file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Algebra/RingQuot.lean | RingQuot.smul_quot | [
{
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"state_before":... | [
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1
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Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.BoundedFormula.realize_top | [
{
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282,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
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Mathlib/Geometry/Euclidean/Sphere/Basic.lean | EuclideanGeometry.Sphere.mk_center_radius | [
{
"state_after": "no goals",
"state_before": "V : Type ?u.1295\nP : Type u_1\ninst✝ : MetricSpace P\ns : Sphere P\n⊢ { center := s.center, radius := s.radius } = s",
"tactic": "ext <;> rfl"
}
] | [
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Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.isOrtho_self | [] | [
306,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
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Mathlib/Data/Bitvec/Lemmas.lean | Bitvec.ofFin_le_ofFin_of_le | [
{
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"state_before": "n : ℕ\ni j : Fin (2 ^ n)\nh : i ≤ j\n⊢ Bitvec.toNat (Bitvec.ofNat n ↑i) ≤ Bitvec.toNat (Bitvec.ofNat n ↑j)",
"tactic": "simp only [toNat_ofNat, Nat.mod_eq_of_lt, Fin.is_lt]"
},
{
"state_after": "no goals",
"s... | [
164,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
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Mathlib/Data/Set/Pointwise/Basic.lean | Set.iUnion_mul_left_image | [] | [
478,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
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Mathlib/Analysis/Calculus/FDeriv/Mul.lean | Differentiable.mul | [] | [
339,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
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Mathlib/Topology/Algebra/Order/IntermediateValue.lean | IsConnected.Icc_subset | [] | [
229,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
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Mathlib/RingTheory/DedekindDomain/Ideal.lean | Ideal.dvd_iff_le | [
{
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655,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
643,
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Mathlib/Topology/Order/Basic.lean | closure_Ici | [] | [
169,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
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Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.singletonSubgraph_le_iff | [
{
"state_after": "ι : Sort ?u.207802\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' : SimpleGraph W\nv : V\nH : Subgraph G\n⊢ v ∈ H.verts → SimpleGraph.singletonSubgraph G v ≤ H",
"state_before": "ι : Sort ?u.207802\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' : SimpleGraph W\nv : V\nH : Subgraph G\n⊢ Sim... | [
858,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
852,
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Mathlib/Order/InitialSeg.lean | InitialSeg.trans_apply | [] | [
131,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
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Std/Data/Int/Lemmas.lean | Int.zero_add | [] | [
228,
95
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
228,
25
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Mathlib/Analysis/Calculus/Deriv/Basic.lean | deriv_id | [] | [
653,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
652,
1
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Mathlib/Order/WellFounded.lean | Acc.induction_bot | [] | [
257,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
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Std/Data/Nat/Gcd.lean | Nat.gcd_ne_zero_left | [] | [
112,
81
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
112,
1
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Mathlib/Data/Nat/Basic.lean | Nat.succ_add_sub_one | [
{
"state_after": "no goals",
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"tactic": "rw [succ_add, succ_sub_one]"
}
] | [
304,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
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src/lean/Init/SimpLemmas.lean | let_val_congr | [] | [
49,
81
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
48,
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Mathlib/Data/Set/Function.lean | Set.piecewise_preimage | [
{
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1469,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1468,
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Mathlib/RingTheory/DedekindDomain/Ideal.lean | FractionalIdeal.exists_not_mem_one_of_ne_bot | [
{
"state_after": "R : Type ?u.159729\nA : Type u_1\nK : Type u_2\ninst✝⁶ : CommRing R\ninst✝⁵ : CommRing A\ninst✝⁴ : Field K\ninst✝³ : IsDomain A\ninst✝² : Algebra A K\ninst✝¹ : IsFractionRing A K\ninst✝ : IsDedekindDomain A\nhNF : ¬IsField A\nI : Ideal A\nhI0 : I ≠ ⊥\nhI1 : I ≠ ⊤\n⊢ ∀ {M : Ideal A}, IsMaximal ... | [
451,
18
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401,
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Mathlib/CategoryTheory/EqToHom.lean | CategoryTheory.Functor.postcomp_map_hEq | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nE : Type u₃\ninst✝ : Category E\nF G : C ⥤ D\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\nH : D ⥤ E\nhx : F.obj X = G.obj X\nhy : F.obj Y = G.obj Y\nhmap : HEq (F.map f) (G.map f)\n⊢ HEq (H.map (F.map f)) (H.map (G.map f))",
"state_b... | [
251,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.iIndepFun.indepFun_prod_range_succ | [] | [
898,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
894,
1
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Mathlib/Order/UpperLower/Basic.lean | bddBelow_upperClosure | [
{
"state_after": "no goals",
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"tactic": "simp_rw [BddBelow, lowerBounds_upperClosure]... | [
1492,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1491,
1
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Mathlib/Topology/MetricSpace/Basic.lean | dist_le_Ico_sum_dist | [
{
"state_after": "no goals",
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"tactic": "induction n, h using Nat.le_induction with\n| base => rw... | [
239,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
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Mathlib/Logic/Basic.lean | ball_congr | [] | [
1035,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1034,
1
] |
Mathlib/RingTheory/Polynomial/Vieta.lean | Multiset.prod_X_sub_X_eq_sum_esymm | [
{
"state_after": "R : Type u_1\ninst✝ : CommRing R\ns : Multiset R\n⊢ prod (map (fun x => X + ↑C (-x)) s) =\n ∑ j in Finset.range (↑card s + 1), (-1) ^ j * (↑C (esymm s j) * X ^ (↑card s - j))",
"state_before": "R : Type u_1\ninst✝ : CommRing R\ns : Multiset R\n⊢ prod (map (fun t => X - ↑C t) s) = ∑ j in... | [
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83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Analysis/NormedSpace/Star/Basic.lean | starₗᵢ_toContinuousLinearEquiv | [] | [
314,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.append_assoc | [
{
"state_after": "no goals",
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"tactic": "induction p with\n| nil => rfl\n| ... | [
273,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
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Mathlib/MeasureTheory/Decomposition/UnsignedHahn.lean | MeasureTheory.hahn_decomposition | [
{
"state_after": "α : Type u_1\ninst✝² : MeasurableSpace α\nμ ν : Measure α\ninst✝¹ : IsFiniteMeasure μ\ninst✝ : IsFiniteMeasure ν\nd : Set α → ℝ := fun s => ↑(ENNReal.toNNReal (↑↑μ s)) - ↑(ENNReal.toNNReal (↑↑ν s))\n⊢ ∃ s,\n MeasurableSet s ∧\n (∀ (t : Set α), MeasurableSet t → t ⊆ s → ↑↑ν t ≤ ↑↑μ t) ∧... | [
181,
56
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39,
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Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.mul_meas_ge_le_pow_norm | [] | [
1794,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1791,
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.preimage_frontier | [] | [
641,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
639,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.associated_rightInverse | [] | [
821,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
819,
1
] |
Mathlib/Topology/Algebra/Order/Floor.lean | tendsto_ceil_right' | [] | [
152,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.vanishingIdeal_closure | [] | [
475,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
1
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Mathlib/Order/Hom/Basic.lean | OrderIso.strictMono | [] | [
1006,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1005,
11
] |
Mathlib/Data/Fintype/Basic.lean | Finset.coe_compl | [] | [
178,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Algebra/Algebra/Tower.lean | Submodule.smul_mem_span_smul_of_mem | [
{
"state_after": "R : Type u\nS : Type v\nA : Type w\nB : Type u₁\nM : Type v₁\ninst✝⁶ : Semiring R\ninst✝⁵ : Semiring S\ninst✝⁴ : AddCommMonoid A\ninst✝³ : Module R S\ninst✝² : Module S A\ninst✝¹ : Module R A\ninst✝ : IsScalarTower R S A\ns : Set S\nt : Set A\nk : S\nhks : k ∈ span R s\nx : A\nhx : x ∈ t\n⊢ 0 ... | [
286,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
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Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.map_sup_comap_of_surjective | [] | [
483,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.two_nsmul_neg_pi_div_two | [
{
"state_after": "no goals",
"state_before": "⊢ 2 • ↑(-π / 2) = ↑π",
"tactic": "rw [two_nsmul_coe_div_two, coe_neg, neg_coe_pi]"
}
] | [
152,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Topology/Algebra/GroupCompletion.lean | UniformSpace.Completion.coe_neg | [] | [
89,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
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Mathlib/Analysis/Convex/Strict.lean | strictConvex_Icc | [] | [
189,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.toOpposite_apply | [] | [
405,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Order/Heyting/Basic.lean | disjoint_compl_compl_left_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.163358\nα : Type u_1\nβ : Type ?u.163364\ninst✝ : HeytingAlgebra α\na b c : α\n⊢ Disjoint (aᶜᶜ) b ↔ Disjoint a b",
"tactic": "simp_rw [← le_compl_iff_disjoint_left, compl_compl_compl]"
}
] | [
917,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
916,
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Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.mem_filter | [] | [
112,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.one_mem | [] | [
129,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
11
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.degree_of_b_ne_zero' | [] | [
328,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.mod_opow_log_lt_self | [
{
"state_after": "case inl\no : Ordinal\nho : o ≠ 0\n⊢ o % 0 ^ log 0 o < o\n\ncase inr\nb o : Ordinal\nho : o ≠ 0\nhb : b ≠ 0\n⊢ o % b ^ log b o < o",
"state_before": "b o : Ordinal\nho : o ≠ 0\n⊢ o % b ^ log b o < o",
"tactic": "rcases eq_or_ne b 0 with (rfl | hb)"
},
{
"state_after": "no goals... | [
382,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.mk_div | [] | [
174,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.lift.tmul | [] | [
481,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
480,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.diff_mem_iff | [] | [
141,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Topology/Separation.lean | normal_separation | [] | [
1711,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1709,
1
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Mathlib/Data/Polynomial/Div.lean | Polynomial.divByMonic_eq_zero_iff | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\ninst✝¹ : CommRing R\np q : R[X]\ninst✝ : Nontrivial R\nhq : Monic q\nh : p /ₘ q = 0\nthis : p %ₘ q + q * (p /ₘ q) = p\n⊢ degree p < degree q",
"state_before": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\nin... | [
262,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.ToPartrec.Code.case_eval | [
{
"state_after": "no goals",
"state_before": "f g : Code\n⊢ eval (case f g) = fun v => Nat.rec (eval f (List.tail v)) (fun y x => eval g (y :: List.tail v)) (List.headI v)",
"tactic": "simp [eval]"
}
] | [
163,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Algebra/Symmetrized.lean | SymAlg.mul_def | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝⁴ : Add α\ninst✝³ : Mul α\ninst✝² : One α\ninst✝¹ : OfNat α 2\ninst✝ : Invertible 2\na b : αˢʸᵐ\n⊢ a * b = ↑sym (⅟2 * (↑unsym a * ↑unsym b + ↑unsym b * ↑unsym a))",
"tactic": "rfl"
}
] | [
204,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.coe_add | [] | [
975,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
974,
1
] |
Mathlib/Analysis/Convex/Quasiconvex.lean | ConvexOn.quasiconvexOn | [] | [
166,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ico_diff_Ico_left | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.155748\nα : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : LocallyFiniteOrder α\na✝ b✝ a b c : α\n⊢ Ico a b \\ Ico a c = Ico (max a c) b",
"tactic": "cases le_total a c with\n| inl h =>\n ext x\n rw [mem_sdiff, mem_Ico, mem_Ico, mem_Ico, max_eq_righ... | [
821,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
815,
1
] |
Mathlib/Data/List/Count.lean | List.filter_eq' | [] | [
288,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Analysis/SpecialFunctions/Stirling.lean | Stirling.stirlingSeq_pow_four_div_stirlingSeq_pow_two_eq | [
{
"state_after": "n : ℕ\nhn : n ≠ 0\nthis : 4 = 2 * 2\n⊢ stirlingSeq n ^ 4 / stirlingSeq (2 * n) ^ 2 * (↑n / (2 * ↑n + 1)) = Wallis.W n",
"state_before": "n : ℕ\nhn : n ≠ 0\n⊢ stirlingSeq n ^ 4 / stirlingSeq (2 * n) ^ 2 * (↑n / (2 * ↑n + 1)) = Wallis.W n",
"tactic": "have : 4 = 2 * 2 := by rfl"
},
{... | [
248,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/LinearAlgebra/BilinearMap.lean | LinearMap.lsmul_injective | [] | [
419,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_subtype_eq_prod_filter | [
{
"state_after": "ι : Type ?u.379810\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ninst✝¹ : CommMonoid β\nf : α → β\np : α → Prop\ninst✝ : DecidablePred p\n⊢ ∏ x in map (Function.Embedding.subtype p) (Finset.subtype p s), f x = ∏ x in filter p s, f x",
"state_before": "ι : Ty... | [
870,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
867,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ici_inj | [] | [
969,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
968,
1
] |
Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.Ioo_eq_zero | [] | [
78,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Topology/DenseEmbedding.lean | DenseInducing.nhdsWithin_neBot | [] | [
132,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
11
] |
Mathlib/FieldTheory/IsAlgClosed/Basic.lean | IsAlgClosure.equivOfEquiv_comp_algebraMap | [] | [
511,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.not_isCycle_one | [] | [
295,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.eq_top_iff' | [] | [
1086,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1085,
1
] |
Mathlib/Topology/Basic.lean | ClusterPt.mono | [] | [
1128,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1127,
1
] |
Mathlib/Algebra/Group/Commute.lean | Commute.pow_left | [] | [
178,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.coe_coeMonoidHom | [] | [
836,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
835,
1
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | ContDiffBump.le_one | [] | [
400,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_two | [] | [
375,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Data/Fintype/Basic.lean | Function.Injective.right_inv_of_invOfMemRange | [] | [
502,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/Algebra/FreeMonoid/Count.lean | FreeMonoid.count_apply | [] | [
85,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.monomial_mul_C | [
{
"state_after": "no goals",
"state_before": "R : Type u\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q : R[X]\n⊢ ↑(monomial n) a * ↑C b = ↑(monomial n) (a * b)",
"tactic": "simp only [← monomial_zero_left, monomial_mul_monomial, add_zero]"
}
] | [
546,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEFinStronglyMeasurable.finStronglyMeasurable_mk | [] | [
1854,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1852,
1
] |
Mathlib/Init/Data/Sigma/Basic.lean | PSigma.eq | [] | [
22,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
20,
11
] |
Mathlib/Init/Algebra/Order.lean | lt_or_gt_of_ne | [] | [
360,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Computability/PartrecCode.lean | Nat.Partrec.Code.curry_inj | [
{
"state_after": "no goals",
"state_before": "c₁ c₂ : Code\nn₁ n₂ : ℕ\nh : curry c₁ n₁ = curry c₂ n₂\n⊢ c₁ = c₂",
"tactic": "injection h"
},
{
"state_after": "c₁ c₂ : Code\nn₁ n₂ : ℕ\nh₁ : c₁ = c₂\nh₂ : pair (Code.const n₁) Code.id = pair (Code.const n₂) Code.id\n⊢ n₁ = n₂",
"state_before": ... | [
689,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.closure_subset_span | [] | [
135,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Data/Matrix/Notation.lean | Matrix.dotProduct_cons | [
{
"state_after": "no goals",
"state_before": "α : Type u\no n m : ℕ\nm' : Type uₘ\nn' : Type uₙ\no' : Type uₒ\na b : ℕ\ninst✝¹ : AddCommMonoid α\ninst✝ : Mul α\nv : Fin (Nat.succ n) → α\nx : α\nw : Fin n → α\n⊢ v ⬝ᵥ vecCons x w = vecHead v * x + vecTail v ⬝ᵥ w",
"tactic": "simp [dotProduct, Fin.sum_univ... | [
155,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.extend_function_finite | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝ : Finite α\ns : Set α\nf : ↑s ↪ β\nh : Nonempty (α ≃ β)\n⊢ Nonempty (↑(sᶜ) ≃ ↑(range ↑fᶜ))",
"state_before": "α : Type u\nβ : Type v\ninst✝ : Finite α\ns : Set α\nf : ↑s ↪ β\nh : Nonempty (α ≃ β)\n⊢ ∃ g, ∀ (x : ↑s), ↑g ↑x = ↑f x",
"tactic": "apply extend_f... | [
1211,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1205,
1
] |
Mathlib/Order/Filter/Partial.lean | Filter.ptendsto_def | [] | [
231,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.Red.Step.sublist | [
{
"state_after": "case not\nα : Type u\nL L₃ L₄ L₁✝ L₂✝ : List (α × Bool)\nx✝ : α\nb✝ : Bool\n⊢ L₁✝ ++ L₂✝ <+ L₁✝ ++ (x✝, b✝) :: (x✝, !b✝) :: L₂✝",
"state_before": "α : Type u\nL L₁ L₂ L₃ L₄ : List (α × Bool)\nH : Step L₁ L₂\n⊢ L₂ <+ L₁",
"tactic": "cases H"
},
{
"state_after": "case not\nα : Ty... | [
383,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/Data/Finset/NatAntidiagonal.lean | Finset.Nat.antidiagonal.fst_le | [
{
"state_after": "n : ℕ\nkl : ℕ × ℕ\nhlk : kl ∈ antidiagonal n\n⊢ ∃ c, n = kl.fst + c",
"state_before": "n : ℕ\nkl : ℕ × ℕ\nhlk : kl ∈ antidiagonal n\n⊢ kl.fst ≤ n",
"tactic": "rw [le_iff_exists_add]"
},
{
"state_after": "n : ℕ\nkl : ℕ × ℕ\nhlk : kl ∈ antidiagonal n\n⊢ n = kl.fst + kl.snd",
... | [
104,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/CategoryTheory/Abelian/Basic.lean | CategoryTheory.Abelian.imageIsoImage_hom_comp_image_ι | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : Abelian C\nX Y : C\nf : X ⟶ Y\n⊢ (imageIsoImage f).hom ≫ Limits.image.ι f = kernel.ι (cokernel.π f)",
"tactic": "simp only [IsImage.isoExt_hom, IsImage.lift_ι, imageStrongEpiMonoFactorisation_m]"
}
] | [
442,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
] |
Mathlib/Algebra/Star/Unitary.lean | unitary.coe_zpow | [
{
"state_after": "case ofNat\nR : Type u_1\ninst✝¹ : GroupWithZero R\ninst✝ : StarSemigroup R\nU : { x // x ∈ unitary R }\na✝ : ℕ\n⊢ ↑(U ^ Int.ofNat a✝) = ↑U ^ Int.ofNat a✝\n\ncase negSucc\nR : Type u_1\ninst✝¹ : GroupWithZero R\ninst✝ : StarSemigroup R\nU : { x // x ∈ unitary R }\na✝ : ℕ\n⊢ ↑(U ^ Int.negSucc a... | [
182,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Algebra/ContinuedFractions/Translations.lean | GeneralizedContinuedFraction.part_num_eq_s_a | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ng : GeneralizedContinuedFraction α\nn : ℕ\ngp : Pair α\ns_nth_eq : Stream'.Seq.get? g.s n = some gp\n⊢ Stream'.Seq.get? (partialNumerators g) n = some gp.a",
"tactic": "simp [partialNumerators, s_nth_eq]"
}
] | [
60,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.comp_smul | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.552397\nR' : Type ?u.552400\n𝕜 : Type u_3\n𝕜₂ : Type u_1\n𝕜₃ : Type ?u.552409\n𝕝 : Type ?u.552412\nE : Type u_4\nE₂ : Type u_2\nE₃ : Type ?u.552421\nF : Type ?u.552424\nG : Type ?u.552427\nι : Type ?u.552430\ninst✝⁶ : SeminormedRing 𝕜\ninst✝⁵ : ... | [
445,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | map_extChartAt_nhdsWithin | [] | [
1178,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1176,
1
] |
Mathlib/Data/List/Basic.lean | List.drop_eq_get_cons | [] | [
2157,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2155,
1
] |
Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | MvPolynomial.weightedHomogeneousComponent_finsupp | [
{
"state_after": "R : Type u_2\nM : Type u_1\ninst✝¹ : CommSemiring R\nσ : Type u_3\ninst✝ : AddCommMonoid M\nw : σ → M\nn : M\nφ ψ : MvPolynomial σ R\n⊢ (Function.support fun m => ↑(weightedHomogeneousComponent w m) φ) ⊆ (fun d => ↑(weightedDegree' w) d) '' ↑(support φ)",
"state_before": "R : Type u_2\nM :... | [
399,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/GroupTheory/Perm/List.lean | List.formPerm_pair | [] | [
71,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | orderOf_inv | [
{
"state_after": "no goals",
"state_before": "G : Type u\nA : Type v\nx✝ y : G\na b : A\nn m : ℕ\ninst✝¹ : Group G\ninst✝ : AddGroup A\ni : ℤ\nx : G\n⊢ orderOf x⁻¹ = orderOf x",
"tactic": "simp [orderOf_eq_orderOf_iff]"
}
] | [
565,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
565,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.ball_zero_absorbs_ball_zero | [
{
"state_after": "case intro.intro\nR : Type ?u.1218120\nR' : Type ?u.1218123\n𝕜 : Type u_1\n𝕜₂ : Type ?u.1218129\n𝕜₃ : Type ?u.1218132\n𝕝 : Type ?u.1218135\nE : Type u_2\nE₂ : Type ?u.1218141\nE₃ : Type ?u.1218144\nF : Type ?u.1218147\nG : Type ?u.1218150\nι : Type ?u.1218153\ninst✝² : NormedField 𝕜\ninst... | [
979,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
973,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasFDerivWithinAt.continuousWithinAt | [] | [
724,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
722,
1
] |
Mathlib/Data/Set/Prod.lean | Set.prod_sdiff_diagonal | [] | [
588,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
587,
1
] |
Mathlib/MeasureTheory/Measure/OpenPos.lean | MeasureTheory.Measure.eqOn_of_ae_eq | [] | [
118,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Std/Data/List/Lemmas.lean | List.erase_of_not_mem | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\na b : α\nl : List α\nh : ¬a = b ∧ ¬a ∈ l\n⊢ List.erase (b :: l) a = b :: l",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\na b : α\nl : List α\nh : ¬a ∈ b :: l\n⊢ List.erase (b :: l) a = b :: l",
"tactic": "rw [mem_cons, not_or] at h"
},
... | [
1054,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1050,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | HasStrictFDerivAt.clm_comp | [] | [
66,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
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