file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/LinearAlgebra/AffineSpace/Midpoint.lean | midpoint_neg_self | [
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Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.lintegral_rpow_sum_coe_nnnorm_sub_le_rpow_tsum | [
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_even_add_odd | [] | [
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Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.le_rpow_add | [
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Mathlib/Order/RelClasses.lean | Set.not_unbounded_iff | [
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543,
37
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542,
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Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.of_mul_of | [
{
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Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | UniformOnFun.hasBasis_uniformity | [] | [
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.coe_smul | [] | [
594,
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593,
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Mathlib/Topology/Basic.lean | continuous_iff_continuousAt | [] | [
1678,
28
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Mathlib/Data/Multiset/Basic.lean | Multiset.Subset.refl | [] | [
393,
61
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Mathlib/GroupTheory/Complement.lean | Subgroup.smul_toEquiv | [] | [
473,
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Std/Data/Int/DivMod.lean | Int.dvd_of_mod_eq_zero | [] | [
673,
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Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.congr_symm_apply | [] | [
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909,
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.PushoutCocone.inl_colimit_cocone | [] | [
1161,
97
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Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.sqrtd_im | [] | [
108,
6
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Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.max | [] | [
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74
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Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.type_pUnit | [] | [
263,
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Mathlib/Analysis/Fourier/FourierTransform.lean | Real.continuous_fourierChar | [] | [
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77
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Mathlib/Data/Fin/Tuple/Basic.lean | Fin.snoc_cast_add | [] | [
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Mathlib/Logic/Basic.lean | xor_false | [
{
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{
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287,
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Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.Multicofork.toSigmaCofork_π | [] | [
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Mathlib/Logic/Function/Basic.lean | Function.eval_apply | [] | [
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Mathlib/Algebra/GroupPower/Lemmas.lean | abs_nsmul | [
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Mathlib/Data/Complex/Exponential.lean | Complex.sin_two_mul | [
{
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.const_mul_right' | [] | [
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42
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Mathlib/Algebra/Associated.lean | Associates.irreducible_mk | [
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Mathlib/Computability/Ackermann.lean | one_lt_ack_succ_right | [
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135,
32
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129,
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Mathlib/Data/Matrix/Basis.lean | Matrix.StdBasisMatrix.mul_of_ne | [
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Mathlib/Data/Rat/Order.lean | Rat.lt_one_iff_num_lt_denom | [
{
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Mathlib/Data/List/Sigma.lean | List.lookupAll_cons_eq | [] | [
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Mathlib/Data/Set/Function.lean | Set.EqOn.inter_preimage_eq | [
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Mathlib/Data/Multiset/Sort.lean | Multiset.sort_singleton | [] | [
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Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | aemeasurable_const | [] | [
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Mathlib/GroupTheory/Torsion.lean | IsTorsion.exponentExists | [] | [
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Mathlib/Topology/UnitInterval.lean | unitInterval.coe_symm_eq | [] | [
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.node | [] | [
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Mathlib/Data/Polynomial/Module.lean | PolynomialModule.map_smul | [
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Mathlib/Data/Sum/Basic.lean | Sum.swap_rightInverse | [] | [
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Mathlib/Init/Data/Sigma/Basic.lean | ex_of_psig | [] | [
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Mathlib/MeasureTheory/Function/SpecialFunctions/Basic.lean | Complex.measurable_sin | [] | [
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Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.edgeSet_mono | [] | [
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Mathlib/Analysis/Normed/Group/AddTorsor.lean | dist_vadd_right | [
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Mathlib/Algebra/GCDMonoid/Basic.lean | dvd_mul | [
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.range_map | [
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Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | EuclideanGeometry.dist_div_tan_angle_of_angle_eq_pi_div_two | [
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Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.independent_span_singleton | [
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Mathlib/CategoryTheory/Skeletal.lean | CategoryTheory.skeleton_skeletal | [
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Mathlib/Combinatorics/Quiver/Path.lean | Quiver.Path.comp_assoc | [
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}
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Mathlib/Topology/LocallyConstant/Basic.lean | IsLocallyConstant.eq_const | [] | [
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55
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Mathlib/Data/Matrix/Block.lean | Matrix.blockDiagonal_transpose | [
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388,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/Data/Fintype/Lattice.lean | Finite.exists_min | [
{
"state_after": "case intro\nα : Type u_1\nβ : Type u_2\ninst✝² : Finite α\ninst✝¹ : Nonempty α\ninst✝ : LinearOrder β\nf : α → β\nval✝ : Fintype α\n⊢ ∃ x₀, ∀ (x : α), f x₀ ≤ f x",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝² : Finite α\ninst✝¹ : Nonempty α\ninst✝ : LinearOrder β\nf : α → β\n⊢ ∃ x₀,... | [
71,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Analysis/LocallyConvex/BalancedCoreHull.lean | balancedCore_mem_nhds_zero | [
{
"state_after": "case intro.intro.intro.intro\n𝕜 : Type u_2\nE : Type u_1\nι : Type ?u.92160\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : AddCommGroup E\ninst✝² : Module 𝕜 E\ninst✝¹ : TopologicalSpace E\ninst✝ : ContinuousSMul 𝕜 E\nU : Set E\nhU : U ∈ 𝓝 0\nr : ℝ\nV : Set E\nhr : 0 < r\nhV : V ∈ 𝓝 0\nhrV... | [
262,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/RingTheory/Derivation/Basic.lean | Derivation.coe_sub_linearMap | [] | [
451,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Topology/Constructions.lean | continuous_isRight | [] | [
880,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
879,
1
] |
Mathlib/Analysis/Normed/Order/Lattice.lean | norm_sup_le_add | [
{
"state_after": "α : Type u_1\ninst✝ : NormedLatticeAddCommGroup α\nx y : α\nh : ‖x ⊔ y - 0 ⊔ 0‖ ≤ ‖x - 0‖ + ‖y - 0‖\n⊢ ‖x ⊔ y‖ ≤ ‖x‖ + ‖y‖",
"state_before": "α : Type u_1\ninst✝ : NormedLatticeAddCommGroup α\nx y : α\n⊢ ‖x ⊔ y‖ ≤ ‖x‖ + ‖y‖",
"tactic": "have h : ‖x ⊔ y - 0 ⊔ 0‖ ≤ ‖x - 0‖ + ‖y - 0‖ := n... | [
156,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | orderOf_one | [
{
"state_after": "no goals",
"state_before": "G : Type u\nA : Type v\nx y : G\na b : A\nn m : ℕ\ninst✝¹ : Monoid G\ninst✝ : AddMonoid A\n⊢ orderOf 1 = 1",
"tactic": "rw [orderOf, ← minimalPeriod_id (x := (1:G)), ← one_mul_eq_id]"
}
] | [
221,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Order/Ideal.lean | Order.Ideal.principal_bot | [] | [
323,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Structure.funMap_apply₁ | [] | [
430,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.ofReal_pow | [] | [
253,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.mem_rootSet_of_ne | [] | [
950,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
948,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.dvd_iff_div_factorization_eq_tsub | [
{
"state_after": "d n : ℕ\nhd : d ≠ 0\nhdn : d ≤ n\n⊢ factorization (n / d) = factorization n - factorization d → d ∣ n",
"state_before": "d n : ℕ\nhd : d ≠ 0\nhdn : d ≤ n\n⊢ d ∣ n ↔ factorization (n / d) = factorization n - factorization d",
"tactic": "refine' ⟨factorization_div, _⟩"
},
{
"stat... | [
591,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
581,
1
] |
Std/Logic.lean | Exists.imp' | [] | [
365,
29
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
363,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.map_apply | [] | [
309,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Std/Data/BinomialHeap.lean | Std.BinomialHeapImp.Heap.realSize_tail? | [
{
"state_after": "α : Type u_1\nle : α → α → Bool\ns' s : Heap α\n⊢ Option.map (fun x => x.snd) (deleteMin le s) = some s' → realSize s = realSize s' + 1",
"state_before": "α : Type u_1\nle : α → α → Bool\ns' s : Heap α\n⊢ tail? le s = some s' → realSize s = realSize s' + 1",
"tactic": "simp only [Heap.... | [
252,
54
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
248,
1
] |
Mathlib/Algebra/Order/Pi.lean | Function.const_le_one | [] | [
151,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.union_add_inter | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.190902\nγ : Type ?u.190905\ninst✝ : DecidableEq α\ns✝ t✝ u : Multiset α\na b : α\ns t : Multiset α\n⊢ s ∪ t + s ∩ t ≤ s + t\n\ncase a\nα : Type u_1\nβ : Type ?u.190902\nγ : Type ?u.190905\ninst✝ : DecidableEq α\ns✝ t✝ u : Multiset α\na b : α\ns t : Multiset α\... | [
1892,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1883,
1
] |
Mathlib/Data/Nat/Dist.lean | Nat.dist_pos_of_ne | [
{
"state_after": "i j : ℕ\nhne : i ≠ j\nh : i < j\n⊢ 0 < j - i",
"state_before": "i j : ℕ\nhne : i ≠ j\nh : i < j\n⊢ 0 < dist i j",
"tactic": "rw [dist_eq_sub_of_le (le_of_lt h)]"
},
{
"state_after": "no goals",
"state_before": "i j : ℕ\nhne : i ≠ j\nh : i < j\n⊢ 0 < j - i",
"tactic": "a... | [
124,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Algebra/GeomSum.lean | geom_sum_Ico_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Ring α\nx : α\nm n : ℕ\nhmn : m ≤ n\n⊢ (∑ i in Ico m n, x ^ i) * (x - 1) = x ^ n - x ^ m",
"tactic": "rw [sum_Ico_eq_sub _ hmn, sub_mul, geom_sum_mul, geom_sum_mul, sub_sub_sub_cancel_right]"
}
] | [
335,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | SubmonoidClass.coe_multiset_prod | [] | [
59,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atTop_diagonal | [
{
"state_after": "ι : Type ?u.282150\nι' : Type ?u.282153\nα : Type u_1\nβ : Type ?u.282159\nγ : Type ?u.282162\ninst✝ : SemilatticeSup α\n⊢ Tendsto (fun a => (a, a)) atTop (atTop ×ˢ atTop)",
"state_before": "ι : Type ?u.282150\nι' : Type ?u.282153\nα : Type u_1\nβ : Type ?u.282159\nγ : Type ?u.282162\ninst... | [
1437,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1435,
1
] |
Mathlib/Order/Bounded.lean | Set.bounded_gt_Ico | [] | [
254,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Std/Data/Array/Lemmas.lean | Array.size_ofFn_go | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nn : Nat\nf : Fin n → α\ni : Nat\nacc : Array α\n⊢ size (ofFn.go f i acc) = size acc + (n - i)",
"tactic": "if hin : i < n then\n unfold ofFn.go\n have : 1 + (n - (i + 1)) = n - i :=\n Nat.sub_sub .. ▸ Nat.add_sub_cancel' (Nat.le_sub_of_add... | [
278,
26
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
267,
9
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.one_apply | [] | [
536,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/Data/Polynomial/Laurent.lean | LaurentPolynomial.commute_T | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\nn : ℤ\nf : R[T;T⁻¹]\nm : ℤ\na : R\n⊢ AddMonoidAlgebra.single (n + (0 + m)) (1 * (a * 1)) = AddMonoidAlgebra.single (0 + m + n) (a * 1 * 1)",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nn : ℤ\nf : R[T;T⁻¹]\nm : ℤ\na : R\n⊢ T n * (↑C a * T m) = ↑C a *... | [
323,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.destruct_cons | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\na : α\ns : WSeq α\n⊢ Computation.destruct (destruct (cons a s)) = Sum.inl (some (a, s))",
"tactic": "simp [destruct, cons, Computation.rmap]"
}
] | [
634,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
633,
1
] |
src/lean/Init/Data/Nat/SOM.lean | Nat.SOM.Mon.append_denote | [
{
"state_after": "no goals",
"state_before": "ctx : Context\nm₁ m₂ : Mon\n⊢ denote ctx (m₁ ++ m₂) = denote ctx m₁ * denote ctx m₂",
"tactic": "match m₁ with\n| [] => simp! [Nat.one_mul]\n| v :: m₁ => simp! [append_denote ctx m₁ m₂, Nat.mul_assoc]"
},
{
"state_after": "no goals",
"state_befor... | [
107,
62
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
104,
1
] |
Mathlib/Data/Polynomial/Div.lean | Polynomial.modByMonic_X_sub_C_eq_C_eval | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na✝ b : R\nn : ℕ\ninst✝ : CommRing R\np✝ q p : R[X]\na : R\n✝ : Nontrivial R\n⊢ p %ₘ (X - ↑C a) = ↑C (eval a p)",
"state_before": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na✝ b : R\nn : ℕ\ninst✝ : CommRing R\np✝ q p : R[X]\na : R\n⊢ p %... | [
437,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | HasDerivAt.hasDerivWithinAt | [] | [
381,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingHom.comp_id | [] | [
324,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/Data/List/Perm.lean | List.perm_nil | [] | [
169,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.copy_eq | [] | [
142,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/MeasureTheory/Lattice.lean | AEMeasurable.const_inf | [] | [
188,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Algebra/BigOperators/Option.lean | Finset.prod_insertNone | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nM : Type u_2\ninst✝ : CommMonoid M\nf : Option α → M\ns : Finset α\n⊢ ∏ x in ↑insertNone s, f x = f none * ∏ x in s, f (some x)",
"tactic": "simp [insertNone]"
}
] | [
31,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.congr_arg | [] | [
134,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/CategoryTheory/Functor/Basic.lean | CategoryTheory.Functor.map_dite | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝³ : Category C\nD : Type u₂\ninst✝² : Category D\nE : Type u₃\ninst✝¹ : Category E\nF : C ⥤ D\nX Y : C\nP : Prop\ninst✝ : Decidable P\nf : P → (X ⟶ Y)\ng : ¬P → (X ⟶ Y)\n⊢ F.map (if h : P then f h else g h) = if h : P then F.map (f h) else F.ma... | [
143,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.not_isRoot_C | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na✝ b : R\nm n : ℕ\ninst✝ : Semiring R\np q r✝ : R[X]\nx r a : R\nhr : r ≠ 0\n⊢ ¬IsRoot (↑C r) a",
"tactic": "simpa using hr"
}
] | [
516,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
1
] |
Mathlib/Topology/Hom/Open.lean | ContinuousOpenMap.coe_comp | [] | [
133,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.isomorphisms.infer_property | [] | [
416,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.div_eq_one | [] | [
292,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
11
] |
Mathlib/Analysis/NormedSpace/Dual.lean | NormedSpace.inclusionInDoubleDual_norm_le | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : SeminormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type ?u.27970\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\n⊢ ‖ContinuousLinearMap.id 𝕜 (Dual 𝕜 E)‖ ≤ 1",
"state_before": "𝕜 : Type u_1\ninst✝⁴... | [
107,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Order/Directed.lean | ScottContinuous.monotone | [
{
"state_after": "α : Type u\nβ : Type v\nι : Sort w\nr r' s : α → α → Prop\ninst✝¹ : Preorder α\na✝ : α\ninst✝ : Preorder β\nf : α → β\nh : ScottContinuous f\na b : α\nhab : a ≤ b\n⊢ f a ≤ f b",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nr r' s : α → α → Prop\ninst✝¹ : Preorder α\na : α\ninst✝ : ... | [
367,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
11
] |
Std/Data/List/Lemmas.lean | List.eraseP_cons_of_neg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na : α\nl : List α\np : α → Bool\nh : ¬p a = true\n⊢ eraseP p (a :: l) = a :: eraseP p l",
"tactic": "simp [eraseP_cons, h]"
}
] | [
935,
68
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
934,
9
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.dvd_ord_proj_of_dvd | [] | [
528,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | div_le_inv_mul_iff | [
{
"state_after": "α : Type u\ninst✝³ : Group α\ninst✝² : LinearOrder α\ninst✝¹ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b c : α\ninst✝ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\n⊢ a * a ≤ b * b ↔ a ≤ b",
"state_before": "α : Type u\ninst✝³ : Group α\nin... | [
1065,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1060,
1
] |
Mathlib/Data/List/Basic.lean | List.mem_enumFrom | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.432423\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nx : α\ni j : ℕ\n⊢ (i, x) ∈ enumFrom j [] → j ≤ i ∧ i < j + length [] ∧ x ∈ []",
"tactic": "simp [enumFrom]"
},
{
"state_after": "ι : Type ?u.432423\nα : Type u\nβ : T... | [
3862,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3846,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_neg_I | [
{
"state_after": "no goals",
"state_before": "⊢ arg (-I) = -(π / 2)",
"tactic": "simp [arg, le_refl]"
}
] | [
210,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Data/Polynomial/Degree/CardPowDegree.lean | Polynomial.cardPowDegree_isEuclidean | [
{
"state_after": "Fq : Type u_1\ninst✝¹ : Field Fq\ninst✝ : Fintype Fq\ncard_pos : 0 < Fintype.card Fq\npow_pos : ∀ (n : ℕ), 0 < ↑(Fintype.card Fq) ^ n\np q : Fq[X]\n⊢ ↑cardPowDegree p < ↑cardPowDegree q ↔ degree p < degree q",
"state_before": "Fq : Type u_1\ninst✝¹ : Field Fq\ninst✝ : Fintype Fq\ncard_pos ... | [
109,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Init/Logic.lean | if_t_t | [] | [
354,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/MeasureTheory/Covering/Differentiation.lean | VitaliFamily.ae_tendsto_average_norm_sub | [
{
"state_after": "case h\nα : Type u_2\ninst✝⁵ : MetricSpace α\nm0 : MeasurableSpace α\nμ : MeasureTheory.Measure α\nv : VitaliFamily μ\nE : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : SecondCountableTopology α\ninst✝² : BorelSpace α\ninst✝¹ : IsLocallyFiniteMeasure μ\nρ : MeasureTheory.Measure α\ninst✝ :... | [
914,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
897,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.add_sub_assoc | [
{
"state_after": "case intro\nm k : Nat\nh : k ≤ m\nn w✝ : Nat\nh✝ : k + w✝ = m\n⊢ n + m - k = n + (m - k)",
"state_before": "m k : Nat\nh : k ≤ m\nn : Nat\n⊢ n + m - k = n + (m - k)",
"tactic": "cases Nat.le.dest h"
},
{
"state_after": "case intro\nm k : Nat\nh : k ≤ m\nn l : Nat\nhl : k + l = ... | [
605,
89
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
602,
11
] |
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