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/GroupTheory/FreeGroup.lean | FreeGroup.Red.inv_of_red_of_ne | [
{
"state_after": "α : Type u\nL L₁ L₂ L₃ L₄ : List (α × Bool)\nx1 : α\nb1 : Bool\nx2 : α\nb2 : Bool\nH1 : (x1, b1) ≠ (x2, b2)\nH2 : Red ((x1, b1) :: L₁) ((x2, b2) :: L₂)\nthis : Red ((x1, b1) :: L₁) ([(x2, b2)] ++ L₂)\n⊢ Red L₁ ((x1, !b1) :: (x2, b2) :: L₂)",
"state_before": "α : Type u\nL L₁ L₂ L₃ L₄ : Lis... | [
375,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/Data/Sigma/Lex.lean | PSigma.Lex.mono_right | [] | [
189,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelIso.coe_fn_mk | [] | [
680,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
678,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.union | [] | [
154,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
11
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.singleton_mul_inter | [] | [
1894,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1893,
1
] |
Mathlib/Analysis/InnerProductSpace/GramSchmidtOrtho.lean | gramSchmidtOrthonormalBasis_inv_triangular | [
{
"state_after": "case pos\n𝕜 : Type u_2\nE : Type u_3\ninst✝⁷ : IsROrC 𝕜\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : InnerProductSpace 𝕜 E\nι : Type u_1\ninst✝⁴ : LinearOrder ι\ninst✝³ : LocallyFiniteOrderBot ι\ninst✝² : IsWellOrder ι fun x x_1 => x < x_1\ninst✝¹ : Fintype ι\ninst✝ : FiniteDimensional 𝕜 E\nh ... | [
388,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | NonarchAddGroupNorm.toNonarchAddGroupSeminorm_eq_coe | [] | [
919,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
918,
1
] |
Mathlib/Data/Real/Cardinality.lean | Cardinal.mk_Ioc_real | [] | [
290,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Algebra/Parity.lean | odd_bit1 | [] | [
320,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
9
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.filter_eq_nil | [] | [
2004,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2001,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.le_radius_of_bound_nnreal | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_3\nE : Type u_1\nF : Type u_2\nG : Type ?u.62997\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSp... | [
142,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Data/Set/Intervals/ProjIcc.lean | Set.IccExtend_range | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝ : LinearOrder α\na b : α\nh : a ≤ b\nx : α\nf : ↑(Icc a b) → β\n⊢ range (IccExtend h f) = range f",
"tactic": "simp only [IccExtend, range_comp f, range_projIcc, image_univ]"
}
] | [
110,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Order/SymmDiff.lean | symmDiff_eq_sup | [
{
"state_after": "ι : Type ?u.66051\nα : Type u_1\nβ : Type ?u.66057\nπ : ι → Type ?u.66062\ninst✝ : GeneralizedBooleanAlgebra α\na b c d : α\nh : a ∆ b = a ⊔ b\n⊢ Disjoint a b",
"state_before": "ι : Type ?u.66051\nα : Type u_1\nβ : Type ?u.66057\nπ : ι → Type ?u.66062\ninst✝ : GeneralizedBooleanAlgebra α\n... | [
444,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
] |
Mathlib/MeasureTheory/Decomposition/SignedHahn.lean | MeasureTheory.SignedMeasure.exists_compl_positive_negative | [
{
"state_after": "case intro.intro.intro\nα : Type u_1\nβ : Type ?u.111089\ninst✝³ : MeasurableSpace α\nM : Type ?u.111095\ninst✝² : AddCommMonoid M\ninst✝¹ : TopologicalSpace M\ninst✝ : OrderedAddCommMonoid M\ns✝ : SignedMeasure α\ni j : Set α\ns : SignedMeasure α\nf : ℕ → ℝ\nleft✝ : Antitone f\nhf₂ : Tendsto ... | [
411,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.map_id | [
{
"state_after": "case H.h.h\nR : Type u_3\ninst✝¹⁸ : CommSemiring R\nR' : Type ?u.944131\ninst✝¹⁷ : Monoid R'\nR'' : Type ?u.944137\ninst✝¹⁶ : Semiring R''\nM : Type u_1\nN : Type u_2\nP : Type ?u.944149\nQ : Type ?u.944152\nS : Type ?u.944155\ninst✝¹⁵ : AddCommMonoid M\ninst✝¹⁴ : AddCommMonoid N\ninst✝¹³ : Ad... | [
770,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
768,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | le_inv | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.47777\nα : Type u_1\nβ : Type ?u.47783\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nha : 0 < a\nhb : 0 < b\n⊢ a ≤ b⁻¹ ↔ b ≤ a⁻¹",
"tactic": "rw [← inv_le_inv (inv_pos.2 hb) ha, inv_inv]"
}
] | [
273,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.inv_preimage | [] | [
188,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Topology/Order/Basic.lean | lt_mem_nhds | [] | [
912,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
1
] |
Mathlib/Algebra/CharP/Basic.lean | ringChar.eq | [] | [
216,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/RingTheory/NonZeroDivisors.lean | map_mem_nonZeroDivisors | [] | [
137,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.snd_one | [] | [
443,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/Data/Setoid/Partition.lean | IndexedPartition.class_of | [] | [
471,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/Algebra/Group/Pi.lean | Function.const_eq_one | [] | [
646,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
645,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.pow_le_pow_of_le_right | [] | [
492,
29
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
482,
1
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.Quotient.mk_surjective | [
{
"state_after": "case mk\nR : Type u_2\nM : Type u_1\nr : R\nx✝ y : M\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\np p' : Submodule R M\nb✝ : M ⧸ p\nx : M\n⊢ ∃ a, mk a = Quot.mk Setoid.r x",
"state_before": "R : Type u_2\nM : Type u_1\nr : R\nx y : M\ninst✝² : Ring R\ninst✝¹ : AddCommGrou... | [
253,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Algebra/DirectSum/Basic.lean | DirectSum.support_of | [] | [
141,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Algebra/Star/Pi.lean | Pi.single_star | [] | [
64,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean | Complex.isBigO_cpow_rpow | [
{
"state_after": "α : Type u_1\nl : Filter α\nf g : α → ℂ\nhl : IsBoundedUnder (fun x x_1 => x ≤ x_1) l fun x => Abs.abs (g x).im\n⊢ (fun x => ↑abs (f x) ^ (g x).re) =ᶠ[l] fun x => ↑abs (f x) ^ (g x).re",
"state_before": "α : Type u_1\nl : Filter α\nf g : α → ℂ\nhl : IsBoundedUnder (fun x x_1 => x ≤ x_1) l ... | [
180,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Real.Ioo_eq_ball | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.200414\nι : Type ?u.200417\ninst✝ : PseudoMetricSpace α\nx y : ℝ\n⊢ Ioo x y = ball ((x + y) / 2) ((y - x) / 2)",
"tactic": "rw [Real.ball_eq_Ioo, ← sub_div, add_comm, ← sub_add, add_sub_cancel', add_self_div_two,\n ← add_... | [
1407,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1405,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.add_assoc_equiv | [] | [
1662,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1661,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.attach_map_val | [] | [
1541,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1540,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.mem_closedBall_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.189364\ninst✝ : PseudoEMetricSpace α\nx y z : α\nε ε₁ ε₂ : ℝ≥0∞\ns t : Set α\n⊢ x ∈ closedBall y ε ↔ y ∈ closedBall x ε",
"tactic": "rw [mem_closedBall', mem_closedBall]"
}
] | [
572,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
1
] |
Mathlib/LinearAlgebra/Determinant.lean | LinearMap.range_lt_top_of_det_eq_zero | [
{
"state_after": "R : Type ?u.1165630\ninst✝¹¹ : CommRing R\nM : Type u_2\ninst✝¹⁰ : AddCommGroup M\ninst✝⁹ : Module R M\nM' : Type ?u.1166221\ninst✝⁸ : AddCommGroup M'\ninst✝⁷ : Module R M'\nι : Type ?u.1166763\ninst✝⁶ : DecidableEq ι\ninst✝⁵ : Fintype ι\ne : Basis ι R M\nA : Type ?u.1167241\ninst✝⁴ : CommRing... | [
355,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/Topology/Basic.lean | tendsto_atTop_of_eventually_const | [] | [
1042,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1040,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iInter_iInter_eq_left | [] | [
739,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
737,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.disjoint_inv_left_iff | [
{
"state_after": "α : Type u_1\nf g h✝ : Perm α\nh : Disjoint f⁻¹ g\n⊢ Disjoint f g",
"state_before": "α : Type u_1\nf g h : Perm α\n⊢ Disjoint f⁻¹ g ↔ Disjoint f g",
"tactic": "refine' ⟨fun h => _, Disjoint.inv_left⟩"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\nf g h✝ : P... | [
103,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Logic/Equiv/List.lean | Encodable.sortedUniv_nodup | [] | [
218,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.QuasiMeasurePreserving.aemeasurable | [] | [
2488,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2487,
11
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.infDist_lt_iff | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.60248\nα : Type u\nβ : Type v\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\ns t u : Set α\nx y : α\nΦ : α → β\nr : ℝ\nhs : Set.Nonempty s\n⊢ infDist x s < r ↔ ∃ y, y ∈ s ∧ dist x y < r",
"tactic": "simp_rw [infDist, ← ENNReal.lt_ofR... | [
522,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_undef | [
{
"state_after": "ι : Type ?u.10878693\n𝕜 : Type ?u.10878696\nE : Type u_1\nF : Type ?u.10878702\nA : Type ?u.10878705\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na b : ℝ\nf g : ℝ → E\nμ : MeasureTheory.Measure ℝ\nh : ¬IntegrableOn f (Ι a b)\n⊢ (∫ (x : ℝ) in a..b, f x ∂μ)... | [
509,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
8
] |
Mathlib/Analysis/MeanInequalities.lean | NNReal.Lp_add_le | [
{
"state_after": "case inl\nι : Type u\ns : Finset ι\nf g : ι → ℝ≥0\nhp : 1 ≤ 1\n⊢ (∑ i in s, (f i + g i) ^ 1) ^ (1 / 1) ≤ (∑ i in s, f i ^ 1) ^ (1 / 1) + (∑ i in s, g i ^ 1) ^ (1 / 1)\n\ncase inr\nι : Type u\ns : Finset ι\nf g : ι → ℝ≥0\np : ℝ\nhp✝ : 1 ≤ p\nhp : 1 < p\n⊢ (∑ i in s, (f i + g i) ^ p) ^ (1 / p) ≤... | [
488,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Filter.lean | BoxIntegral.IntegrationParams.hasBasis_toFilteriUnion | [
{
"state_after": "ι : Type u_1\ninst✝ : Fintype ι\nI✝ J : Box ι\nc c₁ c₂ : ℝ≥0\nr r₁ r₂ : (ι → ℝ) → ↑(Set.Ioi 0)\nπ π₁ π₂ : TaggedPrepartition I✝\nl✝ l₁ l₂ l : IntegrationParams\nI : Box ι\nπ₀ : Prepartition I\nthis :\n ∀ (c : ℝ≥0),\n HasBasis (toFilterDistortioniUnion l I c π₀) (RCond l) fun r =>\n {π... | [
490,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/Order/Heyting/Basic.lean | disjoint_compl_compl_right_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.163829\nα : Type u_1\nβ : Type ?u.163835\ninst✝ : HeytingAlgebra α\na b c : α\n⊢ Disjoint a (bᶜᶜ) ↔ Disjoint a b",
"tactic": "simp_rw [← le_compl_iff_disjoint_right, compl_compl_compl]"
}
] | [
922,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
921,
1
] |
Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.ofMkLE_comp_ofLEMk | [
{
"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\nX : Subobject B\ng : A₂ ⟶ B\ninst✝ : Mono g\nh₁ : mk f ≤ X\nh₂ : X ≤ mk g\n⊢ (underlyingIso f).inv ≫ underlying.map (LE.le.hom h₁ ≫ LE.le.hom h₂) ≫ (underlyingIso g).hom =\... | [
431,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Term.realize_subst | [
{
"state_after": "case var\nL : Language\nL' : Language\nM : Type w\nN : Type ?u.7876\nP : Type ?u.7879\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\ntf : α → Term L β\nv : β → M\n_a✝ : α\n⊢ realize v (subst (var _a✝) tf) = realize (fun a => realize v (tf a)) ... | [
138,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.closure_subset_cthickening | [
{
"state_after": "ι : Sort ?u.112257\nα : Type u\nβ : Type v\ninst✝ : PseudoEMetricSpace α\nδ✝ ε : ℝ\ns t : Set α\nx : α\nδ : ℝ\nE : Set α\n⊢ cthickening (min δ 0) E ⊆ cthickening δ E",
"state_before": "ι : Sort ?u.112257\nα : Type u\nβ : Type v\ninst✝ : PseudoEMetricSpace α\nδ✝ ε : ℝ\ns t : Set α\nx : α\nδ... | [
1149,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1147,
1
] |
Mathlib/Data/Int/Cast/Lemmas.lean | AddMonoidHom.eq_int_castAddHom | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.40880\nι : Type ?u.40883\nα : Type ?u.40886\nβ : Type ?u.40889\nA : Type u_1\ninst✝ : AddGroupWithOne A\nf : ℤ →+ A\nh1 : ↑f 1 = 1\n⊢ ↑f 1 = ↑(castAddHom A) 1",
"tactic": "simp [h1]"
}
] | [
243,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Data/Int/ModEq.lean | Int.ModEq.rfl | [] | [
54,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
11
] |
Mathlib/Algebra/Order/Floor.lean | Nat.floor_le | [] | [
157,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.IsFundamentalDomain.measure_eq_tsum_of_ac | [
{
"state_after": "G : Type u_1\nH✝ : Type ?u.223644\nα : Type u_2\nβ : Type ?u.223650\nE : Type ?u.223653\ninst✝¹⁰ : Group G\ninst✝⁹ : Group H✝\ninst✝⁸ : MulAction G α\ninst✝⁷ : MeasurableSpace α\ninst✝⁶ : MulAction H✝ β\ninst✝⁵ : MeasurableSpace β\ninst✝⁴ : NormedAddCommGroup E\ns t✝ : Set α\nμ : Measure α\nin... | [
287,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.or_exists_succ | [
{
"state_after": "case intro.zero\nm n k : ℕ\np : ℕ → Prop\nhn : p zero\n⊢ p 0 ∨ ∃ n, p (n + 1)\n\ncase intro.succ\nm n✝ k : ℕ\np : ℕ → Prop\nn : ℕ\nhn : p (succ n)\n⊢ p 0 ∨ ∃ n, p (n + 1)",
"state_before": "m n k : ℕ\np : ℕ → Prop\n⊢ (∃ n, p n) → p 0 ∨ ∃ n, p (n + 1)",
"tactic": "rintro ⟨_ | n, hn⟩"
... | [
143,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.nth_succ | [] | [
82,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.distinctConstantsTheory_eq_iUnion | [
{
"state_after": "L : Language\nL' : Language\nM : Type w\nN : Type ?u.204492\nP : Type ?u.204495\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nγ : Type ?u.204523\nn : ℕ\ns : Set α\n⊢ (fun ab =>\n Formula.not (Term.equal (Constants.term (Language.con L ... | [
1151,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1136,
1
] |
Mathlib/Data/Int/Bitwise.lean | Int.bodd_subNatNat | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\n⊢ bodd (subNatNat m n) = xor (Nat.bodd m) (Nat.bodd n)",
"tactic": "apply subNatNat_elim m n fun m n i => bodd i = xor m.bodd n.bodd <;>\nintros i j <;>\nsimp only [Int.bodd, Int.bodd_coe, Nat.bodd_add] <;>\ncases Nat.bodd i <;> simp"
}
] | [
53,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/CategoryTheory/Endofunctor/Algebra.lean | CategoryTheory.Endofunctor.Algebra.id_eq_id | [] | [
106,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.Multicoequalizer.condition | [] | [
871,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
869,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.toList_injective | [] | [
41,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/Algebra/Hom/Group.lean | map_inv | [] | [
429,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.div_self | [] | [
1695,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1694,
11
] |
Mathlib/Analysis/Calculus/UniformLimitsDeriv.lean | uniformCauchySeqOn_ball_of_deriv | [
{
"state_after": "ι : Type u_3\nl : Filter ι\n𝕜 : Type u_1\ninst✝² : IsROrC 𝕜\nG : Type u_2\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : ι → 𝕜 → G\ng : 𝕜 → G\nf' : ι → 𝕜 → G\ng' : 𝕜 → G\nx : 𝕜\nr : ℝ\nhf' : UniformCauchySeqOn f' l (Metric.ball x r)\nhfg : Cauchy (map (fun n => f n x) l)\... | [
501,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | GroupTopology.toTopologicalSpace_iInf | [] | [
1971,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1969,
1
] |
Std/Data/List/Lemmas.lean | List.takeWhile_append_dropWhile | [
{
"state_after": "α : Type u_1\np : α → Bool\nx : α\nxs : List α\n⊢ ((match p x with\n | true => x :: takeWhile p xs\n | false => []) ++\n match p x with\n | true => dropWhile p xs\n | false => x :: xs) =\n x :: xs",
"state_before": "α : Type u_1\np : α → Bool\nx : α\nxs : List α... | [
1768,
100
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1765,
9
] |
Mathlib/Topology/UniformSpace/Basic.lean | comp_le_uniformity | [] | [
451,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Order/Zorn.lean | zorn_superset | [] | [
204,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Data/Set/Finite.lean | Set.finite_prod | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ns : Set α\nt : Set β\n⊢ Set.Finite (s ×ˢ t) ↔ (Set.Finite s ∨ t = ∅) ∧ (Set.Finite t ∨ s = ∅)",
"tactic": "simp only [← not_infinite, Set.infinite_prod, not_or, not_and_or, not_nonempty_iff_eq_empty]"
}
] | [
945,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
944,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_const_sub_Iio | [] | [
237,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | InnerProductGeometry.tan_angle_sub_mul_norm_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⊢ Real.tan (angle x (x - y)) * ‖x‖ = ‖y‖",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : inner x y = 0\... | [
327,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/Topology/NhdsSet.lean | nhdsSet_singleton | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.11780\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t s₁ s₂ t₁ t₂ : Set α\nx : α\ns✝ : Set α\n⊢ s✝ ∈ 𝓝ˢ {x} ↔ s✝ ∈ 𝓝 x",
"state_before": "α : Type u_1\nβ : Type ?u.11780\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t s₁ s₂ t₁... | [
103,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/FieldTheory/Fixed.lean | FixedPoints.linearIndependent_smul_of_linearIndependent | [
{
"state_after": "M : Type u\ninst✝⁴ : Monoid M\nG : Type u\ninst✝³ : Group G\nF : Type v\ninst✝² : Field F\ninst✝¹ : MulSemiringAction M F\ninst✝ : MulSemiringAction G F\nm : M\ns : Finset F\nthis : IsEmpty ↑↑∅\n⊢ (LinearIndependent { x // x ∈ subfield G F } fun i => ↑i) → LinearIndependent F fun i => ↑(toFun ... | [
172,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.toLin_apply | [] | [
521,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.restrict_biUnion | [
{
"state_after": "case refine'_1\nι : Type u_1\nI J J₁✝ J₂ : Box ι\nπ π₁ π₂ : Prepartition I\nx : ι → ℝ\nπi✝ πi₁ πi₂ πi : (J : Box ι) → Prepartition J\nhJ : J ∈ π\nJ₁ : Box ι\nh₁ : J₁ ∈ (πi J).boxes\n⊢ J₁ ∈ (restrict (biUnion π πi) J).boxes\n\ncase refine'_2\nι : Type u_1\nI J J₁ J₂ : Box ι\nπ π₁ π₂ : Prepartit... | [
540,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/Algebra/GCDMonoid/Div.lean | Finset.Nat.gcd_div_id_eq_one | [] | [
50,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisConnection.le_u_l_trans | [] | [
163,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.mul_add_mod_of_lt | [
{
"state_after": "no goals",
"state_before": "m n k a b c : ℕ\nh : c < b\n⊢ (a * b + c) % b = c",
"tactic": "rw [Nat.mul_add_mod, Nat.mod_eq_of_lt h]"
}
] | [
805,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
804,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.filter_dvd_eq_divisors | [
{
"state_after": "case a\nn : ℕ\nh : n ≠ 0\na✝ : ℕ\n⊢ a✝ ∈ filter (fun x => x ∣ n) (range (succ n)) ↔ a✝ ∈ divisors n",
"state_before": "n : ℕ\nh : n ≠ 0\n⊢ filter (fun x => x ∣ n) (range (succ n)) = divisors n",
"tactic": "ext"
},
{
"state_after": "case a\nn : ℕ\nh : n ≠ 0\na✝ : ℕ\n⊢ a✝ ∣ n → a... | [
66,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ici_diff_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.41632\ninst✝ : PartialOrder α\na b c x : α\n⊢ x ∈ Ici a \\ {a} ↔ x ∈ Ioi a",
"tactic": "simp [lt_iff_le_and_ne, eq_comm]"
}
] | [
801,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
800,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.abv_pos_of_not_limZero | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝² : LinearOrderedField α\ninst✝¹ : Ring β\nabv : β → α\ninst✝ : IsAbsoluteValue abv\nf : CauSeq β abv\nhf : ¬LimZero f\nthis : (a : Prop) → Decidable a\n⊢ ∃ K, K > 0 ∧ ∃ i, ∀ (j : ℕ), j ≥ i → K ≤ abv (↑f j)",
"state_before": "α : Type u_1\nβ : Type u_2\nins... | [
508,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.updateColumn_transpose | [
{
"state_after": "case a.h\nl : Type ?u.1226495\nm : Type u_1\nn : Type u_2\no : Type ?u.1226504\nm' : o → Type ?u.1226509\nn' : o → Type ?u.1226514\nR : Type ?u.1226517\nS : Type ?u.1226520\nα : Type v\nβ : Type w\nγ : Type ?u.1226527\nM : Matrix m n α\ni : m\nj : n\nb : n → α\nc : m → α\ninst✝ : DecidableEq m... | [
2824,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2821,
1
] |
Mathlib/Topology/ContinuousOn.lean | nhdsWithin_inter' | [
{
"state_after": "α : Type u_1\nβ : Type ?u.17802\nγ : Type ?u.17805\nδ : Type ?u.17808\ninst✝ : TopologicalSpace α\na : α\ns t : Set α\n⊢ 𝓝 a ⊓ 𝓟 (s ∩ t) = 𝓝 a ⊓ 𝓟 s ⊓ 𝓟 t",
"state_before": "α : Type u_1\nβ : Type ?u.17802\nγ : Type ?u.17805\nδ : Type ?u.17808\ninst✝ : TopologicalSpace α\na : α\ns t :... | [
268,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Order/LocallyFinite.lean | WithTop.Ioc_coe_top | [] | [
1129,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1128,
1
] |
Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.eval₂Hom_comp_C | [
{
"state_after": "case a\nσ : Type u_3\nτ : Type ?u.929356\nR : Type u_1\nS : Type u_2\nT : Type ?u.929365\ninst✝² : CommSemiring R\ninst✝¹ : CommSemiring S\ninst✝ : CommSemiring T\nf✝ : σ → MvPolynomial τ R\nf : R →+* S\ng : σ → S\nr : R\n⊢ ↑(RingHom.comp (eval₂Hom f g) C) r = ↑f r",
"state_before": "σ : T... | [
302,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.Embedding.comap_apply | [] | [
1817,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1816,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.union_inv | [] | [
212,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Algebra/Hom/GroupAction.lean | MulSemiringActionHom.map_mul | [] | [
533,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
11
] |
Mathlib/Order/Grade.lean | grade_strictMono | [] | [
118,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.coe_iSup_of_directed | [
{
"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.280898\ninst✝ : NonUnitalRingHomClass F R S✝\nι : Sort u_1\nhι : Nonempty ι\nS... | [
839,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
837,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Star.lean | HasFDerivWithinAt.star | [] | [
51,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
8
] |
Mathlib/Topology/MetricSpace/Basic.lean | Real.closedBall_eq_Icc | [
{
"state_after": "case h\nα : Type u\nβ : Type v\nX : Type ?u.199537\nι : Type ?u.199540\ninst✝ : PseudoMetricSpace α\nx r y : ℝ\n⊢ y ∈ closedBall x r ↔ y ∈ Icc (x - r) (x + r)",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.199537\nι : Type ?u.199540\ninst✝ : PseudoMetricSpace α\nx r : ℝ\n⊢ closedBa... | [
1402,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1399,
1
] |
Mathlib/RingTheory/JacobsonIdeal.lean | Ideal.jacobson_bot_polynomial_le_sInf_map_maximal | [
{
"state_after": "R : Type u\nS : Type v\ninst✝ : CommRing R\nJ : Ideal R[X]\nj : Ideal R\nhj : j ∈ {J | IsMaximal J} ∧ map C j = J\n⊢ jacobson ⊥ ≤ J",
"state_before": "R : Type u\nS : Type v\ninst✝ : CommRing R\n⊢ jacobson ⊥ ≤ sInf (map C '' {J | IsMaximal J})",
"tactic": "refine' le_sInf fun J => exis... | [
343,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | zpow_left_injective | [
{
"state_after": "case inl\nα : Type u_1\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : LinearOrderedCommGroup α\nn : ℤ\na b : α\nhn : n ≠ 0\nh : 0 < n\n⊢ Function.Injective fun x => x ^ n\n\ncase inr\nα : Type u_1\nM : Type u\nN : Type v\nG : Type w\n... | [
426,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | UniqueDiffOn.eq | [] | [
289,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/AlgebraicTopology/SimplexCategory.lean | SimplexCategory.eq_σ_comp_of_not_injective' | [
{
"state_after": "n : ℕ\nΔ' : SimplexCategory\nθ : [n + 1] ⟶ Δ'\ni : Fin (n + 1)\nhi : ↑(Hom.toOrderHom θ) (↑Fin.castSucc i) = ↑(Hom.toOrderHom θ) (Fin.succ i)\n⊢ θ = σ i ≫ δ (Fin.succ i) ≫ θ",
"state_before": "n : ℕ\nΔ' : SimplexCategory\nθ : [n + 1] ⟶ Δ'\ni : Fin (n + 1)\nhi : ↑(Hom.toOrderHom θ) (↑Fin.ca... | [
635,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
1
] |
Mathlib/GroupTheory/FreeAbelianGroupFinsupp.lean | FreeAbelianGroup.support_of | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\nx : X\n⊢ support (of x) = {x}",
"tactic": "rw [support, toFinsupp_of, Finsupp.support_single_ne_zero _ one_ne_zero]"
}
] | [
173,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_const_smul_right | [
{
"state_after": "α : Type u_2\nβ : Type ?u.553754\nE : Type u_3\nF : Type ?u.553760\nG : Type ?u.553763\nE' : Type u_4\nF' : Type ?u.553769\nG' : Type ?u.553772\nE'' : Type ?u.553775\nF'' : Type ?u.553778\nG'' : Type ?u.553781\nR : Type ?u.553784\nR' : Type ?u.553787\n𝕜 : Type u_1\n𝕜' : Type ?u.553793\ninst✝... | [
1733,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1728,
1
] |
Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.principal_opow_omega | [
{
"state_after": "a b : Ordinal\nm n : ℕ\nha : ↑m < ω\nhb : ↑n < ω\n⊢ ↑(m ^ n) < ω",
"state_before": "a b : Ordinal\nm n : ℕ\nha : ↑m < ω\nhb : ↑n < ω\n⊢ (fun x x_1 => x ^ x_1) ↑m ↑n < ω",
"tactic": "simp_rw [← nat_cast_opow]"
},
{
"state_after": "no goals",
"state_before": "a b : Ordinal\nm... | [
439,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.closure_eq | [] | [
512,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
1
] |
Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.le_mk_of_comm | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝² : Category C\nX✝ Y Z : C\nD : Type u₂\ninst✝¹ : Category D\nB A : C\nX : Subobject B\nf : A ⟶ B\ninst✝ : Mono f\ng : underlying.obj X ⟶ A\nw : g ≫ f = arrow X\n⊢ (g ≫ (underlyingIso f).inv) ≫ arrow (mk f) = arrow X",
"tactic": "simp [w]"
... | [
275,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.biUnion_nonempty | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.529716\ninst✝ : DecidableEq β\ns s₁ s₂ : Finset α\nt t₁ t₂ : α → Finset β\n⊢ (∃ x a, a ∈ s ∧ x ∈ t a) ↔ ∃ x, x ∈ s ∧ ∃ x_1, x_1 ∈ t x",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.529716\ninst✝ : DecidableEq β\ns s₁ s₂ : Finset α\nt t₁ t... | [
3664,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3661,
1
] |
Mathlib/CategoryTheory/CofilteredSystem.lean | CategoryTheory.Functor.isMittagLeffler_of_surjective | [
{
"state_after": "no goals",
"state_before": "J : Type u\ninst✝ : Category J\nF : J ⥤ Type v\ni j✝ k✝ : J\ns : Set (F.obj i)\nh : ∀ ⦃i j : J⦄ (f : i ⟶ j), Function.Surjective (F.map f)\nj k : J\ng : k ⟶ j\n⊢ range (F.map (𝟙 j)) ⊆ range (F.map g)",
"tactic": "rw [map_id, types_id, range_id, (h g).range_... | [
177,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Data/Nat/Choose/Multinomial.lean | Nat.binomial_succ_succ | [
{
"state_after": "α : Type u_1\ns : Finset α\nf : α → ℕ\na b : α\nn : ℕ\ninst✝ : DecidableEq α\nh : a ≠ b\n⊢ choose (succ (f a) + succ (f b)) (succ (f a)) =\n choose (succ (f a) + if b = a then succ (f a) else f b) (succ (f a)) + choose (f a + succ (f b)) (f a)",
"state_before": "α : Type u_1\ns : Finset... | [
136,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.