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/Order/Filter/Basic.lean | Filter.NeBot.comap_of_surj | [] | [
2437,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2435,
1
] |
Mathlib/Analysis/Convex/Between.lean | wbtw_pointReflection | [
{
"state_after": "R : Type u_1\nV : Type u_2\nV' : Type ?u.618495\nP : Type u_3\nP' : Type ?u.618501\ninst✝³ : LinearOrderedField R\ninst✝² : AddCommGroup V\ninst✝¹ : Module R V\ninst✝ : AddTorsor V P\nx y : P\n⊢ ↑(lineMap y (↑(pointReflection R x) y)) 2⁻¹ = x",
"state_before": "R : Type u_1\nV : Type u_2\n... | [
914,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.DominatedFinMeasAdditive.eq_zero_of_measure_zero | [
{
"state_after": "α : Type u_2\nE : Type ?u.100491\nF : Type ?u.100494\nF' : Type ?u.100497\nG : Type ?u.100500\n𝕜 : Type ?u.100503\np : ℝ≥0∞\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace ℝ F\ninst✝⁴ : NormedAddCommGroup F'\ninst✝³ : NormedSpace ℝ... | [
211,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/FieldTheory/Tower.lean | lift_rank_mul_lift_rank | [
{
"state_after": "case intro.mk\nF : Type u\nK : Type v\nA : Type w\ninst✝¹⁰ : CommRing F\ninst✝⁹ : Ring K\ninst✝⁸ : AddCommGroup A\ninst✝⁷ : Algebra F K\ninst✝⁶ : Module K A\ninst✝⁵ : Module F A\ninst✝⁴ : IsScalarTower F K A\ninst✝³ : StrongRankCondition F\ninst✝² : StrongRankCondition K\ninst✝¹ : Module.Free ... | [
65,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/RingTheory/GradedAlgebra/Basic.lean | DirectSum.decompose_symm_one | [] | [
91,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.isPreconnected_setOf_sOppSide | [
{
"state_after": "case inl\nR : Type ?u.516890\nV : Type u_1\nV' : Type ?u.516896\nP : Type u_2\nP' : Type ?u.516902\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : NormedSpace ℝ V\ninst✝¹ : PseudoMetricSpace P\ninst✝ : NormedAddTorsor V P\ns : AffineSubspace ℝ P\nx : P\nh : ↑s = ∅\n⊢ IsPreconnected {y | SOppSide ... | [
948,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
939,
1
] |
Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean | Matrix.SpecialLinearGroup.fin_two_induction | [
{
"state_after": "no goals",
"state_before": "n : Type u\ninst✝³ : DecidableEq n\ninst✝² : Fintype n\nR : Type v\ninst✝¹ : CommRing R\nS : Type ?u.785760\ninst✝ : CommRing S\nP : SL(2, R) → Prop\na b c d : R\nhdet : a * d - b * c = 1\n⊢ det (↑of ![![a, b], ![c, d]]) = 1",
"tactic": "rwa [det_fin_two_of]... | [
312,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/MeasureTheory/PiSystem.lean | generateFrom_measurableSet_of_generatePiSystem | [] | [
268,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Std/Data/List/Lemmas.lean | List.Sublist.reverse | [
{
"state_after": "α✝ : Type u_1\nl₁✝ l₂ l₁ l₂✝ : List α✝\na✝ : α✝\nh : l₁ <+ l₂✝\n⊢ List.reverse l₁ <+ List.reverse l₂✝ ++ [a✝]",
"state_before": "α✝ : Type u_1\nl₁✝ l₂ l₁ l₂✝ : List α✝\na✝ : α✝\nh : l₁ <+ l₂✝\n⊢ List.reverse l₁ <+ List.reverse (a✝ :: l₂✝)",
"tactic": "rw [reverse_cons]"
},
{
"s... | [
386,
85
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
383,
1
] |
Mathlib/Topology/Constructions.lean | Filter.HasBasis.prod_nhds | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type ?u.35295\nδ : Type ?u.35298\nε : Type ?u.35301\nζ : Type ?u.35304\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : TopologicalSpace β\ninst✝³ : TopologicalSpace γ\ninst✝² : TopologicalSpace δ\ninst✝¹ : TopologicalSpace ε\ninst✝ : TopologicalSpace ζ\nιa : Type u_1\nιb : T... | [
544,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.orthogonal_span_singleton_eq_toLin_ker | [
{
"state_after": "case h\nR : Type ?u.1290200\nM : Type ?u.1290203\ninst✝¹⁴ : Semiring R\ninst✝¹³ : AddCommMonoid M\ninst✝¹² : Module R M\nR₁ : Type ?u.1290239\nM₁ : Type ?u.1290242\ninst✝¹¹ : Ring R₁\ninst✝¹⁰ : AddCommGroup M₁\ninst✝⁹ : Module R₁ M₁\nR₂ : Type ?u.1290851\nM₂ : Type ?u.1290854\ninst✝⁸ : CommSem... | [
1232,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1224,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasFDerivAtFilter.tendsto_nhds | [
{
"state_after": "𝕜 : Type u_2\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.394427\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.394522\... | [
719,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
711,
1
] |
Mathlib/Order/Lattice.lean | sup_ind | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : LinearOrder α\na✝ b✝ c d a b : α\np : α → Prop\nha : p a\nhb : p b\nh : a ≤ b\n⊢ p (a ⊔ b)",
"tactic": "rwa [sup_eq_right.2 h]"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : Linea... | [
840,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
838,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.id_comp | [] | [
1285,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1284,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.coe_addEquiv_trans | [] | [
361,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | QuotientAddGroup.equivIocMod_zero | [] | [
843,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.summable_conj | [] | [
584,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
] |
Mathlib/Data/List/Dedup.lean | List.nodup_dedup | [] | [
76,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Data/Nat/Log.lean | Nat.clog_pow | [
{
"state_after": "b x : ℕ\nhb : 1 < b\nz : ℕ\n⊢ b ^ x ≤ b ^ z ↔ x ≤ z",
"state_before": "b x : ℕ\nhb : 1 < b\nz : ℕ\n⊢ clog b (b ^ x) ≤ z ↔ x ≤ z",
"tactic": "rw [← le_pow_iff_clog_le hb]"
},
{
"state_after": "no goals",
"state_before": "b x : ℕ\nhb : 1 < b\nz : ℕ\n⊢ b ^ x ≤ b ^ z ↔ x ≤ z",
... | [
320,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Data/Finset/Prod.lean | Finset.diag_union_offDiag | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.116188\nγ : Type ?u.116191\ninst✝ : DecidableEq α\ns t : Finset α\nx : α × α\n⊢ diag s ∪ offDiag s = s ×ˢ s",
"tactic": "conv_rhs => rw [← filter_union_filter_neg_eq (fun a => a.1 = a.2) (s ×ˢ s)]"
}
] | [
365,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/Logic/Equiv/Set.lean | Equiv.image_eq_iff_eq | [] | [
128,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Data/Set/Basic.lean | Set.not_mem_of_mem_compl | [] | [
1636,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1635,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.comap_lift'_eq2 | [] | [
316,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelIso.bijective | [] | [
803,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
802,
11
] |
Mathlib/Analysis/Convex/Function.lean | StrictConvexOn.dual | [] | [
88,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.isOrtho_orthogonal_right | [] | [
311,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/GroupTheory/Complement.lean | Subgroup.MemRightTransversals.mk''_toEquiv | [] | [
401,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.decide_True | [] | [
29,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
28,
1
] |
Mathlib/Algebra/Associated.lean | of_irreducible_pow | [
{
"state_after": "case inl\nα✝ : Type ?u.76176\nβ : Type ?u.76179\nγ : Type ?u.76182\nδ : Type ?u.76185\nα : Type u_1\ninst✝ : Monoid α\nx : α\nn : ℕ\nhn✝ : n ≠ 1\nhn : n < 1\n⊢ Irreducible (x ^ n) → IsUnit x\n\ncase inr\nα✝ : Type ?u.76176\nβ : Type ?u.76179\nγ : Type ?u.76182\nδ : Type ?u.76185\nα : Type u_1\... | [
221,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.memℒp_indicator_const | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.667132\nG : Type ?u.667135\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\nc✝ : E\nf : α → E\nhf : AEStronglyMeasu... | [
689,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
676,
1
] |
Mathlib/NumberTheory/PythagoreanTriples.lean | coprime_sq_sub_sq_add_of_even_odd | [
{
"state_after": "m n : ℤ\nh : Int.gcd m n = 1\nhm : m % 2 = 0\nhn : n % 2 = 1\nH : ¬Int.gcd (m ^ 2 - n ^ 2) (m ^ 2 + n ^ 2) = 1\n⊢ False",
"state_before": "m n : ℤ\nh : Int.gcd m n = 1\nhm : m % 2 = 0\nhn : n % 2 = 1\n⊢ Int.gcd (m ^ 2 - n ^ 2) (m ^ 2 + n ^ 2) = 1",
"tactic": "by_contra H"
},
{
... | [
353,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
9
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.finite_const_le_meas_of_disjoint_iUnion | [
{
"state_after": "α : Type u_2\nβ : Type ?u.734278\nγ : Type ?u.734281\nδ : Type ?u.734284\nι✝ : Type ?u.734287\nR : Type ?u.734290\nR' : Type ?u.734293\nm0 : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\nμ✝ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set α\nι : Type u_1\ninst✝ : Meas... | [
3582,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3574,
1
] |
Std/Classes/Order.lean | Std.TransCmp.lt_asymm | [] | [
59,
50
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
58,
1
] |
Mathlib/Topology/Algebra/Module/WeakDual.lean | tendsto_iff_forall_eval_tendsto_topDualPairing | [] | [
346,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/Algebra/BigOperators/Fin.lean | Fin.prod_univ_add | [
{
"state_after": "α : Type ?u.65773\nβ : Type ?u.65776\nM : Type u_1\ninst✝ : CommMonoid M\na b : ℕ\nf : Fin (a + b) → M\n⊢ ∏ x : Fin a ⊕ Fin b, f (Equiv.toFun finSumFinEquiv x) =\n (∏ i : Fin a, f (↑(castAdd b) i)) * ∏ i : Fin b, f (↑(natAdd a) i)\n\nα : Type ?u.65773\nβ : Type ?u.65776\nM : Type u_1\ninst✝... | [
202,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pullbackConeOfRightIso_fst | [] | [
1697,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1697,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.subset_inter_iff | [] | [
1789,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1788,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.AECover.biInter_Ici_aecover | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nι : Type u_1\ninst✝² : Countable ι\ninst✝¹ : MeasurableSpace α\nμ : Measure α\ninst✝ : Preorder ι\nφ : ι → Set α\nhφ : AECover μ atTop φ\nx : α\nh : ∀ᶠ (i : ι) in atTop, x ∈ φ i\n⊢ ∀ᶠ (i : ι) in atTop, x ∈ ⋂ (k : ι) (_ : k ∈ Ici i), φ k",
"tact... | [
348,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/Tactic/CancelDenoms.lean | CancelDenoms.mul_subst | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : CommRing α\nn1 n2 k e1 e2 t1 t2 : α\nh1 : n1 * e1 = t1\nh2 : n2 * e2 = t2\nh3 : n1 * n2 = k\n⊢ k * (e1 * e2) = t1 * t2",
"tactic": "rw [← h3, mul_comm n1, mul_assoc n2, ← mul_assoc n1, h1,\n ← mul_assoc n2, mul_comm n2, mul_assoc, h2... | [
40,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/Logic/Function/Iterate.lean | Function.RightInverse.iterate | [] | [
216,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Algebra/ContinuedFractions/TerminatedStable.lean | GeneralizedContinuedFraction.convergents'_stable_of_terminated | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\ng : GeneralizedContinuedFraction K\nn m : ℕ\ninst✝ : DivisionRing K\nn_le_m : n ≤ m\nterminated_at_n : TerminatedAt g n\n⊢ convergents' g m = convergents' g n",
"tactic": "simp only [convergents', convergents'Aux_stable_of_terminated n_le_m ter... | [
96,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | SequentiallyComplete.seq_mem | [] | [
683,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.div_le_div | [] | [
1638,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1637,
21
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.BicartesianSq.of_has_biproduct₁ | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝³ : Category C\nW X Y Z : C\nf : W ⟶ X\ng : W ⟶ Y\nh : X ⟶ Z\ni : Y ⟶ Z\ninst✝² : HasZeroObject C\ninst✝¹ : HasZeroMorphisms C\ninst✝ : HasBinaryBiproduct X Y\n⊢ BicartesianSq biprod.fst biprod.snd 0 0",
"tactic": "convert of_is_biproduct₁ ... | [
971,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
969,
1
] |
Mathlib/Data/List/MinMax.lean | List.mem_argmax_iff | [
{
"state_after": "case intro.intro\nα : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrder β\nf : α → β\nl : List α\no : Option α\na m : α\ninst✝ : DecidableEq α\nhml : m ∈ l\nham : ∀ (a : α), a ∈ l → f a ≤ f m\nhma : ∀ (a : α), a ∈ l → f m ≤ f a → indexOf m l ≤ indexOf a l\n⊢ m ∈ argmax f l",
"state_before": "α ... | [
244,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Topology/MetricSpace/IsometricSMul.lean | Metric.smul_sphere | [] | [
456,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.coe_add | [] | [
357,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Algebra/Module/Zlattice.lean | Zspan.mem_fundamentalDomain | [] | [
59,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | iteratedFDeriv_const_of_ne | [
{
"state_after": "case intro\n𝕜 : 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\nins... | [
140,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.tsum_intervalIntegral_eq_of_summable_norm | [] | [
1067,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1064,
1
] |
Mathlib/Computability/Encoding.lean | Computability.decode_encodeNum | [
{
"state_after": "n : Num\n⊢ decodeNum (encodeNum n) = n",
"state_before": "⊢ ∀ (n : Num), decodeNum (encodeNum n) = n",
"tactic": "intro n"
},
{
"state_after": "case zero\n\n⊢ (if\n (match Num.zero with\n | Num.zero => []\n | Num.pos n => encodePosNum n) =\n []... | [
151,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Dynamics/Ergodic/Ergodic.lean | MeasureTheory.MeasurePreserving.preErgodic_of_preErgodic_conjugate | [
{
"state_after": "α : Type u_1\nm : MeasurableSpace α\nf : α → α\ns✝ : Set α\nμ : Measure α\nβ : Type u_2\nm' : MeasurableSpace β\nμ' : Measure β\ns' : Set β\ng : α → β\nhg : MeasurePreserving g\nhf : PreErgodic f\nf' : β → β\nh_comm : g ∘ f = f' ∘ g\ns : Set β\nhs₀ : MeasurableSet s\nhs₁ : f' ⁻¹' s = s\n⊢ s =ᶠ... | [
95,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.smul_integral_comp_add_mul | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.14885131\n𝕜 : Type ?u.14885134\nE : Type u_1\nF : Type ?u.14885140\nA : Type ?u.14885143\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na b c✝ d✝ : ℝ\nf : ℝ → E\nc d : ℝ\n⊢ (c • ∫ (x : ℝ) in a..b, f (d + c * x)) =... | [
773,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
771,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | real_inner_self_abs | [] | [
609,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
608,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.sub_eq' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.79068\nf g : α → β\nc c₁ c₂ x : α\ninst✝ : AddCommGroup α\nh : Periodic f c\n⊢ f (c - x) = f (-x)",
"tactic": "simpa only [sub_eq_neg_add] using h (-x)"
}
] | [
170,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.limitRecOn_zero | [
{
"state_after": "α : Type ?u.95975\nβ : Type ?u.95978\nγ : Type ?u.95981\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nC : Ordinal → Sort u_2\nH₁ : C 0\nH₂ : (o : Ordinal) → C o → C (succ o)\nH₃ : (o : Ordinal) → IsLimit o → ((o' : Ordinal) → o' < o → C o') → C o\n⊢ Eq.mpr (_ : C 0 = C 0) H₁ = H₁",
... | [
324,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/Topology/Algebra/Module/FiniteDimension.lean | LinearEquiv.coe_toContinuousLinearEquiv_symm | [] | [
381,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.add_le_add_iff_left | [] | [
262,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
11
] |
Mathlib/Data/MvPolynomial/CommRing.lean | MvPolynomial.degrees_neg | [
{
"state_after": "R : Type u\nS : Type v\nσ : Type u_1\na a' a₁ a₂ : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝ : CommRing R\np✝ q p : MvPolynomial σ R\n⊢ (Finset.sup (support p) fun s => ↑toMultiset s) = degrees p",
"state_before": "R : Type u\nS : Type v\nσ : Type u_1\na a' a₁ a₂ : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ... | [
101,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.dvd_iff_mod_eq_zero | [
{
"state_after": "m n : Num\n⊢ ↑n % ↑m = 0 ↔ ↑n % ↑m = ↑0",
"state_before": "m n : Num\n⊢ m ∣ n ↔ n % m = 0",
"tactic": "rw [← dvd_to_nat, Nat.dvd_iff_mod_eq_zero, ← to_nat_inj, mod_to_nat]"
},
{
"state_after": "no goals",
"state_before": "m n : Num\n⊢ ↑n % ↑m = 0 ↔ ↑n % ↑m = ↑0",
"tacti... | [
1715,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1714,
1
] |
Mathlib/Geometry/Manifold/ChartedSpace.lean | chartAt_self_eq | [] | [
536,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/CategoryTheory/Limits/Types.lean | CategoryTheory.Limits.Types.isLimitEquivSections_apply | [] | [
94,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Topology/Semicontinuous.lean | LowerSemicontinuousAt.add' | [
{
"state_after": "α : Type u_1\ninst✝⁴ : TopologicalSpace α\nβ : Type ?u.85283\ninst✝³ : Preorder β\nf✝ g✝ : α → β\nx : α\ns t : Set α\ny z : β\nι : Type ?u.85309\nγ : Type u_2\ninst✝² : LinearOrderedAddCommMonoid γ\ninst✝¹ : TopologicalSpace γ\ninst✝ : OrderTopology γ\nf g : α → γ\nhcont : ContinuousAt (fun p ... | [
457,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.map_eq_iff_sup_ker_eq_of_surjective | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type u_2\nF : Type ?u.1967635\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nI J : Ideal R\nf : R →+* S\nhf : Function.Surjective ↑f\n⊢ map f I = map f J ↔ I ⊔ RingHom.ker f = J ⊔ RingHom.ker f",
"tactic": "rw [← (comap_injective_of_surjective f... | [
2167,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2164,
1
] |
Std/Data/Int/Lemmas.lean | Int.neg_mul_neg | [
{
"state_after": "no goals",
"state_before": "a b : Int\n⊢ -a * -b = a * b",
"tactic": "simp"
}
] | [
473,
71
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
473,
11
] |
Mathlib/Topology/MetricSpace/Kuratowski.lean | KuratowskiEmbedding.embeddingOfSubset_isometry | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nf g : { x // x ∈ lp (fun n => ℝ) ⊤ }\nn : ℕ\nC : ℝ\ninst✝ : MetricSpace α\nx : ℕ → α\na✝ b✝ : α\nH : DenseRange x\na b : α\n⊢ dist (embeddingOfSubset x a) (embeddingOfSubset x b) = dist a b",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nf g : { x... | [
93,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.map_subtype_top | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nR₁ : Type ?u.1539707\nR₂ : Type ?u.1539710\nR₃ : Type ?u.1539713\nR₄ : Type ?u.1539716\nS : Type ?u.1539719\nK : Type ?u.1539722\nK₂ : Type ?u.1539725\nM : Type u_1\nM' : Type ?u.1539731\nM₁ : Type ?u.1539734\nM₂ : Type ?u.1539737\nM₃ : Type ?u.153... | [
1632,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1632,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | Filter.HasBasis.uniformity_closure | [] | [
964,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
962,
1
] |
Mathlib/Data/List/Sigma.lean | List.dedupKeys_cons | [] | [
632,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.floor_neg | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.206564\nα : Type u_1\nβ : Type ?u.206570\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz✝ : ℤ\na : α\nz : ℤ\n⊢ z ≤ ⌊-a⌋ ↔ z ≤ -⌈a⌉",
"tactic": "rw [le_neg, ceil_le, le_floor, Int.cast_neg, le_neg]"
}
] | [
1100,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1099,
1
] |
Mathlib/Data/List/Intervals.lean | List.Ico.self_empty | [] | [
90,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Algebra/Associated.lean | associated_mul_unit_left | [] | [
455,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/Topology/PathConnected.lean | pathConnectedSpace_iff_zerothHomotopy | [
{
"state_after": "X : Type u_1\nY : Type ?u.687930\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx y z : X\nι : Type ?u.687945\nF : Set X\nthis : Setoid X := pathSetoid X\n⊢ PathConnectedSpace X ↔ Nonempty (ZerothHomotopy X) ∧ Subsingleton (ZerothHomotopy X)",
"state_before": "X : Type u_1\nY : ... | [
1106,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1095,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.CommSq.cocone_inr | [] | [
98,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.coe_id | [] | [
374,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsLeast.dual | [] | [
155,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Combinatorics/SetFamily/LYM.lean | Finset.falling_zero_subset | [] | [
149,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.infty_ne_coe | [] | [
105,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Data/Set/Function.lean | Set.LeftInvOn.image_image' | [] | [
1092,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1091,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidHom.mk_coe | [
{
"state_after": "case h\nF : Type ?u.74354\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.74363\nδ : Type ?u.74366\ninst✝⁷ : Preorder α\ninst✝⁶ : Preorder β\ninst✝⁵ : Preorder γ\ninst✝⁴ : Preorder δ\ninst✝³ : MulOneClass α\ninst✝² : MulOneClass β\ninst✝¹ : MulOneClass γ\ninst✝ : MulOneClass δ\nf✝ g f : α →*o β\nh : ... | [
331,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.equivMapDomain_refl' | [
{
"state_after": "case h.h\nα : Type u_1\nβ : Type ?u.141999\nγ : Type ?u.142002\nι : Type ?u.142005\nM : Type u_2\nM' : Type ?u.142011\nN : Type ?u.142014\nP : Type ?u.142017\nG : Type ?u.142020\nH : Type ?u.142023\nR : Type ?u.142026\nS : Type ?u.142029\ninst✝ : Zero M\nx : α →₀ M\na✝ : α\n⊢ ↑(equivMapDomain ... | [
333,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.mem_strictlyPositive | [] | [
613,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
612,
1
] |
Mathlib/Data/Finsupp/ToDfinsupp.lean | Dfinsupp.toFinsupp_toDfinsupp | [] | [
139,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Data/String/Basic.lean | String.length_data | [] | [
199,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean | Real.hasDerivAt_arctan | [] | [
94,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Order/LocallyFinite.lean | Finset.Iio_eq_Ico | [] | [
481,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
480,
1
] |
Mathlib/Algebra/Ring/Commute.lean | Commute.mul_self_eq_mul_self_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : Type x\ninst✝¹ : NonUnitalNonAssocRing R\ninst✝ : NoZeroDivisors R\na b : R\nh : Commute a b\n⊢ a * a = b * b ↔ a = b ∨ a = -b",
"tactic": "rw [← sub_eq_zero, h.mul_self_sub_mul_self_eq, mul_eq_zero, or_comm, sub_eq_ze... | [
87,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Data/List/Nodup.lean | List.forall_mem_ne | [] | [
34,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
1
] |
Mathlib/MeasureTheory/Measure/Regular.lean | MeasurableSet.exists_isOpen_diff_lt | [
{
"state_after": "case intro.intro.intro\nα : Type u_1\nβ : Type ?u.13200\ninst✝² : MeasurableSpace α\ninst✝¹ : TopologicalSpace α\nμ : Measure α\ninst✝ : OuterRegular μ\nA : Set α\nhA : MeasurableSet A\nhA' : ↑↑μ A ≠ ⊤\nε : ℝ≥0∞\nhε : ε ≠ 0\nU : Set α\nhAU : U ⊇ A\nhUo : IsOpen U\nhU : ↑↑μ U < ↑↑μ A + ε\n⊢ ∃ U... | [
280,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.trim_eq_self | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.697521\nm : MeasurableSpace α\nL : Type ?u.697527\nM : Type u_2\nN : Type ?u.697533\ninst✝⁵ : AddCommMonoid L\ninst✝⁴ : TopologicalSpace L\ninst✝³ : AddCommMonoid M\ninst✝² : TopologicalSpace M\ninst✝¹ : AddCommMonoid N\ninst✝ : TopologicalSpace N\nn : Measura... | [
1296,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1294,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_count' | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1693528\nγ : Type ?u.1693531\nδ : Type ?u.1693534\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝ : MeasurableSpace α\nf : α → ℝ≥0∞\nhf : Measurable f\n⊢ (∑' (i : α), ∫⁻ (a : α), f a ∂dirac i) = ∑' (a : α), f a",
"state_before": "α : Type u_1\nβ : Type ?u.1693528\n... | [
1398,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1395,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | tendsto_prod_uniformity_fst | [] | [
1602,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1600,
1
] |
Mathlib/RingTheory/Finiteness.lean | Submodule.fg_span_singleton | [] | [
179,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_div_const_uIcc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\na✝ a b c : α\n⊢ (fun x => x / a) '' [[b, c]] = [[b / a, c / a]]",
"tactic": "simp only [div_eq_mul_inv, image_mul_const_uIcc]"
}
] | [
726,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
725,
1
] |
Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.maximalIdeal_eq_span_p | [
{
"state_after": "case a\np : ℕ\nhp : Fact (Nat.Prime p)\n⊢ maximalIdeal ℤ_[p] ≤ Ideal.span {↑p}\n\ncase a\np : ℕ\nhp : Fact (Nat.Prime p)\n⊢ Ideal.span {↑p} ≤ maximalIdeal ℤ_[p]",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\n⊢ maximalIdeal ℤ_[p] = Ideal.span {↑p}",
"tactic": "apply le_antisymm"
}... | [
606,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
600,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.ConnectedComponent.map_id | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nC : ConnectedComponent G\n⊢ ∀ (v : V), map Hom.id (connectedComponentMk G v) = connectedComponentMk G v",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : Si... | [
2063,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2061,
1
] |
Mathlib/Order/Filter/SmallSets.lean | Filter.eventually_smallSets_forall | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.6026\nι : Sort ?u.6029\nl l' la : Filter α\nlb : Filter β\np : α → Prop\n⊢ (∀ᶠ (s : Set α) in smallSets l, ∀ (x : α), x ∈ s → p x) ↔ ∀ᶠ (x : α) in l, p x",
"tactic": "simpa only [inf_top_eq, eventually_top] using @eventually_smallSe... | [
167,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.mul_re | [] | [
268,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Topology/Instances/AddCircle.lean | AddCircle.addOrderOf_div_of_gcd_eq_one' | [
{
"state_after": "case ofNat\n𝕜 : Type u_1\nB : Type ?u.190115\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\np q : 𝕜\nhp : Fact (0 < p)\nn : ℕ\nhn : 0 < n\na✝ : ℕ\nh : Nat.gcd (Int.natAbs (Int.ofNat a✝)) n = 1\n⊢ addOrderOf ↑(↑(Int.ofNat a✝) / ↑n * p) = n\n\ncase neg... | [
409,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Std/Data/HashMap/WF.lean | Std.HashMap.Imp.WF.out | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : BEq α\ninst✝ : Hashable α\nm : Imp α β\nh : WF m\n⊢ m.size = Bucket.size m.buckets ∧ Bucket.WF m.buckets",
"tactic": "induction h with\n| mk h₁ h₂ => exact ⟨h₁, h₂⟩\n| @empty' _ h => exact ⟨(Bucket.mk_size h).symm, .mk' h... | [
290,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
283,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.