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/NumberTheory/Multiplicity.lean | dvd_geom_sum₂_iff_of_dvd_sub' | [
{
"state_after": "R : Type u_1\nn : ℕ\ninst✝ : CommRing R\na b x✝ y✝ x y p : R\nh : p ∣ x - y\n⊢ p ∣ y - x",
"state_before": "R : Type u_1\nn : ℕ\ninst✝ : CommRing R\na b x✝ y✝ x y p : R\nh : p ∣ x - y\n⊢ p ∣ ∑ i in range n, x ^ i * y ^ (n - 1 - i) ↔ p ∣ ↑n * x ^ (n - 1)",
"tactic": "rw [geom_sum₂_comm,... | [
54,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
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Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.add_pf_add_lt | [
{
"state_after": "no goals",
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"tactic": "simp [*, add_assoc]"
}
] | [
321,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.prod_ne_zero | [
{
"state_after": "no goals",
"state_before": "α β : Type u\nι : Type u_1\nf : ι → Cardinal\n⊢ prod f ≠ 0 ↔ ∀ (i : ι), f i ≠ 0",
"tactic": "simp [prod_eq_zero]"
}
] | [
1068,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1068,
1
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Mathlib/SetTheory/Ordinal/Basic.lean | Cardinal.ord_eq_Inf | [] | [
1346,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1345,
1
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Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.funext | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\np✝ q✝ : R[X]\ninst✝ : Infinite R\np q : R[X]\next : ∀ (r : R), eval r p = eval r q\n⊢ p - q = 0",
"state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝² : CommRing R\ninst✝¹ :... | [
879,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
875,
1
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Mathlib/FieldTheory/Adjoin.lean | IntermediateField.coe_algebraMap_over_bot | [] | [
237,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
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Mathlib/Logic/Function/Basic.lean | Function.update_comp_eq_of_injective | [] | [
639,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
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Mathlib/Data/Option/Basic.lean | Option.casesOn'_none | [] | [
345,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
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Mathlib/Data/List/Basic.lean | List.take_eq_nil_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.177112\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l : List α\nk : ℕ\n⊢ take k l = [] ↔ l = [] ∨ k = 0",
"tactic": "cases l <;> cases k <;> simp [Nat.succ_ne_zero]"
}
] | [
2044,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2043,
1
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Mathlib/Algebra/Group/Conj.lean | MonoidHom.map_isConj | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : Monoid α\ninst✝ : Monoid β\nf : α →* β\na b : α\nc : αˣ\nhc : SemiconjBy (↑c) a b\n⊢ SemiconjBy (↑(↑(Units.map f) c)) (↑f a) (↑f b)",
"tactic": "rw [Units.coe_map, SemiconjBy, ← f.map_mul, hc.eq, f.map_mul]"
}
] | [
62,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
11
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Mathlib/Computability/TMToPartrec.lean | Turing.ToPartrec.Code.exists_code | [
{
"state_after": "case prim\nn✝ : ℕ\nf✝ : Vector ℕ n✝ →. ℕ\nn : ℕ\nf : Vector ℕ n → ℕ\nhf : Nat.Primrec' f\n⊢ ∃ c, ∀ (v : Vector ℕ n), eval c ↑v = pure <$> ↑f v\n\ncase comp\nn : ℕ\nf : Vector ℕ n →. ℕ\nm✝ n✝ : ℕ\nf✝ : Vector ℕ n✝ →. ℕ\ng✝ : Fin n✝ → Vector ℕ m✝ →. ℕ\na✝¹ : Nat.Partrec' f✝\na✝ : ∀ (i : Fin n✝),... | [
392,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.list_prod | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝² : PseudoEMetricSpace α\ninst✝¹ : PseudoEMetricSpace β\ninst✝ : PseudoEMetricSpace γ\nK✝ : ℝ≥0\nf✝ : α → β\nx y : α\nr : ℝ≥0∞\nf : ι → Function.End α\nK : ι → ℝ≥0\nh : ∀ (i : ι), LipschitzWith (K i) (f i)\n⊢ ... | [
295,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
11
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Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Term.realize_var | [] | [
85,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
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Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.quot_liftOn_mk | [] | [
512,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.toGerm_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.443277\nδ : Type ?u.443280\ninst✝³ : MeasurableSpace α\nμ ν : Measure α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α →ₘ[μ] β\n⊢ toGerm f = ↑↑f",
"tactic": "rw [← mk_toGer... | [
383,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd | [
{
"state_after": "case mp\nk : Type u_2\nV : Type u_4\nP : Type u_3\ninst✝⁴ : Ring k\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AffineSpace V P\nι : Type u_1\ninst✝ : Nontrivial k\np : ι → P\nj : ι\nq : P\n⊢ q ∈ affineSpan k (Set.range p) → ∃ s w, q = ↑(Finset.weightedVSubOfPoint s p (p j)) w +ᵥ p ... | [
1176,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1156,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_add | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.12526056\n𝕜 : Type ?u.12526059\nE : Type u_1\nF : Type ?u.12526065\nA : Type ?u.12526068\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na b : ℝ\nf g : ℝ → E\nμ : MeasureTheory.Measure ℝ\nhf : IntervalIntegrable f ... | [
582,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
8
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.nfpBFamily_lt_ord | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.35030\nr : α → α → Prop\no : Ordinal\nf : (a : Ordinal) → a < o → Ordinal → Ordinal\nc : Ordinal\nhc : ℵ₀ < cof c\nhc' : card o < cof c\nhf : ∀ (i : Ordinal) (hi : i < o) (b : Ordinal), b < c → f i hi b < c\na : Ordinal\n⊢ Cardinal.lift (card o) < co... | [
406,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | union_mem_uniformity_sum | [] | [
1775,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1771,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasFDerivAt.isBigO | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\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.387793\ninst✝³ : NormedAddCommGroup G\ninst✝² : Normed... | [
700,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
698,
8
] |
Mathlib/MeasureTheory/Measure/AEDisjoint.lean | MeasureTheory.AEDisjoint.symmetric | [] | [
61,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
11
] |
Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.mk_ne_zero_of_degree_lt | [] | [
219,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/CategoryTheory/Monoidal/OfHasFiniteProducts.lean | CategoryTheory.monoidalOfHasFiniteProducts.tensorHom | [] | [
99,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/RingTheory/Ideal/MinimalPrime.lean | Ideal.minimalPrimes_eq_subsingleton_self | [
{
"state_after": "case h\nR : Type u_1\nS : Type ?u.122062\ninst✝² : CommRing R\ninst✝¹ : CommRing S\nI J✝ : Ideal R\ninst✝ : IsPrime I\nJ : Ideal R\n⊢ J ∈ Ideal.minimalPrimes I ↔ J ∈ {I}",
"state_before": "R : Type u_1\nS : Type ?u.122062\ninst✝² : CommRing R\ninst✝¹ : CommRing S\nI J : Ideal R\ninst✝ : Is... | [
215,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Algebra/Hom/Ring.lean | RingHom.coe_coe | [] | [
460,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_mono_ae | [] | [
1549,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1548,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | mul_lt_mul_of_neg_left | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.82636\ninst✝ : StrictOrderedRing α\na b c : α\nh : b < a\nhc : c < 0\n⊢ c * a < c * b",
"tactic": "simpa only [neg_mul, neg_lt_neg_iff] using mul_lt_mul_of_pos_left h (neg_pos_of_neg hc)"
}
] | [
691,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
690,
1
] |
Mathlib/FieldTheory/IsAlgClosed/Basic.lean | IsAlgClosed.roots_eq_zero_iff | [
{
"state_after": "k : Type u\ninst✝¹ : Field k\ninst✝ : IsAlgClosed k\np : k[X]\nh : roots p = 0\n⊢ p = ↑C (coeff p 0)",
"state_before": "k : Type u\ninst✝¹ : Field k\ninst✝ : IsAlgClosed k\np : k[X]\n⊢ roots p = 0 ↔ p = ↑C (coeff p 0)",
"tactic": "refine' ⟨fun h => _, fun hp => by rw [hp, roots_C]⟩"
... | [
107,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_set_inter_subset | [] | [
376,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | LinearMap.curry_uncurryLeft | [
{
"state_after": "case h.H\nR : Type u\nι : Type u'\nn : ℕ\nM : Fin (Nat.succ n) → Type v\nM₁ : ι → Type v₁\nM₂ : Type v₂\nM₃ : Type v₃\nM' : Type v'\ninst✝⁶ : CommSemiring R\ninst✝⁵ : (i : Fin (Nat.succ n)) → AddCommMonoid (M i)\ninst✝⁴ : AddCommMonoid M'\ninst✝³ : AddCommMonoid M₂\ninst✝² : (i : Fin (Nat.succ... | [
1278,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1274,
1
] |
Std/Data/List/Lemmas.lean | List.subset_nil | [] | [
266,
97
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
265,
1
] |
Mathlib/Algebra/Order/Group/DenselyOrdered.lean | le_of_forall_one_lt_div_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝³ : Group α\ninst✝² : LinearOrder α\ninst✝¹ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\ninst✝ : DenselyOrdered α\na b c : α\nh : ∀ (ε : α), 1 < ε → a / ε ≤ b\nε : α\nε1 : ε < 1\n⊢ a * ε ≤ b",
"tactic": "simpa only [di... | [
39,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
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Mathlib/Data/List/Perm.lean | List.perm_comp_perm | [
{
"state_after": "case h.h\nα : Type uu\nβ : Type vv\nl₁ l₂ : List α\nγ : Type ?u.37152\nδ : Type ?u.37155\nr : α → β → Prop\np : γ → δ → Prop\na c : List α\n⊢ (Perm ∘r Perm) a c = (a ~ c)",
"state_before": "α : Type uu\nβ : Type vv\nl₁ l₂ : List α\nγ : Type ?u.37152\nδ : Type ?u.37155\nr : α → β → Prop\np ... | [
338,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.comapMkQOrderEmbedding_eq | [] | [
504,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
1
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Mathlib/Algebra/GroupPower/Lemmas.lean | nsmul_eq_mul | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.256535\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : NonAssocSemiring R\nn : ℕ\na : R\n⊢ n • a = ↑n * a",
"tactic": "rw [nsmul_eq_mul', (n.cast_commute a).eq]"
}
] | [
511,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
] |
Mathlib/Data/Dfinsupp/NeLocus.lean | Dfinsupp.neLocus_add_left | [] | [
127,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | AddSubgroup.mem_pointwise_smul_iff_inv_smul_mem | [] | [
499,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.filter_eq_bot_of_isEmpty | [] | [
708,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
707,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.map_op_smul' | [] | [
380,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Topology/FiberBundle/Constructions.lean | Bundle.Trivial.eq_trivialization | [] | [
110,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.norm_sub_eq_abs_sub_norm_iff_angle_eq_zero | [
{
"state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y✝ x y : V\nhx : x ≠ 0\nhy : y ≠ 0\nh : ‖x - y‖ = abs (‖x‖ - ‖y‖)\n⊢ angle x y = 0",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y✝ x y : V\nhx : x ≠ 0\nhy : y... | [
333,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/AlgebraicTopology/DoldKan/Normalized.lean | AlgebraicTopology.DoldKan.factors_normalizedMooreComplex_PInfty | [
{
"state_after": "case zero\nA : Type u_2\ninst✝¹ : Category A\ninst✝ : Abelian A\nX : SimplicialObject A\n⊢ Factors (NormalizedMooreComplex.objX X Nat.zero) (HomologicalComplex.Hom.f PInfty Nat.zero)\n\ncase succ\nA : Type u_2\ninst✝¹ : Category A\ninst✝ : Abelian A\nX : SimplicialObject A\nn : ℕ\n⊢ Factors (N... | [
60,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/CategoryTheory/Preadditive/AdditiveFunctor.lean | CategoryTheory.AdditiveFunctor.ofLeftExact_map | [] | [
311,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Algebra/Group/Units.lean | IsUnit.mul_iff | [] | [
712,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
710,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.tendsto_iff_forall_toWeakDualBCNN_tendsto | [
{
"state_after": "Ω : Type u_2\ninst✝⁶ : MeasurableSpace Ω\nR : Type ?u.130020\ninst✝⁵ : SMul R ℝ≥0\ninst✝⁴ : SMul R ℝ≥0∞\ninst✝³ : IsScalarTower R ℝ≥0 ℝ≥0∞\ninst✝² : IsScalarTower R ℝ≥0∞ ℝ≥0∞\ninst✝¹ : TopologicalSpace Ω\ninst✝ : OpensMeasurableSpace Ω\nγ : Type u_1\nF : Filter γ\nμs : γ → FiniteMeasure Ω\nμ :... | [
503,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.total_repr | [] | [
782,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
781,
1
] |
Mathlib/LinearAlgebra/Ray.lean | SameRay.smul | [] | [
189,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.not_mem_of_not_mem_closure | [] | [
811,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
810,
1
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Mathlib/Order/Heyting/Basic.lean | sup_sdiff_self | [] | [
558,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
1
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Mathlib/Data/Set/Lattice.lean | sSup_sUnion | [
{
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2247,
59
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2246,
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Mathlib/Order/CompleteLattice.lean | sInf_eq_bot | [] | [
606,
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605,
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Mathlib/Algebra/Associated.lean | Irreducible.ne_one | [] | [
196,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.linMulLin_comp | [] | [
737,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
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Mathlib/RingTheory/Valuation/Basic.lean | AddValuation.map_le_add | [] | [
692,
31
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691,
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Mathlib/Topology/Order/Basic.lean | le_mem_nhds | [] | [
916,
41
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915,
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Mathlib/LinearAlgebra/AffineSpace/Matrix.lean | AffineBasis.det_smul_coords_eq_cramer_coords | [
{
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175,
95
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171,
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Mathlib/Topology/Basic.lean | dense_iff_closure_eq | [] | [
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26
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604,
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Mathlib/Topology/Order/Basic.lean | pi_Icc_mem_nhds | [] | [
1477,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1476,
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Mathlib/LinearAlgebra/Span.lean | Submodule.iSup_toAddSubmonoid | [
{
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606,
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Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.coeSubtype | [] | [
674,
6
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673,
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Mathlib/Algebra/Star/Basic.lean | commute_star_comm | [
{
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"tactic": "rw [← commute_star_star, star_star]"
}
] | [
167,
38
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166,
1
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Mathlib/Data/Set/NAry.lean | Set.image2_union_left | [
{
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132,
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127,
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Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.sign_eq_sign_of_equiv | [
{
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681,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
678,
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Mathlib/Topology/Order/Basic.lean | nhdsWithin_Ici_neBot | [] | [
250,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
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Mathlib/Algebra/Order/Monoid/Lemmas.lean | cmp_mul_right' | [] | [
1564,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1561,
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.I_mul_I_of_nonzero | [] | [
594,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
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Mathlib/Data/PFun.lean | PFun.fix_fwd | [
{
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"tactic": "rwa [← fix_fwd_eq ha']"
}
] | [
326,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
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Mathlib/Topology/CompactOpen.lean | Homeomorph.continuousMapOfUnique_apply | [] | [
462,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
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Mathlib/Topology/Homotopy/HomotopyGroup.lean | GenLoop.Homotopic.symm | [] | [
180,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
8
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Mathlib/Data/Polynomial/Laurent.lean | LaurentPolynomial.degree_C_mul_T_le | [
{
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"state_before": "R : Type u_1\ninst✝ : Semiring R\nn : ℤ\na : R\n⊢ degree (↑C a * T n) ≤ ↑... | [
547,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
544,
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Mathlib/NumberTheory/Bernoulli.lean | bernoulli'PowerSeries_mul_exp_sub_one | [
{
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"tac... | [
181,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
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Mathlib/RingTheory/Subring/Basic.lean | Subring.ext | [] | [
235,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
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Mathlib/RingTheory/FinitePresentation.lean | AlgHom.FinitePresentation.id | [] | [
504,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
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Mathlib/Combinatorics/Quiver/Cast.lean | Quiver.Hom.cast_cast | [
{
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57,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
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Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.inner_eq_mul_norm_iff_angle_eq_zero | [
{
"state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y✝ x y : V\nhx : x ≠ 0\nhy : y ≠ 0\nh : inner x y = ‖x‖ * ‖y‖\n⊢ angle x y = 0",
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265,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
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Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.trim_measurableSet_eq | [] | [
1307,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1305,
1
] |
Mathlib/Data/List/Basic.lean | List.map₂Right_nil_cons | [] | [
4147,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4146,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.set_integral_nonneg | [] | [
736,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
734,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.castHom_apply | [] | [
335,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/GroupTheory/Finiteness.lean | Submonoid.fg_iff | [
{
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"state_before": "M : Type u_1\nN : Type ?u.1028\ninst✝¹ : Monoid M\ninst✝ : AddMonoid N\nP : Submonoid M\nx✝ : ∃ S, closure S = P ∧ Set.Finite S\nS : Set M\nhS : closure S = P\nhf : Set.Finite S\n⊢ closure ↑(Set.Finite.toFinset hf) = P",
"tactic": "simp [hS]"
}
] | [
62,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
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Mathlib/CategoryTheory/Limits/Shapes/Diagonal.lean | CategoryTheory.Limits.diagonalObjPullbackFstIso_inv_fst_snd | [
{
"state_after": "C : Type u_2\ninst✝⁵ : Category C\nX✝ Y✝ Z✝ : C\ninst✝⁴ : HasPullbacks C\nS T : C\nf✝ : X✝ ⟶ T\ng✝ : Y✝ ⟶ T\ni : T ⟶ S\ninst✝³ : HasPullback i i\ninst✝² : HasPullback f✝ g✝\ninst✝¹ : HasPullback (f✝ ≫ i) (g✝ ≫ i)\ninst✝ :\n HasPullback (diagonal i)\n (map (f✝ ≫ i) (g✝ ≫ i) i i f✝ g✝ (𝟙 S)... | [
339,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
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Mathlib/Analysis/BoxIntegral/Partition/Split.lean | BoxIntegral.Box.splitLower_def | [
{
"state_after": "no goals",
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95,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
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Mathlib/Algebra/Associated.lean | irreducible_mul_units | [
{
"state_after": "α : Type u_1\nβ : Type ?u.91092\nγ : Type ?u.91095\nδ : Type ?u.91098\ninst✝ : Monoid α\na : αˣ\nb : α\n⊢ ¬IsUnit b →\n ((∀ (a_2 b_1 : α), b * ↑a = a_2 * b_1 → IsUnit a_2 ∨ IsUnit b_1) ↔\n ∀ (a b_1 : α), b = a * b_1 → IsUnit a ∨ IsUnit b_1)",
"state_before": "α : Type u_1\nβ : Type... | [
274,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Analysis/Complex/Schwarz.lean | Complex.abs_le_abs_of_mapsTo_ball_self | [
{
"state_after": "case hz\nf : ℂ → ℂ\nc z : ℂ\nR R₁ R₂ : ℝ\nhd : DifferentiableOn ℂ f (ball 0 R)\nh_maps : MapsTo f (ball 0 R) (ball 0 R)\nh₀ : f 0 = 0\nhz : ↑abs z < R\n⊢ z ∈ ball 0 R\n\nf : ℂ → ℂ\nc z : ℂ\nR R₁ R₂ : ℝ\nhd : DifferentiableOn ℂ f (ball 0 R)\nh_maps : MapsTo f (ball 0 R) (ball 0 R)\nh₀ : f 0 = 0... | [
200,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.sinh_three_mul | [
{
"state_after": "x y : ℝ\n⊢ ↑(sinh (3 * x)) = ↑(4 * sinh x ^ 3 + 3 * sinh x)",
"state_before": "x y : ℝ\n⊢ sinh (3 * x) = 4 * sinh x ^ 3 + 3 * sinh x",
"tactic": "rw [← ofReal_inj]"
},
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ ↑(sinh (3 * x)) = ↑(4 * sinh x ^ 3 + 3 * sinh x)"... | [
1457,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1456,
8
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.mul_mono_left | [] | [
768,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
767,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.not_infinitePos_add_infiniteNeg | [] | [
559,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
1
] |
Std/Data/List/Lemmas.lean | List.disjoint_symm | [] | [
1350,
86
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1350,
1
] |
Mathlib/Algebra/Homology/Augment.lean | ChainComplex.augmentTruncate_hom_f_succ | [] | [
177,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Data/Quot.lean | Quotient.map_mk | [] | [
253,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Analysis/Calculus/Deriv/Polynomial.lean | Polynomial.differentiableOn | [] | [
128,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
11
] |
Mathlib/Topology/Order/Basic.lean | tendsto_order_unbounded | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : TopologicalSpace α\ninst✝ : Preorder α\nt : OrderTopology α\nf : β → α\na : α\nx : Filter β\nhu : ∃ u, a < u\nhl : ∃ l, l < a\nh : ∀ (l u : α), l < a → a < u → ∀ᶠ (b : β) in x, l < f b ∧ f b < u\n⊢ ∀ (i : α), i < a → ∀ (i_2 : α), a < i_2 → ∀ᶠ (a : β... | [
985,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
981,
1
] |
Mathlib/Data/Set/Intervals/WithBotTop.lean | WithTop.preimage_coe_Ico | [
{
"state_after": "no goals",
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"tactic": "simp [← Ici_inter_Iio]"
}
] | [
64,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/ModelTheory/LanguageMap.lean | FirstOrder.Language.constantsOnMap_isExpansionOn | [
{
"state_after": "L : Language\nL' : Language\nM : Type w\ninst✝ : Structure L M\nα : Type u'\nβ : Type v'\nf : α → β\nfα : α → M\nfβ : β → M\nh : fβ ∘ f = fα\nthis : Structure (constantsOn α) M := constantsOn.structure fα\n⊢ LHom.IsExpansionOn (LHom.constantsOnMap f) M",
"state_before": "L : Language\nL' :... | [
438,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Order/Hom/Lattice.lean | map_sdiff' | [
{
"state_after": "no goals",
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"tactic": "rw [sdiff... | [
294,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/Topology/Separation.lean | t2_separation | [] | [
876,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
874,
1
] |
Mathlib/Logic/Equiv/TransferInstance.lean | Equiv.pow_def | [] | [
127,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.lipschitz_with_one_iff_forall_dist_image_le_of_mem_cylinder | [
{
"state_after": "case mp\nE : ℕ → Type u_2\nα : Type u_1\ninst✝ : PseudoMetricSpace α\nf : ((n : ℕ) → E n) → α\n⊢ (∀ (x y : (n : ℕ) → E n), dist (f x) (f y) ≤ dist x y) →\n ∀ (x y : (n : ℕ) → E n) (n : ℕ), y ∈ cylinder x n → dist (f x) (f y) ≤ (1 / 2) ^ n\n\ncase mpr\nE : ℕ → Type u_2\nα : Type u_1\ninst✝ :... | [
357,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.refl_prod_refl | [] | [
1031,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1029,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | IsCompact.exists_infDist_eq_dist | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.68670\nα : Type u\nβ : Type v\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\ns t u : Set α\nx✝ y✝ : α\nΦ : α → β\nh : IsCompact s\nhne : Set.Nonempty s\nx y : α\nhys : y ∈ s\nhy : infEdist x s = edist x y\n⊢ infDist x s = dist x y",
... | [
636,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
633,
1
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