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/Algebra/BigOperators/Finprod.lean | finprod_mem_iUnion | [
{
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1065,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Data/Finset/Lattice.lean | Finset.inf_insert | [] | [
339,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
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Mathlib/RingTheory/TensorProduct.lean | TensorProduct.Algebra.smul_def | [] | [
1208,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1207,
1
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | borel_eq_top_of_countable | [
{
"state_after": "α : Type u_1\nβ : Type ?u.26837\nγ : Type ?u.26840\nγ₂ : Type ?u.26843\nδ : Type ?u.26846\nι : Sort y\ns✝ t u : Set α\ninst✝² : TopologicalSpace α\ninst✝¹ : T1Space α\ninst✝ : Countable α\ns : Set α\nx✝ : MeasurableSet s\n⊢ MeasurableSet (⋃ (x : α) (_ : x ∈ s), {x})",
"state_before": "α : ... | [
77,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasDerivAt.csin | [] | [
214,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
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Mathlib/Order/Filter/Prod.lean | Filter.coprod_neBot_left | [] | [
509,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
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Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.X.nat_coe_snd | [] | [
280,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
9
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Mathlib/Data/Set/Pointwise/BigOperators.lean | Set.list_prod_singleton | [] | [
124,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | uniformity_basis_edist_inv_two_pow | [] | [
263,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
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Mathlib/Analysis/SpecialFunctions/Exponential.lean | hasStrictDerivAt_exp_smul_const' | [] | [
419,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
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Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.kernelSubobject_zero | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\nX Y Z : C\ninst✝¹ : HasZeroMorphisms C\nf : X ⟶ Y\ninst✝ : HasKernel f\nA B : C\n⊢ IsIso (kernel.ι 0)",
"tactic": "infer_instance"
}
] | [
194,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.sub_eq_of_eq_add | [] | [
1124,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1123,
11
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Mathlib/CategoryTheory/Sites/Sheaf.lean | CategoryTheory.Presheaf.isSheaf_iff_isLimit | [] | [
177,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
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Mathlib/Algebra/Homology/Additive.lean | ChainComplex.single₀MapHomologicalComplex_inv_app_succ | [] | [
392,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_add | [] | [
377,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/Data/List/Rotate.lean | List.isRotated_nil_iff' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nl l' : List α\n⊢ [] ~r l ↔ [] = l",
"tactic": "rw [isRotated_comm, isRotated_nil_iff, eq_comm]"
}
] | [
497,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
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Mathlib/Computability/TuringMachine.lean | Turing.BlankExtends.trans | [
{
"state_after": "case intro.intro\nΓ : Type u_1\ninst✝ : Inhabited Γ\nl₁ : List Γ\ni j : ℕ\n⊢ BlankExtends l₁ (l₁ ++ List.replicate i default ++ List.replicate j default)",
"state_before": "Γ : Type u_1\ninst✝ : Inhabited Γ\nl₁ l₂ l₃ : List Γ\n⊢ BlankExtends l₁ l₂ → BlankExtends l₂ l₃ → BlankExtends l₁ l₃"... | [
90,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Convex/Between.lean | Wbtw.swap_right_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nV : Type u_2\nV' : Type ?u.218711\nP : Type u_3\nP' : Type ?u.218717\ninst✝⁷ : OrderedRing R\ninst✝⁶ : AddCommGroup V\ninst✝⁵ : Module R V\ninst✝⁴ : AddTorsor V P\ninst✝³ : AddCommGroup V'\ninst✝² : Module R V'\ninst✝¹ : AddTorsor V' P'\ninst✝ : No... | [
396,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
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Std/Data/Int/DivMod.lean | Int.ediv_mul_cancel | [] | [
704,
58
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
703,
11
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Mathlib/Topology/Sheaves/Stalks.lean | TopCat.Presheaf.stalk_mono_of_mono | [] | [
510,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.congr' | [] | [
304,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/Data/Int/Bitwise.lean | Int.testBit_lnot | [
{
"state_after": "no goals",
"state_before": "n k : ℕ\n⊢ testBit (lnot ↑n) k = !testBit (↑n) k",
"tactic": "simp [lnot, testBit]"
},
{
"state_after": "no goals",
"state_before": "n k : ℕ\n⊢ testBit (lnot -[n+1]) k = !testBit -[n+1] k",
"tactic": "simp [lnot, testBit]"
}
] | [
367,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
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Mathlib/Data/Finset/Lattice.lean | Finset.inf_product_right | [] | [
437,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieModuleHom.map_sub | [] | [
741,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_mul_const_Ioi | [] | [
519,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.sUnion_empty | [
{
"state_after": "case a\nz✝ : ZFSet\n⊢ z✝ ∈ ⋃₀ ∅ ↔ z✝ ∈ ∅",
"state_before": "⊢ ⋃₀ ∅ = ∅",
"tactic": "ext"
},
{
"state_after": "no goals",
"state_before": "case a\nz✝ : ZFSet\n⊢ z✝ ∈ ⋃₀ ∅ ↔ z✝ ∈ ∅",
"tactic": "simp"
}
] | [
1070,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1068,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.sizeOf_eq_sizeOf | [
{
"state_after": "no goals",
"state_before": "α : Type uu\nβ : Type vv\nl₁✝ l₂✝ : List α\ninst✝ : SizeOf α\nl₁ l₂ : List α\nh : l₁ ~ l₂\n⊢ sizeOf l₁ = sizeOf l₂",
"tactic": "induction h with | nil => rfl\n| cons _ _ h_sz₁₂ => simp [h_sz₁₂]\n| swap => simp [add_left_comm]\n| trans _ _ h_sz₁₂ h_sz₂₃ => si... | [
322,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.Measure.pi_caratheodory | [
{
"state_after": "ι : Type u_1\nι' : Type ?u.2502507\nα : ι → Type u_2\ninst✝¹ : Fintype ι\nm : (i : ι) → OuterMeasure (α i)\ninst✝ : (i : ι) → MeasurableSpace (α i)\nμ : (i : ι) → Measure (α i)\n⊢ ∀ (i : ι),\n MeasurableSpace.comap (fun b => b i) ((fun a => inst✝ a) i) ≤\n OuterMeasure.caratheodory (Ou... | [
301,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Analysis/VonNeumannAlgebra/Basic.lean | VonNeumannAlgebra.mem_commutant_iff | [] | [
141,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Std/Data/List/Lemmas.lean | List.diff_nil | [] | [
1492,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1492,
9
] |
Mathlib/Data/Complex/Exponential.lean | Real.sin_sub_sin | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ ↑(sin x - sin y) = ↑(2 * sin ((x - y) / 2) * cos ((x + y) / 2))",
"tactic": "simp [sin_sub_sin]"
}
] | [
1214,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1213,
8
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.mem_comap | [] | [
283,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.diff | [] | [
806,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
805,
1
] |
Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.indep_of_indep_of_le_right | [] | [
199,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | GroupNorm.apply_one | [] | [
887,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
886,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.refl_symm | [] | [
374,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/AlgebraicGeometry/PresheafedSpace.lean | AlgebraicGeometry.PresheafedSpace.mk_coe | [] | [
83,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.inf_prod | [] | [
1688,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1687,
1
] |
Mathlib/Data/Set/Intervals/Instances.lean | Set.Icc.coe_eq_one | [
{
"state_after": "α : Type u_1\ninst✝ : OrderedSemiring α\nx : ↑(Icc 0 1)\n⊢ x = 1 ↔ ↑x = 1",
"state_before": "α : Type u_1\ninst✝ : OrderedSemiring α\nx : ↑(Icc 0 1)\n⊢ ↑x = 1 ↔ x = 1",
"tactic": "symm"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedSemiring α... | [
92,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.set_lintegral_max | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1032041\nγ : Type ?u.1032044\nδ : Type ?u.1032047\nm : MeasurableSpace α\nμ ν : Measure α\nf g : α → ℝ≥0∞\nhf : Measurable f\nhg : Measurable g\ns : Set α\n⊢ MeasurableSet {x | g x < f x}\n\nα : Type u_1\nβ : Type ?u.1032041\nγ : Type ?u.1032044\nδ : Type ?u.1032047\n... | [
1257,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1253,
1
] |
Mathlib/LinearAlgebra/SymplecticGroup.lean | SymplecticGroup.coe_J | [] | [
132,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/CategoryTheory/EqToHom.lean | CategoryTheory.congrArg_mpr_hom_left | [
{
"state_after": "case refl\nC : Type u₁\ninst✝ : Category C\nX Z : C\nq : X ⟶ Z\n⊢ Eq.mpr (_ : (X ⟶ Z) = (X ⟶ Z)) q = eqToHom (_ : X = X) ≫ q",
"state_before": "C : Type u₁\ninst✝ : Category C\nX Y Z : C\np : X = Y\nq : Y ⟶ Z\n⊢ Eq.mpr (_ : (X ⟶ Z) = (Y ⟶ Z)) q = eqToHom p ≫ q",
"tactic": "cases p"
}... | [
94,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.inducing | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.57703\nδ : Type ?u.57706\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nh : α ≃ₜ β\n⊢ Inducing (↑(Homeomorph.symm h) ∘ ↑h)",
"tactic": "simp only [sy... | [
229,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
11
] |
Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.eval_gcd_eq_zero | [] | [
334,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.lift_mono | [] | [
101,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.Cofork.IsColimit.homIso_natural | [] | [
588,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
584,
1
] |
Mathlib/Data/Nat/Parity.lean | Odd.of_dvd_nat | [] | [
367,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/Analysis/Calculus/ParametricIntervalIntegral.lean | intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_le | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁶ : IsROrC 𝕜\nμ : MeasureTheory.Measure ℝ\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : CompleteSpace E\nH : Type ?u.684895\ninst✝¹ : NormedAddCommGroup H\ninst✝ : NormedSpace 𝕜 H\na b ε : ℝ\nbound : ℝ → ℝ\nF F... | [
115,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
8
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_const_id_atTop | [] | [
1885,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1884,
1
] |
Mathlib/Topology/ContinuousOn.lean | Continuous.piecewise | [] | [
1211,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1208,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pullback.condition | [] | [
1214,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1212,
1
] |
Mathlib/Combinatorics/Additive/SalemSpencer.lean | mulSalemSpencer_mul_left_iff₀ | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.103189\nα : Type u_1\nβ : Type ?u.103195\n𝕜 : Type ?u.103198\nE : Type ?u.103201\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NoZeroDivisors α\ns : Set α\na : α\nha : a ≠ 0\nhs : MulSalemSpencer ((fun x x_1 => x * x_1) a '' s)\nb c d : α\nhb : b ∈ ... | [
257,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Order/Hom/Bounded.lean | TopHom.cancel_right | [] | [
288,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Combinatorics/SetFamily/Compression/Down.lean | Down.mem_compression | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\n𝒜 ℬ : Finset (Finset α)\ns : Finset α\na : α\n⊢ s ∈ 𝒜 ∧ erase s a ∈ 𝒜 ∨ (∃ a_1, a_1 ∈ 𝒜 ∧ erase a_1 a = s) ∧ ¬s ∈ 𝒜 ↔ s ∈ 𝒜 ∧ erase s a ∈ 𝒜 ∨ insert a s ∈ 𝒜 ∧ ¬s ∈ 𝒜",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\n𝒜 ℬ : Finset (Finset ... | [
174,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Analysis/Normed/Ring/Seminorm.lean | RingNorm.apply_one | [] | [
221,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/CategoryTheory/Limits/Opposites.lean | CategoryTheory.Limits.pushoutIsoUnopPullback_inv_fst | [
{
"state_after": "case a\nC : Type u₁\ninst✝³ : Category C\nJ : Type u₂\ninst✝² : Category J\nX✝ : Type v₂\nX Y Z : C\nf : X ⟶ Z\ng : X ⟶ Y\ninst✝¹ : HasPushout f g\ninst✝ : HasPullback f.op g.op\n⊢ ((pushoutIsoUnopPullback f g).inv.op ≫ pullback.fst).unop = pushout.inl.op.unop",
"state_before": "C : Type u... | [
699,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
694,
1
] |
Mathlib/GroupTheory/Nilpotent.lean | lowerCentralSeries_pi_of_finite | [
{
"state_after": "G : Type ?u.343966\ninst✝³ : Group G\nH : Subgroup G\ninst✝² : Normal H\nη : Type u_1\nGs : η → Type u_2\ninst✝¹ : (i : η) → Group (Gs i)\ninst✝ : Finite η\nn : ℕ\npi : ((i : η) → Subgroup (Gs i)) → Subgroup ((i : η) → Gs i) := fun f => Subgroup.pi Set.univ f\n⊢ lowerCentralSeries ((i : η) → G... | [
799,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
787,
1
] |
Mathlib/GroupTheory/Coset.lean | leftCoset_mem_leftCoset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Group α\ns : Subgroup α\na : α\nha : a ∈ s\n⊢ ∀ (x : α), x ∈ a *l ↑s ↔ x ∈ ↑s",
"tactic": "simp [mem_leftCoset_iff, mul_mem_cancel_left (s.inv_mem ha)]"
}
] | [
224,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Order/CompleteLattice.lean | Monotone.iInf_comp_eq | [] | [
1001,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
999,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.bijOn | [] | [
256,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
11
] |
Mathlib/Data/Multiset/Lattice.lean | Multiset.inf_dedup | [] | [
162,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/GroupTheory/Subsemigroup/Center.lean | Set.subset_center_units | [] | [
89,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Order/Filter/Extr.lean | isMinOn_dual_iff | [] | [
234,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Order/BoundedOrder.lean | min_bot_left | [] | [
835,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
834,
1
] |
Mathlib/Topology/ContinuousOn.lean | continuousWithinAt_update_same | [] | [
798,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
791,
1
] |
Mathlib/Tactic/CategoryTheory/Elementwise.lean | Tactic.Elementwise.forall_congr_forget_Type | [] | [
46,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Topology/LocallyConstant/Algebra.lean | LocallyConstant.charFn_eq_one | [] | [
115,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | HasFDerivWithinAt.cexp | [] | [
130,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Data/Sum/Order.lean | Sum.Lex.lt_def | [] | [
344,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.map_symm_eq_iff_map_eq | [
{
"state_after": "case mp\nG : Type u_2\nG' : Type ?u.263490\ninst✝⁴ : Group G\ninst✝³ : Group G'\nA : Type ?u.263499\ninst✝² : AddGroup A\nH✝ : Subgroup G\nk : Set G\nN : Type u_1\ninst✝¹ : Group N\nP : Type ?u.263526\ninst✝ : Group P\nH : Subgroup N\ne : G ≃* N\n⊢ map (↑e) (map (↑(MulEquiv.symm e)) H) = H\n\n... | [
1491,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1485,
1
] |
Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | deriv_cexp | [] | [
113,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Std/Data/List/Lemmas.lean | List.suffix_of_suffix_length_le | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\nl₁ l₃ l₂ : List α✝\nh₁ : l₁ <:+ l₃\nh₂ : l₂ <:+ l₃\nll : length l₁ ≤ length l₂\n⊢ length (reverse l₁) ≤ length (reverse l₂)",
"tactic": "simp [ll]"
}
] | [
1674,
90
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1671,
1
] |
Mathlib/Data/Matrix/Rank.lean | Matrix.rank_le_height | [] | [
159,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Data/Rat/NNRat.lean | NNRat.coe_list_sum | [] | [
256,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.subset_zeroLocus_vanishingIdeal | [] | [
236,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | Decidable.mul_lt_mul'' | [
{
"state_after": "α : Type u\nβ : Type ?u.59742\ninst✝¹ : StrictOrderedSemiring α\na b c d : α\ninst✝ : DecidableRel fun x x_1 => x ≤ x_1\nh1 : a < c\nh2 : b < d\nh3 : 0 ≤ a\nh4 : 0 ≤ b\nb0 : 0 = b\n⊢ 0 < c * d",
"state_before": "α : Type u\nβ : Type ?u.59742\ninst✝¹ : StrictOrderedSemiring α\na b c d : α\n... | [
556,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
11
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.BoundedFormula.realize_mapTermRel_id | [
{
"state_after": "case falsum\nL : Language\nL' : Language\nM : Type w\nN : Type ?u.71406\nP : Type ?u.71409\ninst✝³ : Structure L M\ninst✝² : Structure L N\ninst✝¹ : Structure L P\nα : Type u'\nβ : Type v'\nn✝¹ l : ℕ\nφ ψ : BoundedFormula L α l\nθ : BoundedFormula L α (Nat.succ l)\nv✝ : α → M\nxs✝¹ : Fin l → M... | [
379,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.hasBasis_nhds_of_ne_top | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.66801\nβ : Type ?u.66804\nγ : Type ?u.66807\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\nxt : x ≠ ⊤\n⊢ HasBasis (𝓝 x) (fun x => 0 < x) fun ε => Icc (x - ε) (x + ε)",
"tactic": "simpa only [pos_iff_ne_zero] using hasBasis_nhd... | [
254,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.BoundedFormula.realize_foldr_inf | [
{
"state_after": "case nil\nL : Language\nL' : Language\nM : Type w\nN : Type ?u.45572\nP : Type ?u.45575\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nn l : ℕ\nφ ψ : BoundedFormula L α l\nθ : BoundedFormula L α (Nat.succ l)\nv✝ : α → M\nxs✝ : Fin l → M\nv : α... | [
295,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.BinaryBicone.binary_cofan_inl_toCocone | [] | [
1040,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1039,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.mem_toAddSubmonoid | [] | [
489,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
1
] |
Mathlib/Topology/Order/Basic.lean | nhds_basis_abs_sub_lt | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrderedAddCommGroup α\ninst✝¹ : OrderTopology α\nl : Filter β\nf g : β → α\ninst✝ : NoMaxOrder α\na : α\n⊢ HasBasis (⨅ (r : α) (_ : r > 0), 𝓟 {b | abs (b - a) < r}) (fun ε => 0 < ε) fun ε => {b | abs (b - a) < ε}"... | [
1915,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1910,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image₂_inter_union_subset | [
{
"state_after": "α : Type u_1\nα' : Type ?u.103900\nβ : Type u_2\nβ' : Type ?u.103906\nγ : Type ?u.103909\nγ' : Type ?u.103912\nδ : Type ?u.103915\nδ' : Type ?u.103918\nε : Type ?u.103921\nε' : Type ?u.103924\nζ : Type ?u.103927\nζ' : Type ?u.103930\nν : Type ?u.103933\ninst✝⁹ : DecidableEq α'\ninst✝⁸ : Decida... | [
541,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
1
] |
Mathlib/Analysis/Asymptotics/Theta.lean | Asymptotics.isTheta_const_smul_left | [] | [
283,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.C_eq_coe_nat | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type u_1\na a' a₁ a₂ : R\ne : ℕ\nn✝ m : σ\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S₁\np q : MvPolynomial σ R\nn : ℕ\n⊢ ↑C ↑n = ↑n",
"tactic": "induction n <;> simp [Nat.succ_eq_add_one... | [
269,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/Algebra/Lie/BaseChange.lean | LieAlgebra.ExtendScalars.bracket_lie_smul | [
{
"state_after": "case refine'_1\nR : Type u\nA : Type w\nL : Type v\ninst✝⁴ : CommRing R\ninst✝³ : CommRing A\ninst✝² : Algebra R A\ninst✝¹ : LieRing L\ninst✝ : LieAlgebra R L\na : A\nx y : A ⊗[R] L\n⊢ ⁅0, a • y⁆ = a • ⁅0, y⁆\n\ncase refine'_2\nR : Type u\nA : Type w\nL : Type v\ninst✝⁴ : CommRing R\ninst✝³ : ... | [
131,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
9
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.FinMeasSupp.of_map | [] | [
1215,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1213,
1
] |
Mathlib/GroupTheory/SemidirectProduct.lean | SemidirectProduct.left_inr | [] | [
145,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.bound | [] | [
294,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/Logic/Basic.lean | dite_ne_left_iff | [
{
"state_after": "α : Sort u_1\nβ : Sort ?u.35535\nσ : α → Sort ?u.35531\nf : α → β\nP Q : Prop\ninst✝¹ : Decidable P\ninst✝ : Decidable Q\na b c : α\nA : P → α\nB : ¬P → α\n⊢ (∃ x, ¬B x = a) ↔ ∃ h, a ≠ B h",
"state_before": "α : Sort u_1\nβ : Sort ?u.35535\nσ : α → Sort ?u.35531\nf : α → β\nP Q : Prop\nins... | [
1161,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1159,
1
] |
Mathlib/GroupTheory/Commutator.lean | Subgroup.commutator_pi_pi_le | [] | [
221,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.lift_down | [
{
"state_after": "α : Type ?u.113662\nβ : Type ?u.113665\nγ : Type ?u.113668\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na : Ordinal\nb : Ordinal\nh : b ≤ lift a\n⊢ card b ≤ card (lift a)",
"state_before": "α : Type ?u.113662\nβ : Type ?u.113665\nγ : Type ?u.113668\nr : α → α → Prop\ns : β → β → ... | [
815,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
813,
1
] |
Mathlib/Data/List/Infix.lean | List.prefix_rfl | [] | [
60,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/AlgebraicTopology/DoldKan/PInfty.lean | AlgebraicTopology.DoldKan.QInfty_comp_PInfty | [
{
"state_after": "case h\nC : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\nn : ℕ\n⊢ HomologicalComplex.Hom.f (QInfty ≫ PInfty) n = HomologicalComplex.Hom.f 0 n",
"state_before": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\n⊢ QInfty ≫ PIn... | [
157,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Data/MvPolynomial/PDeriv.lean | MvPolynomial.pderiv_eq_zero_of_not_mem_vars | [] | [
113,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Topology/Order/Basic.lean | Dense.exists_le' | [
{
"state_after": "case pos\nα : Type u\nβ : Type v\nγ : Type w\ninst✝² : TopologicalSpace α\ninst✝¹ : LinearOrder α\ninst✝ : OrderClosedTopology α\nf g : β → α\ns : Set α\nhs : Dense s\nhbot : ∀ (x : α), IsBot x → x ∈ s\nx : α\nhx : IsBot x\n⊢ ∃ y, y ∈ s ∧ y ≤ x\n\ncase neg\nα : Type u\nβ : Type v\nγ : Type w\n... | [
781,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
775,
1
] |
Mathlib/Algebra/Invertible.lean | mul_right_eq_iff_eq_mul_invOf | [
{
"state_after": "no goals",
"state_before": "α : Type u\nc a b : α\ninst✝¹ : Monoid α\ninst✝ : Invertible c\n⊢ a * c = b ↔ a = b * ⅟c",
"tactic": "rw [← mul_right_inj_of_invertible (c := ⅟c), mul_mul_invOf_self_cancel]"
}
] | [
321,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.BoundedFormula.induction_on_exists_not | [] | [
635,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
626,
1
] |
Std/Data/Rat/Lemmas.lean | Rat.normalize.reduced' | [
{
"state_after": "num : Int\nden g : Nat\nden_nz : den ≠ 0\ne : g = Nat.gcd (Int.natAbs num) den\n⊢ Nat.coprime (Int.natAbs (Int.div num ↑g)) (den / g)",
"state_before": "num : Int\nden g : Nat\nden_nz : den ≠ 0\ne : g = Nat.gcd (Int.natAbs num) den\n⊢ Nat.coprime (Int.natAbs (num / ↑g)) (den / g)",
"ta... | [
18,
35
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
15,
1
] |
Mathlib/RingTheory/Ideal/LocalRing.lean | LocalRing.ResidueField.mapEquiv_trans | [] | [
468,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
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