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/LinearAlgebra/Matrix/SesquilinearForm.lean | LinearMap.toMatrix₂Aux_eq | [
{
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1
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Mathlib/Analysis/Seminorm.lean | Seminorm.smul_comp | [] | [
358,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
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Mathlib/Logic/Denumerable.lean | Denumerable.ofNat_nat | [] | [
127,
6
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126,
1
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Mathlib/Algebra/BigOperators/Multiset/Lemmas.lean | Commute.multiset_sum_right | [
{
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"state_before": "α : Type u_1\ninst✝ : NonUnitalNonAssocSemiring α\ns : M... | [
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.sign_coe_pi_div_two | [
{
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}
] | [
971,
47
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970,
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.IsImage.of_image_eq | [] | [
544,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.map_add_right_Icc | [
{
"state_after": "ι : Type ?u.213211\nα : Type u_1\ninst✝² : OrderedCancelAddCommMonoid α\ninst✝¹ : ExistsAddOfLE α\ninst✝ : LocallyFiniteOrder α\na b c : α\n⊢ ↑(addRightEmbedding c) '' Set.Icc a b = Set.Icc (a + c) (b + c)",
"state_before": "ι : Type ?u.213211\nα : Type u_1\ninst✝² : OrderedCancelAddCommMo... | [
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38
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1048,
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Mathlib/Algebra/GCDMonoid/Basic.lean | gcd_dvd_gcd_mul_right_right | [] | [
496,
42
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495,
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Mathlib/Data/Set/Intervals/Basic.lean | Set.not_mem_Ioi | [] | [
1052,
9
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1051,
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Mathlib/Data/Nat/Order/Basic.lean | Nat.add_eq_min_iff | [
{
"state_after": "m n k l : ℕ\n⊢ m + n = min m n ↔ max m n = 0",
"state_before": "m n k l : ℕ\n⊢ m + n = min m n ↔ m = 0 ∧ n = 0",
"tactic": "rw [← max_eq_zero_iff]"
},
{
"state_after": "no goals",
"state_before": "m n k l : ℕ\n⊢ m + n = min m n ↔ max m n = 0",
"tactic": "cases' le_total... | [
147,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
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src/lean/Init/Core.lean | Setoid.trans | [] | [
1101,
22
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1100,
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Mathlib/Init/Data/Nat/Lemmas.lean | Nat.zero_ne_bit0 | [] | [
147,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
11
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Mathlib/Analysis/Calculus/FDeriv/Prod.lean | HasStrictFDerivAt.fst | [] | [
144,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
11
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Mathlib/Order/OrdContinuous.lean | RightOrdContinuous.map_isLeast | [] | [
182,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
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Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | SmoothManifoldWithCorners.chart_mem_maximalAtlas | [] | [
701,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
699,
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Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.adjoin_le_iff | [] | [
58,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Data/Option/Lemmas.lean | Option.eq_some_iff_get_eq | [
{
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"state_before": "α✝ : Type u_1\no : Option α✝\na : α✝\n⊢ o = some a ↔ ∃ h, get o h = a",
"tactic": "cases o <;> simp"
},
{
"state_after": "no goals",
"state_before": "case none\nα✝ : Type u_1\na : α... | [
65,
27
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
64,
1
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Mathlib/Topology/UniformSpace/Cauchy.lean | UniformContinuous.comp_cauchySeq | [] | [
255,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Topology/Inseparable.lean | inseparable_iff_forall_closed | [
{
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298,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Iic_union_Ici_of_le | [] | [
1211,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1210,
1
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_norm_rpow | [
{
"state_after": "case pos\nα : Type u_1\nE : Type ?u.1675097\nF : Type u_2\nG : Type ?u.1675103\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf : α → F\nhq_pos : 0 < q\nh0 : p = 0\n⊢ snorm (fun x => ‖f x‖... | [
520,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
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Mathlib/Topology/SubsetProperties.lean | NhdsContainBoxes.comm | [] | [
657,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
1
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Mathlib/LinearAlgebra/Basic.lean | LinearMap.map_dfinsupp_sum | [] | [
1148,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1146,
1
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.comp_C | [
{
"state_after": "no goals",
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"tactic": "simp [comp, (C : R →+* _).map_sum]"
}
] | [
546,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.mul_eq_top | [] | [
581,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
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Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.inv_def | [] | [
97,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/IntegralDomain.lean | card_fiber_eq_of_mem_range | [
{
"state_after": "case intro\nR : Type ?u.416251\nG : Type u_2\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDomain R\ninst✝³ : Group G\ninst✝² : Fintype G\nH : Type u_1\ninst✝¹ : Group H\ninst✝ : DecidableEq H\nf : G →* H\ny : H\nhy : y ∈ Set.range ↑f\nx : G\n⊢ card (filter (fun g => ↑f g = ↑f x) univ) = card (filter (fun ... | [
216,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
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Mathlib/Topology/Category/TopCat/Limits/Products.lean | TopCat.embedding_prod_map | [
{
"state_after": "J : Type v\ninst✝ : SmallCategory J\nW X Y Z : TopCat\nf : W ⟶ X\ng : Y ⟶ Z\nhf : Embedding ((forget TopCat).map f)\nhg : Embedding ((forget TopCat).map g)\nthis : Mono f\n⊢ Function.Injective ((forget TopCat).map (prod.map f g))",
"state_before": "J : Type v\ninst✝ : SmallCategory J\nW X ... | [
291,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
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Mathlib/Analysis/Calculus/DiffContOnCl.lean | DiffContOnCl.add | [] | [
94,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.update_eq_single_add_erase | [
{
"state_after": "case h\nι : Type u\nγ : Type w\nβ✝ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝¹ : (i : ι) → Zero (β✝ i)\ns : Finset ι\nx : (i : ↑↑s) → β✝ ↑i\ni✝ : ι\nf✝ : Π₀ (i : ι), β✝ i\nb✝ : β✝ i✝\nj✝ : ι\nβ : ι → Type u_1\ninst✝ : (i : ι) → AddZeroClass (β i)\nf : Π₀ (i : ... | [
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Mathlib/CategoryTheory/Limits/Shapes/Diagonal.lean | CategoryTheory.Limits.pullback_diagonal_map_snd_snd_fst | [
{
"state_after": "no goals",
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"tactic": "simp [condition]"
},
{
"state_after": "no go... | [
113,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
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Mathlib/Analysis/Normed/Group/Basic.lean | nnnorm_mul_le' | [] | [
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42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/SetTheory/ZFC/Basic.lean | PSet.Mem.mk | [] | [
276,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.lift_card_closure_le | [
{
"state_after": "L : Language\nM : Type w\nN : Type ?u.34936\nP : Type ?u.34939\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nS : Substructure L M\ns : Set M\n⊢ lift (#{ x // x ∈ LowerAdjoint.toFun (closure L) s }) ≤ max ℵ₀ (lift (#↑s) + lift (#(i : ℕ) × Functions L i))",
"state_b... | [
334,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
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Mathlib/RingTheory/PowerBasis.lean | PowerBasis.finrank | [
{
"state_after": "no goals",
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Real/Basic.lean | Real.ciInf_const_zero | [
{
"state_after": "case inl\nx y : ℝ\nα : Sort u_1\nh✝ : IsEmpty α\n⊢ (⨅ (x : α), 0) = 0\n\ncase inr\nx y : ℝ\nα : Sort u_1\nh✝ : Nonempty α\n⊢ (⨅ (x : α), 0) = 0",
"state_before": "x y : ℝ\nα : Sort u_1\n⊢ (⨅ (x : α), 0) = 0",
"tactic": "cases isEmpty_or_nonempty α"
},
{
"state_after": "no goals... | [
841,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
838,
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Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.lmapDomain_total | [
{
"state_after": "case h.h\nα : Type u_4\nM : Type u_2\nN : Type ?u.336034\nP : Type ?u.336037\nR : Type u_1\nS : Type ?u.336043\ninst✝¹² : Semiring R\ninst✝¹¹ : Semiring S\ninst✝¹⁰ : AddCommMonoid M\ninst✝⁹ : Module R M\ninst✝⁸ : AddCommMonoid N\ninst✝⁷ : Module R N\ninst✝⁶ : AddCommMonoid P\ninst✝⁵ : Module R... | [
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623,
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Mathlib/Order/Filter/Pi.lean | Filter.pi_mono | [] | [
63,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Computability/EpsilonNFA.lean | εNFA.eval_singleton | [] | [
133,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
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] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.eq_coe_iff | [
{
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"state_before": "α : Type u_1\ninst✝¹ : Monoid α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\na b : α\nn : ℕ\n⊢ multiplicity a b = ↑n ↔ a ^ n ... | [
167,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
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Mathlib/Topology/Category/TopCat/Opens.lean | TopologicalSpace.Opens.mapIso_refl | [] | [
275,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
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] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.trans | [] | [
474,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/Data/List/Infix.lean | List.prefix_iff_eq_take | [] | [
213,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tendsto_inv_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.123804\nγ : Type ?u.123807\na✝ b c d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\nf : Filter α\nm : α → ℝ≥0∞\na : ℝ≥0∞\nh : Tendsto (fun x => (m x)⁻¹) f (𝓝 a⁻¹)\n⊢ Tendsto m f (𝓝 a)",
"tactic": "simpa only [inv_inv] us... | [
538,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Bounded.lean | Set.bounded_gt_inter_not_gt | [] | [
430,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
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Mathlib/Data/Subtype.lean | Subtype.coind_injective | [
{
"state_after": "no goals",
"state_before": "α✝ : Sort ?u.7280\nβ✝ : Sort ?u.7283\nγ : Sort ?u.7286\np✝ q : α✝ → Prop\nα : Sort u_1\nβ : Sort u_2\nf : α → β\np : β → Prop\nh : ∀ (a : α), p (f a)\nhf : Injective f\nx y : α\nhxy : coind f h x = coind f h y\n⊢ f x = f y",
"tactic": "apply congr_arg Subtyp... | [
187,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Summable.neg | [] | [
808,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
807,
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Mathlib/Algebra/Algebra/Basic.lean | Module.algebraMap_end_eq_smul_id | [] | [
626,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
1
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Mathlib/Topology/MetricSpace/MetricSeparated.lean | IsMetricSeparated.symm | [] | [
41,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
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Mathlib/Data/Complex/Exponential.lean | Real.sin_three_mul | [
{
"state_after": "x y : ℝ\n⊢ ↑(sin (3 * x)) = ↑(3 * sin x - 4 * sin x ^ 3)",
"state_before": "x y : ℝ\n⊢ sin (3 * x) = 3 * sin x - 4 * sin x ^ 3",
"tactic": "rw [← ofReal_inj]"
},
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ ↑(sin (3 * x)) = ↑(3 * sin x - 4 * sin x ^ 3)",
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42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1336,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/EulerSineProd.lean | EulerSine.antideriv_sin_comp_const_mul | [
{
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"state_before": "z : ℂ\nn : ℕ\nhz : z ≠ 0\nx : ℝ\n⊢ HasDerivAt (fun y => -Complex.cos (2 * z * ↑y) / (2 * z)) (Compl... | [
62,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/RingTheory/Derivation/Basic.lean | Derivation.map_smul | [] | [
124,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Algebra/CharP/CharAndCard.lean | not_isUnit_prime_of_dvd_card | [] | [
85,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Analysis/NormedSpace/ENorm.lean | ENorm.map_sub_rev | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nV : Type u_2\ninst✝² : NormedField 𝕜\ninst✝¹ : AddCommGroup V\ninst✝ : Module 𝕜 V\ne : ENorm 𝕜 V\nx y : V\n⊢ ↑e (x - y) = ↑e (y - x)",
"tactic": "rw [← neg_sub, e.map_neg]"
}
] | [
116,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
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Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgEquiv.invFun_eq_symm | [] | [
832,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
831,
1
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Mathlib/SetTheory/Game/PGame.lean | PGame.relabel_moveLeft' | [] | [
1152,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1150,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | MeasureTheory.Measure.add_haar_eq_zero_of_disjoint_translates | [
{
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154,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
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Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.liftPropWithinAt_inter' | [
{
"state_after": "H : Type u_2\nM : Type u_1\nH' : Type u_3\nM' : Type u_4\nX : Type ?u.33513\ninst✝⁶ : TopologicalSpace H\ninst✝⁵ : TopologicalSpace M\ninst✝⁴ : ChartedSpace H M\ninst✝³ : TopologicalSpace H'\ninst✝² : TopologicalSpace M'\ninst✝¹ : ChartedSpace H' M'\ninst✝ : TopologicalSpace X\nG : StructureGr... | [
368,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
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Mathlib/Data/Bool/Basic.lean | Bool.and_or_distrib_right | [
{
"state_after": "no goals",
"state_before": "a b c : Bool\n⊢ ((a || b) && c) = (a && c || b && c)",
"tactic": "cases a <;> cases b <;> cases c <;> simp"
}
] | [
187,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
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Mathlib/Algebra/Order/Sub/Canonical.lean | tsub_inj_right | [] | [
282,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.castAdd_zero | [
{
"state_after": "case h.h\nn m : ℕ\nx✝ : Fin n\n⊢ ↑(↑(castAdd 0) x✝) = ↑(↑(cast (_ : n = n)) x✝)",
"state_before": "n m : ℕ\n⊢ ↑(castAdd 0) = ↑(cast (_ : n = n))",
"tactic": "ext"
},
{
"state_after": "case h.h\nn m : ℕ\nx✝ : Fin n\n⊢ ↑(↑(castAdd 0) x✝) = ↑x✝",
"state_before": "case h.h\nn m... | [
1138,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1135,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.le_iterate_of_add_int_le_map | [
{
"state_after": "no goals",
"state_before": "f g : CircleDeg1Lift\nx : ℝ\nm : ℤ\nh : x + ↑m ≤ ↑f x\nn : ℕ\n⊢ x + ↑n * ↑m ≤ (↑f^[n]) x",
"tactic": "simpa only [nsmul_eq_mul, add_right_iterate] using\n (f.commute_add_int m).symm.iterate_le_of_map_le (monotone_id.add_const (m : ℝ)) f.monotone h n"
}
] | [
580,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
577,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.one_lt_rpow_of_pos_of_lt_one_of_neg | [] | [
226,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.find?_some_eq_eq | [
{
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158,
28
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
156,
1
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Mathlib/Algebra/Group/Pi.lean | Pi.mulSingle_sup | [] | [
479,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_map | [] | [
939,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
938,
1
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Mathlib/Topology/Algebra/GroupWithZero.lean | ContinuousOn.div_const | [
{
"state_after": "no goals",
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74,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
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Mathlib/Topology/NoetherianSpace.lean | TopologicalSpace.noetherianSpace_TFAE | [
{
"state_after": "case tfae_1_iff_2\nα : Type u_1\nβ : Type ?u.1862\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\n⊢ NoetherianSpace α ↔ WellFounded fun s t => s < t\n\nα : Type u_1\nβ : Type ?u.1862\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ntfae_1_iff_2 : NoetherianSpace α ↔ WellFoun... | [
104,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
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Mathlib/Data/Real/NNReal.lean | NNReal.coe_sSup | [] | [
495,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
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Mathlib/CategoryTheory/Opposites.lean | CategoryTheory.NatTrans.rightOp_comp | [] | [
441,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
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Mathlib/MeasureTheory/Function/L2Space.lean | MeasureTheory.L2.mem_L1_inner | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.97006\n𝕜 : Type u_3\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : MeasurableSpace α\nμ : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : NormedAddCommGroup F\nf g : { x // x ∈ Lp E 2 }\n⊢ snorm (fun x => inner (↑↑f x) (↑↑g x)) 1 μ < ⊤... | [
191,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
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Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.adjoin_image | [
{
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"state_before": "R : Type u\nA : Type v\nB : Type w\ni... | [
221,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/MeasureTheory/Group/Integration.lean | MeasureTheory.lintegral_eq_zero_of_isMulLeftInvariant | [
{
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226,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
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] |
Mathlib/Data/Nat/PartENat.lean | PartENat.add_left_cancel_iff | [
{
"state_after": "no goals",
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"tactic": "rw [add_comm a, add_comm a, PartENat.add_right_cancel_iff ha]"
}
] | [
541,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
11
] |
Mathlib/Data/Set/Prod.lean | Set.univ_pi_subset_univ_pi_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nα : ι → Type u_1\nβ : ι → Type ?u.156455\ns s₁ s₂ : Set ι\nt t₁ t₂ : (i : ι) → Set (α i)\ni : ι\n⊢ pi univ t₁ ⊆ pi univ t₂ ↔ (∀ (i : ι), t₁ i ⊆ t₂ i) ∨ ∃ i, t₁ i = ∅",
"tactic": "simp [pi_subset_pi_iff]"
}
] | [
833,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
832,
1
] |
Mathlib/Data/Pi/Lex.lean | Pi.ofLex_apply | [] | [
63,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | lcm_one_left | [] | [
797,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
] |
Mathlib/Data/List/Basic.lean | List.foldl_eq_foldr | [
{
"state_after": "ι : Type ?u.249628\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf : α → α → α\nhcomm : Commutative f\nhassoc : Associative f\na b : α\nl : List α\n⊢ f b (foldl f a l) = f b (foldr f a l)",
"state_before": "ι : Type ?u.249628\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type... | [
2715,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2712,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.restrictSymm | [] | [
1263,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1262,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.sUnion_pair | [] | [
1184,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1183,
1
] |
Mathlib/Analysis/Convex/Quasiconvex.lean | MonotoneOn.quasiconcaveOn | [] | [
189,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Computability/Partrec.lean | Partrec.nat_casesOn_right | [
{
"state_after": "α : Type u_2\nβ : Type ?u.130006\nγ : Type ?u.130009\nσ : Type u_1\ninst✝³ : Primcodable α\ninst✝² : Primcodable β\ninst✝¹ : Primcodable γ\ninst✝ : Primcodable σ\nf : α → ℕ\ng : α → σ\nh : α → ℕ →. σ\nhf : Computable f\nhg : Computable g\nhh : Partrec₂ h\na : α\n⊢ Nat.rec (Part.some (g a)) (fu... | [
594,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | AddSubmonoid.mem_bsupr_iff_exists_dfinsupp | [] | [
1997,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1993,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.coe_symm_trans | [] | [
854,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
852,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.range_eq_map | [
{
"state_after": "case h\nG : Type u_1\nG' : Type ?u.457281\ninst✝⁴ : Group G\ninst✝³ : Group G'\nA : Type ?u.457290\ninst✝² : AddGroup A\nN : Type u_2\nP : Type ?u.457299\ninst✝¹ : Group N\ninst✝ : Group P\nK : Subgroup G\nf : G →* N\nx✝ : N\n⊢ x✝ ∈ range f ↔ x✝ ∈ map f ⊤",
"state_before": "G : Type u_1\nG... | [
2603,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2603,
1
] |
Mathlib/Analysis/SpecialFunctions/Arsinh.lean | Filter.Tendsto.arsinh | [] | [
211,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Order/Interval.lean | NonemptyInterval.coe_top_interval | [] | [
650,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
1
] |
Mathlib/Topology/MetricSpace/Holder.lean | HolderWith.dist_le | [] | [
263,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.comp_assoc | [] | [
184,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.eval_X | [] | [
1148,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1147,
1
] |
Mathlib/Logic/Encodable/Basic.lean | Encodable.nonempty_encodable | [] | [
469,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
] |
Mathlib/Order/RelClasses.lean | WellFoundedGT.fix_eq | [] | [
457,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.mkPiRing_eq_iff | [
{
"state_after": "R : Type u\nι : Type u'\nn : ℕ\nM : Fin (Nat.succ n) → Type v\nM₁ : ι → Type v₁\nM₂ : Type v₂\nM₃ : Type v₃\nM' : Type v'\ninst✝⁷ : CommSemiring R\ninst✝⁶ : (i : ι) → AddCommMonoid (M₁ i)\ninst✝⁵ : (i : Fin (Nat.succ n)) → AddCommMonoid (M i)\ninst✝⁴ : AddCommMonoid M₂\ninst✝³ : (i : Fin (Nat.... | [
1081,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1075,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.sup_subgroupOf_eq | [] | [
3166,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3164,
1
] |
Mathlib/Data/Real/GoldenRatio.lean | goldConj_mul_gold | [
{
"state_after": "⊢ φ * ψ = -1",
"state_before": "⊢ ψ * φ = -1",
"tactic": "rw [mul_comm]"
},
{
"state_after": "no goals",
"state_before": "⊢ φ * ψ = -1",
"tactic": "exact gold_mul_goldConj"
}
] | [
72,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.ToPartrec.Code.zero'_eval | [
{
"state_after": "no goals",
"state_before": "⊢ eval zero' = fun v => pure (0 :: v)",
"tactic": "simp [eval]"
}
] | [
143,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_blockDiagonal | [
{
"state_after": "m : Type ?u.1756003\nn : Type u_2\ninst✝⁶ : DecidableEq n\ninst✝⁵ : Fintype n\ninst✝⁴ : DecidableEq m\ninst✝³ : Fintype m\nR : Type v\ninst✝² : CommRing R\no : Type u_1\ninst✝¹ : Fintype o\ninst✝ : DecidableEq o\nM : o → Matrix n n R\n⊢ ∑ x : Perm (n × o), ↑↑(↑sign x) * ∏ x_1 : n × o, blockDia... | [
643,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
575,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.union_empty | [
{
"state_after": "no goals",
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"tactic": "simp"
}
] | [
1437,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1436,
1
] |
Mathlib/GroupTheory/Sylow.lean | Sylow.exists_subgroup_card_pow_prime_le | [
{
"state_after": "no goals",
"state_before": "G : Type u\nα : Type v\nβ : Type w\ninst✝¹ : Group G\ninst✝ : Fintype G\np : ℕ\n_hp✝ : Fact (Nat.Prime p)\nn m : ℕ\nhdvd : p ^ m ∣ Fintype.card G\nH : Subgroup G\nhH : Fintype.card { x // x ∈ H } = p ^ n\nhnm✝ : n ≤ m\nhnm : n < m\nh0m : 0 < m\n_wf : m - 1 < m\n... | [
650,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
635,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasFDerivWithinAt.congr | [] | [
884,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
882,
1
] |
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