d e : α\nm n : ℤ\na : α\n⊢ a / 3 + a / 3 + a / 3 = a",
"tactic": "rw [div_add_div_same, div_add_div_same, ← two_mul, ← add_one_mul 2 a, two_add_one_eq_three,\n mu... | [
549,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
1
] |
Mathlib/Topology/Sheaves/LocalPredicate.lean | TopCat.PrelocalPredicate.sheafifyOf | [
{
"state_after": "no goals",
"state_before": "X : TopCat\nT✝ T : ↑X → Type v\nP : PrelocalPredicate T\nU : Opens ↑X\nf : (x : { x // x ∈ U }) → T ↑x\nh : pred P f\nx : { x // x ∈ U }\n⊢ pred P fun x => f ((fun x => { val := ↑x, property := (_ : ↑x ∈ ↑U) }) x)",
"tactic": "convert h"
}
] | [
165,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioi_subset_Ioc_union_Ioi | [] | [
1291,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1290,
1
] |
Mathlib/Data/Set/Prod.lean | Set.pi_eq_empty | [
{
"state_after": "case h\nι : Type u_1\nα : ι → Type u_2\nβ : ι → Type ?u.115563\ns s₁ s₂ : Set ι\nt t₁ t₂ : (i : ι) → Set (α i)\ni : ι\nhs : i ∈ s\nht : t i = ∅\nf : (i : ι) → α i\n⊢ f ∈ pi s t ↔ f ∈ ∅",
"state_before": "ι : Type u_1\nα : ι → Type u_2\nβ : ι → Type ?u.115563\ns s₁ s₂ : Set ι\nt t₁ t₂ : (i ... | [
676,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
673,
1
] |
Mathlib/Analysis/SpecialFunctions/Arsinh.lean | Real.arsinh_bijective | [] | [
129,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Analysis/Calculus/Inverse.lean | ApproximatesLinearOn.toLocalHomeomorph_source | [] | [
508,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Mathlib/Data/Set/Prod.lean | Set.mem_prod_eq | [] | [
55,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Std/Data/List/Init/Lemmas.lean | List.tail?_nil | [] | [
29,
54
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
29,
9
] |
Mathlib/LinearAlgebra/Matrix/Trace.lean | Matrix.trace_fin_three | [
{
"state_after": "ι : Type ?u.43106\nm : Type ?u.43109\nn : Type ?u.43112\np : Type ?u.43115\nα : Type ?u.43118\nR : Type u_1\nS : Type ?u.43124\ninst✝³ : Fintype m\ninst✝² : Fintype n\ninst✝¹ : Fintype p\ninst✝ : AddCommMonoid R\nA : Matrix (Fin 3) (Fin 3) R\n⊢ trace A = A 0 0 + (A 1 1 + (A 2 2 + 0))",
"st... | [
200,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | OrderIso.map_atTop | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.52291\nι' : Type ?u.52294\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.52303\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ne : α ≃o β\n⊢ map (↑e) atTop = atTop",
"tactic": "rw [← e.comap_atTop, map_comap_of_surjective e.surjective]"
}
] | [
413,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.closure_sUnion | [] | [
736,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
1
] |
Mathlib/AlgebraicTopology/ExtraDegeneracy.lean | SSet.Augmented.StandardSimplex.shiftFun_0 | [] | [
158,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.sUnion_empty | [] | [
1080,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1079,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.tendsto_sup | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.315768\nι : Sort x\nf : α → β\nx₁ x₂ : Filter α\ny : Filter β\n⊢ Tendsto f (x₁ ⊔ x₂) y ↔ Tendsto f x₁ y ∧ Tendsto f x₂ y",
"tactic": "simp only [Tendsto, map_sup, sup_le_iff]"
}
] | [
3023,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3021,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.summable_norm_mul_pow | [
{
"state_after": "case intro.intro.intro.intro\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.202797\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpa... | [
288,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.angle_const_sub | [
{
"state_after": "no goals",
"state_before": "V : Type u_1\nP : Type ?u.41135\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nv v₁ v₂ v₃ : V\n⊢ ∠ (v - v₁) (v - v₂) (v - v₃) = ∠ v₁ v₂ v₃",
"tactic": "simpa only [vsub_eq_sub] using angle... | [
118,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Data/Num/Lemmas.lean | PosNum.add_one | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.30620\nn : PosNum\n⊢ n + 1 = succ n",
"tactic": "cases n <;> rfl"
}
] | [
86,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.sqLe_cancel | [
{
"state_after": "case a\nd✝ : ℤ\nc d x y z w : ℕ\nzw : SqLe y d x c\nh : SqLe (x + z) c (y + w) d\n⊢ ¬c * z * z > d * w * w",
"state_before": "d✝ : ℤ\nc d x y z w : ℕ\nzw : SqLe y d x c\nh : SqLe (x + z) c (y + w) d\n⊢ SqLe z c w d",
"tactic": "apply le_of_not_gt"
},
{
"state_after": "case a\nd... | [
460,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.map_eq_comap_of_inverse | [] | [
2538,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2536,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.infsep_eq_iInf | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type ?u.62378\ninst✝¹ : PseudoMetricSpace α\nx y z : α\ns t : Set α\ninst✝ : Decidable (Set.Nontrivial s)\nhs : Set.Nontrivial s\n⊢ infsep s = ⨅ (d : ↑(offDiag s)), uncurry dist ↑d\n\ncase inr\nα : Type u_1\nβ : Type ?u.62378\ninst✝¹ : PseudoMetricSpace α\nx y z : α... | [
461,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/MeasureTheory/Measure/Haar/NormedSpace.lean | MeasureTheory.Measure.integral_comp_inv_smul_of_nonneg | [
{
"state_after": "no goals",
"state_before": "E : Type u_2\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 : NormedSpac... | [
109,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.isBigO_id | [] | [
666,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
665,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.X_pow_sub_one_mul_cyclotomic_dvd_X_pow_sub_one_of_dvd | [
{
"state_after": "R : Type u_1\ninst✝ : CommRing R\nd n : ℕ\nh : d ∈ Nat.properDivisors n\nhdn : d < n\n⊢ (X ^ d - 1) * cyclotomic n R ∣ X ^ n - 1",
"state_before": "R : Type u_1\ninst✝ : CommRing R\nd n : ℕ\nh : d ∈ Nat.properDivisors n\n⊢ (X ^ d - 1) * cyclotomic n R ∣ X ^ n - 1",
"tactic": "have hdn ... | [
455,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.isCountablyGenerated_iff_exists_antitone_basis | [
{
"state_after": "case mp\nα : Type u_1\nβ : Type ?u.110685\nγ : Type ?u.110688\nι : Type ?u.110691\nι' : Sort ?u.110694\nf : Filter α\n⊢ IsCountablyGenerated f → ∃ x, HasAntitoneBasis f x\n\ncase mpr\nα : Type u_1\nβ : Type ?u.110685\nγ : Type ?u.110688\nι : Type ?u.110691\nι' : Sort ?u.110694\nf : Filter α\n⊢... | [
1172,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1165,
1
] |
Mathlib/Algebra/Lie/Abelian.lean | lie_abelian_iff_equiv_lie_abelian | [] | [
83,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | PSet.not_nonempty_empty | [
{
"state_after": "no goals",
"state_before": "⊢ ¬PSet.Nonempty ∅",
"tactic": "simp [PSet.Nonempty]"
}
] | [
416,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | uniformContinuous_inf_dom_left₂ | [
{
"state_after": "α✝ : Type ua\nβ✝ : Type ub\nγ✝ : Type uc\nδ : Type ud\nι : Sort ?u.158569\ninst✝² : UniformSpace α✝\ninst✝¹ : UniformSpace β✝\ninst✝ : UniformSpace γ✝\nα : Type ?u.158596\nβ : Type ?u.158602\nγ : Type ?u.158608\nf : α → β → γ\nua1 ua2 : UniformSpace α\nub1 ub2 : UniformSpace β\nuc1 : UniformSp... | [
1660,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1650,
1
] |
Mathlib/RingTheory/Localization/Submodule.lean | IsLocalization.coeSubmodule_bot | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\ninst✝³ : CommRing R\nM : Submonoid R\nS : Type u_1\ninst✝² : CommRing S\ninst✝¹ : Algebra R S\nP : Type ?u.27701\ninst✝ : CommRing P\n⊢ coeSubmodule S ⊥ = ⊥",
"tactic": "rw [coeSubmodule, Submodule.map_bot]"
}
] | [
53,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
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