file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.IsNormal.bsup | [
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Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_lt_one_iff | [] | [
671,
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Mathlib/MeasureTheory/Function/AEEqOfIntegral.lean | MeasureTheory.ae_eq_zero_restrict_of_forall_set_integral_eq_zero_real | [
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Mathlib/Data/Multiset/Basic.lean | Multiset.pmap_cons | [] | [
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Mathlib/Data/Int/Order/Basic.lean | Int.ediv_eq_ediv_of_mul_eq_mul | [
{
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{
"... | [
487,
87
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Mathlib/Data/Set/Function.lean | Set.RightInvOn.congr_right | [] | [
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33
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Mathlib/Algebra/AddTorsor.lean | vsub_sub_vsub_comm | [
{
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"tactic": "rw [← vsub_vadd_eq_vsub_sub, vsub_vadd_comm, vsub_vadd_eq_vsub_sub]"
}
] | [
277,
70
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Mathlib/Topology/Category/Profinite/Basic.lean | Profinite.coe_id | [] | [
133,
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Mathlib/Order/SuccPred/Basic.lean | Order.succ_mono | [] | [
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71
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278,
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Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.nnnorm_equiv_symm_const | [
{
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Mathlib/Analysis/NormedSpace/HahnBanach/Separation.lean | geometric_hahn_banach_point_closed | [] | [
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Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.to_submodule_injective | [
{
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Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiffWithinAt.contDiffOn | [] | [
661,
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Mathlib/Data/Polynomial/IntegralNormalization.lean | Polynomial.integralNormalization_coeff | [
{
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Mathlib/Algebra/Jordan/Basic.lean | aux1 | [
{
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Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.rpow_le_one_of_one_le_of_neg | [
{
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{
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685,
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.continuousWithinAt | [] | [
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34
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1896,
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Mathlib/Analysis/NormedSpace/Star/Basic.lean | selfAdjoint.nnnorm_pow_two_pow | [] | [
280,
30
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Mathlib/Order/Filter/AtTopBot.lean | Filter.exists_lt_of_tendsto_atBot | [] | [
536,
46
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Mathlib/Data/Polynomial/DenomsClearable.lean | denomsClearable_C_mul_X_pow | [
{
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Mathlib/Order/JordanHolder.lean | CompositionSeries.bot_le | [] | [
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40
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Mathlib/Data/List/MinMax.lean | List.index_of_argmax | [
{
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{
... | [
225,
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.embDomain_single | [
{
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Mathlib/Topology/ContinuousFunction/Algebra.lean | ContinuousMap.inf_eq | [
{
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"tactic": "s... | [
937,
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Mathlib/Order/Cover.lean | not_covby | [] | [
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Mathlib/Data/Finset/Lattice.lean | Finset.max'_lt_iff | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1372,
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Mathlib/LinearAlgebra/Dual.lean | Subspace.dualCoannihilator_top | [
{
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"tactic": "rw [dualCoannihilator, dualAnnihilator_top, comap_bot, Module.eval_ker]"
}
] | [
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_add_left' | [
{
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Mathlib/Data/Seq/Computation.lean | Computation.map_id | [
{
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711,
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Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.set_lintegral_deterministic | [
{
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392,
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Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSpace.ext | [] | [
262,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
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Mathlib/Data/Multiset/Basic.lean | Multiset.countp_cons_of_neg | [] | [
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69
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Std/Data/List/Basic.lean | List.tails_eq_tailsTR | [
{
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},
{
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Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | coplanar_singleton | [] | [
656,
37
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Mathlib/Topology/Order/Basic.lean | Antitone.map_sInf_of_continuousAt | [] | [
2750,
9
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Mathlib/Algebra/Homology/Additive.lean | CategoryTheory.NatTrans.mapHomologicalComplex_naturality | [
{
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Mathlib/RingTheory/Nilpotent.lean | nilpotent_iff_mem_prime | [
{
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Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Memℒp.toLp_neg | [] | [
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6
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Mathlib/Data/Set/Prod.lean | Set.prod_subset_iff | [] | [
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81
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Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoUniformlyOn.comp | [
{
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Mathlib/Init/Logic.lean | InvImage.trans | [] | [
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Mathlib/Data/Finset/Sups.lean | Finset.infs_left_comm | [] | [
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Mathlib/Algebra/Tropical/Basic.lean | Tropical.untrop_div | [] | [
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Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.factorThruKernelSubobject_comp_kernelSubobjectIso | [
{
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Mathlib/CategoryTheory/StructuredArrow.lean | CategoryTheory.CostructuredArrow.mono_of_mono_left | [] | [
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32
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Mathlib/Order/Cover.lean | covby_iff_wcovby_and_ne | [] | [
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60
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Mathlib/Data/List/AList.lean | AList.lookup_eq_none | [] | [
170,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Data/Polynomial/Expand.lean | Polynomial.expand_injective | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹ : CommSemiring R\nS : Type v\ninst✝ : CommSemiring S\np q n : ℕ\nhn : 0 < n\ng g' : R[X]\nH : ↑(expand R n) g = ↑(expand R n) g'\nk : ℕ\n⊢ coeff g k = coeff g' k",
"tactic": "rw [← coeff_expand_mul hn, H, coeff_expand_mul hn]"
}
] | [
134,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Topology/Order/Basic.lean | IsClosed.sSup_mem | [] | [
2636,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2634,
1
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.restrict_univ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.808029\nδ : Type ?u.808032\ninst✝¹ : MeasurableSpace α\nK : Type ?u.808038\ninst✝ : Zero β\nf : α →ₛ β\n⊢ restrict f univ = f",
"tactic": "simp [restrict]"
}
] | [
759,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
1
] |
Mathlib/Data/PFunctor/Univariate/M.lean | PFunctor.M.bisim | [
{
"state_after": "F : PFunctor\nX : Type ?u.72703\nf : X → Obj F X\nP : PFunctor\nα : Type u\nR : M P → M P → Prop\nh :\n ∀ (x y : M P),\n R x y → ∃ a f f', dest x = { fst := a, snd := f } ∧ dest y = { fst := a, snd := f' } ∧ ∀ (i : B P a), R (f i) (f' i)\nx y : M P\nh' : R x y\n⊢ x = y",
"state_before"... | [
742,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
728,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.monic_of_b_eq_one | [
{
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"state_before": "R : Type u_1\nS : Type ?u.561206\nF : Type ?u.561209\nK : Type ?u.561212... | [
255,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Analysis/InnerProductSpace/Adjoint.lean | ContinuousLinearMap.adjoint_inner_left | [] | [
125,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.mem_map | [] | [
1229,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1228,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | RingHom.kerLift_injective | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nf✝ f : R →+* S\na✝ b✝ : R ⧸ ker f\na b : R\nh : ↑f a = ↑f b\n⊢ a - b ∈ ker f",
"tactic": "rw [mem_ker, map_sub, h, sub_self]"
}
] | [
41,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.aeval_algEquiv | [] | [
289,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Tactic/Abel.lean | Mathlib.Tactic.Abel.term_atom_pfg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddCommGroup α\nx x' : α\nh : x = x'\n⊢ x = termg 1 x' 0",
"tactic": "simp [termg, h]"
}
] | [
240,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_const_mul_pow_atTop_iff | [
{
"state_after": "case refine'_1\nι : Type ?u.223673\nι' : Type ?u.223676\nα : Type u_1\nβ : Type ?u.223682\nγ : Type ?u.223685\ninst✝ : LinearOrderedSemifield α\nl : Filter β\nf : β → α\nr c : α\nn : ℕ\nh : Tendsto (fun x => c * x ^ n) atTop atTop\n⊢ n ≠ 0\n\ncase refine'_2\nι : Type ?u.223673\nι' : Type ?u.22... | [
1066,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1060,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisConnection.le_iff_le | [] | [
91,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Analysis/Hofer.lean | hofer | [
{
"state_after": "X : Type u_1\ninst✝¹ : MetricSpace X\ninst✝ : CompleteSpace X\nx : X\nε : ℝ\nε_pos : 0 < ε\nϕ : X → ℝ\ncont : Continuous ϕ\nnonneg : ∀ (y : X), 0 ≤ ϕ y\nH : ¬∃ ε', ε' > 0 ∧ ∃ x', ε' ≤ ε ∧ d x' x ≤ 2 * ε ∧ ε * ϕ x ≤ ε' * ϕ x' ∧ ∀ (y : X), d x' y ≤ ε' → ϕ y ≤ 2 * ϕ x'\n⊢ False",
"state_befor... | [
113,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.tendsto_inf_right | [] | [
2996,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2994,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.add_lt_add_of_lt_of_le' | [
{
"state_after": "case inl\nx y z : EReal\nh : x < y\nh' : z ≤ z\nhbot : z ≠ ⊥\nhtop : z = ⊤ → z = ⊤ → x = ⊥\n⊢ x + z < y + z\n\ncase inr\nx y z t : EReal\nh : x < y\nh' : z ≤ t\nhbot : t ≠ ⊥\nhtop : t = ⊤ → z = ⊤ → x = ⊥\nhlt : z < t\n⊢ x + z < y + t",
"state_before": "x y z t : EReal\nh : x < y\nh' : z ≤ ... | [
712,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
704,
1
] |
Mathlib/Topology/Order/Basic.lean | map_coe_Ioo_atTop | [] | [
2511,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2510,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.Disjoint.inv_right | [] | [
97,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.Equalizer.ι_normNoninc | [] | [
981,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
981,
1
] |
Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.HomotopicWith.symm | [] | [
568,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
1
] |
Mathlib/Order/Monotone/Monovary.lean | Monovary.monovaryOn | [] | [
62,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
11
] |
Mathlib/Data/Nat/Digits.lean | Nat.ofDigits_mod | [] | [
520,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/Topology/Semicontinuous.lean | ContinuousAt.comp_upperSemicontinuousWithinAt | [] | [
841,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
838,
1
] |
Mathlib/Data/MvPolynomial/PDeriv.lean | MvPolynomial.pderiv_one | [] | [
90,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/NumberTheory/Padics/PadicNorm.lean | padicNorm.sum_lt | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nα : Type u_1\nF : α → ℚ\nt : ℚ\ns : Finset α\n⊢ ∀ ⦃a : α⦄ {s : Finset α},\n ¬a ∈ s →\n (Finset.Nonempty s → (∀ (i : α), i ∈ s → padicNorm p (F i) < t) → padicNorm p (∑ i in s, F i) < t) →\n Finset.Nonempty (insert a s) →\n (∀ (i : α), i ∈... | [
328,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | ContinuousOn.aemeasurable | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nE : Type ?u.1668784\nF : Type ?u.1668787\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : TopologicalSpace α\ninst✝³ : OpensMeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : TopologicalSpace β\ninst✝ : BorelSpace β\nf : α → β\ns : Set α\nμ ... | [
502,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
] |
Mathlib/Data/Real/Irrational.lean | Nat.Prime.irrational_sqrt | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : Prime p\n⊢ Part.get (multiplicity ↑p ↑p) (_ : multiplicity.Finite ↑p ↑p) % 2 = 1",
"tactic": "simp [multiplicity.multiplicity_self\n (mt isUnit_iff_dvd_one.1 (mt Int.coe_nat_dvd.1 hp.not_dvd_one))]"
}
] | [
106,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Order/WithBot.lean | WithTop.map_toDual | [] | [
749,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
747,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.mul_invOf_self_assoc | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.9084\nm : Type u\nn : Type u'\nα : Type v\ninst✝³ : Fintype n\ninst✝² : DecidableEq n\ninst✝¹ : CommRing α\nA : Matrix n n α\nB : Matrix n m α\ninst✝ : Invertible A\n⊢ A ⬝ (⅟A ⬝ B) = B",
"tactic": "rw [← Matrix.mul_assoc, Matrix.mul_invOf_self, M... | [
87,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
11
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_sub_const_Icc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\n⊢ (fun x => x - a) '' Icc b c = Icc (b - a) (c - a)",
"tactic": "simp [sub_eq_neg_add]"
}
] | [
391,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/Order/GameAdd.lean | WellFounded.sym2_gameAdd | [] | [
221,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Analysis/Convex/Segment.lean | segment_eq_Icc | [] | [
505,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.mulVec_diagonal | [] | [
1703,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1701,
1
] |
Mathlib/Algebra/Lie/Solvable.lean | LieAlgebra.LieIdeal.solvable_iff_le_radical | [] | [
289,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/MeasureTheory/Measure/Regular.lean | MeasureTheory.Measure.InnerRegular.smul | [
{
"state_after": "α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\np q : Set α → Prop\nU✝ : Set α\nε : ℝ≥0∞\nH : InnerRegular μ p q\nc : ℝ≥0∞\nU : Set α\nhU : q U\nr : ℝ≥0∞\nhr : r < ↑↑(c • μ) U\n⊢ ∃ K, K ⊆ U ∧ p K ∧ r < ↑↑(c • μ) K",
"state_before": "α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\np... | [
187,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderIso.toEquiv_symm | [] | [
890,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
889,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Maximal.lean | MaximalSpectrum.toPrimeSpectrum_injective | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : CommRing R\nx✝¹ x✝ : MaximalSpectrum R\nasIdeal✝¹ : Ideal R\nIsMaximal✝¹ : Ideal.IsMaximal asIdeal✝¹\nasIdeal✝ : Ideal R\nIsMaximal✝ : Ideal.IsMaximal asIdeal✝\nh :\n toPrimeSpectrum { asIdeal := asIdeal✝¹, IsMaximal := IsMaximal✝¹ } =\n ... | [
63,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Data/List/Rotate.lean | List.nthLe_rotate | [] | [
277,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.order_pow | [
{
"state_after": "case zero\nΓ✝ : Type ?u.1298389\nR : Type u_2\ninst✝³ : OrderedCancelAddCommMonoid Γ✝\nΓ : Type u_1\ninst✝² : LinearOrderedCancelAddCommMonoid Γ\ninst✝¹ : Semiring R\ninst✝ : NoZeroDivisors R\nx : HahnSeries Γ R\n⊢ order (x ^ Nat.zero) = Nat.zero • order x\n\ncase succ\nΓ✝ : Type ?u.1298389\nR... | [
927,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
921,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_vector | [
{
"state_after": "no goals",
"state_before": "α✝ β α : Type u\nn : ℕ\n⊢ (#Fin n → α) = (#α) ^ n",
"tactic": "simp"
}
] | [
1956,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1955,
1
] |
Mathlib/Order/Concept.lean | Concept.snd_subset_snd_iff | [
{
"state_after": "case refine'_1\nι : Sort ?u.9043\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.9052\nκ : ι → Sort ?u.9057\nr : α → β → Prop\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\nc d : Concept α β r\nh : c.snd ⊆ d.snd\n⊢ d ≤ c\n\ncase refine'_2\nι : Sort ?u.9043\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.9052\nκ : ι → S... | [
250,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.div_lt_iff_lt_mul | [
{
"state_after": "k x y : Nat\nHk : 0 < k\n⊢ ¬y ≤ x / k ↔ ¬y * k ≤ x",
"state_before": "k x y : Nat\nHk : 0 < k\n⊢ x / k < y ↔ x < y * k",
"tactic": "rw [← Nat.not_le, ← Nat.not_le]"
},
{
"state_after": "no goals",
"state_before": "k x y : Nat\nHk : 0 < k\n⊢ ¬y ≤ x / k ↔ ¬y * k ≤ x",
"ta... | [
298,
74
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
297,
1
] |
Mathlib/Data/Set/Finite.lean | Set.finite_mem_finset | [] | [
977,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
976,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.add | [] | [
1078,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1075,
1
] |
Mathlib/Topology/Separation.lean | exists_open_with_compact_closure | [
{
"state_after": "case intro.intro\nα : Type u\nβ : Type v\ninst✝⁴ : TopologicalSpace α\nγ : Type ?u.140885\ninst✝³ : TopologicalSpace β\ninst✝² : TopologicalSpace γ\ninst✝¹ : LocallyCompactSpace α\ninst✝ : T2Space α\nx : α\nK : Set α\nhKc : IsCompact K\nhxK : K ∈ 𝓝 x\n⊢ ∃ U, IsOpen U ∧ x ∈ U ∧ IsCompact (clos... | [
1408,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1404,
1
] |
Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.limNthHom_add | [] | [
601,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
599,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_mem_iff_measure_eq | [] | [
3178,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3176,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsGLB.insert | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ns✝ t : Set α\na✝ b✝ : α\ninst✝ : SemilatticeInf γ\na b : γ\ns : Set γ\nhs : IsGLB s b\n⊢ IsGLB ({a} ∪ s) (a ⊓ b)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : Preorder α\... | [
955,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
952,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.mk'_mem_iff | [
{
"state_after": "case mp\nR : Type u_1\ninst✝⁴ : CommSemiring R\nM : Submonoid R\nS : Type u_2\ninst✝³ : CommSemiring S\ninst✝² : Algebra R S\nP : Type ?u.672634\ninst✝¹ : CommSemiring P\ninst✝ : IsLocalization M S\nx : R\ny : { x // x ∈ M }\nI : Ideal S\nh : mk' S x y ∈ I\n⊢ ↑(algebraMap R S) x ∈ I\n\ncase mp... | [
339,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/Order/Cover.lean | Covby.unique_left | [] | [
447,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Mathlib/Order/MinMax.lean | Monotone.map_min | [] | [
261,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.nndist_eq_iSup | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.308003\nα : Type u\nβ : Type v\nγ : Type w\ninst✝² : TopologicalSpace α\ninst✝¹ : PseudoMetricSpace β\ninst✝ : PseudoMetricSpace γ\nf g : α →ᵇ β\nx : α\nC : ℝ\n⊢ (⨆ (x : α), dist (↑f x) (↑g x)) = ↑(⨆ (x : α), nndist (↑f x) (↑g x))",
"tactic": "si... | [
260,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Data/List/Zip.lean | List.zipWith_nil_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type u_2\nγ : Type u_1\nδ : Type ?u.385\nε : Type ?u.388\nf : α → β → γ\nl : List α\n⊢ zipWith f l [] = []",
"tactic": "simp"
}
] | [
50,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.le_comap_of_map_le | [] | [
288,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
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