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/Data/Polynomial/Eval.lean | Polynomial.monomial_comp | [] | [
586,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.subset_span | [] | [
65,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/CategoryTheory/Bicategory/NaturalTransformation.lean | CategoryTheory.OplaxNatTrans.whiskerRight_naturality_comp | [
{
"state_after": "B : Type u₁\ninst✝¹ : Bicategory B\nC : Type u₂\ninst✝ : Bicategory C\nF G H : OplaxFunctor B C\nη : OplaxNatTrans F G\nθ : OplaxNatTrans G H\na b c : B\na' : C\nf : a ⟶ b\ng : b ⟶ c\nh : (↑G.toPrelaxFunctor).obj c ⟶ a'\n⊢ (OplaxFunctor.mapComp F f g ▷ app η c ≫\n (α_ ((↑F.toPrelaxFun... | [
144,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Std/Data/List/Lemmas.lean | List.nil_eq_append | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\na b : List α✝\n⊢ [] = a ++ b ↔ a = [] ∧ b = []",
"tactic": "rw [eq_comm, append_eq_nil]"
}
] | [
118,
30
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
117,
9
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_add_const_Iio | [] | [
104,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Algebra/BigOperators/RingEquiv.lean | RingEquiv.map_sum | [] | [
56,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
11
] |
Mathlib/LinearAlgebra/Matrix/Circulant.lean | Matrix.conjTranspose_circulant | [
{
"state_after": "case a.h\nα : Type u_1\nβ : Type ?u.7051\nm : Type ?u.7054\nn : Type u_2\nR : Type ?u.7060\ninst✝¹ : Star α\ninst✝ : AddGroup n\nv : n → α\ni✝ x✝ : n\n⊢ (circulant v)ᴴ i✝ x✝ = circulant (star fun i => v (-i)) i✝ x✝",
"state_before": "α : Type u_1\nβ : Type ?u.7051\nm : Type ?u.7054\nn : Ty... | [
88,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.inter_sdiff_self | [
{
"state_after": "α : Type u_1\nβ : Type ?u.221592\nγ : Type ?u.221595\ninst✝ : DecidableEq α\ns t u v : Finset α\na b : α\ns₁ s₂ : Finset α\n⊢ ∀ (x : α), ¬(x ∈ s₁ ∧ x ∈ s₂ ∧ ¬x ∈ s₁)",
"state_before": "α : Type u_1\nβ : Type ?u.221592\nγ : Type ?u.221595\ninst✝ : DecidableEq α\ns t u v : Finset α\na b : α\... | [
2049,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2047,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.signAux_swap_zero_one | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : DecidableEq α\nn : ℕ\nhn : 2 ≤ n\n⊢ 0 < 2",
"tactic": "decide"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : DecidableEq α\nn : ℕ\nhn : 2 ≤ n\n⊢ 1 < 2",
"tactic": "decide"
}... | [
457,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
9
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | Submodule.sup_orthogonal_inf_of_completeSpace | [
{
"state_after": "case h\n𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.757872\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : InnerProductSpace ℝ F\nK K₁ K₂ : Submodule 𝕜 E\nh : K₁ ≤ K₂\ninst✝ : CompleteSpace { x // x ∈ K₁ }\nx : E\n⊢ x ∈... | [
743,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
734,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPushout.of_is_bilimit' | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\nZ X Y P : C\nf : Z ⟶ X\ng : Z ⟶ Y\ninl : X ⟶ P\ninr : Y ⟶ P\ninst✝¹ : HasZeroObject C\ninst✝ : HasZeroMorphisms C\nb : BinaryBicone X Y\nh : BinaryBicone.IsBilimit b\n⊢ IsPushout (b.inl ≫ b.fst) 0 0 (0 ≫ 0)",
"state_before": "C : Type u₁\ninst✝² : Category... | [
831,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
828,
1
] |
Std/Data/Int/DivMod.lean | Int.div_self | [
{
"state_after": "a : Int\nH : a ≠ 0\nthis : div (1 * a) a = 1\n⊢ div a a = 1",
"state_before": "a : Int\nH : a ≠ 0\n⊢ div a a = 1",
"tactic": "have := Int.mul_div_cancel 1 H"
},
{
"state_after": "no goals",
"state_before": "a : Int\nH : a ≠ 0\nthis : div (1 * a) a = 1\n⊢ div a a = 1",
"... | [
223,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
222,
19
] |
Std/Data/Int/Lemmas.lean | Int.le_of_sub_nonpos | [
{
"state_after": "a b : Int\nh✝ : a - b ≤ 0\nh : a - b + b ≤ 0 + b\n⊢ a ≤ b",
"state_before": "a b : Int\nh : a - b ≤ 0\n⊢ a ≤ b",
"tactic": "have h := Int.add_le_add_right h b"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nh✝ : a - b ≤ 0\nh : a - b + b ≤ 0 + b\n⊢ a ≤ b",
"... | [
932,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
930,
11
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Equiv.summable_iff_of_support | [] | [
255,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Data/Finsupp/NeLocus.lean | Finsupp.neLocus_eq_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nM : Type ?u.2977\nN : Type u_2\nP : Type ?u.2983\ninst✝² : DecidableEq α\ninst✝¹ : DecidableEq N\ninst✝ : Zero N\nf✝ g✝ f g : α →₀ N\nh : f = g\n⊢ neLocus f f = ∅",
"tactic": "simp only [neLocus, Ne.def, eq_self_iff_true, not_true, Finset.filte... | [
64,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.toLinAlgEquiv_toMatrixAlgEquiv | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁹ : CommSemiring R\nl : Type ?u.2268827\nm : Type ?u.2268830\nn : Type u_3\ninst✝⁸ : Fintype n\ninst✝⁷ : Fintype m\ninst✝⁶ : DecidableEq n\nM₁ : Type u_2\nM₂ : Type ?u.2268854\ninst✝⁵ : AddCommMonoid M₁\ninst✝⁴ : AddCommMonoid M₂\ninst✝³ : Mod... | [
737,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
1
] |
Mathlib/Order/Cover.lean | Wcovby.eq_or_eq | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type ?u.16370\ninst✝ : PartialOrder α\na b c : α\nh : a ⩿ b\nh2✝ : a ≤ c\nh3 : c ≤ b\nh2 : a = c\n⊢ c = a ∨ c = b\n\ncase inr\nα : Type u_1\nβ : Type ?u.16370\ninst✝ : PartialOrder α\na b c : α\nh : a ⩿ b\nh2✝ : a ≤ c\nh3 : c ≤ b\nh2 : a < c\n⊢ c = a ∨ c = b",
"... | [
162,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/RingTheory/DedekindDomain/Factorization.lean | Ideal.finprod_heightOneSpectrum_factorization | [
{
"state_after": "R : Type u_1\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDomain R\ninst✝³ : IsDedekindDomain R\nK : Type ?u.253124\ninst✝² : Field K\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nv : HeightOneSpectrum R\nI : Ideal R\nhI : I ≠ 0\n⊢ Associates.mk (∏ᶠ (v : HeightOneSpectrum R), maxPowDividing v I) = As... | [
168,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.coeFn_injective | [] | [
117,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/CategoryTheory/Preadditive/AdditiveFunctor.lean | CategoryTheory.AdditiveFunctor.forget_obj_of | [] | [
221,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Data/List/Rotate.lean | List.prod_rotate_eq_one_of_prod_eq_one | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Group α\nx✝¹ : prod [] = 1\nx✝ : ℕ\n⊢ prod (rotate [] x✝) = 1",
"tactic": "simp"
},
{
"state_after": "α : Type u\ninst✝ : Group α\na : α\nl : List α\nhl : prod (a :: l) = 1\nn : ℕ\nthis : n % length (a :: l) ≤ length (a :: l)\n⊢ p... | [
183,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.snd_comp_prod | [] | [
1113,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1111,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | hasFTaylorSeriesUpToOn_top_iff | [
{
"state_after": "case mp\n𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nX : Type uX\ninst✝¹ : ... | [
249,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Data/String/Basic.lean | String.le_iff_toList_le | [] | [
120,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.le_bmex_of_forall | [
{
"state_after": "α : Type ?u.382605\nβ : Type ?u.382608\nγ : Type ?u.382611\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no : Ordinal\nf : (a : Ordinal) → a < o → Ordinal\na : Ordinal\nH : ∀ (b : Ordinal), b < a → ∃ i hi, f i hi = b\nh : bmex o f < a\n⊢ False",
"state_before": "α : Type ?u.382605\... | [
2079,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2076,
1
] |
Mathlib/Topology/FiberBundle/Basic.lean | FiberPrebundle.continuousOn_of_comp_right | [
{
"state_after": "ι : Type ?u.65679\nB : Type u_2\nF : Type u_4\nX✝ : Type ?u.65688\ninst✝⁴ : TopologicalSpace X✝\nE : B → Type u_3\ninst✝³ : TopologicalSpace B\ninst✝² : TopologicalSpace F\ninst✝¹ : (x : B) → TopologicalSpace (E x)\na : FiberPrebundle F E\ne : Pretrivialization F TotalSpace.proj\nX : Type u_1\... | [
934,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
917,
1
] |
Mathlib/Analysis/Complex/OperatorNorm.lean | Complex.reClm_nnnorm | [] | [
50,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Order/Circular.lean | sbtw_iff_btw_not_btw | [] | [
187,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.dist_lt_iff | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nE : Type ?u.78801\ninst✝³ : TopologicalSpace α\ninst✝² : CompactSpace α\ninst✝¹ : MetricSpace β\ninst✝ : NormedAddCommGroup E\nf g : C(α, β)\nC : ℝ\nC0 : 0 < C\n⊢ (∀ (x : α), dist (↑(mkOfCompact f) x) (↑(mkOfCompact g) x) < C) ↔ ∀ (x : α), dist (↑f x) (↑g x) < C",
... | [
157,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.isSt_st' | [] | [
354,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/MeasureTheory/Function/ContinuousMapDense.lean | BoundedContinuousFunction.toLp_denseRange | [
{
"state_after": "α : Type u_1\ninst✝¹⁰ : MeasurableSpace α\ninst✝⁹ : TopologicalSpace α\ninst✝⁸ : NormalSpace α\ninst✝⁷ : BorelSpace α\nE : Type u_2\ninst✝⁶ : NormedAddCommGroup E\nμ : MeasureTheory.Measure α\np : ℝ≥0∞\ninst✝⁵ : SecondCountableTopologyEither α E\n_i : Fact (1 ≤ p)\nhp : p ≠ ⊤\n𝕜 : Type u_3\ni... | [
375,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingHom.coe_coe_ringHom | [] | [
221,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Data/Set/Prod.lean | Set.prod_self_ssubset_prod_self | [] | [
95,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Data/Nat/Fib.lean | Nat.fib_zero | [] | [
79,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Combinatorics/Pigeonhole.lean | Fintype.exists_card_fiber_lt_of_card_lt_nsmul | [] | [
402,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/MeasureTheory/Function/EssSup.lean | ENNReal.essSup_const_mul | [] | [
319,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.add_mul_mod_self_right | [
{
"state_after": "no goals",
"state_before": "x y z : Nat\n⊢ (x + y * z) % z = x % z",
"tactic": "rw [Nat.mul_comm, add_mul_mod_self_left]"
}
] | [
502,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
501,
9
] |
Mathlib/Analysis/PSeries.lean | Finset.le_sum_condensed | [
{
"state_after": "case h.e'_3\nM : Type u_1\ninst✝ : OrderedAddCommMonoid M\nf : ℕ → M\nhf : ∀ ⦃m n : ℕ⦄, 0 < m → m ≤ n → f n ≤ f m\nn : ℕ\n⊢ ∑ k in range (2 ^ n), f k = f 0 + ∑ k in Ico 1 (2 ^ n), f k",
"state_before": "M : Type u_1\ninst✝ : OrderedAddCommMonoid M\nf : ℕ → M\nhf : ∀ ⦃m n : ℕ⦄, 0 < m → m ≤ ... | [
69,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Data/Fin/Tuple/Reflection.lean | FinVec.seq_eq | [
{
"state_after": "m n✝ : ℕ\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.1470\nn : ℕ\nf : Fin (n + 1) → α → β\nv : Fin (n + 1) → α\ni : Fin (n + 1)\n⊢ Matrix.vecCons (f 0 (v 0)) (fun i => Matrix.vecTail f i (Matrix.vecTail v i)) i = f i (v i)",
"state_before": "m n✝ : ℕ\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.1... | [
55,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.map_div | [] | [
1552,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1551,
11
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.coe_pow | [] | [
393,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | ContDiff.cos | [] | [
970,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
969,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.lift_umax' | [] | [
701,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.mapDomain_smul | [] | [
1582,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1580,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.mem_ball_self | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.25444\nι : Type ?u.25447\ninst✝ : PseudoMetricSpace α\nx y z : α\nδ ε ε₁ ε₂ : ℝ\ns : Set α\nh : 0 < ε\n⊢ x ∈ ball x ε",
"tactic": "rwa [mem_ball, dist_self]"
}
] | [
429,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.Subsingleton.isWf | [] | [
474,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
11
] |
Mathlib/Data/Polynomial/Inductions.lean | Polynomial.divX_mul_X_add | [
{
"state_after": "no goals",
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}
] | [
53,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
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Mathlib/Order/CompleteLattice.lean | iSup₂_comm | [
{
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1147,
51
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1144,
1
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.sum_const_nat | [
{
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1760,
25
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1757,
1
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Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | Matrix.toBilin'Aux_stdBasis | [
{
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100,
18
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80,
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Mathlib/Data/Finsupp/Fin.lean | Finsupp.cons_succ | [] | [
54,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
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Mathlib/CategoryTheory/Limits/Shapes/FiniteLimits.lean | CategoryTheory.Limits.hasFiniteLimits_of_hasFiniteLimits_of_size | [
{
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"state_before": "C : Type u\ninst✝ : Category C\nh ... | [
81,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
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Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.nfp_monotone | [] | [
469,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
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Mathlib/Order/Disjoint.lean | Disjoint.mono_right | [] | [
77,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
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Mathlib/Algebra/Module/Torsion.lean | Submodule.smul_coe_torsionBy | [] | [
254,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
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Mathlib/Data/Fin/Basic.lean | Fin.zero_ne_one | [] | [
843,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
842,
1
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | differentiableOn_id | [] | [
1029,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1028,
1
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Mathlib/Topology/Algebra/UniformConvergence.lean | UniformFun.hasBasis_nhds_one | [] | [
163,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
11
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Mathlib/Analysis/Convex/Basic.lean | Antitone.convex_lt | [] | [
401,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
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Mathlib/Data/Set/Intervals/Pi.lean | Set.image_update_Ioo_left | [
{
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}
] | [
176,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
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Mathlib/Order/SuccPred/Basic.lean | Order.pred_ne_top | [] | [
905,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
904,
1
] |
Mathlib/Data/Real/ENNReal.lean | OrderIso.invENNReal_symm_apply | [] | [
1534,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1532,
1
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Mathlib/Analysis/Calculus/ParametricIntegral.lean | hasFDerivAt_integral_of_dominated_loc_of_lip | [
{
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167,
75
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154,
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Mathlib/Data/Nat/Fib.lean | Nat.le_fib_self | [
{
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"tactic": "induction' five_le_n with n five_le_n IH"
},
{
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136,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
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Mathlib/Order/RelIso/Basic.lean | RelIso.surjective | [] | [
811,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
810,
11
] |
Mathlib/RingTheory/DedekindDomain/Basic.lean | Ring.DimensionLEOne.eq_bot_of_lt | [] | [
85,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
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Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.coe_sum | [] | [
773,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
771,
1
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Mathlib/Order/UpperLower/Basic.lean | isUpperSet_setOf | [] | [
277,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Midpoint.lean | midpoint_eq_iff | [] | [
104,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.iUnion_null_iff' | [
{
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135,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.mem_vsub | [] | [
609,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
608,
1
] |
Mathlib/Algebra/Category/GroupCat/Biproducts.lean | AddCommGroupCat.biprodIsoProd_inv_comp_fst | [] | [
85,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.continuous_sub_left | [
{
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451,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
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Mathlib/Data/Polynomial/Monic.lean | Polynomial.isUnit_leadingCoeff_mul_right_eq_zero_iff | [
{
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537,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
524,
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Mathlib/Analysis/Convex/Side.lean | AffineSubspace.wSameSide_smul_vsub_vadd_right | [] | [
339,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Std/Data/Char.lean | String.csize_pos | [
{
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"state_before": "c : Char\n⊢ 0 < csize c",
"tactic": "rcases csize_eq c with _|_|_|_ <;> simp_all"
}
] | [
18,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
17,
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Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.sum_fiberwise | [
{
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635,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
632,
1
] |
Mathlib/ModelTheory/Definability.lean | Set.Definable.preimage_comp | [
{
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"state_before": "M : Type w\nA : Set M\nL : Language\ninst✝ ... | [
159,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Order/CompleteLattice.lean | sSup_insert | [] | [
506,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/CategoryTheory/Sites/Sheaf.lean | CategoryTheory.Presheaf.isSheaf_iff_isSheaf' | [
{
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633,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
615,
1
] |
Mathlib/CategoryTheory/Limits/Constructions/ZeroObjects.lean | CategoryTheory.Limits.zeroCoprodIso_inv | [] | [
125,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.coe_rpow_of_ne_zero | [
{
"state_after": "x : ℝ≥0\nh : x ≠ 0\ny : ℝ\n⊢ Option.some x ^ y = ↑(x ^ y)",
"state_before": "x : ℝ≥0\nh : x ≠ 0\ny : ℝ\n⊢ ↑x ^ y = ↑(x ^ y)",
"tactic": "rw [← ENNReal.some_eq_coe]"
},
{
"state_after": "no goals",
"state_before": "x : ℝ≥0\nh : x ≠ 0\ny : ℝ\n⊢ (if x = 0 ∧ y < 0 then ⊤ else ↑... | [
355,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.comp_measurable | [] | [
404,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Data/Set/Intervals/OrdConnectedComponent.lean | Set.mem_ordConnectedComponent_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrder α\ns t : Set α\nx y z : α\n⊢ y ∈ ordConnectedComponent s x ↔ x ∈ ordConnectedComponent s y",
"tactic": "rw [mem_ordConnectedComponent, mem_ordConnectedComponent, uIcc_comm]"
}
] | [
86,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/RingTheory/FreeCommRing.lean | FreeCommRing.isSupported_neg | [] | [
194,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Algebra/CharP/Basic.lean | ringChar.eq_zero | [] | [
239,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/GroupTheory/Perm/ViaEmbedding.lean | Equiv.Perm.viaEmbedding_apply | [] | [
35,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.subset_iInter₂_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.60356\nγ : Type ?u.60359\nι : Sort u_2\nι' : Sort ?u.60365\nι₂ : Sort ?u.60368\nκ : ι → Sort u_3\nκ₁ : ι → Sort ?u.60378\nκ₂ : ι → Sort ?u.60383\nκ' : ι' → Sort ?u.60388\ns : Set α\nt : (i : ι) → κ i → Set α\n⊢ (s ⊆ ⋂ (i : ι) (j : κ i),... | [
322,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiff.one_of_succ | [] | [
1468,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1467,
1
] |
Mathlib/Topology/VectorBundle/Constructions.lean | Trivialization.prod_apply | [] | [
118,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/CategoryTheory/Closed/Cartesian.lean | CategoryTheory.CartesianClosed.uncurry_natural_right | [] | [
194,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | IsCompact.measurableSet | [] | [
330,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.closure_isCycle | [
{
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"tactic": "classical\n cases nonempty_fintype β\n exact\n top_le_iff.mp (le_trans (ge_of_eq closure_isSwap) (closure_mono f... | [
1613,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1609,
1
] |
Mathlib/Data/Option/Basic.lean | Option.pmap_eq_some_iff | [
{
"state_after": "case none\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.12874\nδ : Type ?u.12877\np : α → Prop\nf : (a : α) → p a → β\ny : β\nhf : ∀ (a : α), a ∈ none → p a\n⊢ pmap f none hf = some y ↔ ∃ a H, f a (_ : p a) = y\n\ncase some\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.12874\nδ : Type ?u.12877\np : α → ... | [
252,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Data/Multiset/Powerset.lean | Multiset.mem_powersetLenAux | [
{
"state_after": "α : Type u_1\nn : ℕ\nl : List α\ns : Multiset α\n⊢ ∀ (a : List α), (∃ a_1, (a_1 <+ l ∧ length a_1 = n) ∧ a_1 ~ a) ↔ (∃ l_1, l_1 ~ a ∧ l_1 <+ l) ∧ length a = n",
"state_before": "α : Type u_1\nn : ℕ\nl : List α\ns : Multiset α\n⊢ ∀ (a : List α),\n Quotient.mk (isSetoid α) a ∈ powersetLen... | [
191,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image₂_subset | [
{
"state_after": "α : Type u_1\nα' : Type ?u.12205\nβ : Type u_2\nβ' : Type ?u.12211\nγ : Type u_3\nγ' : Type ?u.12217\nδ : Type ?u.12220\nδ' : Type ?u.12223\nε : Type ?u.12226\nε' : Type ?u.12229\nζ : Type ?u.12232\nζ' : Type ?u.12235\nν : Type ?u.12238\ninst✝⁷ : DecidableEq α'\ninst✝⁶ : DecidableEq β'\ninst✝⁵... | [
83,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | Right.self_le_inv | [] | [
492,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.IntegrableOn.right_of_union | [] | [
180,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.int_cast_re | [] | [
440,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Basis.toDual_total_left | [
{
"state_after": "R : Type u\nM : Type v\nK : Type u₁\nV : Type u₂\nι : Type w\ninst✝³ : CommSemiring R\ninst✝² : AddCommMonoid M\ninst✝¹ : Module R M\ninst✝ : DecidableEq ι\nb : Basis ι R M\nf : ι →₀ R\ni : ι\n⊢ ∑ d in f.support, ↑(↑(toDual b) (↑f d • ↑b d)) (↑b i) = ↑f i",
"state_before": "R : Type u\nM :... | [
310,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
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