file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Analysis/Normed/Field/Basic.lean | norm_pow_le' | [
{
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"tactic": "simpa only [NNReal.coe_pow, coe_nnnorm] using NNReal.coe_mono (nnnorm_pow_le' a h)"
}
] | [
377,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
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Mathlib/Algebra/IndicatorFunction.lean | Set.indicator_smul_apply | [
{
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496,
39
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492,
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Mathlib/RingTheory/FiniteType.lean | RingHom.FiniteType.of_finite | [] | [
250,
51
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249,
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Mathlib/Data/Multiset/Bind.lean | Multiset.mem_sigma | [
{
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352,
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351,
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Mathlib/MeasureTheory/Measure/AEDisjoint.lean | MeasureTheory.AEDisjoint.union_right_iff | [
{
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"tactic": "simp [union_eq_iUnion, and_comm]"
}
] | [
114,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
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Mathlib/CategoryTheory/Abelian/Generator.lean | CategoryTheory.Abelian.has_injective_coseparator | [
{
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55,
38
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Measurable.infEdist | [] | [
1652,
30
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Mathlib/GroupTheory/Index.lean | Subgroup.index_iInf_ne_zero | [
{
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"state_before": "G : Type u_2\ninst✝¹ : Group G\nH K L : Subgroup G\nι : Type u_1\ninst✝ : Finite ι\nf : ι → Sub... | [
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474,
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Mathlib/GroupTheory/Sylow.lean | Sylow.prime_pow_dvd_card_normalizer | [] | [
588,
87
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585,
1
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Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.liftAux_tmul | [] | [
456,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
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Mathlib/Data/List/FinRange.lean | List.nodup_ofFn | [
{
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},
{
"state_after": "case refin... | [
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25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Normed/Group/Basic.lean | tendsto_norm' | [
{
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1080,
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Mathlib/CategoryTheory/Idempotents/Basic.lean | CategoryTheory.Idempotents.isIdempotentComplete_iff_of_equivalence | [
{
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"state... | [
183,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
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Mathlib/CategoryTheory/Abelian/Pseudoelements.lean | CategoryTheory.Abelian.Pseudoelement.ModuleCat.eq_range_of_pseudoequal | [
{
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495,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.const_mul | [] | [
439,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
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Mathlib/Analysis/Convex/Basic.lean | convex_Ioc | [] | [
303,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
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Mathlib/CategoryTheory/Limits/Opposites.lean | CategoryTheory.Limits.hasColimitsOfShape_of_hasLimitsOfShape_op | [] | [
310,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
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Mathlib/Order/Cover.lean | Wcovby.of_image | [] | [
117,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
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Mathlib/Data/Set/Function.lean | Set.LeftInvOn.eq | [] | [
1030,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1029,
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Mathlib/Order/Heyting/Basic.lean | sdiff_le_sdiff | [] | [
674,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
673,
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Mathlib/LinearAlgebra/AffineSpace/Midpoint.lean | midpoint_vadd_midpoint | [] | [
98,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Logic/Function/Basic.lean | Function.LeftInverse.eq_rightInverse | [
{
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"tactic": "rw [h₂.comp_eq_id, comp.right_id]"
},
{
"state_after": "no goals",
"state_before": "α : Sor... | [
393,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
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Mathlib/Order/Bounded.lean | Set.bounded_ge_inter_ge | [] | [
417,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
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Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.subgroupMap_surjective | [] | [
3436,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3434,
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Mathlib/MeasureTheory/Measure/Lebesgue/Complex.lean | Complex.volume_preserving_equiv_real_prod | [] | [
52,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.cokernelZeroIsoTarget_hom | [
{
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"tactic": "simp"
},
{
"state_after": "case h\nC : Type u\ninst✝² : Category C\ninst✝¹ : HasZeroMorphisms C\nX Y : C\nf : X ⟶ Y\n... | [
807,
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805,
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Mathlib/SetTheory/Cardinal/Cofinality.lean | RelIso.cof_eq | [] | [
119,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
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Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.comap_comp | [] | [
611,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
610,
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Mathlib/Data/QPF/Univariate/Basic.lean | Qpf.Fix.ind_rec | [
{
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Mathlib/Data/Set/Function.lean | Set.SurjOn.bijOn_subset | [
{
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Mathlib/Data/List/Card.lean | List.mem_of_mem_remove | [
{
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"t... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Group/Basic.lean | div_eq_div_iff_mul_eq_mul | [
{
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"tactic": "rw [div_eq_iff_eq_... | [
1020,
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1018,
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Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.Compacts.carrier_eq_coe | [] | [
76,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/FieldTheory/RatFunc.lean | RatFunc.eval_algebraMap | [
{
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"tactic": "si... | [
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Mathlib/MeasureTheory/Function/Jacobian.lean | MeasureTheory.addHaar_image_le_lintegral_abs_det_fderiv | [
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906,
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.mapRange.addEquiv_refl | [] | [
2202,
27
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Mathlib/Algebra/Lie/IdealOperations.lean | LieSubmodule.lie_mem_lie | [] | [
115,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.single_apply_ne_zero | [
{
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Mathlib/Order/CompleteLattice.lean | iSup_exists | [] | [
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38
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Mathlib/Algebra/Order/Ring/Lemmas.lean | le_of_mul_le_of_one_le_of_nonneg_left | [] | [
941,
41
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Mathlib/Data/List/Lemmas.lean | List.foldl_range_subset_of_range_subset | [
{
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Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_neg_Ici | [] | [
134,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
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Mathlib/Data/Finset/Basic.lean | Multiset.toFinset_eq | [] | [
3128,
32
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Mathlib/Algebra/Group/Basic.lean | mul_right_ne_self | [] | [
195,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
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Mathlib/Data/List/Chain.lean | List.Chain'.iff_mem | [] | [
189,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
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Mathlib/Analysis/Calculus/ContDiffDef.lean | iteratedFDeriv_succ_eq_comp_right | [
{
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1614,
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Mathlib/Data/Set/Countable.lean | Set.Countable.of_subsingleton | [] | [
241,
39
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240,
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Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.HasLimit.lift_isoOfNatIso_inv | [] | [
374,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
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Mathlib/Computability/Language.lean | Language.nil_mem_kstar | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.36899\nγ : Type ?u.36902\nl✝ m : Language α\na b x : List α\nl : Language α\nx✝ : List α\nh : x✝ ∈ []\n⊢ x✝ ∈ l",
"tactic": "contradiction"
}
] | [
133,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ring.exists_not_isUnit_of_not_isField | [
{
"state_after": "α : Type u\nβ : Type v\nR : Type u_1\ninst✝¹ : CommSemiring R\ninst✝ : Nontrivial R\nhf : ¬IsField R\nthis : ¬∀ {a : R}, a ≠ 0 → ∃ b, a * b = 1\n⊢ ∃ x _hx, ¬IsUnit x",
"state_before": "α : Type u\nβ : Type v\nR : Type u_1\ninst✝¹ : CommSemiring R\ninst✝ : Nontrivial R\nhf : ¬IsField R\n⊢ ∃... | [
749,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
743,
1
] |
Mathlib/Topology/Connected.lean | IsPreconnected.constant_of_mapsTo | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.149420\nπ : ι → Type ?u.149425\ninst✝² : TopologicalSpace α\ns t u v : Set α\ninst✝¹ : TopologicalSpace β\nS : Set α\nhS : IsPreconnected S\nT : Set β\ninst✝ : DiscreteTopology ↑T\nf : α → β\nhc : ContinuousOn f S\nhTm : MapsTo f S T\nx y : α\nhx : x ∈ S\nhy... | [
1613,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1608,
1
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Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.memℒp_of_cauchy_tendsto | [
{
"state_after": "α : Type u_2\nE : Type u_1\nF : Type ?u.8218613\nG : Type ?u.8218616\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nhp : 1 ≤ p\nf : ℕ → α → E\nhf : ∀ (n : ℕ), Memℒp (f n) p\nf_lim : α → E\... | [
1528,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1513,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.xy_modEq_of_modEq | [
{
"state_after": "no goals",
"state_before": "a b c : ℕ\na1 : 1 < a\nb1 : 1 < b\nh : a ≡ b [MOD c]\n⊢ xn a1 0 ≡ xn b1 0 [MOD c] ∧ yn a1 0 ≡ yn b1 0 [MOD c]",
"tactic": "constructor <;> rfl"
},
{
"state_after": "a b c : ℕ\na1 : 1 < a\nb1 : 1 < b\nh : a ≡ b [MOD c]\n⊢ a ≡ b [MOD c] ∧ 1 ≡ 1 [MOD c]... | [
838,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
828,
1
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Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidHom.one_comp | [] | [
493,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
] |
Mathlib/Topology/UrysohnsBounded.lean | exists_bounded_mem_Icc_of_closed_of_le | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : NormalSpace X\ns t : Set X\nhs : IsClosed s\nht : IsClosed t\nhd : Disjoint s t\na b : ℝ\nhle : a ≤ b\nf : X →ᵇ ℝ\nhfs : EqOn (↑f) 0 s\nhft : EqOn (↑f) 1 t\nhf01 : ∀ (x : X), ↑f x ∈ Icc 0 1\nx : X\nhx : x ∈ s\n⊢... | [
59,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/LinearAlgebra/Matrix/Basis.lean | Basis.toMatrix_reindex | [
{
"state_after": "case a.h\nι : Type u_1\nι' : Type u_4\nκ : Type ?u.637514\nκ' : Type ?u.637517\nR : Type u_2\nM : Type u_3\ninst✝⁷ : CommSemiring R\ninst✝⁶ : AddCommMonoid M\ninst✝⁵ : Module R M\nR₂ : Type ?u.637710\nM₂ : Type ?u.637713\ninst✝⁴ : CommRing R₂\ninst✝³ : AddCommGroup M₂\ninst✝² : Module R₂ M₂\ne... | [
271,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.maximal_of_no_maximal | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝¹ : Semiring α\nI : Ideal α\na b : α\nR : Type u\ninst✝ : Semiring R\nP : Ideal R\nhmax : ∀ (m : Ideal R), P < m → ¬IsMaximal m\nJ : Ideal R\nhPJ : P < J\nhnonmax : ¬J = ⊤\n⊢ False",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : Semiring α\nI : Ideal α\na b... | [
358,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/Topology/Maps.lean | Inducing.isOpen_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.6214\nδ : Type ?u.6217\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α → β\nhf : Inducing f\ns : Set α\n⊢ IsOpen s ↔ ∃ t, IsOpen t ∧ f ⁻¹' t = s",
... | [
175,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/RingTheory/Coprime/Lemmas.lean | IsCoprime.prod_right | [
{
"state_after": "no goals",
"state_before": "R : Type u\nI : Type v\ninst✝ : CommSemiring R\nx y z : R\ns : I → R\nt : Finset I\n⊢ (∀ (i : I), i ∈ t → IsCoprime x (s i)) → IsCoprime x (∏ i in t, s i)",
"tactic": "simpa only [isCoprime_comm] using IsCoprime.prod_left (R := R)"
}
] | [
61,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Data/List/OfFn.lean | List.last_ofFn_succ | [] | [
146,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Topology/ContinuousFunction/Basic.lean | ContinuousMap.continuous | [] | [
139,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
11
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.sum_mem | [] | [
80,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/LinearAlgebra/FreeModule/Basic.lean | Module.free_iff_set | [] | [
66,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Data/Polynomial/Reverse.lean | Polynomial.reflect_add | [
{
"state_after": "case a\nR : Type u_1\ninst✝ : Semiring R\nf✝ f g : R[X]\nN n✝ : ℕ\n⊢ coeff (reflect N (f + g)) n✝ = coeff (reflect N f + reflect N g) n✝",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nf✝ f g : R[X]\nN : ℕ\n⊢ reflect N (f + g) = reflect N f + reflect N g",
"tactic": "ext"
},
{... | [
137,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.top_mul' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.84274\nβ : Type ?u.84277\na b c d : ℝ≥0∞\nr p q : ℝ≥0\n⊢ ⊤ * a = if a = 0 then 0 else ⊤",
"tactic": "convert WithTop.top_mul' a"
}
] | [
555,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/Topology/Order/Basic.lean | Ioo_subset_closure_interior | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : TopologicalSpace α\ninst✝¹ : LinearOrder α\ninst✝ : OrderClosedTopology α\na b : α\n⊢ Ioo a b ⊆ closure (interior (Ioo a b))",
"tactic": "simp only [interior_Ioo, subset_closure]"
}
] | [
325,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Order/Lattice.lean | inf_lt_of_right_lt | [] | [
424,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/Algebra/Invertible.lean | invOf_neg | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝³ : Monoid α\ninst✝² : HasDistribNeg α\na : α\ninst✝¹ : Invertible a\ninst✝ : Invertible (-a)\n⊢ -a * -⅟a = 1",
"tactic": "simp"
}
] | [
259,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | squeeze_zero' | [] | [
1441,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1439,
1
] |
Mathlib/Data/Set/Semiring.lean | Set.up_union | [] | [
130,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.mem_coe | [] | [
110,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiff_one_iff_fderiv | [] | [
1678,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1677,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.measurePreserving_funUnique | [
{
"state_after": "ι : Type ?u.5846526\nι' : Type ?u.5846529\nα✝ : ι → Type ?u.5846534\ninst✝¹ : Fintype ι\nm✝ : (i : ι) → OuterMeasure (α✝ i)\nβ : Type u\nm : MeasurableSpace β\nμ : Measure β\nα : Type v\ninst✝ : Unique α\ne : (α → β) ≃ᵐ β := MeasurableEquiv.funUnique α β\n⊢ MeasurePreserving ↑e",
"state_be... | [
784,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
775,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.add_eq_max | [] | [
732,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
728,
1
] |
Mathlib/Order/Filter/FilterProduct.lean | Filter.Germ.coe_lt | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nφ : Ultrafilter α\ninst✝ : Preorder β\nf g : α → β\n⊢ ↑f < ↑g ↔ ∀* (x : α), f x < g x",
"tactic": "simp only [lt_iff_le_not_le, eventually_and, coe_le, eventually_not, EventuallyLE]"
}
] | [
65,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Analysis/Convex/Exposed.lean | IsExposed.isCompact | [] | [
193,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
11
] |
Mathlib/Analysis/SpecialFunctions/Sqrt.lean | HasDerivAt.sqrt | [] | [
91,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Algebra/Opposites.lean | MulOpposite.unop_sub | [] | [
314,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.subset_sInter_iff | [] | [
1067,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1066,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.diag_list_sum | [] | [
687,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
686,
1
] |
Mathlib/Data/Set/Intervals/OrdConnectedComponent.lean | Set.ordConnectedProj_eq | [
{
"state_after": "case mp\nα : Type u_1\ninst✝ : LinearOrder α\ns t : Set α\nx✝ y✝ z : α\nx y : ↑s\nh : ordConnectedProj s x = ordConnectedProj s y\n⊢ [[↑x, ↑y]] ⊆ s\n\ncase mpr\nα : Type u_1\ninst✝ : LinearOrder α\ns t : Set α\nx✝ y✝ z : α\nx y : ↑s\nh : [[↑x, ↑y]] ⊆ s\n⊢ ordConnectedProj s x = ordConnectedPro... | [
135,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.le_op_norm_mul_prod_of_le | [] | [
449,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Mathlib/Data/Finset/Powerset.lean | Finset.powersetLen_self | [
{
"state_after": "case a\nα : Type u_1\ns✝ t s a✝ : Finset α\n⊢ a✝ ∈ powersetLen (card s) s ↔ a✝ ∈ {s}",
"state_before": "α : Type u_1\ns✝ t s : Finset α\n⊢ powersetLen (card s) s = {s}",
"tactic": "ext"
},
{
"state_after": "case a\nα : Type u_1\ns✝ t s a✝ : Finset α\n⊢ a✝ ⊆ s ∧ card a✝ = card s... | [
277,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Algebra/Hom/NonUnitalAlg.lean | NonUnitalAlgHom.prod_fst_snd | [] | [
362,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/NumberTheory/RamificationInertia.lean | Ideal.IsDedekindDomain.ramificationIdx_ne_zero | [
{
"state_after": "R : Type u\ninst✝³ : CommRing R\nS : Type v\ninst✝² : CommRing S\nf : R →+* S\np : Ideal R\nP : Ideal S\ninst✝¹ : IsDomain S\ninst✝ : IsDedekindDomain S\nhp0 : map f p ≠ ⊥\nhP : IsPrime P\nle : map f p ≤ P\nhP0 : P ≠ ⊥\n⊢ ramificationIdx f p P ≠ 0",
"state_before": "R : Type u\ninst✝³ : Co... | [
175,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Data/Sigma/Basic.lean | PSigma.subtype_ext_iff | [] | [
262,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.BoundedFormula.semanticallyEquivalent_not_not | [
{
"state_after": "no goals",
"state_before": "L : Language\nT : Theory L\nα : Type w\nn : ℕ\nφ ψ : BoundedFormula L α n\nM : Theory.ModelType T\nv : α → ↑M\nxs : Fin n → ↑M\n⊢ Realize (φ ⇔ ∼∼φ) v xs",
"tactic": "simp"
}
] | [
523,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
522,
1
] |
Mathlib/Analysis/Asymptotics/SpecificAsymptotics.lean | Asymptotics.IsBigO.trans_tendsto_norm_atTop | [
{
"state_after": "case intro.intro\n𝕜 : Type u_2\ninst✝ : NormedLinearOrderedField 𝕜\nα : Type u_1\nu v : α → 𝕜\nl : Filter α\nhuv : u =O[l] v\nhu : Tendsto (fun x => ‖u x‖) l atTop\nc : ℝ\nhc : 0 < c\nhcuv : IsBigOWith c l u v\n⊢ Tendsto (fun x => ‖v x‖) l atTop",
"state_before": "𝕜 : Type u_2\ninst✝ :... | [
97,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Topology/Basic.lean | IsOpen.union | [
{
"state_after": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns s₁ s₂ t : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\nh₁ : IsOpen s₁\nh₂ : IsOpen s₂\n⊢ IsOpen (⋃ (b : Bool), bif b then s₁ else s₂)",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns s₁ s₂ t : Set α\np p₁ p₂ : α → Prop\n... | [
156,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/CategoryTheory/Monad/Adjunction.lean | CategoryTheory.Monad.left_comparison | [] | [
127,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.pair_preimage | [] | [
422,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.eq_iInf_of_mem_iff_exists_mem | [] | [
791,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
789,
1
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.HasIntegral.of_mul | [
{
"state_after": "ι : Type u\nE : Type v\nF : Type w\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\nI J : Box ι\nπ : TaggedPrepartition I\ninst✝ : Fintype ι\nl : IntegrationParams\nf g : (ι → ℝ) → E\nvol : ι →ᵇᵃ[⊤] E →L[ℝ] F\ny y' : F\na : ℝ\nh... | [
212,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Order/Hom/Lattice.lean | SupBotHom.cancel_left | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.109835\nι : Type ?u.109838\nα : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.109850\ninst✝⁷ : Sup α\ninst✝⁶ : Bot α\ninst✝⁵ : Sup β\ninst✝⁴ : Bot β\ninst✝³ : Sup γ\ninst✝² : Bot γ\ninst✝¹ : Sup δ\ninst✝ : Bot δ\ng : SupBotHom β γ\nf₁ f₂ : SupBot... | [
821,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
819,
1
] |
Mathlib/Topology/Instances/Nat.lean | Nat.dist_cast_real | [] | [
35,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/Deprecated/Submonoid.lean | Additive.isAddSubmonoid_iff | [] | [
71,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Std/Data/List/Lemmas.lean | List.infix_append' | [
{
"state_after": "α : Type u_1\nl₁ l₂ l₃ : List α\n⊢ l₂ <:+: l₁ ++ l₂ ++ l₃",
"state_before": "α : Type u_1\nl₁ l₂ l₃ : List α\n⊢ l₂ <:+: l₁ ++ (l₂ ++ l₃)",
"tactic": "rw [← List.append_assoc]"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl₁ l₂ l₃ : List α\n⊢ l₂ <:+: l₁ ++ ... | [
1566,
47
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1565,
9
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.pow_apply | [
{
"state_after": "case zero\nR : Type ?u.509735\nn : ℕ\n⊢ ↑(pow Nat.zero) n = if Nat.zero = 0 ∧ n = 0 then 0 else n ^ Nat.zero\n\ncase succ\nR : Type ?u.509735\nn n✝ : ℕ\n⊢ ↑(pow (succ n✝)) n = if succ n✝ = 0 ∧ n = 0 then 0 else n ^ succ n✝",
"state_before": "R : Type ?u.509735\nk n : ℕ\n⊢ ↑(pow k) n = if k... | [
766,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
762,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.IsPath.of_append_left | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v w : V\np : Walk G u v\nq : Walk G v w\n⊢ List.Nodup (support p ++ List.tail (support q)) → List.Nodup (support p)",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGr... | [
995,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
992,
1
] |
Mathlib/Analysis/Calculus/TangentCone.lean | uniqueDiffWithinAt_convex | [
{
"state_after": "case intro\n𝕜 : Type ?u.165851\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type ?u.165857\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type ?u.165952\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_1\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace ℝ G... | [
405,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
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