file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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|---|---|---|---|---|---|---|
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.map_bot | [] | [
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25
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Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.mkPiField_zero | [
{
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919,
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Mathlib/MeasureTheory/Covering/VitaliFamily.lean | VitaliFamily.eventually_filterAt_mem_sets | [
{
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255,
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Mathlib/Topology/Algebra/Order/ProjIcc.lean | Continuous.Icc_extend' | [] | [
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.pos_of_mem_ball | [] | [
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26
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424,
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Mathlib/Topology/Algebra/Order/IntermediateValue.lean | ContinuousOn.surjOn_uIcc | [
{
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Mathlib/Topology/UniformSpace/Separation.lean | UniformSpace.uniformity_quotient | [] | [
286,
6
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284,
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Mathlib/Data/Finset/Pointwise.lean | Finset.empty_vsub | [] | [
1473,
20
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1472,
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Mathlib/Combinatorics/Additive/Etransform.lean | Finset.mulEtransformLeft_one | [
{
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] | [
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89
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Mathlib/Analysis/InnerProductSpace/PiL2.lean | OrthonormalBasis.orthogonalProjection_eq_sum | [
{
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461,
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457,
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Mathlib/Logic/Basic.lean | Not.imp_symm | [] | [
263,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
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Mathlib/Topology/UniformSpace/Completion.lean | UniformSpace.Completion.uniformContinuous_map₂ | [] | [
713,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_eq_one_iff_of_norm_one | [
{
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Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.norm_p_pow | [] | [
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95
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316,
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Mathlib/Algebra/Order/Field/Basic.lean | le_inv_of_neg | [
{
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"tactic": "rw [← inv_le_inv_of_neg (inv_lt_zero.2 hb) ha, inv_inv]"
}
] | [
768,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Data/Int/DivMod.lean | Int.mod_def | [
{
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] | [
323,
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Mathlib/Topology/NoetherianSpace.lean | Inducing.noetherianSpace | [] | [
80,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.ord_aleph'_eq_enum_card | [
{
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"state_before": "⊢ ord ∘ aleph' = enumOrd {b | ord (card b) = b}",
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375,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Hom/NonUnitalAlg.lean | NonUnitalAlgHom.ext | [] | [
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28
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Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.centroid_univ | [
{
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853,
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Mathlib/Order/CompleteBooleanAlgebra.lean | sInf_sup_sInf | [] | [
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27
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Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.map_sub | [] | [
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16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Heyting/Basic.lean | himp_inf_distrib | [
{
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] | [
405,
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Mathlib/LinearAlgebra/Quotient.lean | Submodule.comap_liftQ | [
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Mathlib/Order/Hom/Basic.lean | lt_map_inv_iff | [
{
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Mathlib/Data/Polynomial/Monic.lean | Polynomial.not_monic_zero_iff | [] | [
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Mathlib/Data/Seq/Parallel.lean | Computation.map_parallel | [
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | LocalHomeomorph.isLittleO_congr | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Complex/Basic.lean | Complex.ofReal_bit0 | [
{
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}
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.coe_prod | [] | [
779,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/TensorProduct.lean | LinearMap.baseChange_zero | [
{
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Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.fiber_subset_ofLE | [
{
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Mathlib/Data/Set/Intervals/Pi.lean | Set.image_mulSingle_Icc_right | [] | [
256,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Idempotents/Karoubi.lean | CategoryTheory.Idempotents.Karoubi.hom_eq_zero_iff | [] | [
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14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Module/Submodule/Bilinear.lean | Submodule.map₂_span_span | [
{
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | GaloisConnection.l_ciSup_set | [
{
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Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSet.ite' | [
{
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | mem_map_indicator_ae_iff_mem_map_restrict_ae_of_zero_mem | [
{
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.sub_comp | [
{
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Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.map_injective_of_injective | [
{
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Mathlib/Analysis/Calculus/Deriv/Comp.lean | HasStrictDerivAt.comp | [
{
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Mathlib/Combinatorics/Additive/Etransform.lean | Finset.mulEtransformLeft.card | [
{
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}
] | [
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77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
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Mathlib/Algebra/Order/Ring/Lemmas.lean | neg_of_mul_pos_right | [] | [
572,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
1
] |
Mathlib/Analysis/Asymptotics/SuperpolynomialDecay.lean | Asymptotics.superpolynomialDecay_param_pow_mul_iff | [
{
"state_after": "case zero\nα : Type u_1\nβ : Type u_2\nl : Filter α\nk f g g' : α → β\ninst✝² : TopologicalSpace β\ninst✝¹ : LinearOrderedField β\ninst✝ : OrderTopology β\nhk : Tendsto k l atTop\n⊢ SuperpolynomialDecay l k (k ^ Nat.zero * f) ↔ SuperpolynomialDecay l k f\n\ncase succ\nα : Type u_1\nβ : Type u_... | [
302,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Differentiable.ccos | [] | [
336,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/Geometry/Manifold/ChartedSpace.lean | modelProd_range_prod_id | [
{
"state_after": "H✝ : Type u\nH'✝ : Type ?u.49184\nM : Type ?u.49187\nM' : Type ?u.49190\nM'' : Type ?u.49193\nH : Type u_1\nH' : Type u_2\nα : Type u_3\nf : H → α\n⊢ (range fun p => (f p.fst, p.snd)) = range fun p => (f p.fst, p.snd)",
"state_before": "H✝ : Type u\nH'✝ : Type ?u.49184\nM : Type ?u.49187\n... | [
688,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
1
] |
Mathlib/MeasureTheory/Decomposition/SignedHahn.lean | MeasureTheory.SignedMeasure.restrictNonposSeq_lt | [
{
"state_after": "α : Type u_1\nβ : Type ?u.20255\ninst✝³ : MeasurableSpace α\nM : Type ?u.20261\ninst✝² : AddCommMonoid M\ninst✝¹ : TopologicalSpace M\ninst✝ : OrderedAddCommMonoid M\ns : SignedMeasure α\ni j : Set α\nn : ℕ\nhn :\n ¬restrict s (i \\ ⋃ (k : ℕ) (_ : k ≤ n), MeasureTheory.SignedMeasure.restrictN... | [
186,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
9
] |
Mathlib/Data/Multiset/Fold.lean | Multiset.fold_bind | [
{
"state_after": "case empty\nα : Type u_2\nβ : Type ?u.10571\nop : α → α → α\nhc : IsCommutative α op\nha : IsAssociative α op\nι : Type u_1\nt : ι → Multiset α\nb : ι → α\nb₀ : α\n⊢ fold op (fold op b₀ (map b 0)) (bind 0 t) = fold op b₀ (map (fun i => fold op (b i) (t i)) 0)\n\ncase cons\nα : Type u_2\nβ : Ty... | [
91,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Algebra/ModEq.lean | AddCommGroup.ModEq.sub_left_cancel' | [] | [
255,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
11
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biproduct.ι_desc | [] | [
444,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
1
] |
Mathlib/Algebra/Order/SMul.lean | inv_smul_le_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.105112\n𝕜 : Type u_1\nR : Type ?u.105118\nM : Type u_2\nN : Type ?u.105124\ninst✝⁵ : LinearOrderedSemifield 𝕜\ninst✝⁴ : OrderedAddCommMonoid M\ninst✝³ : OrderedAddCommMonoid N\ninst✝² : MulActionWithZero 𝕜 M\ninst✝¹ : MulActionWithZero 𝕜 N\ninst✝... | [
248,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Logic/Equiv/Fin.lean | finSuccAboveEquiv_symm_apply_last | [
{
"state_after": "m n : ℕ\nx : { x // x ≠ Fin.last n }\n⊢ some (↑(OrderIso.symm (finSuccAboveEquiv (Fin.last n))) x) = some (Fin.castLT ↑x (_ : ↑↑x < n))",
"state_before": "m n : ℕ\nx : { x // x ≠ Fin.last n }\n⊢ ↑(OrderIso.symm (finSuccAboveEquiv (Fin.last n))) x = Fin.castLT ↑x (_ : ↑↑x < n)",
"tactic... | [
257,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Hom.map_le_range | [] | [
868,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
867,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.isSubordinate_single | [] | [
337,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/RingTheory/WittVector/Defs.lean | WittVector.ext_iff | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nR : Type u_1\nx y : 𝕎 R\nh : x = y\nn : ℕ\n⊢ coeff x n = coeff y n",
"tactic": "rw [h]"
}
] | [
91,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.mul_lt_of_lt_div | [
{
"state_after": "no goals",
"state_before": "a b r : ℝ≥0\nh : a < b / r\nhr : r = 0\n⊢ False",
"tactic": "simp [hr] at h"
}
] | [
849,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
848,
1
] |
Mathlib/Analysis/ODE/PicardLindelof.lean | PicardLindelof.FunSpace.dist_next_apply_le_of_le | [
{
"state_after": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\nv : PicardLindelof E\nf : FunSpace v\ninst✝ : CompleteSpace E\nf₁ f₂ : FunSpace v\nn : ℕ\nd : ℝ\nt : ↑(Icc v.tMin v.tMax)\nh : ∀ (t : ↑(Icc v.tMin v.tMax)), ‖toFun f₁ t - toFun f₂ t‖ ≤ (↑v.L * abs (↑t - ↑v.t₀)) ^ n / ↑n ! *... | [
322,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Algebra/Order/Sub/Defs.lean | le_tsub_add_add | [
{
"state_after": "α : Type u_1\nβ : Type ?u.11136\ninst✝⁴ : Preorder α\ninst✝³ : AddCommSemigroup α\ninst✝² : Sub α\ninst✝¹ : OrderedSub α\na b c d : α\ninst✝ : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1\n⊢ b + a ≤ b + c + (a - c)",
"state_before": "α : Type u_1\nβ : Type ?u.11136\ninst✝... | [
154,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image₂_inter_subset_right | [
{
"state_after": "α : Type u_3\nα' : Type ?u.44339\nβ : Type u_1\nβ' : Type ?u.44345\nγ : Type u_2\nγ' : Type ?u.44351\nδ : Type ?u.44354\nδ' : Type ?u.44357\nε : Type ?u.44360\nε' : Type ?u.44363\nζ : Type ?u.44366\nζ' : Type ?u.44369\nν : Type ?u.44372\ninst✝⁸ : DecidableEq α'\ninst✝⁷ : DecidableEq β'\ninst✝⁶... | [
223,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.smul_zero_subset | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.904200\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.904209\ninst✝³ : Zero α\ninst✝² : Zero β\ninst✝¹ : SMulWithZero α β\ninst✝ : DecidableEq β\ns✝ : Finset α\nt : Finset β\ns : Finset α\n⊢ s • 0 ⊆ 0",
"tactic": "simp [subset_iff, mem_smul]"
}
] | [
2097,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2097,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | div_lt_iff | [] | [
172,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Order/LocallyFinite.lean | Ioc_toDual | [
{
"state_after": "α : Type u_1\nβ : Type ?u.113413\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : LocallyFiniteOrder α\na b : α\n⊢ Ioc (↑toDual a) (↑toDual b) = Ico b a",
"state_before": "α : Type u_1\nβ : Type ?u.113413\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : LocallyFiniteOrder α\na b : α\n⊢... | [
845,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
1
] |
Mathlib/Analysis/Convex/Basic.lean | Convex.prod | [] | [
116,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Data/Finset/Preimage.lean | Finset.preimage_compl | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ninst✝³ : DecidableEq α\ninst✝² : DecidableEq β\ninst✝¹ : Fintype α\ninst✝ : Fintype β\nf : α → β\ns : Finset β\nhf : Injective f\n⊢ ↑(preimage (sᶜ) f (_ : InjOn f (f ⁻¹' ↑(sᶜ)))) = ↑(preimage s f (_ : InjOn f (f ⁻¹... | [
79,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.principal_empty | [] | [
674,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
673,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | mul_self_add_mul_self_eq_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.216729\ninst✝ : LinearOrderedRing α\na b c x y : α\n⊢ x * x + y * y = 0 ↔ x = 0 ∧ y = 0",
"tactic": "rw [add_eq_zero_iff', mul_self_eq_zero, mul_self_eq_zero] <;> apply mul_self_nonneg"
}
] | [
1213,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1212,
1
] |
Mathlib/Order/CompactlyGenerated.lean | CompleteLattice.coatomic_of_top_compact | [] | [
500,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/GroupTheory/Sylow.lean | Sylow.normal_of_normalizer_normal | [
{
"state_after": "no goals",
"state_before": "G : Type u\nα : Type v\nβ : Type w\ninst✝² : Group G\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : Finite (Sylow p G)\nP : Sylow p G\nhn : Normal (normalizer ↑P)\n⊢ Normal ↑P",
"tactic": "rw [← normalizer_eq_top, ← normalizer_sup_eq_top' P le_normalizer, sup_... | [
727,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
725,
1
] |
Mathlib/Data/List/Nodup.lean | List.nodup_middle | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nl l₁✝ l₂✝ : List α\nr : α → α → Prop\na✝ b a : α\nl₁ l₂ : List α\n⊢ Nodup (l₁ ++ a :: l₂) ↔ Nodup (a :: (l₁ ++ l₂))",
"tactic": "simp only [nodup_append, not_or, and_left_comm, and_assoc, nodup_cons, mem_append,\n disjoint_cons_right... | [
237,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
src/lean/Init/Control/Lawful.lean | StateT.run_bind | [
{
"state_after": "no goals",
"state_before": "m : Type u_1 → Type u_2\nσ α β : Type u_1\ninst✝ : Monad m\nx : StateT σ m α\nf : α → StateT σ m β\ns : σ\n⊢ run (x >>= f) s = do\n let p ← run x s\n run (f p.fst) p.snd",
"tactic": "simp [bind, StateT.bind, run]"
}
] | [
252,
32
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
250,
9
] |
Mathlib/GroupTheory/SpecificGroups/Dihedral.lean | DihedralGroup.sr_mul_sr | [] | [
98,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Geometry/Euclidean/Sphere/Basic.lean | EuclideanGeometry.Cospherical.subset | [
{
"state_after": "case intro.intro\nV : Type ?u.7090\nP : Type u_1\ninst✝ : MetricSpace P\nps₁ ps₂ : Set P\nhs : ps₁ ⊆ ps₂\nc : P\nr : ℝ\nhcr : ∀ (p : P), p ∈ ps₂ → dist p c = r\n⊢ Cospherical ps₁",
"state_before": "V : Type ?u.7090\nP : Type u_1\ninst✝ : MetricSpace P\nps₁ ps₂ : Set P\nhs : ps₁ ⊆ ps₂\nhc :... | [
179,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Logic/Unique.lean | Pi.default_def | [] | [
193,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Analysis/InnerProductSpace/PiL2.lean | Complex.isometryOfOrthonormal_apply | [
{
"state_after": "ι : Type ?u.1373375\nι' : Type ?u.1373378\n𝕜 : Type ?u.1373381\ninst✝⁹ : IsROrC 𝕜\nE : Type ?u.1373387\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : InnerProductSpace 𝕜 E\nE' : Type ?u.1373407\ninst✝⁶ : NormedAddCommGroup E'\ninst✝⁵ : InnerProductSpace 𝕜 E'\nF : Type u_1\ninst✝⁴ : NormedAddComm... | [
677,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | ContinuousLinearMap.aestronglyMeasurable_comp₂ | [] | [
1801,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1798,
1
] |
Mathlib/Data/Nat/Pow.lean | Nat.pow_dvd_pow_iff_le_right | [
{
"state_after": "no goals",
"state_before": "x k l : ℕ\nw : 1 < x\n⊢ x ^ k ∣ x ^ l ↔ k ≤ l",
"tactic": "rw [pow_dvd_pow_iff_pow_le_pow (lt_of_succ_lt w), pow_le_iff_le_right w]"
}
] | [
212,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Algebra/Ring/BooleanRing.lean | toBoolAlg_mul | [] | [
342,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.inv | [
{
"state_after": "no goals",
"state_before": "q : ℚ\nx y : ℝ\nh : Irrational x\n⊢ Irrational x⁻¹⁻¹",
"tactic": "rwa [inv_inv]"
}
] | [
398,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
11
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.replicate_zero | [] | [
891,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
891,
9
] |
Mathlib/Data/Set/Sups.lean | Set.sups_subset | [] | [
86,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Order/BooleanAlgebra.lean | sup_eq_sdiff_sup_sdiff_sup_inf | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.41421\nw x y z : α\ninst✝ : GeneralizedBooleanAlgebra α\n⊢ x \\ y ⊔ y \\ x ⊔ x ⊓ y = (x \\ y ⊔ y \\ x ⊔ x) ⊓ (x \\ y ⊔ y \\ x ⊔ y)",
"tactic": "rw [sup_inf_left]"
},
{
"state_after": "no goals",
"state_before": "α : Type u... | [
471,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/Algebra/Free.lean | FreeSemigroup.mk_mul_mk | [] | [
483,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/Data/List/Basic.lean | List.lookmap_nil | [] | [
3289,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3288,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.of_mul_add_left_left | [
{
"state_after": "R : Type u\ninst✝ : CommSemiring R\nx y z : R\nh : IsCoprime (x + y * z) y\n⊢ IsCoprime x y",
"state_before": "R : Type u\ninst✝ : CommSemiring R\nx y z : R\nh : IsCoprime (y * z + x) y\n⊢ IsCoprime x y",
"tactic": "rw [add_comm] at h"
},
{
"state_after": "no goals",
"state... | [
206,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Analysis/Convex/Topology.lean | Convex.add_smul_mem_interior | [] | [
229,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.aestronglyMeasurable | [] | [
452,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Data/Int/Bitwise.lean | Int.testBit_ldiff | [
{
"state_after": "no goals",
"state_before": "m n : ℤ\nk : ℕ\n⊢ testBit (ldiff' m n) k = (testBit m k && !testBit n k)",
"tactic": "rw [← bitwise_diff, testBit_bitwise]"
}
] | [
356,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | Valuation.map_sub_le | [
{
"state_after": "K : Type ?u.1744962\nF : Type ?u.1744965\nR : Type u_2\ninst✝³ : DivisionRing K\nΓ₀ : Type u_1\nΓ'₀ : Type ?u.1744977\nΓ''₀ : Type ?u.1744980\ninst✝² : LinearOrderedCommMonoidWithZero Γ''₀\ninst✝¹ : Ring R\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nv : Valuation R Γ₀\nx✝ y✝ z x y : R\ng : (fu... | [
308,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | limsSup_nhds | [] | [
168,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.Quotient.restrictScalarsEquiv_mk | [] | [
239,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.liftRel_inl_inl | [
{
"state_after": "case inl\nα : Type u\nα' : Type w\nβ : Type v\nβ' : Type x\nγ : Type u_1\nδ : Type u_2\nr r₁ r₂ : α → γ → Prop\ns s₁ s₂ : β → δ → Prop\na : α\nb : β\nc : γ\nd : δ\nx : α ⊕ β\ny : γ ⊕ δ\na✝ : r a c\n⊢ r a c",
"state_before": "α : Type u\nα' : Type w\nβ : Type v\nβ' : Type x\nγ : Type u_1\nδ... | [
400,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Std/Data/Int/DivMod.lean | Int.ofNat_emod | [] | [
241,
84
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
241,
20
] |
Mathlib/RingTheory/Adjoin/FG.lean | Subalgebra.FG.prod | [
{
"state_after": "case intro\nR : Type u\nA : Type v\nB : Type w\ninst✝⁴ : CommSemiring R\ninst✝³ : Semiring A\ninst✝² : Algebra R A\ninst✝¹ : Semiring B\ninst✝ : Algebra R B\nS : Subalgebra R A\nT : Subalgebra R B\nhS : FG S\nhT : FG T\ns : Set A\nhs : Set.Finite s ∧ Algebra.adjoin R s = S\n⊢ FG (Subalgebra.pr... | [
141,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Order/WithBot.lean | WithTop.some_le_some | [] | [
833,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
832,
1
] |
Mathlib/RingTheory/PolynomialAlgebra.lean | PolyEquivTensor.toFunLinear_mul_tmul_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nA : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\na₁ a₂ : A\np₁ p₂ : R[X]\n⊢ ↑(toFunLinear R A) ((a₁ * a₂) ⊗ₜ[R] (p₁ * p₂)) = ↑(toFunLinear R A) (a₁ ⊗ₜ[R] p₁) * ↑(toFunLinear R A) (a₂ ⊗ₜ[R] p₂)",
"tactic": "classi... | [
111,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Topology/DenseEmbedding.lean | DenseRange.induction_on | [] | [
338,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_inv_lt_iff_of_neg | [
{
"state_after": "no goals",
"state_before": "x y z : ℝ\nhx : 0 < x\nhy : 0 < y\nhz : z < 0\n⊢ x ^ z⁻¹ < y ↔ y ^ z < x",
"tactic": "convert lt_rpow_inv_iff_of_neg (Real.rpow_pos_of_pos hx z⁻¹) (Real.rpow_pos_of_pos hy z) hz <;>\nsimp [← Real.rpow_mul hx.le, ← Real.rpow_mul hy.le, ne_of_lt hz]"
}
] | [
461,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_image_le_lift | [] | [
2004,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2002,
1
] |
Mathlib/Topology/Basic.lean | mem_closure_iff_nhds | [] | [
1333,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1332,
1
] |
Mathlib/Data/Subtype.lean | Subtype.equivalence | [] | [
251,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
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