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/CategoryTheory/Abelian/Exact.lean | CategoryTheory.Abelian.Exact.unop_iff | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝¹ : Category C\ninst✝ : Abelian C\nX✝ Y✝ Z✝ : C\nf✝ : X✝ ⟶ Y✝\ng✝ : Y✝ ⟶ Z✝\nX Y Z : Cᵒᵖ\ng : X ⟶ Y\nf : Y ⟶ Z\ne : Exact f.unop g.unop\n⊢ Exact g f",
"tactic": "rwa [← f.op_unop, ← g.op_unop, ← Exact.op_iff] at e"
},
{
"state_after... | [
320,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Algebra/Hom/Ring.lean | RingHom.congr_arg | [] | [
528,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
1
] |
Mathlib/RingTheory/Noetherian.lean | isNoetherianRing_of_ringEquiv | [] | [
597,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.head_pure | [] | [
161,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Data/Real/Pi/Wallis.lean | Real.Wallis.W_eq_integral_sin_pow_div_integral_sin_pow | [
{
"state_after": "k : ℕ\n⊢ 2 / π * W k = 2 / π * ∏ x in range k, (2 * ↑x + 2) / (2 * ↑x + 3) / ((2 * ↑x + 1) / (2 * ↑x + 2))",
"state_before": "k : ℕ\n⊢ (π / 2)⁻¹ * W k = (∫ (x : ℝ) in 0 ..π, sin x ^ (2 * k + 1)) / ∫ (x : ℝ) in 0 ..π, sin x ^ (2 * k)",
"tactic": "rw [integral_sin_pow_even, integral_sin_... | [
87,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Algebra/Order/Monoid/Canonical/Defs.lean | le_mul_of_le_right | [] | [
200,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.const_mul_left | [] | [
1451,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1449,
1
] |
Mathlib/Logic/Equiv/Set.lean | Equiv.eq_preimage_iff_image_eq | [] | [
136,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.mapRange_id | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.296719\nm inst✝⁵ : MeasurableSpace α\ninst✝⁴ : MeasurableSpace β\nM : Type u_2\ninst✝³ : AddCommMonoid M\ninst✝² : TopologicalSpace M\nv : VectorMeasure α M\nN : Type ?u.296766\ninst✝¹ : AddCommMonoid N\ninst✝ : TopologicalSpace N\ni✝ : Set α\na✝ : MeasurableS... | [
627,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | PseudoMetricSpace.replaceTopology_eq | [
{
"state_after": "case h.dist.h.h\nα : Type u\nβ : Type v\nX : Type ?u.167309\nι : Type ?u.167312\ninst✝ : PseudoMetricSpace α\nγ : Type u_1\nU : TopologicalSpace γ\nm : PseudoMetricSpace γ\nH : U = UniformSpace.toTopologicalSpace\nx✝¹ x✝ : γ\n⊢ dist x✝¹ x✝ = dist x✝¹ x✝",
"state_before": "α : Type u\nβ : T... | [
1268,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1265,
1
] |
Mathlib/Order/Filter/NAry.lean | Filter.map_map₂ | [
{
"state_after": "α : Type u_3\nα' : Type ?u.36106\nβ : Type u_4\nβ' : Type ?u.36112\nγ : Type u_2\nγ' : Type ?u.36118\nδ : Type u_1\nδ' : Type ?u.36124\nε : Type ?u.36127\nε' : Type ?u.36130\nm✝ : α → β → γ\nf f₁ f₂ : Filter α\ng g₁ g₂ : Filter β\nh h₁ h₂ : Filter γ\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\nu : Set γ... | [
266,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Std/Data/List/Lemmas.lean | List.get?_set_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na : α\nn : Nat\nl : List α\n⊢ get? (set l n a) n = (fun x => a) <$> get? l n",
"tactic": "simp only [set_eq_modifyNth, get?_modifyNth_eq]"
}
] | [
797,
50
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
796,
1
] |
Mathlib/Algebra/Group/Units.lean | Units.eq_inv_mul_iff_mul_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Monoid α\na✝ b c✝ u : αˣ\na c : α\nh : a = ↑b⁻¹ * c\n⊢ ↑b * a = c",
"tactic": "rw [h, mul_inv_cancel_left]"
},
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Monoid α\na✝ b c✝ u : αˣ\na c : α\nh : ↑b * a = c... | [
329,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.derivative_X_add_C_sq | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝ : CommSemiring R\nc : R\n⊢ ↑derivative ((X + ↑C c) ^ 2) = ↑C 2 * (X + ↑C c)",
"tactic": "rw [derivative_sq, derivative_X_add_C, mul_one]"
}
] | [
531,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Localization.induction_on | [] | [
378,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Algebra/FreeMonoid/Count.lean | FreeMonoid.countp_of' | [
{
"state_after": "α : Type u_1\np : α → Prop\ninst✝ : DecidablePred p\nx : α\n⊢ (if p x = (true = true) then 1 else 0) = if p x then ↑Multiplicative.ofAdd 1 else ↑Multiplicative.ofAdd 0",
"state_before": "α : Type u_1\np : α → Prop\ninst✝ : DecidablePred p\nx : α\n⊢ ↑(countp p) (of x) = if p x then ↑Multipl... | [
68,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.add_le_add' | [
{
"state_after": "case mk.mk.mk.mk.intro.intro\nα✝ β✝ : Type u\na✝ : Cardinal\nα : Type u_1\nb✝ : Cardinal\nβ : Type u_1\nc✝ : Cardinal\nγ : Type u_1\nd✝ : Cardinal\nδ : Type u_1\ne₁ : α ↪ β\ne₂ : γ ↪ δ\n⊢ Quot.mk Setoid.r α + Quot.mk Setoid.r γ ≤ Quot.mk Setoid.r β + Quot.mk Setoid.r δ",
"state_before": "α... | [
661,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
9
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.K'.elim_stack | [] | [
1276,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1276,
1
] |
Mathlib/GroupTheory/Archimedean.lean | AddSubgroup.exists_isLeast_pos | [
{
"state_after": "case this\nG : Type u_1\ninst✝¹ : LinearOrderedAddCommGroup G\ninst✝ : Archimedean G\nH : AddSubgroup G\nhbot : H ≠ ⊥\na : G\nh₀ : 0 < a\nhd : Disjoint (↑H) (Ioo 0 a)\nhex : ∀ (g : G), g > 0 → ∃ n, g ∈ Ioc (n • a) ((n + 1) • a)\n⊢ ∃ n, Set.Nonempty (↑H ∩ Ioc (n • a) ((n + 1) • a))\n\nG : Type ... | [
89,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Data/Bundle.lean | Bundle.TotalSpace.proj_mk | [] | [
70,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Homeomorph.toMeasurableEquiv_symm_coe | [] | [
932,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
930,
1
] |
Mathlib/Topology/Inseparable.lean | SeparationQuotient.mk_eq_mk | [] | [
430,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/Data/List/Sublists.lean | List.sublists_eq_sublistsAux | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nl : List α\n⊢ Array.toList\n (foldr\n (fun a arr =>\n Array.foldl (fun r l => Array.push (Array.push r l) (a :: l)) (Array.mkEmpty (Array.size arr * 2)) arr 0\n (Array.size arr))\n #[[]] l) =\n foldr\n (fun a r ... | [
147,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Analysis/Calculus/Deriv/Polynomial.lean | Polynomial.fderiv | [] | [
181,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
11
] |
Mathlib/Topology/Instances/NNReal.lean | NNReal.tendsto_atTop_zero_of_summable | [
{
"state_after": "f : ℕ → ℝ≥0\nhf : Summable f\n⊢ Tendsto f cofinite (𝓝 0)",
"state_before": "f : ℕ → ℝ≥0\nhf : Summable f\n⊢ Tendsto f atTop (𝓝 0)",
"tactic": "rw [← Nat.cofinite_eq_atTop]"
},
{
"state_after": "no goals",
"state_before": "f : ℕ → ℝ≥0\nhf : Summable f\n⊢ Tendsto f cofinite... | [
243,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.not_sOppSide_bot | [] | [
238,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.singleton_val | [] | [
677,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
676,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.ceil_add_le | [
{
"state_after": "F : Type ?u.217435\nα : Type u_1\nβ : Type ?u.217441\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na✝ a b : α\n⊢ a + b ≤ ↑⌈a⌉ + ↑⌈b⌉",
"state_before": "F : Type ?u.217435\nα : Type u_1\nβ : Type ?u.217441\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na✝ a b : α\n⊢... | [
1181,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1179,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | InnerProductGeometry.angle_sub_eq_arcsin_of_inner_eq_zero | [
{
"state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : inner x (-y) = 0\nh0 : x ≠ 0 ∨ y ≠ 0\n⊢ angle x (x - y) = Real.arcsin (‖y‖ / ‖x - y‖)",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : inner x... | [
243,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Init/Data/Quot.lean | EqvGen.is_equivalence | [] | [
27,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
26,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | rank_map_le | [
{
"state_after": "no goals",
"state_before": "K : Type u\nV V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.51468\nR : Type u\ninst✝⁶ : Ring R\nM : Type v\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\nM' : Type v'\ninst✝³ : AddCommGroup M'\ninst✝... | [
181,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.prod_top | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\ninst✝³ : NonUnitalNonAssocSemiring R\nM : Subsemigroup R\ninst✝² : NonUnitalNonAssocSemiring S\ninst✝¹ : NonUnitalNonAssocSemiring T\nF : Type ?u.267604\ninst✝ : NonUnitalRingHomClass F R S\ns : NonUnitalSubsemiring R\nx : R ×... | [
804,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
802,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.reindexFinsetRange_apply | [
{
"state_after": "case mk\nι : Type u_2\nι' : Type ?u.423699\nR : Type u_3\nR₂ : Type ?u.423705\nK : Type ?u.423708\nM : Type u_1\nM' : Type ?u.423714\nM'' : Type ?u.423717\nV : Type u\nV' : Type ?u.423722\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\ninst✝³ : AddCommMonoid M'\ninst✝² : M... | [
536,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
1
] |
Mathlib/Topology/Bases.lean | isTopologicalBasis_pi | [
{
"state_after": "case refine'_1\nι : Type u_1\nX : ι → Type u_2\ninst✝ : (i : ι) → TopologicalSpace (X i)\nT : (i : ι) → Set (Set (X i))\ncond : ∀ (i : ι), IsTopologicalBasis (T i)\n⊢ ∀ (u : Set ((i : ι) → X i)), u ∈ {S | ∃ U F, (∀ (i : ι), i ∈ F → U i ∈ T i) ∧ S = Set.pi (↑F) U} → IsOpen u\n\ncase refine'_2\n... | [
467,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | fderivWithin_csinh | [] | [
545,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
] |
Mathlib/CategoryTheory/Sites/Sheaf.lean | CategoryTheory.Presheaf.isLimit_iff_isSheafFor_presieve | [] | [
196,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Data/Fin/Tuple/Sort.lean | Tuple.comp_perm_comp_sort_eq_comp_sort | [
{
"state_after": "n : ℕ\nα : Type u_1\ninst✝ : LinearOrder α\nf : Fin n → α\nσ : Equiv.Perm (Fin n)\n⊢ f ∘ ↑(σ * sort (f ∘ ↑σ)) = f ∘ ↑(sort f)",
"state_before": "n : ℕ\nα : Type u_1\ninst✝ : LinearOrder α\nf : Fin n → α\nσ : Equiv.Perm (Fin n)\n⊢ (f ∘ ↑σ) ∘ ↑(sort (f ∘ ↑σ)) = f ∘ ↑(sort f)",
"tactic": ... | [
169,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.hausdorffDist_nonneg | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.72517\nα : Type u\nβ : Type v\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\ns t u : Set α\nx y : α\nΦ : α → β\n⊢ 0 ≤ hausdorffDist s t",
"tactic": "simp [hausdorffDist]"
}
] | [
692,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.fst_comp_prod | [] | [
1107,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1105,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.bot_eq_zero | [] | [
554,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.le_centralizer | [] | [
2398,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2397,
1
] |
Mathlib/Data/List/Rotate.lean | List.Nodup.rotate_eq_self_iff | [
{
"state_after": "case mp\nα : Type u\nl : List α\nhl : Nodup l\nn : ℕ\n⊢ rotate l n = l → n % length l = 0 ∨ l = []\n\ncase mpr\nα : Type u\nl : List α\nhl : Nodup l\nn : ℕ\n⊢ n % length l = 0 ∨ l = [] → rotate l n = l",
"state_before": "α : Type u\nl : List α\nhl : Nodup l\nn : ℕ\n⊢ rotate l n = l ↔ n % l... | [
411,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/Order/Monotone/Basic.lean | StrictAntiOn.eq_iff_eq | [] | [
793,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
791,
1
] |
Mathlib/SetTheory/Lists.lean | Lists'.mem_equiv_left | [] | [
446,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.uniformity_edist | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.158749\nι : Type ?u.158752\ninst✝ : PseudoMetricSpace α\n⊢ 𝓤 α = ⨅ (ε : ℝ≥0∞) (_ : ε > 0), 𝓟 {p | edist p.fst p.snd < ε}",
"tactic": "simp only [PseudoMetricSpace.uniformity_dist, dist_nndist, edist_nndist,\n Metric.uni... | [
1166,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1164,
1
] |
Mathlib/Analysis/Convex/StoneSeparation.lean | not_disjoint_segment_convexHull_triple | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nι : Type ?u.443\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\ns t : Set E\np q u v x y z : E\nhz : z ∈ segment 𝕜 x y\nhu : u ∈ segment 𝕜 x p\nhv : v ∈ segment 𝕜 y q\n⊢ ∃ x, x ∈ segment 𝕜 u v ∧ x ∈ ↑(convexHull 𝕜).toOrderHom {p,... | [
82,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.llift_apply | [] | [
428,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/MeasureTheory/Measure/AEMeasurable.lean | MeasureTheory.Measure.map_mono_of_aemeasurable | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.4971036\nα : Type u_1\nβ : Type ?u.4971042\nγ : Type ?u.4971045\nδ : Type u_2\nR : Type ?u.4971051\nm0 : MeasurableSpace α\ninst✝³ : MeasurableSpace β\ninst✝² : MeasurableSpace γ\ninst✝¹ : MeasurableSpace δ\nf✝ g : α → β\nμ ν : Measure α\ninst✝ : Zer... | [
375,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.zero_toOuterMeasure | [] | [
751,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
750,
1
] |
Mathlib/Data/Complex/Module.lean | realPart_smul | [
{
"state_after": "A : Type u_1\ninst✝³ : AddCommGroup A\ninst✝² : Module ℂ A\ninst✝¹ : StarAddMonoid A\ninst✝ : StarModule ℂ A\nz : ℂ\na : A\n⊢ ↑ℜ ((↑z.re + ↑z.im * I) • a) = z.re • ↑ℜ a - z.im • ↑ℑ a",
"state_before": "A : Type u_1\ninst✝³ : AddCommGroup A\ninst✝² : Module ℂ A\ninst✝¹ : StarAddMonoid A\nin... | [
500,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.restrict_ofFunction | [
{
"state_after": "α : Type ?u.156969\nm : Set α → ℝ≥0∞\nm_empty : m ∅ = 0\ns : Set α\nhm : Monotone m\n⊢ m ∅ = 0",
"state_before": "α : Type ?u.156969\nm : Set α → ℝ≥0∞\nm_empty : m ∅ = 0\ns : Set α\nhm : Monotone m\n⊢ (fun t => m (t ∩ s)) ∅ = 0",
"tactic": "simp"
},
{
"state_after": "no goals",... | [
818,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
812,
1
] |
Mathlib/Data/Multiset/Nodup.lean | Multiset.Nodup.add_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.5533\nγ : Type ?u.5536\nr : α → α → Prop\ns t : Multiset α\na : α\nd₁ : Nodup s\nd₂ : Nodup t\n⊢ Nodup (s + t) ↔ Disjoint s t",
"tactic": "simp [nodup_add, d₁, d₂]"
}
] | [
127,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.refl_trans | [] | [
403,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | padicNormE.defn | [
{
"state_after": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nf : PadicSeq p\nε : ℚ\nhε : 0 < ε\n⊢ ∃ N,\n ∀ (i : ℕ),\n i ≥ N →\n Quotient.lift PadicSeq.norm (_ : ∀ {f g : PadicSeq p}, f ≈ g → PadicSeq.norm f = PadicSeq.norm g)\n (Padic.mk f - ↑(↑f i)) <\n ε",
"state_before": "p : ℕ... | [
620,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
] |
Mathlib/Data/Dfinsupp/Order.lean | Dfinsupp.le_def | [] | [
55,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | Padic.complete'' | [
{
"state_after": "case intro\np : ℕ\ninst✝ : Fact (Nat.Prime p)\nf : CauSeq ℚ_[p] ↑padicNormE\nx : ℚ_[p]\nhx : ∀ (ε : ℚ), ε > 0 → ∃ N, ∀ (i : ℕ), i ≥ N → ↑padicNormE (x - ↑f i) < ε\n⊢ ∃ q, ∀ (ε : ℚ), ε > 0 → ∃ N, ∀ (i : ℕ), i ≥ N → ↑padicNormE (↑f i - q) < ε",
"state_before": "p : ℕ\ninst✝ : Fact (Nat.Prime... | [
757,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
751,
1
] |
Mathlib/Topology/Filter.lean | Filter.nhds_iInf | [
{
"state_after": "ι : Sort u_2\nα : Type u_1\nβ : Type ?u.9675\nX : Type ?u.9678\nY : Type ?u.9681\nf : ι → Filter α\n⊢ Filter.lift' (⨅ (i : ι), f i) (Iic ∘ 𝓟) = ⨅ (i : ι), Filter.lift' (f i) (Iic ∘ 𝓟)",
"state_before": "ι : Sort u_2\nα : Type u_1\nβ : Type ?u.9675\nX : Type ?u.9678\nY : Type ?u.9681\nf :... | [
138,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Topology/Constructions.lean | continuous_toDual | [] | [
160,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Probability/Independence/ZeroOne.lean | ProbabilityTheory.indep_limsup_self | [] | [
115,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Topology/Algebra/ContinuousMonoidHom.lean | PontryaginDual.map_apply | [] | [
456,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/Data/Finset/Basic.lean | List.mem_toFinset | [] | [
3252,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3251,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.pred_top_lt_iff | [] | [
891,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
890,
1
] |
Mathlib/Algebra/Hom/Ring.lean | RingHom.coe_one | [] | [
739,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
738,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/InverseDeriv.lean | Real.differentiableWithinAt_arccos_Ici | [] | [
166,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Algebra/Lie/Character.lean | LieAlgebra.lieCharacter_apply_lie' | [
{
"state_after": "no goals",
"state_before": "R : Type u\nL : Type v\ninst✝² : CommRing R\ninst✝¹ : LieRing L\ninst✝ : LieAlgebra R L\nχ : LieCharacter R L\nx y : L\n⊢ ⁅↑χ x, ↑χ y⁆ = 0",
"tactic": "rw [LieRing.of_associative_ring_bracket, mul_comm, sub_self]"
}
] | [
53,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/MeasureTheory/Function/Jacobian.lean | MeasureTheory.addHaar_image_le_lintegral_abs_det_fderiv_aux1 | [
{
"state_after": "E : Type u_1\nF : Type ?u.755569\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : FiniteDimensional ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ns : Set E\nf : E → E\nf' : E → E →L[ℝ] E\ninst✝² : MeasurableSpace E\ninst✝¹ : BorelSpace E\nμ : Measure E\ninst✝ ... | [
885,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
805,
1
] |
Mathlib/Data/Nat/Sqrt.lean | Nat.sqrt_lt | [] | [
96,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Order/Disjoint.lean | IsCompl.inf_left_le_of_le_sup_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : DistribLattice α\ninst✝ : BoundedOrder α\na b x y z : α\nh : IsCompl x y\nhle : a ≤ b ⊔ y\n⊢ b ⊓ x ⊔ y ⊓ x = b ⊓ x",
"tactic": "rw [h.symm.inf_eq_bot, sup_bot_eq]"
}
] | [
514,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.Tendsto.atTop_mul_const | [] | [
1045,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1043,
1
] |
Mathlib/Logic/Basic.lean | Decidable.not_forall | [] | [
683,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
11
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.inv_insert | [] | [
259,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.nullMeasurableSet_empty | [] | [
112,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Data/Finmap.lean | Finmap.Disjoint.symm | [] | [
660,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
] |
Mathlib/Algebra/Group/Basic.lean | div_mul_eq_div_div | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.39118\nG : Type ?u.39121\ninst✝ : DivisionCommMonoid α\na b c d : α\n⊢ a / (b * c) = a / b / c",
"tactic": "simp"
}
] | [
560,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
560,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.min_insert | [] | [
1253,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1252,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | hasFDerivWithinAt_congr_set' | [
{
"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.440170\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.440265\... | [
787,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
778,
1
] |
Mathlib/Order/WithBot.lean | WithBot.ofDual_symm_apply | [] | [
929,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
928,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/WideEqualizers.lean | CategoryTheory.Limits.wideEqualizer.trident_π_app_zero | [] | [
597,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
1
] |
Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.ofMkLEMk_comp_ofMkLE | [
{
"state_after": "C : Type u₁\ninst✝³ : Category C\nX✝ Y Z : C\nD : Type u₂\ninst✝² : Category D\nB A₁ A₂ : C\nf : A₁ ⟶ B\ninst✝¹ : Mono f\ng : A₂ ⟶ B\ninst✝ : Mono g\nX : Subobject B\nh₁ : mk f ≤ mk g\nh₂ : mk g ≤ X\n⊢ (underlyingIso f).inv ≫ underlying.map (LE.le.hom h₁ ≫ LE.le.hom h₂) =\n (underlyingIso f... | [
440,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/MeasureTheory/Group/Action.lean | MeasureTheory.measure_smul_null | [
{
"state_after": "no goals",
"state_before": "G : Type u_2\nM : Type ?u.42834\nα : Type u_1\ns✝ : Set α\nm : MeasurableSpace α\ninst✝⁴ : Group G\ninst✝³ : MulAction G α\ninst✝² : MeasurableSpace G\ninst✝¹ : MeasurableSMul G α\nc✝ : G\nμ : Measure α\ninst✝ : SMulInvariantMeasure G α μ\ns : Set α\nh : ↑↑μ s =... | [
200,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Algebra/Category/Ring/Basic.lean | CommRingCat.ringHom_comp_eq_comp | [] | [
541,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
] |
Mathlib/Topology/Inseparable.lean | SeparationQuotient.surjective_mk | [] | [
434,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_lt_of_lt_one_of_le_of_pos | [] | [
826,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
824,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.union_eq_left_iff_subset | [] | [
1466,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1465,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.mapRange.addMonoidHom_id | [] | [
2169,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2167,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.conjTranspose_ratCast_smul | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.1027257\nm : Type u_2\nn : Type u_3\no : Type ?u.1027266\nm' : o → Type ?u.1027271\nn' : o → Type ?u.1027276\nR : Type u_1\nS : Type ?u.1027282\nα : Type v\nβ : Type w\nγ : Type ?u.1027289\ninst✝³ : DivisionRing R\ninst✝² : AddCommGroup α\ninst✝¹ : S... | [
2230,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2228,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiffOn_succ_iff_fderiv_of_open | [
{
"state_after": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\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\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nX : Type uX\ninst✝¹ : NormedAdd... | [
1154,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1150,
1
] |
Mathlib/Data/Multiset/Sum.lean | Multiset.disjSum_strictMono_left | [] | [
99,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.subset_biUnion_of_mem | [] | [
867,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
864,
1
] |
Mathlib/Algebra/Algebra/Basic.lean | LinearMap.ker_restrictScalars | [] | [
953,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
951,
1
] |
Std/Data/List/Lemmas.lean | List.getLast_singleton | [] | [
470,
62
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
470,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | fderivWithin_mul_const' | [] | [
444,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
] |
Mathlib/Order/SupIndep.lean | CompleteLattice.independent_iff_supIndep_univ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.67094\nι : Type u_2\nι' : Type ?u.67100\ninst✝¹ : CompleteLattice α\ninst✝ : Fintype ι\nf : ι → α\n⊢ Independent f ↔ Finset.SupIndep Finset.univ f",
"tactic": "classical\n simp [Finset.supIndep_iff_disjoint_erase, CompleteLattice.I... | [
383,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/Data/Polynomial/Module.lean | PolynomialModule.map_single | [] | [
251,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Algebra/Lie/Nilpotent.lean | LieAlgebra.non_trivial_center_of_isNilpotent | [] | [
600,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
1
] |
Mathlib/Deprecated/Submonoid.lean | powers.isSubmonoid | [] | [
165,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Order/SuccPred/Basic.lean | WithTop.succ_coe_of_ne_top | [] | [
1063,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1062,
1
] |
Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.X.coe_nat | [
{
"state_after": "no goals",
"state_before": "q : ℕ+\nn : ℕ\n⊢ ↑↑n = ↑n",
"tactic": "ext <;> simp"
}
] | [
339,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | NNReal.continuousAt_rpow | [
{
"state_after": "x : ℝ≥0\ny : ℝ\nh : x ≠ 0 ∨ 0 < y\nthis : (fun p => p.fst ^ p.snd) = toNNReal ∘ (fun p => p.fst ^ p.snd) ∘ fun p => (↑p.fst, p.snd)\n⊢ ContinuousAt (fun p => p.fst ^ p.snd) (x, y)",
"state_before": "x : ℝ≥0\ny : ℝ\nh : x ≠ 0 ∨ 0 < y\n⊢ ContinuousAt (fun p => p.fst ^ p.snd) (x, y)",
"ta... | [
450,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioi_diff_Ioi | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.61599\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\n⊢ Ioi a \\ Ioi b = Ioc a b",
"tactic": "rw [diff_eq, compl_Ioi, Ioi_inter_Iic]"
}
] | [
1088,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1088,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.