file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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src/lean/Init/Classical.lean | Classical.skolem | [] | [
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50
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Mathlib/Order/UpperLower/Basic.lean | UpperSet.coe_compl | [] | [
798,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
797,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.card_disjSups_le | [] | [
449,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | sq_le_one_iff | [] | [
585,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
584,
1
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Mathlib/Order/Filter/NAry.lean | Filter.map_map₂_distrib_right | [] | [
341,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_restrict_of_ae | [] | [
2834,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2833,
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Mathlib/Algebra/Parity.lean | even_two | [
{
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"tactic": "rw[one_add_one_eq_two]"
}
] | [
277,
33
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Mathlib/Data/PNat/Basic.lean | PNat.bit1_le_bit0 | [] | [
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Mathlib/Data/MvPolynomial/Division.lean | MvPolynomial.divMonomial_monomial_mul | [] | [
87,
20
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Mathlib/Algebra/Order/ToIntervalMod.lean | toIocDiv_apply_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b c : α\nn : ℤ\na : α\n⊢ a - -1 • p ∈ Set.Ioc a (a + p)",
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}
] | [
201,
54
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_diff_add_inter | [] | [
141,
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_eq_singleton_iff | [
{
"state_after": "case refine'_1\nα : Type u_1\nβ : Type ?u.31757\ninst✝ : PartialOrder α\na b c : α\nh : Icc a b = {c}\n⊢ a = c ∧ b = c\n\ncase refine'_2\nα : Type u_1\nβ : Type ?u.31757\ninst✝ : PartialOrder α\na b c : α\n⊢ a = c ∧ b = c → Icc a b = {c}",
"state_before": "α : Type u_1\nβ : Type ?u.31757\n... | [
771,
21
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Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.ext_iff | [] | [
343,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
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Mathlib/AlgebraicTopology/SimplicialObject.lean | CategoryTheory.CosimplicialObject.δ_comp_δ_self' | [
{
"state_after": "C : Type u\ninst✝ : Category C\nX : CosimplicialObject C\nn : ℕ\ni : Fin (n + 2)\n⊢ δ X i ≫ δ X (↑Fin.castSucc i) = δ X i ≫ δ X (Fin.succ i)",
"state_before": "C : Type u\ninst✝ : Category C\nX : CosimplicialObject C\nn : ℕ\ni : Fin (n + 2)\nj : Fin (n + 3)\nH : j = ↑Fin.castSucc i\n⊢ δ X ... | [
516,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
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Mathlib/Analysis/Calculus/Inverse.lean | HasStrictFDerivAt.eventually_right_inverse | [] | [
643,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
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Mathlib/SetTheory/ZFC/Basic.lean | PSet.Equiv.trans | [] | [
202,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.sameCycle_extendDomain | [
{
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"tactic": "rw [← extendDomain_zpow, exten... | [
236,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
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Mathlib/MeasureTheory/Integral/CircleTransform.lean | Complex.circleTransformDeriv_periodic | [
{
"state_after": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nz w : ℂ\nf : ℂ → E\nthis : ∀ (c : ℂ) (R : ℝ), Periodic (circleMap c R) (2 * π)\n⊢ Periodic (circleTransformDeriv R z w f) (2 * π)",
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60,
14
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53,
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Mathlib/Data/Sum/Basic.lean | Sum.inl_ne_inr | [] | [
164,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
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Mathlib/Data/Vector/Basic.lean | Vector.ext | [
{
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48,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Data/PairingHeap.lean | Std.PairingHeapImp.Heap.WF.merge | [] | [
245,
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] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
239,
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Mathlib/Logic/Denumerable.lean | Denumerable.ofNat_encode | [] | [
75,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.sup | [] | [
649,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
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Mathlib/Analysis/Normed/Group/Basic.lean | norm_ofAdd | [] | [
2218,
6
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2217,
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Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.mem_coe | [] | [
79,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
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Mathlib/RingTheory/Artinian.lean | isArtinian_of_tower | [
{
"state_after": "R : Type u_1\nS : Type u_2\nM : Type u_3\ninst✝⁶ : CommRing R\ninst✝⁵ : Ring S\ninst✝⁴ : AddCommGroup M\ninst✝³ : Algebra R S\ninst✝² : Module S M\ninst✝¹ : Module R M\ninst✝ : IsScalarTower R S M\nh : WellFounded fun x x_1 => x < x_1\n⊢ WellFounded fun x x_1 => x < x_1",
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337,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
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Mathlib/Data/Seq/Computation.lean | Computation.mem_promises | [] | [
441,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
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Std/Data/AssocList.lean | Std.AssocList.findEntry?_eq | [] | [
112,
68
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
111,
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Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.affineCombination_affineCombinationSingleWeights | [
{
"state_after": "k : Type u_3\nV : Type u_4\nP : Type u_2\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\nS : AffineSpace V P\nι : Type u_1\ns : Finset ι\nι₂ : Type ?u.451416\ns₂ : Finset ι₂\ninst✝ : DecidableEq ι\np : ι → P\ni : ι\nhi : i ∈ s\n⊢ ∀ (i2 : ι), i2 ∈ s → i2 ≠ i → affineCombinationS... | [
752,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
748,
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Mathlib/Topology/Algebra/Module/FiniteDimension.lean | LinearMap.continuous_iff_isClosed_ker | [] | [
183,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
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Mathlib/Algebra/Invertible.lean | mul_invOf_self_assoc | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝¹ : Monoid α\na b : α\ninst✝ : Invertible a\n⊢ a * (⅟a * b) = b",
"tactic": "rw [← mul_assoc, mul_invOf_self, one_mul]"
}
] | [
131,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
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Mathlib/Order/Ideal.lean | Order.Ideal.IsMaximal.isCoatom' | [] | [
241,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
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Mathlib/Data/Nat/PartENat.lean | PartENat.toWithTop_top | [] | [
554,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
1
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Mathlib/Topology/LocallyConstant/Basic.lean | LocallyConstant.coe_desc | [] | [
521,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
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Mathlib/Topology/Sheaves/Stalks.lean | TopCat.Presheaf.stalkFunctor_map_injective_of_app_injective | [
{
"state_after": "case intro.intro.intro\nC : Type u\ninst✝³ : Category C\ninst✝² : HasColimits C\nX Y Z : TopCat\ninst✝¹ : ConcreteCategory C\ninst✝ : PreservesFilteredColimits (forget C)\nF G : Presheaf C X\nf : F ⟶ G\nh : ∀ (U : Opens ↑X), Function.Injective ((forget C).map (f.app U.op))\nx : ↑X\nt : (forget... | [
447,
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436,
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.restrict_nondegenerate_iff_isCompl_orthogonal | [] | [
1458,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1455,
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] |
Mathlib/Order/Lattice.lean | inf_congr_left | [] | [
544,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
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Mathlib/NumberTheory/RamificationInertia.lean | Ideal.Quotient.algebraMap_quotient_pow_ramificationIdx | [] | [
465,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
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Mathlib/Order/Filter/Basic.lean | Filter.Tendsto.of_tendsto_comp | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.312157\nι : Sort x\nf : α → β\ng : β → γ\na : Filter α\nb : Filter β\nc : Filter γ\nhfg : a ≤ comap (g ∘ f) c\nhg : comap g c ≤ b\n⊢ a ≤ comap f b",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.312157\nι : Sort x\nf : α → ... | [
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2964,
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Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.coprod.desc_comp | [
{
"state_after": "case h₁\nC : Type u\ninst✝¹ : Category C\nX✝ Y✝ V W X Y : C\ninst✝ : HasBinaryCoproduct X Y\nf : V ⟶ W\ng : X ⟶ V\nh : Y ⟶ V\n⊢ inl ≫ desc g h ≫ f = inl ≫ desc (g ≫ f) (h ≫ f)\n\ncase h₂\nC : Type u\ninst✝¹ : Category C\nX✝ Y✝ V W X Y : C\ninst✝ : HasBinaryCoproduct X Y\nf : V ⟶ W\ng : X ⟶ V\n... | [
829,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
827,
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Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.le_translationNumber_of_add_int_le | [
{
"state_after": "no goals",
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"tactic": "simp only [coe_pow, mul_comm (m : ℝ), ← Nat.cast_add_one, f.le_iterate_of_add_int_le_map h]"
}
] | [
838,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.smul_def | [] | [
678,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
677,
11
] |
Mathlib/Data/List/Join.lean | List.join_concat | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1306\nL : List (List α)\nl : List α\n⊢ join (concat L l) = join L ++ l",
"tactic": "simp"
}
] | [
45,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.L1.continuous_integral | [
{
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745,
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Mathlib/Analysis/InnerProductSpace/l2Space.lean | HilbertBasis.repr_apply_apply | [
{
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441,
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_unique | [] | [
1490,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffOn.continuousOn_fderivWithin_apply | [
{
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Mathlib/RingTheory/Polynomial/Opposites.lean | Polynomial.opRingEquiv_symm_C | [] | [
78,
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Mathlib/MeasureTheory/Function/UniformIntegrable.lean | MeasureTheory.UniformIntegrable.spec' | [
{
"state_after": "case intro.intro.intro\nα : Type u_1\nβ : Type u_2\nι : Type u_3\nm : MeasurableSpace α\nμ : Measure α\ninst✝ : NormedAddCommGroup β\np : ℝ≥0∞\nf : ι → α → β\nhp : p ≠ 0\nhp' : p ≠ ⊤\nhf : ∀ (i : ι), StronglyMeasurable (f i)\nε : ℝ\nhε : 0 < ε\nhfu : UnifIntegrable f p μ\nM : ℝ≥0\nhM : ∀ (i : ... | [
892,
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859,
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Mathlib/Analysis/NormedSpace/ContinuousLinearMap.lean | ContinuousLinearMap.antilipschitz_of_bound | [] | [
140,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
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Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.head_terminates_of_head_tail_terminates | [
{
"state_after": "case mk.intro\nα : Type u\nβ : Type v\nγ : Type w\ns : WSeq α\nT : Terminates (head (tail s))\na : Option (α × WSeq α)\nh : a ∈ destruct (tail s)\n⊢ Terminates (destruct s)",
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Mathlib/RingTheory/Artinian.lean | isArtinian_of_quotient_of_artinian | [] | [
330,
84
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328,
1
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Mathlib/Data/Fin/Basic.lean | Fin.exists_succ_eq_iff | [
{
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"tactic": "convert @exists_succAbove_eq_iff n 0 x"
}
] | [
2181,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2180,
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Mathlib/Topology/Algebra/UniformGroup.lean | DenseInducing.extend_Z_bilin_key | [
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Mathlib/Analysis/Convex/Strict.lean | Set.OrdConnected.strictConvex | [
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Mathlib/Data/Finite/Card.lean | Finite.card_eq_zero_of_injective | [] | [
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.mul_const | [] | [
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.sum_comapDomain | [
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Mathlib/Data/TwoPointing.lean | TwoPointing.pi_fst | [] | [
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Mathlib/CategoryTheory/GlueData.lean | CategoryTheory.GlueData.t'_iji | [
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Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.coe_addMonoidHom_trans | [] | [
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Mathlib/Data/Finset/Basic.lean | Multiset.toFinset_subset | [
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Mathlib/Combinatorics/Colex.lean | Colex.hom_fin_le_iff | [
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Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.iSup_induction | [
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Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.comp_id | [] | [
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Mathlib/Data/Multiset/FinsetOps.lean | Multiset.ndunion_le | [
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Mathlib/Algebra/Regular/Basic.lean | Units.isRegular | [] | [
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Mathlib/Algebra/Module/LinearMap.lean | LinearMap.coe_copy | [] | [
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Mathlib/CategoryTheory/Monoidal/Opposite.lean | CategoryTheory.MonoidalOpposite.op_inj_iff | [] | [
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Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.map_update_sum | [] | [
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.cos_sub_pi | [] | [
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Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.pow_apply_eq_self_of_apply_eq_self | [
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Mathlib/LinearAlgebra/Basic.lean | Submodule.map_to_add_submonoid' | [] | [
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Mathlib/LinearAlgebra/AffineSpace/Slope.lean | slope_sub_smul | [
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Mathlib/Data/Seq/Seq.lean | Stream'.Seq1.map_join' | [
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Mathlib/Data/Set/Function.lean | Set.LeftInvOn.mapsTo | [
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Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.toOpen_res | [] | [
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Mathlib/Order/RelClasses.lean | comm_of | [] | [
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Mathlib/Topology/UniformSpace/Matrix.lean | Matrix.uniformity | [
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Mathlib/Topology/FiberBundle/Basic.lean | FiberBundleCore.continuous_totalSpaceMk | [] | [
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Mathlib/Data/Vector/Basic.lean | Vector.get_cons_succ | [
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Mathlib/Data/Polynomial/Taylor.lean | Polynomial.taylor_coeff | [
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Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.mod_eq_zero | [
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Mathlib/Data/Nat/ModEq.lean | Nat.ModEq.add_left | [] | [
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Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.surjective | [] | [
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Std/Data/Int/Lemmas.lean | Int.le_total | [
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Mathlib/Data/Complex/Basic.lean | Complex.abs_zpow | [] | [
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Mathlib/Order/CompleteLattice.lean | iSup_ite | [] | [
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Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.HasZeroObject.zeroIsoTerminal_inv | [
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Mathlib/Data/Matrix/Basic.lean | Matrix.conjTranspose_nsmul | [
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Mathlib/Data/Nat/Count.lean | Nat.count_succ_eq_succ_count_iff | [
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Mathlib/CategoryTheory/Monoidal/Braided.lean | CategoryTheory.braiding_rightUnitor_aux₂ | [
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Mathlib/Algebra/ContinuedFractions/Computation/Translations.lean | GeneralizedContinuedFraction.IntFractPair.get?_seq1_eq_succ_get?_stream | [] | [
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Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_add_toIcoDiv_zsmul | [
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Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.SurjectiveOnWith.mono | [
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Mathlib/Topology/LocallyFinite.lean | LocallyFinite.subset | [] | [
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Mathlib/Order/Interval.lean | Interval.coe_pure | [] | [
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Mathlib/MeasureTheory/Decomposition/Jordan.lean | MeasureTheory.JordanDecomposition.zero_posPart | [] | [
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Mathlib/Data/Real/ENNReal.lean | ENNReal.toNNReal_pos_iff | [
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Mathlib/CategoryTheory/Subterminal.lean | CategoryTheory.isSubterminal_of_mono_terminal_from | [
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82,
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