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/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.isPath_def | [] | [
884,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
883,
1
] |
Mathlib/Order/Basic.lean | le_of_forall_lt | [] | [
537,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
536,
1
] |
Mathlib/Order/Heyting/Boundary.lean | Coheyting.boundary_sup_le | [
{
"state_after": "α : Type u_1\ninst✝ : CoheytingAlgebra α\na b : α\n⊢ a ⊓ ￢(a ⊔ b) ⊔ b ⊓ ￢(a ⊔ b) ≤ ∂ a ⊔ ∂ b",
"state_before": "α : Type u_1\ninst✝ : CoheytingAlgebra α\na b : α\n⊢ ∂ (a ⊔ b) ≤ ∂ a ⊔ ∂ b",
"tactic": "rw [boundary, inf_sup_right]"
},
{
"state_after": "no goals",
"state_befor... | [
96,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | Right.one_lt_mul_of_le_of_lt | [] | [
960,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
957,
1
] |
Mathlib/Algebra/Order/Monoid/Canonical/Defs.lean | le_one_iff_eq_one | [] | [
240,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.zero_re | [] | [
170,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
9
] |
Mathlib/Algebra/FreeMonoid/Count.lean | FreeMonoid.countp_of | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\np : α → Prop\ninst✝ : DecidablePred p\nx : α\n⊢ ↑(countp p) (of x) = if p x then ↑Multiplicative.ofAdd 1 else 1",
"tactic": "rw [countp_of', ofAdd_zero]"
}
] | [
72,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.Lf.not_gt | [] | [
794,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.abs_self_eq_nnrealPart_add_nnrealPart_neg | [
{
"state_after": "case h\nF : Type ?u.1620901\nα : Type u\nβ : Type v\nγ : Type w\ninst✝ : TopologicalSpace α\nf : α →ᵇ ℝ\nx : α\n⊢ (abs ∘ ↑f) x = (toReal ∘ ↑(nnrealPart f) + toReal ∘ ↑(nnrealPart (-f))) x",
"state_before": "F : Type ?u.1620901\nα : Type u\nβ : Type v\nγ : Type w\ninst✝ : TopologicalSpace α... | [
1624,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1620,
1
] |
Mathlib/Analysis/NormedSpace/Int.lean | Int.nnnorm_coe_units | [
{
"state_after": "no goals",
"state_before": "e : ℤˣ\n⊢ ‖↑e‖₊ = 1",
"tactic": "obtain rfl | rfl := units_eq_one_or e <;>\n simp only [Units.coe_neg_one, Units.val_one, nnnorm_neg, nnnorm_one]"
}
] | [
31,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
29,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.le_iff_specializes | [] | [
936,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
935,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.associated_left_inverse | [
{
"state_after": "no goals",
"state_before": "S : Type u_3\nR : Type u_1\nR₁ : Type ?u.423118\nM : Type u_2\ninst✝⁷ : Ring R\ninst✝⁶ : CommRing R₁\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\ninst✝³ : Module R₁ M\ninst✝² : CommSemiring S\ninst✝¹ : Algebra S R\ninst✝ : Invertible 2\nB₁ : BilinForm R M\nQ :... | [
804,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
801,
1
] |
Mathlib/Data/Setoid/Basic.lean | Setoid.le_def | [] | [
78,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.nontrivial_of_nonZeroDivisors | [
{
"state_after": "R : Type u_1\ninst✝² : Ring R\nS : Submonoid R\ninst✝¹ : OreSet S\ninst✝ : Nontrivial R\nhS : S ≤ R⁰\nh : 0 /ₒ 1 = 1 /ₒ 1\n⊢ False",
"state_before": "R : Type u_1\ninst✝² : Ring R\nS : Submonoid R\ninst✝¹ : OreSet S\ninst✝ : Nontrivial R\nhS : S ≤ R⁰\nh : 0 = 1\n⊢ False",
"tactic": "rw... | [
873,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
870,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.eq_insertNth_iff | [] | [
703,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
701,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.associated_iff_normalizedFactors_eq_normalizedFactors | [
{
"state_after": "α : Type u_1\ninst✝³ : CancelCommMonoidWithZero α\ninst✝² : DecidableEq α\ninst✝¹ : NormalizationMonoid α\ninst✝ : UniqueFactorizationMonoid α\nx y : α\nhx : x ≠ 0\nhy : y ≠ 0\nh : x ~ᵤ y\n⊢ normalizedFactors x = normalizedFactors y",
"state_before": "α : Type u_1\ninst✝³ : CancelCommMonoi... | [
737,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
731,
1
] |
Mathlib/Logic/IsEmpty.lean | isEmpty_ulift | [
{
"state_after": "no goals",
"state_before": "α✝ : Sort ?u.3602\nβ : Sort ?u.3605\nγ : Sort ?u.3608\nα : Type u_1\n⊢ IsEmpty (ULift α) ↔ IsEmpty α",
"tactic": "simp only [← not_nonempty_iff, nonempty_ulift]"
}
] | [
191,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | GroupTopology.toTopologicalSpace_bot | [] | [
1925,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1924,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.mem_mk | [] | [
109,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Std/Data/List/Lemmas.lean | List.forIn_eq_forIn | [] | [
1475,
78
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1475,
9
] |
Mathlib/Algebra/Category/GroupCat/EpiMono.lean | CommGroupCat.ker_eq_bot_of_mono | [] | [
416,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/Topology/Basic.lean | Disjoint.closure_left | [] | [
433,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | HomologicalComplex.d_comp_d | [
{
"state_after": "case pos\nι : Type u_1\nV : Type u\ninst✝¹ : Category V\ninst✝ : HasZeroMorphisms V\nc : ComplexShape ι\nC : HomologicalComplex V c\ni j k : ι\nhij : ComplexShape.Rel c i j\n⊢ d C i j ≫ d C j k = 0\n\ncase neg\nι : Type u_1\nV : Type u\ninst✝¹ : Category V\ninst✝ : HasZeroMorphisms V\nc : Comp... | [
79,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Data/MvPolynomial/Comap.lean | MvPolynomial.comapEquiv_coe | [] | [
121,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | norm_mul₃_le | [] | [
482,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/CategoryTheory/Sites/Sheafification.lean | CategoryTheory.GrothendieckTopology.isoSheafify_inv | [
{
"state_after": "case a\nC : Type u\ninst✝³ : Category C\nJ : GrothendieckTopology C\nD : Type w\ninst✝² : Category D\ninst✝¹ : ∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : Cover J X), HasMultiequalizer (Cover.index S P)\ninst✝ : ∀ (X : C), HasColimitsOfShape (Cover J X)ᵒᵖ D\nP : Cᵒᵖ ⥤ D\nhP : Presheaf.IsSheaf J P\n⊢ toSheafi... | [
581,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
578,
1
] |
Mathlib/GroupTheory/GroupAction/FixingSubgroup.lean | fixingSubmonoid_union | [] | [
86,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/RingTheory/Ideal/Cotangent.lean | Ideal.toCotangent_eq_zero | [] | [
84,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Topology/Separation.lean | SeparatedNhds.mono | [] | [
160,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.map_ceil | [
{
"state_after": "no goals",
"state_before": "F : Type u_3\nα : Type u_1\nβ : Type u_2\ninst✝⁴ : LinearOrderedSemiring α\ninst✝³ : LinearOrderedSemiring β\ninst✝² : FloorSemiring α\ninst✝¹ : FloorSemiring β\ninst✝ : RingHomClass F α β\na✝ : α\nb : β\nf : F\nhf : StrictMono ↑f\na : α\nn : ℕ\n⊢ ↑f a ≤ ↑n ↔ a ... | [
1513,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1512,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.angle_add_angle_eq_pi_of_angle_eq_pi | [
{
"state_after": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np1 p2 p3 p4 : P\nh : InnerProductGeometry.angle (p2 -ᵥ p3) (p4 -ᵥ p3) = π\n⊢ ∠ p1 p3 p2 + ∠ p1 p3 p4 = π",
"state_before": "V : Type u_1\nP : Type... | [
196,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
8
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.one_le_iff_ne_zero | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.180072\nβ : Type ?u.180075\nγ : Type ?u.180078\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no : Ordinal\n⊢ 1 ≤ o ↔ o ≠ 0",
"tactic": "rw [one_le_iff_pos, Ordinal.pos_iff_ne_zero]"
}
] | [
1081,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1080,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_lt_of_lt_one_of_le' | [] | [
864,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
862,
1
] |
Mathlib/GroupTheory/GroupAction/BigOperators.lean | Multiset.smul_prod | [] | [
67,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Data/Pi/Interval.lean | Pi.card_Iio | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : ι → Type u_2\ninst✝⁴ : DecidableEq ι\ninst✝³ : Fintype ι\ninst✝² : (i : ι) → DecidableEq (α i)\ninst✝¹ : (i : ι) → PartialOrder (α i)\ninst✝ : (i : ι) → LocallyFiniteOrderBot (α i)\nb : (i : ι) → α i\n⊢ Finset.card (Iio b) = ∏ i : ι, Finset.car... | [
80,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Topology/Sheaves/SheafOfFunctions.lean | TopCat.Presheaf.toTypes_isSheaf | [
{
"state_after": "X : TopCat\nT : ↑X → Type u\nι : Type u\nU : ι → Opens ↑X\nsf : (i : ι) → (forget (Type u)).obj ((presheafToTypes X T).obj (U i).op)\nhsf : IsCompatible (presheafToTypes X T) U sf\nindex : { x // x ∈ iSup U } → ι\nindex_spec : ∀ (x : { x // x ∈ iSup U }), ↑x ∈ U (index x)\n⊢ ∃! s, IsGluing (pr... | [
79,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_preimage_of_subset_range | [
{
"state_after": "α β : Type u\nf : α → β\ns : Set β\nh : s ⊆ range f\n⊢ lift (#↑s) ≤ lift (#↑(f ⁻¹' s))",
"state_before": "α β : Type u\nf : α → β\ns : Set β\nh : s ⊆ range f\n⊢ (#↑s) ≤ (#↑(f ⁻¹' s))",
"tactic": "rw [← lift_id (#↑(f ⁻¹' s)), ← lift_id (#↑(s))]"
},
{
"state_after": "no goals",
... | [
2199,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2196,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | affineSpan_eq_affineSpan_lineMap_units | [
{
"state_after": "k : Type u_1\nV : Type u_3\nP : Type u_2\ninst✝⁴ : Ring k\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AffineSpace V P\ninst✝ : Nontrivial k\ns : Set P\np : P\nhp : p ∈ s\nw : ↑s → kˣ\nthis : s = Set.range Subtype.val\n⊢ affineSpan k (Set.range fun q => ↑(AffineMap.lineMap p ↑q) ↑(w... | [
1197,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1184,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.mul_pos_iff | [] | [
614,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.mem_span_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\na b : α\ninst✝ : CommSemiring α\nI : Ideal α\nx y x✝ : α\n⊢ x✝ * y = x ↔ x = y * x✝",
"tactic": "rw [eq_comm, mul_comm]"
}
] | [
499,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Mathlib/Data/Set/Basic.lean | Set.diff_union_inter | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns✝ s₁ s₂ t✝ t₁ t₂ u s t : Set α\n⊢ s ∩ t ∪ s \\ t = s",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns✝ s₁ s₂ t✝ t₁ t₂ u s t : Set α\n⊢ s \\ t ∪ s ∩ t = s",
"tactic": "rw [union_comm]"
},
{
"s... | [
1872,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1870,
1
] |
Mathlib/Analysis/Seminorm.lean | coe_normSeminorm | [] | [
1201,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1200,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.sin_sub_pi | [] | [
394,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
Mathlib/Algebra/Homology/ComplexShape.lean | ComplexShape.down'_mk | [] | [
189,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.comapDomain_add | [
{
"state_after": "case h\nα : Type u_3\nβ : Type u_1\nγ : Type ?u.306308\nι : Type ?u.306311\nM : Type u_2\nM' : Type ?u.306317\nN : Type ?u.306320\nP : Type ?u.306323\nG : Type ?u.306326\nH : Type ?u.306329\nR : Type ?u.306332\nS : Type ?u.306335\ninst✝ : AddZeroClass M\nf : α → β\nv₁ v₂ : β →₀ M\nhv₁ : Set.In... | [
763,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
1
] |
Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.mk_le_mk | [] | [
193,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Topology/Order/Basic.lean | tendsto_comp_coe_Ioi_atBot | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na b : α\ns : Set α\nl : Filter β\nf : α → β\n⊢ Tendsto (fun x => f ↑x) atBot l ↔ Tendsto (f ∘ Subtype.val) atBot l",
"state_before": "α : Type u\nβ :... | [
2547,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2545,
1
] |
Mathlib/Data/Set/Function.lean | Set.piecewise_le_piecewise | [
{
"state_after": "no goals",
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1424,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1421,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_union_add_inter₀ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.294414\nγ : Type ?u.294417\nδ : Type ?u.294420\nι : Type ?u.294423\nR : Type ?u.294426\nR' : Type ?u.294429\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t s : S... | [
1709,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1706,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_mul | [
{
"state_after": "no goals",
"state_before": "b x y : ℝ\nhx : x ≠ 0\nhy : y ≠ 0\n⊢ logb b (x * y) = logb b x + logb b y",
"tactic": "simp_rw [logb, log_mul hx hy, add_div]"
}
] | [
69,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.cos_antiperiodic | [
{
"state_after": "θ : Angle\n⊢ cos (θ + ↑π) = -cos θ",
"state_before": "⊢ Function.Antiperiodic cos ↑π",
"tactic": "intro θ"
},
{
"state_after": "case h\nx✝ : ℝ\n⊢ cos (↑x✝ + ↑π) = -cos ↑x✝",
"state_before": "θ : Angle\n⊢ cos (θ + ↑π) = -cos θ",
"tactic": "induction θ using Real.Angle.in... | [
414,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.zero_iff_num_zero | [
{
"state_after": "no goals",
"state_before": "a b c q : ℚ\nx✝ : q = 0\n⊢ q.num = 0",
"tactic": "simp [*]"
}
] | [
422,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Order/Zorn.lean | zorn_superset_nonempty | [] | [
210,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Data/Fintype/Card.lean | card_finset_fin_le | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.11098\nβ : Type ?u.11101\nγ : Type ?u.11104\nn : ℕ\ns : Finset (Fin n)\n⊢ card s ≤ n",
"tactic": "simpa only [Fintype.card_fin] using s.card_le_univ"
}
] | [
324,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_smul_le | [] | [
1102,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1101,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.diam_thickening_le | [
{
"state_after": "case pos\nι : Sort ?u.126772\nα✝ : Type u\nβ : Type v\ninst✝¹ : PseudoEMetricSpace α✝\nδ ε : ℝ\ns✝ t : Set α✝\nx : α✝\nα : Type u_1\ninst✝ : PseudoMetricSpace α\ns : Set α\nhε : 0 ≤ ε\nhs : Bounded s\n⊢ diam (thickening ε s) ≤ diam s + 2 * ε\n\ncase neg\nι : Sort ?u.126772\nα✝ : Type u\nβ : Ty... | [
1231,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1223,
1
] |
Mathlib/Data/List/Zip.lean | List.zip_map_left | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.23064\nε : Type ?u.23067\nf : α → γ\nl₁ : List α\nl₂ : List β\n⊢ zip (map f l₁) l₂ = map (Prod.map f id) (zip l₁ l₂)",
"tactic": "rw [← zip_map, map_id]"
}
] | [
131,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
src/lean/Init/Data/Array/Basic.lean | Array.toArrayLit_eq | [
{
"state_after": "case h\nα : Type u_1\nas : Array α\nn : Nat\nhsz : size as = n\n⊢ as.data = (toArrayLit as n hsz).data",
"state_before": "α : Type u_1\nas : Array α\nn : Nat\nhsz : size as = n\n⊢ as = toArrayLit as n hsz",
"tactic": "apply ext'"
},
{
"state_after": "case h\nα : Type u_1\nas : ... | [
757,
85
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
744,
1
] |
Mathlib/Topology/Inseparable.lean | Inseparable.mem_open_iff | [] | [
365,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/Topology/Sequences.lean | SeqCompactSpace.tendsto_subseq | [] | [
279,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/MeasureTheory/Measure/Regular.lean | Set.exists_isOpen_le_add | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type ?u.11634\ninst✝² : MeasurableSpace α\ninst✝¹ : TopologicalSpace α\nμ✝ : Measure α\nA : Set α\nμ : Measure α\ninst✝ : OuterRegular μ\nε : ℝ≥0∞\nhε : ε ≠ 0\nH : ↑↑μ A = ⊤\n⊢ ∃ U, U ⊇ A ∧ IsOpen U ∧ ↑↑μ U ≤ ↑↑μ A + ε\n\ncase inr\nα : Type u_1\nβ : Type ?u.11634\ni... | [
272,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.addHom_ext' | [] | [
1030,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1028,
1
] |
Mathlib/Topology/Algebra/Order/Compact.lean | IsCompact.exists_local_min_mem_open | [] | [
479,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
] |
Mathlib/Order/BooleanAlgebra.lean | Bool.compl_eq_bnot | [] | [
800,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
799,
1
] |
Mathlib/Order/Filter/NAry.lean | Filter.map₂_right_comm | [
{
"state_after": "α : Type u_4\nα' : Type ?u.39127\nβ : Type u_5\nβ' : Type ?u.39133\nγ : Type u_3\nγ' : Type ?u.39139\nδ : Type u_2\nδ' : Type u_6\nε : Type u_1\nε' : Type ?u.39151\nm✝ : α → β → γ\nf f₁ f₂ : Filter α\ng g₁ g₂ : Filter β\nh h₁ h₂ : Filter γ\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\nu : Set γ\nv : Set ... | [
323,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.proj_pi | [] | [
1251,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1250,
1
] |
Mathlib/Topology/Maps.lean | OpenEmbedding.isOpenMap | [] | [
553,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.coe_toWeakDualBCNN | [] | [
451,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_eq_top | [] | [
1068,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1067,
1
] |
Mathlib/RingTheory/WittVector/Defs.lean | WittVector.wittMul_vars | [] | [
408,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/RepresentationTheory/Action.lean | Action.functorCategoryMonoidalEquivalence.inv_counit_app_hom | [] | [
669,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
667,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.relindex_iInf_ne_zero | [] | [
458,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
] |
Mathlib/Data/List/Nodup.lean | List.nthLe_index_of | [] | [
178,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.uniformEmbedding_toProdMulOpposite | [] | [
579,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
578,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.iUnion_div_right_image | [] | [
750,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
749,
1
] |
Mathlib/Control/Functor.lean | Functor.of_mem_supp | [] | [
302,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.coe_range | [] | [
2990,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2989,
1
] |
Mathlib/Analysis/Convex/Segment.lean | segment_eq_image | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.58852\nG : Type ?u.58855\nι : Type ?u.58858\nπ : ι → Type ?u.58863\ninst✝⁵ : OrderedRing 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : AddCommGroup F\ninst✝² : AddCommGroup G\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\nx y z : E\... | [
199,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/CategoryTheory/Adjunction/Reflective.lean | CategoryTheory.Functor.essImage.unit_isIso | [
{
"state_after": "C : Type u₁\nD : Type u₂\nE : Type u₃\ninst✝³ : Category C\ninst✝² : Category D\ninst✝¹ : Category E\ni : D ⥤ C\ninst✝ : Reflective i\nA : C\nh : A ∈ essImage i\n⊢ (ofRightAdjoint i).unit.app A =\n (getIso h).inv ≫ (ofRightAdjoint i).unit.app (i.obj (witness h)) ≫ (leftAdjoint i ⋙ i).map (g... | [
84,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Algebra/DirectSum/Module.lean | DirectSum.toModule_lof | [] | [
123,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.map_multiset_prod | [] | [
1191,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1190,
11
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.not_isDiag_of_mem_edgeFinset | [] | [
902,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
901,
1
] |
Mathlib/Order/Heyting/Regular.lean | Heyting.Regular.coe_sdiff | [] | [
250,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Data/Polynomial/Splits.lean | Polynomial.splits_X_pow | [] | [
167,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Analysis/Convex/Function.lean | convexOn_iff_div | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.760703\nα : Type ?u.760706\nβ : Type u_3\nι : Type ?u.760712\ninst✝⁴ : LinearOrderedField 𝕜\ninst✝³ : AddCommMonoid E\ninst✝² : OrderedAddCommMonoid β\ninst✝¹ : SMul 𝕜 E\ninst✝ : SMul 𝕜 β\ns : Set E\nf : E → β\nh : ∀ ⦃x : E⦄, x ∈ s → ∀ ⦃y : E⦄, y ∈ s... | [
1052,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1043,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.sup_neBot | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.62053\nι : Sort x\nf✝ g✝ : Filter α\ns t : Set α\nf g : Filter α\n⊢ NeBot (f ⊔ g) ↔ NeBot f ∨ NeBot g",
"tactic": "simp only [neBot_iff, not_and_or, Ne.def, sup_eq_bot_iff]"
}
] | [
513,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
9
] |
Mathlib/LinearAlgebra/Dual.lean | Subspace.dualRestrict_comp_dualLift | [
{
"state_after": "case h.h\nK : Type u\nV : Type v\ninst✝² : Field K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nW✝ W : Subspace K V\nφ : Module.Dual K { x // x ∈ W }\nx : { x // x ∈ W }\n⊢ ↑(↑(comp (dualRestrict W) (dualLift W)) φ) x = ↑(↑1 φ) x",
"state_before": "K : Type u\nV : Type v\ninst✝² : Field K... | [
1032,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1030,
1
] |
Mathlib/Algebra/ModEq.lean | AddCommGroup.sub_modEq_iff_modEq_add' | [] | [
273,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.get_set_same | [
{
"state_after": "case mk\nn : ℕ\nα : Type u_1\nβ : Type ?u.57781\nγ : Type ?u.57784\ni : Fin n\na : α\nval✝ : List α\nproperty✝ : List.length val✝ = n\n⊢ get (set { val := val✝, property := property✝ } i a) i = a",
"state_before": "n : ℕ\nα : Type u_1\nβ : Type ?u.57781\nγ : Type ?u.57784\nv : Vector α n\n... | [
595,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.disjoint_pure_atTop | [] | [
101,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Logic/Basic.lean | forall₃_imp | [] | [
634,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
632,
1
] |
Mathlib/Topology/Separation.lean | t0Space_iff_not_inseparable | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u\nβ : Type v\ninst✝¹ : TopologicalSpace α✝\nα : Type u\ninst✝ : TopologicalSpace α\n⊢ T0Space α ↔ ∀ (x y : α), x ≠ y → ¬Inseparable x y",
"tactic": "simp only [t0Space_iff_inseparable, Ne.def, not_imp_not]"
}
] | [
188,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | Real.differentiable_exp | [] | [
195,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.SimpleFunc.tendsto_approxOn_range_Lp | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.804606\nβ : Type ?u.804609\nι : Type ?u.804612\nE : Type ?u.804615\nF : Type ?u.804618\n𝕜 : Type ?u.804621\ninst✝⁵ : MeasurableSpace β\ninst✝⁴ : MeasurableSpace E\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\nq : ℝ\np : ℝ≥0∞\ninst✝¹... | [
201,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Order/GaloisConnection.lean | OrderIso.bddAbove_image | [] | [
433,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/Algebra/Homology/ShortExact/Preadditive.lean | CategoryTheory.Splitting.split_add | [
{
"state_after": "𝒜 : Type u_2\ninst✝² : Category 𝒜\nA B C A' B' C' : 𝒜\nf : A ⟶ B\ng : B ⟶ C\nf' : A' ⟶ B'\ng' : B' ⟶ C'\ninst✝¹ : Preadditive 𝒜\ninst✝ : HasBinaryBiproducts 𝒜\nh : Splitting f g\n⊢ (h.iso.hom ≫ biprod.fst) ≫ f + g ≫ biprod.inr ≫ h.iso.inv = 𝟙 B",
"state_before": "𝒜 : Type u_2\ninst✝... | [
280,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.top_subgroupOf | [] | [
1645,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1644,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiff_iff_ftaylorSeries | [
{
"state_after": "case mp\n𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nX : Type uX\ninst✝¹ : ... | [
1640,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1635,
1
] |
Mathlib/Combinatorics/Composition.lean | Composition.sizeUpTo_index_le | [
{
"state_after": "n : ℕ\nc : Composition n\nj : Fin n\nH : ¬sizeUpTo c ↑(index c j) ≤ ↑j\n⊢ False",
"state_before": "n : ℕ\nc : Composition n\nj : Fin n\n⊢ sizeUpTo c ↑(index c j) ≤ ↑j",
"tactic": "by_contra H"
},
{
"state_after": "n : ℕ\nc : Composition n\nj : Fin n\ni : Fin (length c) := index... | [
356,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/Analysis/Calculus/Deriv/Polynomial.lean | Polynomial.differentiableWithinAt_aeval | [] | [
117,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
11
] |
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