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/Divisibility/Basic.lean | one_dvd | [] | [
130,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
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Mathlib/CategoryTheory/Extensive.lean | CategoryTheory.BinaryCofan.mono_inr_of_isVanKampen | [
{
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241,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
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Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.type_lt | [] | [
220,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
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Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | LiouvilleWith.sub_nat_iff | [
{
"state_after": "no goals",
"state_before": "p q x y : ℝ\nr : ℚ\nm : ℤ\nn : ℕ\n⊢ LiouvilleWith p (x - ↑n) ↔ LiouvilleWith p x",
"tactic": "rw [← Rat.cast_coe_nat, sub_rat_iff]"
}
] | [
283,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
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Mathlib/CategoryTheory/Generator.lean | CategoryTheory.isSeparator_coprod_of_isSeparator_left | [
{
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"state_before": "C : Type u₁\ninst✝³ : Category C\nD : Type u₂\ninst✝² : Category D\ninst✝¹ : HasZeroMorphisms C\nG H : C\ninst✝ : HasBinaryCoproduct G H\nhG : IsSeparator G\n⊢ {G} ⊆ {G, H}",
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] | [
564,
64
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Mathlib/Data/Complex/Basic.lean | Complex.bit0_im | [] | [
217,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
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Mathlib/GroupTheory/Subsemigroup/Basic.lean | Subsemigroup.mem_sInf | [] | [
250,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
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Mathlib/Data/Set/Sups.lean | Set.empty_sups | [] | [
133,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.SimpleFunc.integral_eq_sum_of_subset | [
{
"state_after": "α : Type u_2\nE : Type ?u.107493\nF : Type u_1\n𝕜 : Type ?u.107499\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace ℝ F\np : ℝ≥0∞\nG : Type ?u.107601\nF' : Type ?u.107604\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedAddCommGroup F'\ninst✝¹ : NormedSpace ℝ ... | [
343,
68
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332,
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Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.StronglyMeasurable.stronglyMeasurableAtFilter | [] | [
73,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
11
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Mathlib/RingTheory/IntegralClosure.lean | IsIntegralClosure.isIntegral | [] | [
844,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
842,
11
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.natTrailingDegree_nat_cast | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b : R\nn✝ m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nn : ℕ\n⊢ natTrailingDegree ↑n = 0",
"tactic": "simp only [← C_eq_nat_cast, natTrailingDegree_C]"
}
] | [
249,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.IsImage.inter_eq_of_inter_eq_of_eqOn | [] | [
576,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
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Mathlib/Data/Set/Equitable.lean | Set.equitableOn_iff_exists_le_le_add_one | [
{
"state_after": "α : Type u_1\nβ : Type ?u.456\ns : Set α\nf : α → ℕ\n⊢ EquitableOn s f → ∃ b, ∀ (a : α), a ∈ s → b ≤ f a ∧ f a ≤ b + 1",
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"tactic": "refine' ⟨_, fun ... | [
57,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
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Mathlib/CategoryTheory/Idempotents/Karoubi.lean | CategoryTheory.Idempotents.Karoubi.hom_ext_iff | [
{
"state_after": "case mp\nC : Type u_1\ninst✝ : Category C\nP Q : Karoubi C\nf g : P ⟶ Q\n⊢ f = g → f.f = g.f\n\ncase mpr\nC : Type u_1\ninst✝ : Category C\nP Q : Karoubi C\nf g : P ⟶ Q\n⊢ f.f = g.f → f = g",
"state_before": "C : Type u_1\ninst✝ : Category C\nP Q : Karoubi C\nf g : P ⟶ Q\n⊢ f = g ↔ f.f = g... | [
115,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
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Mathlib/Algebra/Invertible.lean | invOf_mul | [
{
"state_after": "no goals",
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"tactic": "simp [← mul_assoc]"
}
] | [
296,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
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Mathlib/Topology/Bornology/Constructions.lean | Bornology.forall_isBounded_image_eval_iff | [] | [
109,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
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Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.log_one_right | [] | [
376,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
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Mathlib/Algebra/Group/Prod.lean | MonoidHom.coe_prodMap | [] | [
609,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
608,
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.cycleOf_mul_of_apply_right_eq_self | [
{
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1125,
62
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Mathlib/Topology/Algebra/Module/LocallyConvex.lean | LocallyConvexSpace.ofBases | [] | [
66,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
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Mathlib/Data/Multiset/Basic.lean | Multiset.filterMap_map | [] | [
2154,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2152,
1
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Mathlib/Data/Matrix/Basic.lean | Matrix.conjTranspose_intCast_smul | [
{
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24
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2210,
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Mathlib/RingTheory/HahnSeries.lean | HahnSeries.single_zero_mul_eq_smul | [
{
"state_after": "case coeff.h\nΓ : Type u_2\nR : Type u_1\ninst✝¹ : OrderedCancelAddCommMonoid Γ\ninst✝ : Semiring R\nr : R\nx : HahnSeries Γ R\nx✝ : Γ\n⊢ coeff (↑(single 0) r * x) x✝ = coeff (r • x) x✝",
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760,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
757,
1
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Mathlib/Data/Complex/Exponential.lean | Real.cosh_add_sinh | [
{
"state_after": "x y : ℝ\n⊢ ↑(cosh x + sinh x) = ↑(exp x)",
"state_before": "x y : ℝ\n⊢ cosh x + sinh x = exp x",
"tactic": "rw [← ofReal_inj]"
},
{
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"state_before": "x y : ℝ\n⊢ ↑(cosh x + sinh x) = ↑(exp x)",
"tactic": "simp"
}
] | [
1403,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1403,
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Mathlib/Data/Finset/Lattice.lean | Finset.codisjoint_inf_right | [] | [
558,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
11
] |
Mathlib/Algebra/Order/Group/Defs.lean | inv_mul_le_one_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Group α\ninst✝¹ : LE α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b c d : α\n⊢ b ≤ a * 1 ↔ b ≤ a",
"tactic": "rw [mul_one]"
}
] | [
149,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
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Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | LinearMap.nondegenerate_toMatrix_iff | [] | [
732,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
729,
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Mathlib/Topology/Sequences.lean | mem_closure_iff_seq_limit | [
{
"state_after": "X : Type u_1\nY : Type ?u.2722\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : FrechetUrysohnSpace X\ns : Set X\na : X\n⊢ a ∈ seqClosure s ↔ ∃ x, (∀ (n : ℕ), x n ∈ s) ∧ Tendsto x atTop (𝓝 a)",
"state_before": "X : Type u_1\nY : Type ?u.2722\ninst✝² : TopologicalSpace X\... | [
137,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
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Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.polar_add_left | [] | [
267,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_abs_atBot_atTop | [] | [
939,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
938,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.ext_hom | [] | [
753,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
751,
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] |
Mathlib/Analysis/ODE/PicardLindelof.lean | PicardLindelof.FunSpace.continuous_vComp | [
{
"state_after": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nv : PicardLindelof E\nf : FunSpace v\nthis : Continuous ((fun x => (↑x, toFun f x)) ∘ proj v)\n⊢ Continuous (vComp f)",
"state_before": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nv : PicardLin... | [
234,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
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] |
Mathlib/LinearAlgebra/Pi.lean | LinearMap.iInf_ker_proj | [
{
"state_after": "R : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nι' : Type x'\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M₂\ninst✝⁴ : Module R M₂\ninst✝³ : AddCommMonoid M₃\ninst✝² : Module R M₃\nφ : ι → Type i\ninst✝¹ : (i : ι)... | [
108,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
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Mathlib/Algebra/Periodic.lean | Function.Periodic.neg | [
{
"state_after": "no goals",
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"tactic": "simpa only [sub_eq_add_neg, Periodic] using h.sub_eq"
}
] | [
174,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
11
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.denom_div_dvd | [
{
"state_after": "case pos\nK : Type u\ninst✝ : Field K\np q : K[X]\nhq : q = 0\n⊢ denom (↑(algebraMap K[X] (RatFunc K)) p / ↑(algebraMap K[X] (RatFunc K)) q) ∣ q\n\ncase neg\nK : Type u\ninst✝ : Field K\np q : K[X]\nhq : ¬q = 0\n⊢ denom (↑(algebraMap K[X] (RatFunc K)) p / ↑(algebraMap K[X] (RatFunc K)) q) ∣ q"... | [
1231,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1226,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.mem_join | [] | [
317,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/LinearAlgebra/Determinant.lean | AlternatingMap.map_basis_eq_zero_iff | [
{
"state_after": "case intro\nR : Type u_2\ninst✝⁷ : CommRing R\nM : Type u_3\ninst✝⁶ : AddCommGroup M\ninst✝⁵ : Module R M\nM' : Type ?u.2607358\ninst✝⁴ : AddCommGroup M'\ninst✝³ : Module R M'\nι✝ : Type ?u.2607900\ninst✝² : DecidableEq ι✝\ninst✝¹ : Fintype ι✝\ne✝ : Basis ι✝ R M\nι : Type u_1\ninst✝ : Finite ι... | [
590,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
584,
1
] |
Mathlib/Data/QPF/Univariate/Basic.lean | Qpf.Fix.rec_eq | [
{
"state_after": "F : Type u → Type u\ninst✝ : Functor F\nq : Qpf F\nα : Type u\ng : F α → α\nx : F (Fix F)\nthis : recF g ∘ fixToW = rec g\n⊢ rec g (mk x) = g (rec g <$> x)",
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296,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Algebra/Star/SelfAdjoint.lean | isSelfAdjoint_add_star_self | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nA : Type ?u.12261\ninst✝¹ : AddCommMonoid R\ninst✝ : StarAddMonoid R\nx : R\n⊢ IsSelfAdjoint (x + star x)",
"tactic": "simp only [isSelfAdjoint_iff, add_comm, star_add, star_star]"
}
] | [
146,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
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Mathlib/Data/List/Range.lean | List.chain'_range_succ | [
{
"state_after": "α : Type u\nr : ℕ → ℕ → Prop\nn : ℕ\n⊢ Chain' r (range n ++ [n]) ↔ ∀ (m : ℕ), m < n → r m (succ m)",
"state_before": "α : Type u\nr : ℕ → ℕ → Prop\nn : ℕ\n⊢ Chain' r (range (succ n)) ↔ ∀ (m : ℕ), m < n → r m (succ m)",
"tactic": "rw [range_succ]"
},
{
"state_after": "case zero\... | [
104,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
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Mathlib/RingTheory/Finiteness.lean | Submodule.FG.prod | [
{
"state_after": "no goals",
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58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
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Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.mem_inf | [
{
"state_after": "no goals",
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"tactic": "simp only [inf_def, mem_biUnion, mem_restri... | [
577,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
575,
1
] |
Mathlib/LinearAlgebra/TensorAlgebra/Basic.lean | TensorAlgebra.ι_comp_lift | [
{
"state_after": "no goals",
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"tactic": "convert (lif... | [
131,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/LinearAlgebra/PiTensorProduct.lean | PiTensorProduct.reindex_trans | [
{
"state_after": "case a\nι : Type u_1\nι₂ : Type u_2\nι₃ : Type u_3\nR : Type u_4\ninst✝⁷ : CommSemiring R\nR₁ : Type ?u.488461\nR₂ : Type ?u.488464\ns : ι → Type ?u.488469\ninst✝⁶ : (i : ι) → AddCommMonoid (s i)\ninst✝⁵ : (i : ι) → Module R (s i)\nM : Type u_5\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nE... | [
510,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
1
] |
Mathlib/Data/Polynomial/EraseLead.lean | Polynomial.card_support_eq | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\nf : R[X]\nn : ℕ\n⊢ card (support f) = n → ∃ k x hk hx, f = ∑ i : Fin n, ↑C (x i) * X ^ k i",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nf : R[X]\nn : ℕ\n⊢ card (support f) = n ↔ ∃ k x hk hx, f = ∑ i : Fin n, ↑C (x i) * X ^ k i",
"tactic": "refi... | [
351,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | Differentiable.mul_const | [] | [
438,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | AddValuation.valuation_apply | [] | [
655,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
654,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.Ico_eq_Iio | [] | [
1286,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1285,
11
] |
Mathlib/Order/CompleteLattice.lean | le_sSup_iff | [] | [
169,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Topology/NoetherianSpace.lean | TopologicalSpace.noetherianSpace_iff_of_homeomorph | [] | [
133,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | UniformSpace.mem_ball_self | [] | [
621,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
620,
1
] |
Mathlib/Topology/Order/Basic.lean | frontier_Ioo | [
{
"state_after": "no goals",
"state_before": "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\na b : α\nh : a < b\n⊢ frontier (Ioo a b) = {a, b}",
"tactic": "rw [frontier, closure_Ioo h.ne, ... | [
2369,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2368,
1
] |
Mathlib/Order/Max.lean | IsTop.snd | [] | [
428,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.one_le_pi_div_two | [
{
"state_after": "⊢ 1 ≤ choose exists_cos_eq_zero",
"state_before": "⊢ 1 ≤ π / 2",
"tactic": "rw [Real.pi, mul_div_cancel_left _ (two_ne_zero' ℝ)]"
},
{
"state_after": "no goals",
"state_before": "⊢ 1 ≤ choose exists_cos_eq_zero",
"tactic": "exact (Classical.choose_spec exists_cos_eq_zer... | [
145,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Data/Multiset/Dedup.lean | Multiset.dedup_ext | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.9380\ninst✝ : DecidableEq α\ns t : Multiset α\n⊢ dedup s = dedup t ↔ ∀ (a : α), a ∈ s ↔ a ∈ t",
"tactic": "simp [Nodup.ext]"
}
] | [
130,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.of_coe | [] | [
392,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
] |
Mathlib/Data/Set/Sups.lean | Set.sups_eq_empty | [] | [
143,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Data/Part.lean | Part.ne_none_iff | [
{
"state_after": "case mp\nα : Type u_1\nβ : Type ?u.5585\nγ : Type ?u.5588\no : Part α\n⊢ o ≠ none → ∃ x, o = some x\n\ncase mpr\nα : Type u_1\nβ : Type ?u.5585\nγ : Type ?u.5588\no : Part α\n⊢ (∃ x, o = some x) → o ≠ none",
"state_before": "α : Type u_1\nβ : Type ?u.5585\nγ : Type ?u.5588\no : Part α\n⊢ o... | [
209,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Logic/Basic.lean | bex_imp | [
{
"state_after": "no goals",
"state_before": "α : Sort u_1\nr p q : α → Prop\nP Q : (x : α) → p x → Prop\nb : Prop\n⊢ (∃ x h, P x h) → b ↔ ∀ (x : α) (h : p x), P x h → b",
"tactic": "simp"
}
] | [
1076,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1076,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.bit1_comp | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q r : R[X]\n⊢ comp (bit1 p) q = bit1 (comp p q)",
"tactic": "simp only [bit1, add_comp, bit0_comp, one_comp]"
}
] | [
649,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.support_mono | [] | [
447,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_add_eq_left_of_natDegree_lt | [] | [
703,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
701,
1
] |
Mathlib/Topology/MetricSpace/MetricSeparated.lean | IsMetricSeparated.empty_left | [] | [
50,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Analysis/Complex/UnitDisc/Basic.lean | Complex.UnitDisc.im_conj | [] | [
243,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Data/Set/Intervals/Monoid.lean | Set.image_const_add_Ioo | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝¹ : OrderedCancelAddCommMonoid M\ninst✝ : ExistsAddOfLE M\na b c d : M\n⊢ (fun x => a + x) '' Ioo b c = Ioo (a + b) (a + c)",
"tactic": "simp only [add_comm a, image_add_const_Ioo]"
}
] | [
142,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/MeasureTheory/Integral/RieszMarkovKakutani.lean | exists_lt_rieszContentAux_add_pos | [
{
"state_after": "case intro.intro.intro\nX : Type u_1\ninst✝ : TopologicalSpace X\nΛ : (X →ᵇ ℝ≥0) →ₗ[ℝ≥0] ℝ≥0\nK : Compacts X\nε : ℝ≥0\nεpos : 0 < ε\nα : ℝ≥0\nα_hyp : α < rieszContentAux Λ K + ε\nf : X →ᵇ ℝ≥0\nf_hyp : f ∈ {f | ∀ (x : X), x ∈ K → 1 ≤ ↑f x} ∧ ↑Λ f = α\n⊢ ∃ f, (∀ (x : X), x ∈ K → 1 ≤ ↑f x) ∧ ↑Λ f... | [
93,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | StrictAntiOn.mul_const' | [] | [
1429,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1427,
1
] |
Std/Data/RBMap/WF.lean | Std.RBNode.Ordered.balLeft | [
{
"state_after": "α : Type u_1\ncmp : α → α → Ordering\nl : RBNode α\nv : α\nr : RBNode α\nlv : All (fun x => cmpLT cmp x v) l\nvr : All (fun x => cmpLT cmp v x) r\nhl : Ordered cmp l\nhr : Ordered cmp r\n⊢ Ordered cmp\n (match l with\n | node red a x b => node red (node black a x b) v r\n | l =>\n ... | [
250,
27
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
240,
11
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.toSet_sdiff | [
{
"state_after": "x y : ZFSet\n⊢ toSet (ZFSet.sep (fun z => ¬z ∈ y) x) = toSet x \\ toSet y",
"state_before": "x y : ZFSet\n⊢ toSet (x \\ y) = toSet x \\ toSet y",
"tactic": "change (ZFSet.sep (fun z => z ∉ y) x).toSet = _"
},
{
"state_after": "case h\nx y x✝ : ZFSet\n⊢ x✝ ∈ toSet (ZFSet.sep (fu... | [
1163,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1160,
1
] |
Mathlib/Algebra/Field/Basic.lean | div_add_same | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.2192\nK : Type ?u.2195\ninst✝ : DivisionSemiring α\na b c d : α\nh : b ≠ 0\n⊢ (a + b) / b = a / b + 1",
"tactic": "rw [← div_self h, add_div]"
}
] | [
43,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | Arity.const_succ | [] | [
102,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.apply_le_nfpBFamily | [
{
"state_after": "case refine'_1\no : Ordinal\nf : (b : Ordinal) → b < o → Ordinal → Ordinal\nho : o ≠ 0\nH : ∀ (i : Ordinal) (hi : i < o), IsNormal (f i hi)\na : Ordinal\nb : Ordinal\nh : ∀ (i : Ordinal) (hi : i < o), f i hi b ≤ nfpBFamily o f a\n⊢ b ≤ nfpBFamily o f a\n\ncase refine'_2\no : Ordinal\nf : (b : ... | [
336,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.not_mem_Ici | [] | [
1044,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1043,
1
] |
Std/Data/Array/Init/Lemmas.lean | Array.foldrM_eq_foldrM_data | [
{
"state_after": "no goals",
"state_before": "m : Type u_1 → Type u_2\nα : Type u_3\nβ : Type u_1\ninst✝ : Monad m\nf : α → β → m β\ninit : β\narr : Array α\n⊢ foldrM f init arr (size arr) = List.foldrM f init arr.data",
"tactic": "rw [foldrM_eq_reverse_foldlM_data, List.foldlM_reverse]"
}
] | [
69,
58
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
66,
1
] |
Mathlib/Data/Fintype/Card.lean | Finite.injective_iff_surjective | [] | [
630,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
626,
1
] |
Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.uniformInducing_equivBoundedOfCompact | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nE : Type ?u.908\ninst✝³ : TopologicalSpace α\ninst✝² : CompactSpace α\ninst✝¹ : MetricSpace β\ninst✝ : NormedAddCommGroup E\n⊢ ∀ (s : Set (C(α, β) × C(α, β))),\n (∃ i,\n (IsCompact i.fst ∧ ∃ i_1, 0 < i_1 ∧ {p | dist p.fst p.snd ≤ i_1} ⊆ i.snd) ∧\n ... | [
71,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.inv_bind | [] | [
1077,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1076,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Star.lean | fderivWithin_star | [] | [
103,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.MulticospanIndex.fstPiMap_π | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\nI : MulticospanIndex C\ninst✝¹ : HasProduct I.left\ninst✝ : HasProduct I.right\nb : I.R\n⊢ fstPiMap I ≫ Pi.π I.right b = Pi.π I.left (fstTo I b) ≫ fst I b",
"tactic": "simp [fstPiMap]"
}
] | [
230,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/RingTheory/DiscreteValuationRing/Basic.lean | DiscreteValuationRing.irreducible_of_span_eq_maximalIdeal | [
{
"state_after": "R✝ : Type u\ninst✝⁵ : CommRing R✝\ninst✝⁴ : IsDomain R✝\ninst✝³ : DiscreteValuationRing R✝\nR : Type u_1\ninst✝² : CommRing R\ninst✝¹ : LocalRing R\ninst✝ : IsDomain R\nϖ : R\nhϖ : ϖ ≠ 0\nh : maximalIdeal R = span {ϖ}\nh2 : ¬IsUnit ϖ\n⊢ Irreducible ϖ",
"state_before": "R✝ : Type u\ninst✝⁵ ... | [
92,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.coe_centralizer | [] | [
522,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
] |
Mathlib/Data/Complex/Module.lean | Complex.finrank_real_complex_fact | [] | [
201,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.eq_or_mem_iff_mem | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ns : WSeq α\na a' : α\ns' : WSeq α\nc : Computation (Option (α × WSeq α))\ne : destruct s = c\n⊢ some (a', s') ∈ c → (a ∈ s ↔ a = a' ∨ a ∈ s')",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : WSeq α\na a' : α\ns' : WSeq α\n⊢ some (a', s') ∈ dest... | [
955,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
935,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean | CategoryTheory.Limits.hasStrictTerminalObjects_of_terminal_is_strict | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nI : C\nh : ∀ (A : C) (f : I ⟶ A), IsIso f\nI' A : C\nf : I' ⟶ A\nhI' : IsTerminal I'\nthis : IsIso (IsTerminal.from hI' I ≫ f)\n⊢ (inv (IsTerminal.from hI' I ≫ f) ≫ IsTerminal.from hI' I) ≫ f = 𝟙 A",
"tactic": "rw [assoc, IsI... | [
266,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | hasFDerivWithinAt_inter | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.236817\ninst✝³ : NormedAddCommGroup G\ninst✝² : Normed... | [
484,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
] |
Mathlib/Analysis/Complex/Polynomial.lean | Complex.exists_root | [
{
"state_after": "f : ℂ[X]\nhf : ∀ (z : ℂ), ¬IsRoot f z\n⊢ degree f ≤ 0",
"state_before": "f : ℂ[X]\nhf : 0 < degree f\n⊢ ∃ z, IsRoot f z",
"tactic": "contrapose! hf"
},
{
"state_after": "case intro\nf : ℂ[X]\nhf : ∀ (z : ℂ), ¬IsRoot f z\nthis : Metric.Bounded (Set.range (fun x => eval x f)⁻¹)\n... | [
38,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Mathlib/Topology/UniformSpace/Equicontinuity.lean | equicontinuous_iff_continuous | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nκ : Type ?u.79183\nX : Type u_2\nY : Type ?u.79189\nZ : Type ?u.79192\nα : Type u_3\nβ : Type ?u.79198\nγ : Type ?u.79201\n𝓕 : Type ?u.79204\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : TopologicalSpace Y\ninst✝³ : TopologicalSpace Z\ninst✝² : UniformSp... | [
260,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | max_div_div_right | [] | [
609,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
608,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.digits_getLast | [
{
"state_after": "case pos\nn b m : ℕ\nh : 1 < b\np : digits b m ≠ []\nq : digits b (m / b) ≠ []\nhm : m = 0\n⊢ List.getLast (digits b m) p = List.getLast (digits b (m / b)) q\n\ncase neg\nn b m : ℕ\nh : 1 < b\np : digits b m ≠ []\nq : digits b (m / b) ≠ []\nhm : ¬m = 0\n⊢ List.getLast (digits b m) p = List.get... | [
321,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/Algebra/GCDMonoid/Finset.lean | Finset.lcm_dvd_iff | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.1482\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizedGCDMonoid α\ns s₁ s₂ : Finset β\nf : β → α\na : α\n⊢ (∀ (b : α), b ∈ Multiset.map f s.val → b ∣ a) ↔ ∀ (b : β), b ∈ s → f b ∣ a",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.14... | [
68,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.deriv_eq_enumOrd | [
{
"state_after": "case h.e'_3.h.e'_1\nf : Ordinal → Ordinal\nH : IsNormal f\n⊢ fixedPoints f = ⋂ (i : Unit), fixedPoints f",
"state_before": "f : Ordinal → Ordinal\nH : IsNormal f\n⊢ deriv f = enumOrd (fixedPoints f)",
"tactic": "convert derivFamily_eq_enumOrd fun _ : Unit => H"
},
{
"state_afte... | [
555,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
1
] |
Mathlib/Logic/Lemmas.lean | dite_ite_distrib_right | [] | [
63,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_sum_fin_lt | [] | [
1138,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1134,
1
] |
Mathlib/Data/List/Sort.lean | List.perm_insertionSort | [
{
"state_after": "no goals",
"state_before": "α : Type uu\nr : α → α → Prop\ninst✝ : DecidableRel r\nb : α\nl : List α\n⊢ insertionSort r (b :: l) ~ b :: l",
"tactic": "simpa [insertionSort] using (perm_orderedInsert _ _ _).trans ((perm_insertionSort l).cons b)"
}
] | [
246,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Algebra/Order/Monoid/Canonical/Defs.lean | pos_of_gt | [] | [
307,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_pempty | [] | [
1923,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1922,
1
] |
Mathlib/Order/Compare.lean | Ordering.Compares.cmp_eq | [] | [
176,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.kernelSubobject_factors | [
{
"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\nW : C\nh : W ⟶ X\nw : h ≫ f = 0\n⊢ kernel.lift f h w ≫ MonoOver.arrow (MonoOver.mk' (kernel.ι f)) = h",
"tactic": "simp"
}
] | [
120,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Data/Set/Sigma.lean | Set.singleton_sigma_singleton | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nι' : Type ?u.8240\nα : ι → Type u_2\nβ : ι → Type ?u.8250\ns s₁ s₂ : Set ι\nt t₁ t₂ : (i : ι) → Set (α i)\nu : Set ((i : ι) × α i)\nx : (i : ι) × α i\ni j : ι\na✝ : α i\na : (i : ι) → α i\n⊢ (Set.Sigma {i} fun i => {a i}) = {{ fst := i, snd := a i ... | [
131,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
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