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/LinearAlgebra/BilinearForm.lean | BilinForm.IsAlt.neg_eq | [
{
"state_after": "R : Type ?u.957968\nM : Type ?u.957971\ninst✝¹⁸ : Semiring R\ninst✝¹⁷ : AddCommMonoid M\ninst✝¹⁶ : Module R M\nR₁ : Type u_1\nM₁ : Type u_2\ninst✝¹⁵ : Ring R₁\ninst✝¹⁴ : AddCommGroup M₁\ninst✝¹³ : Module R₁ M₁\nR₂ : Type ?u.958619\nM₂ : Type ?u.958622\ninst✝¹² : CommSemiring R₂\ninst✝¹¹ : AddC... | [
968,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
964,
1
] |
Mathlib/Data/List/Cycle.lean | List.prev_cons_cons_eq | [] | [
226,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidHom.coe_one | [] | [
481,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
480,
1
] |
Mathlib/Algebra/Group/OrderSynonym.lean | toDual_one | [] | [
104,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.vadd_domain | [] | [
514,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.appendFun_comp' | [] | [
272,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/Combinatorics/Quiver/Path.lean | Prefunctor.mapPath_toPath | [] | [
239,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Analysis/Complex/ReImTopology.lean | Complex.quotientMap_re | [] | [
65,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.Measure.haveLebesgueDecomposition_spec | [
{
"state_after": "α : Type u_1\nβ : Type ?u.2715\nm : MeasurableSpace α\nμ✝ ν✝ μ ν : Measure α\nh : HaveLebesgueDecomposition μ ν\n⊢ Measurable (Classical.choose (_ : ∃ p, Measurable p.snd ∧ p.fst ⟂ₘ ν ∧ μ = p.fst + withDensity ν p.snd)).snd ∧\n (Classical.choose (_ : ∃ p, Measurable p.snd ∧ p.fst ⟂ₘ ν ∧ μ =... | [
106,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Topology/ContinuousOn.lean | nhdsWithin_subtype | [] | [
493,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
] |
Mathlib/Topology/Inseparable.lean | Specializes.mem_open | [] | [
120,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Expr.of_cancel_eq | [
{
"state_after": "ctx : Context\na b c d : Expr\nh : Poly.cancel (toNormPoly a) (toNormPoly b) = (toPoly c, toPoly d)\nthis : Poly.denote_eq ctx (Poly.cancel (toNormPoly a) (toNormPoly b)) = Poly.denote_eq ctx (toNormPoly a, toNormPoly b)\n⊢ (denote ctx a = denote ctx b) = (denote ctx c = denote ctx d)",
"s... | [
545,
18
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
541,
1
] |
Mathlib/Order/BoundedOrder.lean | Ne.bot_lt | [] | [
398,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/Algebra/Hom/Ring.lean | NonUnitalRingHom.ext_iff | [] | [
185,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Algebra/BigOperators/Pi.lean | Fintype.prod_apply | [] | [
62,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | IsPreconnected.intermediate_value_Iic | [] | [
164,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Topology/Category/TopCat/OpenNhds.lean | TopologicalSpace.OpenNhds.map_id_obj' | [] | [
122,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Std/Data/List/Lemmas.lean | List.foldl_hom | [
{
"state_after": "no goals",
"state_before": "α₁ : Type u_1\nα₂ : Type u_2\nβ : Type u_3\nf : α₁ → α₂\ng₁ : α₁ → β → α₁\ng₂ : α₂ → β → α₂\nl : List β\ninit : α₁\nH : ∀ (x : α₁) (y : β), g₂ (f x) y = f (g₁ x y)\n⊢ foldl g₂ (f init) l = f (foldl g₁ init l)",
"tactic": "induction l generalizing init <;> si... | [
1419,
48
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1417,
1
] |
Mathlib/AlgebraicGeometry/SheafedSpace.lean | AlgebraicGeometry.SheafedSpace.id_base | [] | [
120,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Data/Polynomial/Splits.lean | Polynomial.map_rootOfSplits' | [] | [
204,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Analysis/InnerProductSpace/Calculus.lean | contDiffAt_norm | [
{
"state_after": "𝕜 : Type ?u.131195\nE : Type u_1\nF : Type ?u.131201\ninst✝⁷ : IsROrC 𝕜\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : InnerProductSpace 𝕜 E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace ℝ F\ninst✝² : NormedSpace ℝ E\nG : Type ?u.131330\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedS... | [
177,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Algebra/Module/Torsion.lean | Submodule.exists_isTorsionBy | [
{
"state_after": "R : Type u_2\nM : Type u_1\ninst✝³ : CommSemiring R\ninst✝² : AddCommMonoid M\ninst✝¹ : Module R M\ninst✝ : (x : M) → Decidable (x = 0)\np : R\nhM : IsTorsion' M { x // x ∈ Submonoid.powers p }\nd : ℕ\nhd : d ≠ 0\ns : Fin d → M\nhs : span R (Set.range s) = ⊤\noj : Option (Fin d) := List.argmax... | [
801,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
788,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | hasDerivWithinAt_congr_set | [] | [
314,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Analysis/Calculus/FDerivMeasurable.lean | FDerivMeasurableAux.le_of_mem_a | [
{
"state_after": "case intro.intro\n𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nK : Set (E →L[𝕜] F)\nr ε : ℝ\nL : E →L[𝕜] F\nx y z : E\nhy : y ∈ clo... | [
163,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/RingTheory/LaurentSeries.lean | LaurentSeries.powerSeriesPart_coeff | [] | [
72,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.homothety_def | [] | [
793,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
791,
1
] |
Std/Data/String/Lemmas.lean | Substring.Valid.isEmpty | [
{
"state_after": "no goals",
"state_before": "x✝ : Substring\nh✝ : Valid x✝\nl m r : List Char\nh : ValidFor l m r x✝\n⊢ Substring.isEmpty x✝ = true ↔ toString x✝ = \"\"",
"tactic": "simp [h.isEmpty, h.toString, ext_iff]"
}
] | [
979,
85
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
978,
1
] |
Mathlib/MeasureTheory/Measure/Regular.lean | MeasureTheory.Measure.Regular.map | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝⁷ : MeasurableSpace α\ninst✝⁶ : TopologicalSpace α\nμ : Measure α\ninst✝⁵ : OpensMeasurableSpace α\ninst✝⁴ : MeasurableSpace β\ninst✝³ : TopologicalSpace β\ninst✝² : T2Space β\ninst✝¹ : BorelSpace β\ninst✝ : Regular μ\nf : α ≃ₜ β\nthis : OuterRegular (map (↑f) ... | [
541,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
11
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.Measure.ae_eval_ne | [] | [
450,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
1
] |
Mathlib/Data/Num/Lemmas.lean | PosNum.size_to_nat | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.330131\nn : PosNum\n⊢ ↑(size (bit0 n)) = Nat.size ↑(bit0 n)",
"tactic": "rw [size, succ_to_nat, size_to_nat n, cast_bit0, Nat.size_bit0 <| ne_of_gt <| to_nat_pos n]"
},
{
"state_after": "no goals",
"state_before": "α : Type ?u.330131\... | [
572,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Std/Data/Int/Lemmas.lean | Int.lt_sub_right_of_add_lt | [
{
"state_after": "a b c : Int\nh✝ : a + b < c\nh : a + b + -b < c + -b\n⊢ a < c - b",
"state_before": "a b c : Int\nh : a + b < c\n⊢ a < c - b",
"tactic": "have h := Int.add_lt_add_right h (-b)"
},
{
"state_after": "no goals",
"state_before": "a b c : Int\nh✝ : a + b < c\nh : a + b + -b < c ... | [
1061,
38
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1059,
11
] |
Mathlib/Control/Traversable/Equiv.lean | Equiv.lawfulFunctor | [] | [
74,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
11
] |
Mathlib/LinearAlgebra/Dual.lean | Submodule.dualQuotEquivDualAnnihilator_symm_apply_mk | [] | [
1288,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1286,
1
] |
Mathlib/RingTheory/Ideal/Over.lean | Ideal.comap_ne_bot_of_algebraic_mem | [] | [
277,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableEquiv.self_comp_symm | [] | [
1259,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1258,
1
] |
Mathlib/Algebra/Opposites.lean | AddOpposite.op_one | [] | [
373,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.mapRange.addEquiv_symm | [] | [
2217,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2215,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/WideEqualizers.lean | CategoryTheory.Limits.wideEqualizer.trident_ι | [] | [
591,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
590,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.coe_ofLinearIsometry_symm | [] | [
1111,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1108,
1
] |
Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | MonotoneOn.integrableOn_of_measure_ne_top | [
{
"state_after": "X : Type u_1\nY : Type ?u.1757356\nE : Type u_2\nR : Type ?u.1757362\ninst✝¹⁰ : MeasurableSpace X\ninst✝⁹ : TopologicalSpace X\ninst✝⁸ : MeasurableSpace Y\ninst✝⁷ : TopologicalSpace Y\ninst✝⁶ : NormedAddCommGroup E\nf : X → E\nμ : MeasureTheory.Measure X\ns : Set X\ninst✝⁵ : BorelSpace X\ninst... | [
334,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.spanSingleton_mul_le_iff | [
{
"state_after": "R : Type u_1\ninst✝⁷ : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝⁶ : CommRing P\ninst✝⁵ : Algebra R P\nloc : IsLocalization S P\nR₁ : Type ?u.1734695\ninst✝⁴ : CommRing R₁\nK : Type ?u.1734701\ninst✝³ : Field K\ninst✝² : Algebra R₁ K\ninst✝¹ : IsFractionRing R₁ K\ninst✝ : IsDomain R₁\nx ... | [
1538,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1530,
1
] |
Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.lim_mul_lim | [
{
"state_after": "α : Type u_1\ninst✝³ : LinearOrderedField α\nβ : Type u_2\ninst✝² : Ring β\nabv : β → α\ninst✝¹ : IsAbsoluteValue abv\ninst✝ : IsComplete β abv\nf g : CauSeq β abv\nh : const abv (lim f * lim g) - f * g = (const abv (lim f) - f) * g + const abv (lim f) * (const abv (lim g) - g)\n⊢ LimZero (con... | [
386,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Algebra/Ring/Divisibility.lean | dvd_sub_self_left | [] | [
152,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Algebra/DirectSum/Basic.lean | DirectSum.add_apply | [] | [
102,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_umax_eq | [
{
"state_after": "no goals",
"state_before": "α β : Type u\na : Cardinal\nb : Cardinal\n⊢ lift a = lift b ↔ lift a = lift b",
"tactic": "rw [← lift_lift.{v, w, u}, ← lift_lift.{u, w, v}, lift_inj]"
}
] | [
1156,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1154,
1
] |
Mathlib/Data/Nat/Pow.lean | Nat.one_lt_pow' | [] | [
78,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Topology/UrysohnsLemma.lean | Urysohns.CU.approx_mem_Icc_right_left | [
{
"state_after": "case zero\nX : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : NormalSpace X\nc✝ : CU X\nx : X\nc : CU X\n⊢ approx Nat.zero c x ∈ Icc (approx Nat.zero (right c) x) (approx Nat.zero (left c) x)\n\ncase succ\nX : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : NormalSpace X\nc✝ : CU X\nx : X\nn : ... | [
197,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_lt | [] | [
357,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/GroupTheory/GroupAction/Defs.lean | toMul_smul | [] | [
1175,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1174,
1
] |
Mathlib/Data/List/Cycle.lean | List.prev_cons_cons_of_ne | [] | [
238,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | Int.coe_nat_pow | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.267168\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\nn m : ℕ\n⊢ ↑(n ^ m) = ↑n ^ m",
"tactic": "induction' m with m _ <;> simp"
}
] | [
547,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
] |
Mathlib/Data/Nat/Dist.lean | Nat.dist_zero_right | [] | [
71,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.range_one | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.124150\nδ : Type ?u.124153\ninst✝² : MeasurableSpace α\ninst✝¹ : Nonempty α\ninst✝ : One β\nx : β\n⊢ x ∈ SimpleFunc.range 1 ↔ x ∈ {1}",
"tactic": "simp [eq_comm]"
}
] | [
544,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
] |
Mathlib/Data/List/Basic.lean | List.mem_filter_of_mem | [
{
"state_after": "case inl\nι : Type ?u.372560\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\np : α → Bool\na : α\nl : List α\nh1 : p a = true\nh : a ∈ a :: l\n⊢ a ∈ filter p (a :: l)\n\ncase inr\nι : Type ?u.372560\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\np : α → Bool\... | [
3548,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3543,
1
] |
Mathlib/Order/Concept.lean | intentClosure_iUnion | [] | [
110,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Data/List/MinMax.lean | List.argmax_cons | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝ : LinearOrder β\nf✝ : α → β\nl✝ : List α\no : Option α\na✝ m : α\nf : α → β\na : α\nl hd : List α\ntl : α\nih : argmax f (a :: hd) = Option.casesOn (argmax f hd) (some a) fun c => if f a < f c then some c else some a\n⊢ (Option.casesOn (Option.casesOn (argmax ... | [
196,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_quotient_mk'' | [] | [
500,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/Data/Set/Basic.lean | Set.Nontrivial.mono | [] | [
2462,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2460,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | Complex.continuousAt_ofReal_cpow_const | [] | [
419,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/Order/WithBot.lean | WithTop.coe_ne_top | [] | [
611,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
610,
1
] |
Std/Data/Rat/Lemmas.lean | Rat.normalize_num_den | [
{
"state_after": "n : Int\nd : Nat\nz : d ≠ 0\nn' : Int\nd' : Nat\nz' : d' ≠ 0\nc : Nat.coprime (Int.natAbs n') d'\nh : normalize n d = mk' n' d'\nthis : ∃ d_1, d_1 ≠ 0 ∧ n = (normalize n d).num * ↑d_1 ∧ d = (normalize n d).den * d_1\n⊢ ∃ m, m ≠ 0 ∧ n = n' * ↑m ∧ d = d' * m",
"state_before": "n : Int\nd : N... | [
80,
52
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
78,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.FinMeasSupp.of_lintegral_ne_top | [
{
"state_after": "α : Type u_1\nβ : Type ?u.921719\nγ : Type ?u.921722\nδ : Type ?u.921725\nm : MeasurableSpace α\ninst✝¹ : Zero β\ninst✝ : Zero γ\nμ : Measure α\nf✝ : α →ₛ β\nf : α →ₛ ℝ≥0∞\nh : lintegral f μ ≠ ⊤\nb : ℝ≥0∞\nhb : b ≠ 0\n⊢ ↑↑μ (↑f ⁻¹' {b}) < ⊤",
"state_before": "α : Type u_1\nβ : Type ?u.9217... | [
1264,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1260,
1
] |
Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.exists_elementaryEmbedding_card_eq | [
{
"state_after": "case inl\nL : Language\nT : Theory L\nα : Type w\nn : ℕ\nM : Type w'\ninst✝ : Structure L M\niM : Infinite M\nκ : Cardinal\nh1 : ℵ₀ ≤ κ\nh2 : lift (card L) ≤ lift κ\nh✝ : lift κ ≤ lift (#M)\n⊢ ∃ N, (Nonempty (↑N ↪ₑ[L] M) ∨ Nonempty (M ↪ₑ[L] ↑N)) ∧ (#↑N) = κ\n\ncase inr\nL : Language\nT : Theor... | [
272,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.integralSum_biUnionTagged | [
{
"state_after": "ι : Type u\nE : Type v\nF : Type w\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nI J✝ : Box ι\nπ✝ : TaggedPrepartition I\nf : (ι → ℝ) → E\nvol : ι →ᵇᵃ[⊤] E →L[ℝ] F\nπ : Prepartition I\nπi : (J : Box ι) → TaggedPrepartition J\n... | [
89,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Data/Polynomial/Monic.lean | Polynomial.Monic.natDegree_map | [
{
"state_after": "R : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝² : Semiring R\ninst✝¹ : Semiring S\ninst✝ : Nontrivial S\nP : R[X]\nhmo : Monic P\nf : R →+* S\n⊢ coeff (Polynomial.map f P) (natDegree P) ≠ 0",
"state_before": "R : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝² : Semir... | [
309,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.dist | [] | [
1461,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1458,
11
] |
Mathlib/ModelTheory/Basic.lean | Equiv.toFun_inducedStructureEquiv_Symm | [
{
"state_after": "L : Language\nM : Type ?u.318087\nN : Type ?u.318090\ninst✝ : Structure L M\ne : M ≃ N\nthis : Structure L N := inducedStructure e\n⊢ (a : N) → (fun x => M) a",
"state_before": "L : Language\nM : Type ?u.318087\nN : Type ?u.318090\ninst✝ : Structure L M\ne : M ≃ N\n⊢ (a : N) → (fun x => M)... | [
1055,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1051,
1
] |
Mathlib/Data/List/Basic.lean | List.reverse_singleton | [] | [
602,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
601,
1
] |
Mathlib/Analysis/Calculus/Conformal/NormedSpace.lean | ConformalAt.comp | [
{
"state_after": "case intro.intro\nX : Type u_3\nY : Type u_1\nZ : Type u_2\ninst✝⁵ : NormedAddCommGroup X\ninst✝⁴ : NormedAddCommGroup Y\ninst✝³ : NormedAddCommGroup Z\ninst✝² : NormedSpace ℝ X\ninst✝¹ : NormedSpace ℝ Y\ninst✝ : NormedSpace ℝ Z\nf : X → Y\ng : Y → Z\nx : X\nhg : ConformalAt g (f x)\nf' : X →L... | [
108,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Data/Finsupp/Antidiagonal.lean | Finsupp.antidiagonal_filter_snd_eq | [
{
"state_after": "case a.mk\nα : Type u\nf g : α →₀ ℕ\nD : (p : (α →₀ ℕ) × (α →₀ ℕ)) → Decidable (p.snd = g)\na b : α →₀ ℕ\n⊢ (a, b) ∈ Finset.filter (fun p => p.snd = g) (antidiagonal f) ↔ (a, b) ∈ if g ≤ f then {(f - g, g)} else ∅",
"state_before": "α : Type u\nf g : α →₀ ℕ\nD : (p : (α →₀ ℕ) × (α →₀ ℕ)) →... | [
87,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Combinatorics/SimpleGraph/Regularity/Equitabilise.lean | Finpartition.equitabilise_isEquipartition | [] | [
162,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.wellFounded_lt | [] | [
874,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
873,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | Finset.prod_add_prod_le' | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : Type ?u.177392\nβ : Type ?u.177395\nM : Type ?u.177398\nN : Type ?u.177401\nG : Type ?u.177404\nk : Type ?u.177407\nR : Type u_2\ninst✝ : CanonicallyOrderedCommSemiring R\nf g h : ι → R\ns : Finset ι\ni : ι\nhi : i ∈ s\nh2i : g i + h i ≤ f i\nh... | [
680,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
670,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left' | [] | [
904,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
901,
1
] |
Mathlib/Algebra/Algebra/Hom.lean | AlgHom.map_pow | [] | [
262,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
11
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ioc_subset_Ioc_right | [] | [
203,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.toNatOrdinal_min | [] | [
191,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.restrict_boxes_of_le | [
{
"state_after": "ι : Type u_1\nI J J₁ J₂ : Box ι\nπ✝ π₁ π₂ : Prepartition I\nx : ι → ℝ\nπi πi₁ πi₂ : (J : Box ι) → Prepartition J\nπ : Prepartition I\nh : I ≤ J\n⊢ Finset.biUnion (Finset.image (fun J' => ↑J ⊓ ↑J') π.boxes) Option.toFinset = π.boxes",
"state_before": "ι : Type u_1\nI J J₁ J₂ : Box ι\nπ✝ π₁ ... | [
517,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.support_zero | [] | [
1134,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1133,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.moveLeft_neg | [
{
"state_after": "case mk\nα✝ β✝ : Type u_1\na✝¹ : α✝ → PGame\na✝ : β✝ → PGame\ni : RightMoves (mk α✝ β✝ a✝¹ a✝)\n⊢ moveLeft (-mk α✝ β✝ a✝¹ a✝) (↑toLeftMovesNeg i) = -moveRight (mk α✝ β✝ a✝¹ a✝) i",
"state_before": "x : PGame\ni : RightMoves x\n⊢ moveLeft (-x) (↑toLeftMovesNeg i) = -moveRight x i",
"tac... | [
1267,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1265,
1
] |
Mathlib/Topology/Category/TopCat/Opens.lean | TopologicalSpace.Opens.map_functor_eq' | [] | [
396,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.exists_of_mem_join | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\na : α\n⊢ ∀ (ss : WSeq α),\n a ∈ ss →\n ∀ (s : WSeq α) (S : WSeq (WSeq α)), append s (join S) = ss → a ∈ append s (join S) → a ∈ s ∨ ∃ s, s ∈ S ∧ a ∈ s",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\na : α\n⊢ ∀ {S : WSeq (WSeq α)}, a ∈ join... | [
1470,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1437,
1
] |
Mathlib/AlgebraicTopology/SimplicialObject.lean | CategoryTheory.SimplicialObject.δ_comp_σ_self' | [
{
"state_after": "C : Type u\ninst✝ : Category C\nX : SimplicialObject C\nn : ℕ\ni : Fin (n + 1)\n⊢ σ X i ≫ δ X (↑Fin.castSucc i) = 𝟙 (X.obj [n].op)",
"state_before": "C : Type u\ninst✝ : Category C\nX : SimplicialObject C\nn : ℕ\nj : Fin (n + 2)\ni : Fin (n + 1)\nH : j = ↑Fin.castSucc i\n⊢ σ X i ≫ δ X j =... | [
166,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/CategoryTheory/Generator.lean | CategoryTheory.isCoseparator_prod | [
{
"state_after": "case refine'_1\nC : Type u₁\ninst✝³ : Category C\nD : Type u₂\ninst✝² : Category D\ninst✝¹ : HasZeroMorphisms C\nG H : C\ninst✝ : HasBinaryProduct G H\nh : IsCoseparator (G ⨯ H)\nX Y : C\nu v : X ⟶ Y\nhuv : ∀ (G_1 : C), G_1 ∈ {G, H} → ∀ (h : Y ⟶ G_1), u ≫ h = v ≫ h\n⊢ u = v\n\ncase refine'_2\n... | [
599,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
Mathlib/GroupTheory/Subsemigroup/Membership.lean | Subsemigroup.mem_iSup_of_directed | [
{
"state_after": "ι : Sort u_2\nM : Type u_1\nA : Type ?u.35\nB : Type ?u.38\ninst✝ : Mul M\nS : ι → Subsemigroup M\nhS : Directed (fun x x_1 => x ≤ x_1) S\nx : M\n⊢ (x ∈ ⨆ (i : ι), S i) → ∃ i, x ∈ S i",
"state_before": "ι : Sort u_2\nM : Type u_1\nA : Type ?u.35\nB : Type ?u.38\ninst✝ : Mul M\nS : ι → Subs... | [
56,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.MonoFactorisation.kernel_ι_comp | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\ninst✝¹ : HasZeroMorphisms C\nX Y : C\nf : X ⟶ Y\ninst✝ : HasKernel f\nF : MonoFactorisation f\n⊢ kernel.ι f ≫ F.e = 0",
"tactic": "rw [← cancel_mono F.m, zero_comp, Category.assoc, F.fac, kernel.condition]"
}
] | [
964,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
962,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.le_of_inf_neBot | [] | [
106,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Algebra/Group/OrderSynonym.lean | toLex_one | [] | [
244,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/CategoryTheory/Conj.lean | CategoryTheory.Iso.conjAut_hom | [] | [
137,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | Submodule.orthogonal_orthogonal_eq_closure | [
{
"state_after": "case refine'_1\n𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.781831\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : InnerProductSpace ℝ F\nK : Submodule 𝕜 E\ninst✝ : CompleteSpace E\n⊢ Kᗮᗮ ≤ topologicalClosure K\n\ncase ... | [
787,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
780,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.angle_le_pi | [] | [
140,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
8
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf_image | [] | [
344,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/AlgebraicTopology/DoldKan/GammaCompN.lean | AlgebraicTopology.DoldKan.N₁Γ₀_hom_app_f_f | [
{
"state_after": "C : Type u_2\ninst✝² : Category C\ninst✝¹ : Preadditive C\ninst✝ : HasFiniteCoproducts C\nK : ChainComplex C ℕ\nn : ℕ\n⊢ HomologicalComplex.Hom.f\n ((Splitting.toKaroubiNondegComplexIsoN₁ (Γ₀.splitting K)).inv ≫\n (toKaroubi (ChainComplex C ℕ)).map (Γ₀NondegComplexIso K).hom).f\n... | [
108,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Data/PNat/Xgcd.lean | PNat.XgcdType.flip_y | [] | [
202,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Order/BooleanAlgebra.lean | himp_eq | [] | [
580,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_subset_Ici_iff | [] | [
586,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidHom.comp_mul | [] | [
536,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/MeasureTheory/Measure/AEMeasurable.lean | AEMeasurable.ae_mem_imp_eq_mk | [] | [
64,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Algebra/Group/Basic.lean | mul_mul_mul_comm | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.6182\nβ : Type ?u.6185\nG : Type u_1\ninst✝ : CommSemigroup G\na b c d : G\n⊢ a * b * (c * d) = a * c * (b * d)",
"tactic": "simp only [mul_left_comm, mul_assoc]"
}
] | [
110,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.toLin'_apply' | [] | [
313,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
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