file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Order/Synonym.lean | ofLex_symm_eq | [] | [
183,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Data/Set/Finite.lean | Set.finite_isBot | [] | [
1427,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1426,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.adjoin_zero | [] | [
687,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
686,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.isCaratheodory_union | [
{
"state_after": "α : Type u\nm : OuterMeasure α\ns s₁ s₂ : Set α\nh₁ : IsCaratheodory m s₁\nh₂ : IsCaratheodory m s₂\nt : Set α\n⊢ ↑m (t ∩ s₁ ∩ s₂) + ↑m ((t ∩ s₁) \\ s₂) + (↑m (t \\ s₁ ∩ s₂) + ↑m ((t \\ s₁) \\ s₂)) =\n ↑m (t ∩ s₁ ∩ s₂) + ↑m ((t ∩ s₁) \\ s₂) + ↑m (t ∩ (s₂ \\ s₁)) + ↑m (t \\ (s₁ ∪ s₂))",
... | [
971,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
966,
1
] |
Mathlib/Data/List/Basic.lean | List.nthLe_reverse' | [
{
"state_after": "ι : Type ?u.97720\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l : List α\nn : ℕ\nhn : n < length (reverse l)\nhn' : length l - 1 - n < length l\n⊢ nthLe l (length l - 1 - n) hn' = nthLe (reverse l) n hn",
"state_before": "ι : Type ?u.97720\nα : Type u\nβ : Type v\nγ : Type w\nδ ... | [
1470,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1466,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.minFac_sq_le_self | [] | [
417,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/CategoryTheory/Monoidal/End.lean | CategoryTheory.μ_naturality | [] | [
132,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Topology/Sober.lean | IsGenericPoint.inseparable | [] | [
84,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
11
] |
Std/Data/List/Lemmas.lean | List.isPrefix.sublist | [] | [
1607,
20
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1606,
11
] |
Mathlib/GroupTheory/Subsemigroup/Center.lean | Set.inv_mem_center₀ | [
{
"state_after": "case inl\nM : Type u_1\ninst✝ : GroupWithZero M\nha : 0 ∈ center M\n⊢ 0⁻¹ ∈ center M\n\ncase inr\nM : Type u_1\ninst✝ : GroupWithZero M\na : M\nha : a ∈ center M\nha0 : a ≠ 0\n⊢ a⁻¹ ∈ center M",
"state_before": "M : Type u_1\ninst✝ : GroupWithZero M\na : M\nha : a ∈ center M\n⊢ a⁻¹ ∈ cente... | [
112,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Topology/Instances/AddCircle.lean | toIcoMod_eventuallyEq_toIocMod | [
{
"state_after": "𝕜 : Type u_1\nB : Type ?u.15815\ninst✝³ : LinearOrderedAddCommGroup 𝕜\ninst✝² : Archimedean 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\np : 𝕜\nhp : 0 < p\na x : 𝕜\nhx : ↑x ≠ ↑a\n⊢ IsOpen (⋃ (z : ℤ), Ioo (a + z • p) (a + p + z • p))",
"state_before": "𝕜 : Type u_1\nB : ... | [
103,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.comap_monotone | [
{
"state_after": "ι : Sort ?u.167405\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : Subgraph G\na b : V\nG' : SimpleGraph W\nf : G →g G'\nH H' : Subgraph G'\nh : H ≤ H'\n⊢ Subgraph.comap f H ≤ Subgraph.comap f H'",
"state_before": "ι : Sort ?u.167405\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : ... | [
703,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
694,
1
] |
Mathlib/Topology/Basic.lean | not_mem_of_not_mem_closure | [] | [
424,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/Deprecated/Subgroup.lean | Multiplicative.isSubgroup_iff | [
{
"state_after": "case mk.mk\nG : Type ?u.3681\nH : Type ?u.3684\nA : Type u_1\na a₁ a₂ b c : G\ninst✝¹ : Group G\ninst✝ : AddGroup A\ns : Set A\nh₃ : ∀ {a : Multiplicative A}, a ∈ s → a⁻¹ ∈ s\nh₁ : 1 ∈ s\nh₂ : ∀ {a b : Multiplicative A}, a ∈ s → b ∈ s → a * b ∈ s\n⊢ IsAddSubgroup s",
"state_before": "G : T... | [
82,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.PolyCnstr.eq_true_of_isValid | [
{
"state_after": "case mk\nctx : Context\neq✝ : Bool\nlhs✝ rhs✝ : Poly\n⊢ isValid { eq := eq✝, lhs := lhs✝, rhs := rhs✝ } = true → denote ctx { eq := eq✝, lhs := lhs✝, rhs := rhs✝ } = True",
"state_before": "ctx : Context\nc : PolyCnstr\n⊢ isValid c = true → denote ctx c = True",
"tactic": "cases c"
}... | [
659,
29
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
652,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.norm_sub_map_le_sub | [] | [
426,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Topology/Basic.lean | isOpen_interior | [] | [
290,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/CategoryTheory/Monoidal/Mon_.lean | Mon_.id_hom' | [] | [
127,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/GroupTheory/Perm/ViaEmbedding.lean | Equiv.Perm.viaEmbeddingHom_apply | [] | [
48,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.EventuallyLE.le_iff_eq | [] | [
1689,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1687,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | tendstoLocallyUniformlyOn_iff_forall_isCompact | [] | [
753,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
751,
1
] |
Mathlib/Topology/Support.lean | HasCompactSupport.smul_left | [
{
"state_after": "X : Type ?u.20432\nα : Type u_1\nα' : Type ?u.20438\nβ : Type ?u.20441\nγ : Type ?u.20444\nδ : Type ?u.20447\nM : Type u_2\nE : Type ?u.20453\nR : Type u_3\ninst✝³ : TopologicalSpace α\ninst✝² : MonoidWithZero R\ninst✝¹ : AddMonoid M\ninst✝ : DistribMulAction R M\nf : α → R\nf' : α → M\nx : α\... | [
259,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Analysis/Calculus/Series.lean | hasFDerivAt_tsum | [
{
"state_after": "case this\nα : Type u_1\nβ : Type ?u.43853\n𝕜 : Type u_2\nE : Type u_3\nF : Type u_4\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : CompleteSpace F\nu : α → ℝ\ninst✝ : NormedSpace 𝕜 F\nf : α → E → F\nf' : α → E → E →L[𝕜... | [
160,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Data/Num/Lemmas.lean | PosNum.le_iff_cmp | [
{
"state_after": "m n : PosNum\n⊢ Ordering.swap (cmp m n) = Ordering.lt ↔ cmp m n = Ordering.gt",
"state_before": "m n : PosNum\n⊢ cmp n m = Ordering.lt ↔ cmp m n = Ordering.gt",
"tactic": "rw [← cmp_swap]"
},
{
"state_after": "no goals",
"state_before": "m n : PosNum\n⊢ Ordering.swap (cmp m... | [
830,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
829,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | hasFDerivWithinAt_pi' | [] | [
422,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.ulower_up | [] | [
1267,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1265,
1
] |
Mathlib/Analysis/Convex/Complex.lean | convex_halfspace_re_ge | [] | [
35,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.disjoint_sdiff_inter | [] | [
2356,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2355,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioo_eq_empty_of_le | [] | [
398,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.closure_empty | [] | [
1242,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1241,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | mem_zpowers_iff_mem_range_orderOf | [
{
"state_after": "no goals",
"state_before": "G : Type u\nA : Type v\nx y : G\na b : A\nn m : ℕ\ninst✝³ : Group G\ninst✝² : AddGroup A\ninst✝¹ : Finite G\ninst✝ : DecidableEq G\n⊢ y ∈ zpowers x ↔ y ∈ Finset.image ((fun x x_1 => x ^ x_1) x) (Finset.range (orderOf x))",
"tactic": "rw [← mem_powers_iff_mem... | [
832,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
830,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.zero_lt_one | [] | [
415,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.prod.diag_map_fst_snd | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\nX✝ Y✝ X Y : C\ninst✝¹ : HasBinaryProduct X Y\ninst✝ : HasBinaryProduct (X ⨯ Y) (X ⨯ Y)\n⊢ diag (X ⨯ Y) ≫ map fst snd = 𝟙 (X ⨯ Y)",
"tactic": "simp"
}
] | [
809,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
808,
1
] |
Mathlib/Algebra/Algebra/Basic.lean | RingHom.algebraMap_toAlgebra | [] | [
276,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Data/Real/ConjugateExponents.lean | Real.IsConjugateExponent.sub_one_pos | [] | [
59,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Order/LocallyFinite.lean | Finset.subtype_Ioc_eq | [] | [
1276,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1275,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.adjoin_rootSet_isSplittingField | [] | [
543,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.tan_pi_sub | [] | [
1311,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1310,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinitesimal_neg | [] | [
706,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
705,
9
] |
Mathlib/Algebra/Order/Ring/Defs.lean | bit1_lt_bit1 | [] | [
905,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
904,
1
] |
Std/Data/List/Lemmas.lean | List.exists_of_mem_join | [] | [
186,
75
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
186,
1
] |
Mathlib/Topology/QuasiSeparated.lean | IsQuasiSeparated.of_quasiSeparatedSpace | [] | [
128,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Data/Set/Image.lean | Set.range_comp | [] | [
722,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
720,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.map_snd_darts | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V\np : Walk G u v\n⊢ List.map (fun x => x.snd) (darts p) = List.tail (support p)",
"tactic": "simpa using congr_arg List.tail (cons_map_snd_darts p)"
... | [
727,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
726,
1
] |
Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean | Matrix.SpecialLinearGroup.SL2_inv_expl_det | [
{
"state_after": "n : Type u\ninst✝³ : DecidableEq n\ninst✝² : Fintype n\nR : Type v\ninst✝¹ : CommRing R\nS : Type ?u.737904\ninst✝ : CommRing S\nA : SL(2, R)\n⊢ vecCons ![↑A 1 1, -↑A 0 1] ![![-↑A 1 0, ↑A 0 0]] 1 1 * vecCons ![↑A 1 1, -↑A 0 1] ![![-↑A 1 0, ↑A 0 0]] 0 0 -\n vecCons ![↑A 1 1, -↑A 0 1] ![![-... | [
294,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.bot_add | [] | [
644,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
643,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderIso.isCompl_iff | [] | [
1373,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1372,
1
] |
Mathlib/Analysis/SpecificLimits/Normed.lean | Real.summable_pow_div_factorial | [
{
"state_after": "α : Type ?u.2025885\nβ : Type ?u.2025888\nι : Type ?u.2025891\nx : ℝ\nA : 0 < ↑⌊‖x‖⌋₊ + 1\n⊢ Summable fun n => x ^ n / ↑n !",
"state_before": "α : Type ?u.2025885\nβ : Type ?u.2025888\nι : Type ?u.2025891\nx : ℝ\n⊢ Summable fun n => x ^ n / ↑n !",
"tactic": "have A : (0 : ℝ) < ⌊‖x‖⌋₊ +... | [
675,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.arrowCongr_apply | [] | [
2329,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2325,
1
] |
Mathlib/Order/Compare.lean | cmp_self_eq_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.19132\ninst✝ : LinearOrder α\nx y : α\n⊢ cmp x x = eq",
"tactic": "rw [cmp_eq_eq_iff]"
}
] | [
244,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.range_toAddSubmonoid | [] | [
1207,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1205,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.subtypeDomain_zero | [] | [
1043,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1042,
1
] |
Mathlib/Topology/Bornology/Constructions.lean | Bornology.cobounded_pi | [] | [
104,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Topology/MetricSpace/CauSeqFilter.lean | isCauSeq_iff_cauchySeq | [] | [
90,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.pullback_id | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF : C ⥤ D\nX Y Z : C\nf : Y ⟶ X\nS R : Sieve X\n⊢ pullback (𝟙 X) S = S",
"tactic": "simp [Sieve.ext_iff]"
}
] | [
464,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Log.lean | Complex.log_im | [
{
"state_after": "no goals",
"state_before": "x : ℂ\n⊢ (log x).im = arg x",
"tactic": "simp [log]"
}
] | [
39,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Algebra/GroupPower/Ring.lean | Units.eq_or_eq_neg_of_sq_eq_sq | [] | [
312,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
11
] |
Mathlib/Data/Set/Intervals/Group.lean | Set.add_mem_Ioc_iff_right | [] | [
93,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Algebra/Category/Mon/FilteredColimits.lean | MonCat.FilteredColimits.colimit_one_eq | [
{
"state_after": "case h\nJ : Type v\ninst✝¹ : SmallCategory J\nF : J ⥤ MonCat\ninst✝ : IsFiltered J\nj : J\n⊢ ∃ k f g, ↑(F.map f) { fst := Nonempty.some (_ : Nonempty J), snd := 1 }.snd = ↑(F.map g) { fst := j, snd := 1 }.snd",
"state_before": "J : Type v\ninst✝¹ : SmallCategory J\nF : J ⥤ MonCat\ninst✝ : ... | [
110,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.rightMoves_mk | [] | [
152,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.BoundedFormula.IsQF.induction_on_sup_not | [] | [
589,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
581,
1
] |
Mathlib/NumberTheory/Bernoulli.lean | bernoulli'_four | [
{
"state_after": "A : Type ?u.188932\ninst✝¹ : CommRing A\ninst✝ : Algebra ℚ A\nthis : Nat.choose 4 2 = 6\n⊢ bernoulli' 4 = -1 / 30",
"state_before": "A : Type ?u.188932\ninst✝¹ : CommRing A\ninst✝ : Algebra ℚ A\n⊢ bernoulli' 4 = -1 / 30",
"tactic": "have : Nat.choose 4 2 = 6 := by decide"
},
{
... | [
135,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.map_join | [
{
"state_after": "case bisim\nα : Type u\nβ : Type v\nγ : Type w\nf : α → β\nS : WSeq (WSeq α)\n⊢ Seq.IsBisimulation fun s1 s2 => ∃ s S, s1 = append s (map f (join S)) ∧ s2 = append s (join (map (map f) S))\n\ncase r\nα : Type u\nβ : Type v\nγ : Type w\nf : α → β\nS : WSeq (WSeq α)\n⊢ ∃ s S_1, map f (join S) = ... | [
1761,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1747,
1
] |
Mathlib/Order/Zorn.lean | zorn_partialOrder | [] | [
164,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.comap_top | [] | [
855,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
854,
1
] |
Mathlib/Data/Set/Sups.lean | Set.sups_union_left | [] | [
161,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/MeasureTheory/Group/Integration.lean | MeasureTheory.integral_div_left_eq_self | [
{
"state_after": "𝕜 : Type ?u.79010\nM : Type ?u.79013\nα : Type ?u.79016\nG : Type u_1\nE : Type u_2\nF : Type ?u.79025\ninst✝⁹ : MeasurableSpace G\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : CompleteSpace E\ninst✝⁵ : NormedAddCommGroup F\nμ✝ : Measure G\nf✝ : G → E\ng : G\ninst✝⁴ : Gro... | [
194,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.Infinitesimal.neg | [
{
"state_after": "no goals",
"state_before": "x : ℝ*\nhx : Infinitesimal x\n⊢ Infinitesimal (-x)",
"tactic": "simpa only [neg_zero] using hx.neg"
}
] | [
701,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
8
] |
Mathlib/Data/Matrix/Kronecker.lean | Matrix.mul_kronecker_mul | [] | [
362,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.adjoin_span | [] | [
212,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Data/Set/NAry.lean | Set.image2_image_left | [
{
"state_after": "case h\nα : Type u_4\nα' : Type ?u.33962\nβ : Type u_3\nβ' : Type ?u.33968\nγ : Type u_2\nγ' : Type ?u.33974\nδ : Type u_1\nδ' : Type ?u.33980\nε : Type ?u.33983\nε' : Type ?u.33986\nζ : Type ?u.33989\nζ' : Type ?u.33992\nν : Type ?u.33995\nf✝ f' : α → β → γ\ng✝ g' : α → β → γ → δ\ns s' : Set ... | [
288,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | comap_norm_nhds_one | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.451724\n𝕜 : Type ?u.451727\nα : Type ?u.451730\nι : Type ?u.451733\nκ : Type ?u.451736\nE : Type u_1\nF : Type ?u.451742\nG : Type ?u.451745\ninst✝² : SeminormedGroup E\ninst✝¹ : SeminormedGroup F\ninst✝ : SeminormedGroup G\ns : Set E\na a₁ a₂ b b₁... | [
1041,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1040,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.val_le_iff | [] | [
385,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
1
] |
Mathlib/Data/List/Sort.lean | List.mergeSort_eq_insertionSort | [] | [
460,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Mathlib/Deprecated/Subgroup.lean | Group.closure_mono | [] | [
562,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
561,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.Subsingleton.atTop_eq | [
{
"state_after": "ι : Type ?u.24415\nι' : Type ?u.24418\nα✝ : Type ?u.24421\nβ : Type ?u.24424\nγ : Type ?u.24427\nα : Type u_1\ninst✝¹ : Subsingleton α\ninst✝ : Preorder α\ns : Set α\nhs : s ∈ atTop\nx : α\n⊢ x ∈ s",
"state_before": "ι : Type ?u.24415\nι' : Type ?u.24418\nα✝ : Type ?u.24421\nβ : Type ?u.24... | [
295,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/RingTheory/Finiteness.lean | Module.Finite.of_restrictScalars_finite | [
{
"state_after": "R✝ : Type ?u.395725\nA✝ : Type ?u.395728\nB : Type ?u.395731\nM✝ : Type ?u.395734\nN : Type ?u.395737\ninst✝¹¹ : Semiring R✝\ninst✝¹⁰ : AddCommMonoid M✝\ninst✝⁹ : Module R✝ M✝\ninst✝⁸ : AddCommMonoid N\ninst✝⁷ : Module R✝ N\nR : Type u_1\nA : Type u_2\nM : Type u_3\ninst✝⁶ : CommSemiring R\nin... | [
593,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
1
] |
Mathlib/Data/Quot.lean | Quotient.lift_mk | [] | [
311,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Data/PFunctor/Multivariate/W.lean | MvPFunctor.w_cases | [] | [
237,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Algebra/Module/Injective.lean | Module.injective_object_of_injective_module | [
{
"state_after": "case intro\nR : Type u\ninst✝³ : Ring R\nQ : TypeMax\ninst✝² : AddCommGroup Q\ninst✝¹ : Module R Q\ninst✝ : Injective R Q\nX✝ Y✝ : ModuleCat R\ng : X✝ ⟶ ModuleCat.mk Q\nf : X✝ ⟶ Y✝\nmn : CategoryTheory.Mono f\nh : ↑Y✝ →ₗ[R] ↑(ModuleCat.mk Q)\neq1 : ∀ (x : ↑X✝), ↑h (↑f x) = ↑g x\n⊢ ∃ h, f ≫ h =... | [
71,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/GroupTheory/Congruence.lean | Con.induction_on | [] | [
342,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
11
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.BoundedFormula.realize_relabelEquiv | [
{
"state_after": "L : Language\nL' : Language\nM : Type w\nN : Type ?u.163438\nP : Type ?u.163441\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nn l : ℕ\nφ✝ ψ : BoundedFormula L α l\nθ : BoundedFormula L α (Nat.succ l)\nv✝ : α → M\nxs✝ : Fin l → M\ng : α ≃ β\nk... | [
496,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/Topology/Semicontinuous.lean | upperSemicontinuous_const | [] | [
728,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
727,
1
] |
Mathlib/Order/SymmDiff.lean | IsCompl.symmDiff_eq_top | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.56328\nα : Type u_1\nβ : Type ?u.56334\nπ : ι → Type ?u.56339\ninst✝ : CoheytingAlgebra α\na✝ a b : α\nh : IsCompl a b\n⊢ a ∆ b = ⊤",
"tactic": "rw [h.eq_hnot, hnot_symmDiff_self]"
}
] | [
359,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.closure_induction | [] | [
353,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.normSq_star | [
{
"state_after": "no goals",
"state_before": "S : Type ?u.588276\nT : Type ?u.588279\nR : Type u_1\ninst✝ : CommRing R\nr x y z : R\na b c : ℍ[R]\n⊢ ↑normSq (star a) = ↑normSq a",
"tactic": "simp [normSq_def']"
}
] | [
1211,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1211,
1
] |
Mathlib/Analysis/MeanInequalitiesPow.lean | Real.zpow_arith_mean_le_arith_mean_zpow | [] | [
96,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Algebra/Opposites.lean | MulOpposite.op_sub | [] | [
309,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Complex.deriv_sinh | [] | [
132,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Combinatorics/Additive/SalemSpencer.lean | mulSalemSpencer_insert | [
{
"state_after": "F : Type ?u.68556\nα : Type u_1\nβ : Type ?u.68562\n𝕜 : Type ?u.68565\nE : Type ?u.68568\ninst✝ : CancelCommMonoid α\ns : Set α\na : α\n⊢ (MulSalemSpencer s ∧\n (∀ ⦃b c : α⦄, b ∈ s → c ∈ s → a * b = c * c → a = b) ∧ ∀ ⦃b c : α⦄, b ∈ s → c ∈ s → b * c = a * a → b = c) →\n MulSalemSpenc... | [
164,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Data/Polynomial/Splits.lean | Polynomial.splits_of_splits_id | [
{
"state_after": "no goals",
"state_before": "F : Type u\nK : Type v\nL : Type w\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Field F\ni : K →+* L\nf x✝¹ : K[X]\nhu : IsUnit x✝¹\nx✝ : Splits (RingHom.id K) x✝¹\n⊢ 0 ≤ 1",
"tactic": "decide"
},
{
"state_after": "no goals",
"state_before": "F :... | [
418,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | PadicSeq.add_eq_max_of_ne | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nf g : PadicSeq p\nhfgne : norm f ≠ norm g\nhfg : ¬f + g ≈ 0\nhf : f ≈ 0\nthis : LimZero (f - 0)\n⊢ norm (f + g) = max (norm f) (norm g)",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nf g : PadicSeq p\nhfgne : norm f ≠ norm g\nhfg : ¬f + g ≈ 0\nhf : f ≈ 0... | [
457,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
] |
Mathlib/Data/Multiset/Fintype.lean | Multiset.coe_mem | [] | [
92,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | HomologicalComplex.Hom.next_eq | [
{
"state_after": "ι : Type u_1\nV : Type u\ninst✝¹ : Category V\ninst✝ : HasZeroMorphisms V\nc : ComplexShape ι\nC C₁ C₂ C₃ : HomologicalComplex V c\nf : Hom C₁ C₂\ni : ι\nw : ComplexShape.Rel c i (ComplexShape.next c i)\n⊢ next f i = (xNextIso C₁ w).hom ≫ HomologicalComplex.Hom.f f (ComplexShape.next c i) ≫ (x... | [
541,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.prodComm_symm | [] | [
134,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Topology/SubsetProperties.lean | OpenEmbedding.locallyCompactSpace | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.150029\nπ : ι → Type ?u.150034\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ns t : Set α\ninst✝ : LocallyCompactSpace β\nf : α → β\nhf : OpenEmbedding f\nthis : ∀ (x : α), HasBasis (𝓝 x) (fun s => (s ∈ 𝓝 (f x) ∧ IsCompact s) ∧ s ⊆ range f) fun... | [
1210,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1200,
11
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.isConj_of_support_equiv | [
{
"state_after": "ι : Type ?u.3024744\nα : Type u_1\nβ : Type ?u.3024750\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nσ τ : Perm α\nf : { x // x ∈ ↑(support σ) } ≃ { x // x ∈ ↑(support τ) }\nhf :\n ∀ (x : α) (hx : x ∈ ↑(support σ)),\n ↑(↑f { val := ↑σ x, property := (_ : ↑σ x ∈ support σ) }) = ↑τ ↑(↑f { val ... | [
1720,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1705,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.lf_of_lf_of_lt | [] | [
588,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
587,
1
] |
Mathlib/Data/Prod/Basic.lean | Prod.swap_swap_eq | [] | [
183,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Combinatorics/SimpleGraph/Clique.lean | SimpleGraph.is3Clique_triple_iff | [
{
"state_after": "α : Type u_1\nG H : SimpleGraph α\nn : ℕ\ns : Finset α\ninst✝ : DecidableEq α\na b c : α\n⊢ ((Set.Pairwise (↑{c}) G.Adj ∧ ∀ (b_1 : α), b_1 ∈ ↑{c} → b ≠ b_1 → Adj G b b_1) ∧\n ∀ (b_1 : α), b_1 ∈ insert b ↑{c} → a ≠ b_1 → Adj G a b_1) ∧\n Finset.card {a, b, c} = 3 ↔\n Adj G a b ∧ ... | [
137,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.