file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/LinearAlgebra/Finrank.lean | FiniteDimensional.finrank_le_finrank_of_rank_le_rank | [
{
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"state_before": "K : Type u\nV : Type v\ninst✝⁴ : Ring K\ninst✝³ : AddCommGroup V\ninst✝² : Module K V\nV₂ : Type v'\ninst✝¹ : AddCommGroup V₂\ninst✝ : Module K V₂\nh : lift (Module.rank K V) ≤ lift (Module.rank K V₂)\nh' : Module.rank K V₂ < ℵ₀\n⊢ finrank K V ≤ finrank K V₂",
... | [
94,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.all_singleton | [] | [
465,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.add_lt_top | [] | [
533,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
9
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Mathlib/Algebra/GroupWithZero/Basic.lean | mul_eq_left₀ | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.11158\nM₀ : Type u_1\nG₀ : Type ?u.11164\nM₀' : Type ?u.11167\nG₀' : Type ?u.11170\nF : Type ?u.11173\nF' : Type ?u.11176\ninst✝ : CancelMonoidWithZero M₀\na b c : M₀\nha : a ≠ 0\n⊢ a * b = a ↔ b = 1",
"tactic": "rw [Iff.comm, ← mul_right_inj' ha... | [
203,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
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Mathlib/Topology/Category/TopCat/Limits/Products.lean | TopCat.range_prod_map | [
{
"state_after": "case h\nJ : Type v\ninst✝ : SmallCategory J\nW X Y Z : TopCat\nf : W ⟶ Y\ng : X ⟶ Z\nx : (forget TopCat).obj (Y ⨯ Z)\n⊢ x ∈ Set.range ((forget TopCat).map (prod.map f g)) ↔\n x ∈\n (forget TopCat).map prod.fst ⁻¹' Set.range ((forget TopCat).map f) ∩\n (forget TopCat).map prod.sn... | [
274,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.pred_le_self | [
{
"state_after": "α : Type ?u.81368\nβ : Type ?u.81371\nγ : Type ?u.81374\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no : Ordinal\nh : ∃ a, o = succ a\na : Ordinal\ne : o = succ a\n⊢ pred o ≤ o",
"state_before": "α : Type ?u.81368\nβ : Type ?u.81371\nγ : Type ?u.81374\nr : α → α → Prop\ns : β → β... | [
182,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Topology/UniformSpace/UniformEmbedding.lean | closure_image_mem_nhds_of_uniformInducing | [
{
"state_after": "case intro.intro.intro.intro\nα : Type u\nβ : Type v\nγ : Type w\ninst✝² : UniformSpace α\ninst✝¹ : UniformSpace β\ninst✝ : UniformSpace γ\ns : Set (α × α)\ne : α → β\nb : β\nhe₁ : UniformInducing e\nhe₂ : DenseInducing e\nhs✝ : s ∈ 𝓤 α\nU : Set (β × β)\nhs : Prod.map e e ⁻¹' U ⊆ s\nhU : U ∈ ... | [
258,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Data/Multiset/Powerset.lean | Multiset.powersetAux_eq_map_coe | [] | [
35,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/Algebra/Module/LocalizedModule.lean | LocalizedModule.mk_cancel | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝² : CommSemiring R\nS : Submonoid R\nM : Type v\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\ns : { x // x ∈ S }\nm : M\n⊢ 1 • 1 • s • m = 1 • s • m",
"tactic": "simp"
}
] | [
407,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | IsBoundedBilinearMap.continuous_right | [] | [
422,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
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Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.strictMono_iff_injective | [] | [
158,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
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Mathlib/Topology/Order/Hom/Esakia.lean | EsakiaHom.coe_comp | [] | [
328,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/RingTheory/Polynomial/Bernstein.lean | bernsteinPolynomial.eval_at_1 | [
{
"state_after": "R : Type u_1\ninst✝ : CommRing R\nn ν : ℕ\n⊢ Polynomial.eval 1 (↑(choose n ν) * X ^ ν * (1 - X) ^ (n - ν)) = if ν = n then 1 else 0",
"state_before": "R : Type u_1\ninst✝ : CommRing R\nn ν : ℕ\n⊢ Polynomial.eval 1 (bernsteinPolynomial R n ν) = if ν = n then 1 else 0",
"tactic": "rw [be... | [
105,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
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Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.smul_mem_pointwise_smul_iff | [] | [
415,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/Data/List/Basic.lean | List.indexOf_lt_length | [] | [
1209,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1207,
1
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Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.coe_toAddEquiv | [] | [
358,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Std/Data/String/Lemmas.lean | String.prev_of_valid | [
{
"state_after": "cs : List Char\nc : Char\ncs' : List Char\n⊢ (if { byteIdx := utf8Len cs + csize c } = 0 then 0\n else utf8PrevAux (cs ++ c :: cs') 0 { byteIdx := utf8Len cs + csize c }) =\n { byteIdx := utf8Len cs }",
"state_before": "cs : List Char\nc : Char\ncs' : List Char\n⊢ prev { data := cs +... | [
286,
37
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
283,
1
] |
Mathlib/LinearAlgebra/QuotientPi.lean | Submodule.quotientPi_aux.right_inv | [
{
"state_after": "ι : Type u_1\nR : Type u_3\ninst✝⁸ : CommRing R\nMs : ι → Type u_2\ninst✝⁷ : (i : ι) → AddCommGroup (Ms i)\ninst✝⁶ : (i : ι) → Module R (Ms i)\nN : Type ?u.135340\ninst✝⁵ : AddCommGroup N\ninst✝⁴ : Module R N\nNs : ι → Type ?u.135847\ninst✝³ : (i : ι) → AddCommGroup (Ns i)\ninst✝² : (i : ι) → ... | [
114,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Std/Data/Int/Lemmas.lean | Int.ofNat_mul_negSucc' | [] | [
59,
98
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
59,
15
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Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.IsAtomic.relabel | [] | [
696,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
694,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.coeff_C | [] | [
657,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.val_add_one | [
{
"state_after": "case inl\nn✝ m n : ℕ\n⊢ ↑(last n + 1) = if last n = last n then 0 else ↑(last n) + 1\n\ncase inr\nn✝ m n : ℕ\ni : Fin (n + 1)\nh : i < last n\n⊢ ↑(i + 1) = if i = last n then 0 else ↑i + 1",
"state_before": "n✝ m n : ℕ\ni : Fin (n + 1)\n⊢ ↑(i + 1) = if i = last n then 0 else ↑i + 1",
"... | [
759,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
755,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.sInf_toSubalgebra | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.678241\nR : Type u_2\nA : Type u_1\nB : Type ?u.678250\ninst✝⁹ : CommSemiring R\ninst✝⁸ : StarRing R\ninst✝⁷ : Semiring A\ninst✝⁶ : Algebra R A\ninst✝⁵ : StarRing A\ninst✝⁴ : StarModule R A\ninst✝³ : Semiring B\ninst✝² : Algebra R B\ninst✝¹ : StarRin... | [
681,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
679,
1
] |
Mathlib/CategoryTheory/Bicategory/Basic.lean | CategoryTheory.Bicategory.pentagon_hom_inv_inv_inv_hom | [
{
"state_after": "B : Type u\ninst✝ : Bicategory B\na b c d e : B\nf : a ⟶ b\ng : b ⟶ c\nh : c ⟶ d\ni : d ⟶ e\n⊢ ((α_ f g (h ≫ i)).inv ≫ (α_ f g (h ≫ i)).hom ≫ f ◁ (α_ g h i).inv ≫ (α_ f (g ≫ h) i).inv) ≫ (α_ f g h).inv ▷ i =\n ((α_ f g (h ≫ i)).inv ≫ (α_ (f ≫ g) h i).inv ≫ (α_ f g h).hom ▷ i) ≫ (α_ f g h).i... | [
297,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.neighborSet_compl | [
{
"state_after": "case h\nι : Sort ?u.146524\n𝕜 : Type ?u.146527\nV : Type u\nW : Type v\nX : Type w\nG✝ : SimpleGraph V\nG' : SimpleGraph W\na b c u v✝ w✝ : V\ne : Sym2 V\nG : SimpleGraph V\nv w : V\n⊢ w ∈ neighborSet (Gᶜ) v ↔ w ∈ neighborSet G vᶜ \\ {v}",
"state_before": "ι : Sort ?u.146524\n𝕜 : Type ?u... | [
1003,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1000,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Uniform.lean | Pmf.uniformOfFinset_apply_of_not_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.5033\nγ : Type ?u.5036\ns : Finset α\nhs : Finset.Nonempty s\na : α\nha : ¬a ∈ s\n⊢ ↑(uniformOfFinset s hs) a = 0",
"tactic": "simp [ha]"
}
] | [
63,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | Ideal.Quotient.mkₐ_surjective | [] | [
230,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Combinatorics/Quiver/Cast.lean | Quiver.Path.cast_cast | [
{
"state_after": "U : Type u_1\ninst✝ : Quiver U\nu'' v'' : U\np : Path u'' v''\n⊢ cast (_ : u'' = u'') (_ : v'' = v'') (cast (_ : u'' = u'') (_ : v'' = v'') p) = cast (_ : u'' = u'') (_ : v'' = v'') p",
"state_before": "U : Type u_1\ninst✝ : Quiver U\nu v u' v' u'' v'' : U\np : Path u v\nhu : u = u'\nhv : ... | [
106,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.coe_one | [] | [
402,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Topology/Constructions.lean | continuous_uncurry_left | [] | [
494,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.IsStrongLimit.ne_zero | [] | [
864,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
863,
1
] |
Std/Data/String/Lemmas.lean | Substring.Valid.foldl | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nf : α → Char → α\ninit : α\nx✝ : Substring\nh✝ : Valid x✝\nw✝² w✝¹ w✝ : List Char\nh : ValidFor w✝² w✝¹ w✝ x✝\n⊢ Substring.foldl f init x✝ = List.foldl f init (toString x✝).data",
"tactic": "simp [h.foldl, h.toString]"
}
] | [
1054,
74
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1053,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Ring.lean | summable_sum_mul_antidiagonal_of_summable_mul | [
{
"state_after": "ι : Type ?u.27646\nκ : Type ?u.27649\nR : Type ?u.27652\nα : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : NonUnitalNonAssocSemiring α\nf g : ℕ → α\ninst✝¹ : T3Space α\ninst✝ : TopologicalSemiring α\nh : Summable fun x => f (↑x.snd).fst * g (↑x.snd).snd\n⊢ Summable fun n => ∑ kl in Nat.antid... | [
213,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.Injective.of_comp_iff | [] | [
134,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Algebra/Order/Monoid/WithZero/Defs.lean | WithZero.zero_le | [] | [
53,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Topology/LocallyConstant/Basic.lean | LocallyConstant.mulIndicator_of_mem | [] | [
558,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.add_one_lt_exp_of_nonzero | [
{
"state_after": "case inl\nx : ℝ\nhx : x ≠ 0\nh : x < 0\n⊢ x + 1 < exp x\n\ncase inr\nx : ℝ\nhx : x ≠ 0\nh : x > 0\n⊢ x + 1 < exp x",
"state_before": "x : ℝ\nhx : x ≠ 0\n⊢ x + 1 < exp x",
"tactic": "cases' lt_or_gt_of_ne hx with h h"
},
{
"state_after": "no goals",
"state_before": "case inr... | [
1984,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1981,
1
] |
Mathlib/Order/CompleteLattice.lean | lt_iInf_iff | [] | [
925,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
924,
1
] |
Mathlib/Algebra/Lie/Basic.lean | lie_add | [] | [
122,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/RingTheory/Finiteness.lean | Module.Finite.of_surjective | [
{
"state_after": "R : Type u_1\nA : Type ?u.386467\nB : Type ?u.386470\nM : Type u_2\nN : Type u_3\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\ninst✝¹ : AddCommMonoid N\ninst✝ : Module R N\nhM : Finite R M\nf : M →ₗ[R] N\nhf : Surjective ↑f\n⊢ Submodule.FG (Submodule.map f ⊤)",
"stat... | [
563,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
560,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.factorization_prime_le_iff_dvd | [
{
"state_after": "d n : ℕ\nhd : d ≠ 0\nhn : n ≠ 0\n⊢ (∀ (p : ℕ), Prime p → ↑(factorization d) p ≤ ↑(factorization n) p) ↔ factorization d ≤ factorization n",
"state_before": "d n : ℕ\nhd : d ≠ 0\nhn : n ≠ 0\n⊢ (∀ (p : ℕ), Prime p → ↑(factorization d) p ≤ ↑(factorization n) p) ↔ d ∣ n",
"tactic": "rw [← ... | [
466,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | AnalyticOn.sub | [] | [
601,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
599,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.reindexFinsetRange_repr_self | [
{
"state_after": "case h.mk\nι : Type u_3\nι' : Type ?u.425289\nR : Type u_1\nR₂ : Type ?u.425295\nK : Type ?u.425298\nM : Type u_2\nM' : Type ?u.425304\nM'' : Type ?u.425307\nV : Type u\nV' : Type ?u.425312\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\ninst✝³ : AddCommMonoid M'\ninst✝² :... | [
545,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
] |
Mathlib/Analysis/InnerProductSpace/PiL2.lean | OrthonormalBasis.map_apply | [] | [
473,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
11
] |
Mathlib/Topology/Algebra/Ring/Basic.lean | TopologicalSemiring.continuousNeg_of_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝² : TopologicalSpace α\ninst✝¹ : NonAssocRing α\ninst✝ : ContinuousMul α\n⊢ Continuous fun a => -a",
"tactic": "simpa using (continuous_const.mul continuous_id : Continuous fun x : α => -1 * x)"
}
] | [
68,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.div_subset_div | [] | [
684,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
683,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.eval_monomial | [] | [
1138,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1137,
1
] |
Mathlib/Order/SymmDiff.lean | symmDiff_snd | [] | [
830,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
828,
1
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.integralSum_biUnion_partition | [
{
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102,
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92,
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Mathlib/Analysis/Calculus/ContDiff.lean | contDiff_zero_fun | [
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Mathlib/Order/BoundedOrder.lean | OrderBot.ext_bot | [
{
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439,
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Std/Data/Int/DivMod.lean | Int.emod_add_ediv | [
{
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{
"state_after": "m n : Nat\n⊢ ↑m % ↑(succ n) + ↑(s... | [
311,
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Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_deriv_eq_sub' | [
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.toFinsupp_X | [] | [
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Mathlib/Topology/Algebra/Monoid.lean | ContinuousWithinAt.mul | [] | [
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27
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227,
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Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.le_one_iff_exists_coeIdeal | [
{
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680,
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Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.lower_iso | [] | [
511,
28
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510,
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Mathlib/Logic/Equiv/Defs.lean | Equiv.permCongr_trans | [
{
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451,
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Mathlib/Analysis/SpecialFunctions/Pow/Complex.lean | Complex.cpow_def_of_ne_zero | [] | [
44,
12
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Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.homothety_add | [
{
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832,
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Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | MeasureTheory.LocallyIntegrable.aestronglyMeasurable | [
{
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202,
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Mathlib/Analysis/Complex/Schwarz.lean | Complex.dist_le_div_mul_dist_of_mapsTo_ball | [
{
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160,
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Mathlib/Analysis/Convex/Topology.lean | segment_subset_closure_openSegment | [
{
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89,
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Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean | tendsto_rpow_mul_exp_neg_mul_atTop_nhds_0 | [
{
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},
... | [
114,
83
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111,
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Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.coeff_one | [
{
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] | [
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75
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Mathlib/Logic/Equiv/List.lean | Encodable.length_sortedUniv | [] | [
213,
23
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Mathlib/CategoryTheory/Limits/ConcreteCategory.lean | CategoryTheory.Limits.Concrete.multiequalizer_ext | [
{
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98,
91
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Mathlib/FieldTheory/RatFunc.lean | RatFunc.algebraMap_X | [] | [
1424,
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1423,
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Mathlib/Data/Set/Basic.lean | Set.not_mem_empty | [] | [
426,
5
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Mathlib/ModelTheory/LanguageMap.lean | FirstOrder.Language.coe_con | [] | [
583,
6
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Mathlib/Data/List/Cycle.lean | Cycle.length_coe | [] | [
578,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
577,
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Mathlib/Topology/Algebra/Field.lean | IsPreconnected.eq_of_sq_eq | [
{
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164,
57
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157,
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Mathlib/MeasureTheory/Integral/RieszMarkovKakutani.lean | riesz_content_aux_image_nonempty | [
{
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60,
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Mathlib/Data/Num/Lemmas.lean | Num.bit_to_nat | [
{
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] | [
718,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
718,
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Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.signAux_swap_zero_one' | [
{
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449,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
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Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.unique | [] | [
460,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
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Mathlib/Data/Multiset/Lattice.lean | Multiset.le_sup | [] | [
67,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
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Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.coe_starAe | [] | [
728,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
727,
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Mathlib/Data/Set/Basic.lean | Disjoint.union_right | [] | [
2957,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2956,
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Mathlib/Algebra/FreeAlgebra.lean | FreeAlgebra.lift_unique | [
{
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356,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.FinStronglyMeasurable.exists_set_sigmaFinite | [
{
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Mathlib/Data/Matrix/Notation.lean | Matrix.transpose_empty_rows | [] | [
196,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
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Mathlib/Topology/Algebra/InfiniteSum/Order.lean | summable_abs_iff | [
{
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258,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
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Mathlib/CategoryTheory/Extensive.lean | CategoryTheory.NatTrans.equifibered_of_isIso | [] | [
72,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
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Std/Data/String/Lemmas.lean | Substring.Valid.contains | [
{
"state_after": "no goals",
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"tactic": "simp [h.contains, h.toString]"
}
] | [
1066,
77
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1065,
1
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Mathlib/Algebra/Module/Submodule/Lattice.lean | Submodule.eq_bot_iff | [] | [
95,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
11
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.polar_sub_right | [
{
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"tactic":... | [
308,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
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Mathlib/RingTheory/Localization/AsSubring.lean | Localization.subalgebra.mem_range_mapToFractionRing_iff_ofField | [
{
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126,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
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Mathlib/LinearAlgebra/InvariantBasisNumber.lean | card_eq_of_linearEquiv | [] | [
195,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
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Mathlib/Topology/UniformSpace/Basic.lean | uniformity_mulOpposite | [] | [
1528,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1526,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.volume_Ico | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.117608\ninst✝ : Fintype ι\na b : ℝ\n⊢ ↑↑volume (Ico a b) = ofReal (b - a)",
"tactic": "simp [volume_val]"
}
] | [
83,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_dite | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.394402\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf✝ g✝ : α → β\ninst✝ : CommMonoid β\ns : Finset α\np : α → Prop\nhp : DecidablePred p\nf : (x : α) → p x → β\ng : (x : α) → ¬p x → β\nx : { x // x ∈ filter p s }\n⊢ p ↑x",
"t... | [
988,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
983,
1
] |
Mathlib/Order/Filter/Archimedean.lean | Filter.Tendsto.atTop_zsmul_neg_const | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nR : Type u_1\nl : Filter α\nf✝ : α → R\nr : R\ninst✝¹ : LinearOrderedAddCommGroup R\ninst✝ : Archimedean R\nf : α → ℤ\nhr : r < 0\nhf : Tendsto f l atTop\n⊢ Tendsto (fun x => f x • r) l atBot",
"tactic": "simpa using hf.atTop_zsmul_const (neg_p... | [
240,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/CategoryTheory/Localization/Construction.lean | CategoryTheory.Localization.Construction.uniq | [
{
"state_after": "C : Type u_1\ninst✝¹ : Category C\nW : MorphismProperty C\nD : Type u_4\ninst✝ : Category D\nG : C ⥤ D\nhG : MorphismProperty.IsInvertedBy W G\nG₁ G₂ : MorphismProperty.Localization W ⥤ D\nh : MorphismProperty.Q W ⋙ G₁ = MorphismProperty.Q W ⋙ G₂\nh' : Quotient.functor (relations W) ⋙ G₁ = Quo... | [
210,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Analysis/Analytic/Linear.lean | ContinuousLinearMap.hasFPowerSeriesAt | [] | [
62,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
11
] |
Mathlib/Algebra/Ring/Regular.lean | isLeftRegular_of_non_zero_divisor | [
{
"state_after": "α : Type u_1\ninst✝ : NonUnitalNonAssocRing α\nk : α\nh : ∀ (x : α), k * x = 0 → x = 0\nx y : α\nh' : k * x = k * y\n⊢ k * (x - y) = 0",
"state_before": "α : Type u_1\ninst✝ : NonUnitalNonAssocRing α\nk : α\nh : ∀ (x : α), k * x = 0 → x = 0\n⊢ IsLeftRegular k",
"tactic": "refine' fun x... | [
26,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
23,
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Mathlib/CategoryTheory/Monoidal/Opposite.lean | CategoryTheory.op_tensorObj | [] | [
189,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Order/LocallyFinite.lean | WithBot.Icc_coe_coe | [] | [
1160,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1159,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arcsin_lt_iff_lt_sin | [] | [
177,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.965333\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf g : E → F\np pf pg ... | [
837,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
830,
1
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