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 |
|---|---|---|---|---|---|---|
Std/Data/Fin/Lemmas.lean | Fin.div_val | [] | [
15,
65
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
14,
9
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Mathlib/LinearAlgebra/Span.lean | Submodule.iSup_induction' | [
{
"state_after": "R : Type u_2\nR₂ : Type ?u.218812\nK : Type ?u.218815\nM : Type u_3\nM₂ : Type ?u.218821\nV : Type ?u.218824\nS : Type ?u.218827\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nx✝ : M\np✝ p' : Submodule R M\ninst✝² : Semiring R₂\nσ₁₂ : R →+* R₂\ninst✝¹ : AddCommMonoid M₂\n... | [
649,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
639,
1
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Mathlib/Data/Set/Finite.lean | Set.Finite.toFinset_subset | [
{
"state_after": "no goals",
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"tactic": "rw [← Finset.coe_subset, Finite.coe_toFinset]"
}
] | [
189,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
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Mathlib/Analysis/NormedSpace/Banach.lean | ContinuousLinearEquiv.coe_ofBijective | [
{
"state_after": "case h\n𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nf✝ : E →L[𝕜] F\ninst✝¹ : CompleteSpace F\ninst✝ : CompleteSpace E\nf : E →L[𝕜] F\nhinj :... | [
383,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
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Mathlib/LinearAlgebra/Pi.lean | LinearMap.pi_ext_iff | [] | [
184,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
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Mathlib/Algebra/Order/Ring/Defs.lean | strictMono_mul_left_of_pos | [] | [
582,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
581,
1
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.tendsto_integral_of_dominated_convergence | [
{
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999,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
992,
1
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Mathlib/Order/MinMax.lean | le_min_iff | [] | [
37,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
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Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.mapRange.linearEquiv_trans | [] | [
871,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
867,
1
] |
Mathlib/Order/SymmDiff.lean | compl_bihimp_self | [] | [
378,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.pos_size_of_mem | [
{
"state_after": "case nil\nα : Type u_1\ninst✝¹ : LE α\ninst✝ : DecidableRel fun x x_1 => x ≤ x_1\nx : α\nh : Sized nil\nh_mem : x ∈ nil\n⊢ 0 < size nil\n\ncase node\nα : Type u_1\ninst✝¹ : LE α\ninst✝ : DecidableRel fun x x_1 => x ≤ x_1\nx : α\nsize✝ : ℕ\nl✝ : Ordnode α\nx✝ : α\nr✝ : Ordnode α\nh : Sized (nod... | [
574,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
1
] |
Mathlib/Data/Option/Basic.lean | Option.map_pbind | [
{
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"tactic": "cases ... | [
159,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Analysis/Convex/Basic.lean | convex_Ici | [] | [
252,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Analysis/Calculus/Series.lean | hasFDerivAt_tsum_of_isPreconnected | [
{
"state_after": "no goals",
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138,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
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Mathlib/Combinatorics/Catalan.lean | catalan_three | [
{
"state_after": "⊢ ∑ i : Fin (Nat.succ 2), catalan ↑i * catalan (2 - ↑i) = 5",
"state_before": "⊢ catalan 3 = 5",
"tactic": "unfold catalan"
},
{
"state_after": "no goals",
"state_before": "⊢ ∑ i : Fin (Nat.succ 2), catalan ↑i * catalan (2 - ↑i) = 5",
"tactic": "rfl"
}
] | [
151,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
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Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.toMatrix'_smul | [
{
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997,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
995,
1
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Mathlib/CategoryTheory/Limits/Shapes/Images.lean | CategoryTheory.Limits.ImageMap.mk.injEq' | [
{
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784,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
778,
1
] |
Mathlib/Analysis/LocallyConvex/BalancedCoreHull.lean | mem_balancedHull_iff | [] | [
112,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/ModelTheory/FinitelyGenerated.lean | FirstOrder.Language.Equiv.cg_iff | [] | [
284,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Data/Nat/Interval.lean | Nat.Ico_succ_left_eq_erase_Ico | [
{
"state_after": "case a\na b c x : ℕ\n⊢ x ∈ Ico (succ a) b ↔ x ∈ erase (Ico a b) a",
"state_before": "a b c : ℕ\n⊢ Ico (succ a) b = erase (Ico a b) a",
"tactic": "ext x"
},
{
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"state_before": "case a\na b c x : ℕ\n⊢ x ∈ Ico (succ a) b ↔ x ∈ erase (Ico a b) a",
... | [
253,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.withTopEquiv_symm_top | [] | [
721,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
720,
1
] |
Std/Data/List/Lemmas.lean | List.Chain.imp | [] | [
1797,
17
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1795,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | VectorBundleCore.mem_trivChange_source | [] | [
662,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.pellZd_im | [] | [
210,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.vsub_le_vsub_right | [] | [
1152,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1151,
1
] |
Mathlib/Data/Real/Sqrt.lean | Real.coe_sqrt | [
{
"state_after": "no goals",
"state_before": "x✝ y : ℝ\nx : ℝ≥0\n⊢ ↑(↑NNReal.sqrt x) = sqrt ↑x",
"tactic": "rw [Real.sqrt, Real.toNNReal_coe]"
}
] | [
184,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Data/Multiset/Range.lean | Multiset.self_mem_range_succ | [] | [
62,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.hasIntegral_iff | [
{
"state_after": "no goals",
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200,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
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Mathlib/RepresentationTheory/Action.lean | Action.Iso.conj_ρ | [
{
"state_after": "V : Type (u + 1)\ninst✝ : LargeCategory V\nG : MonCat\nM N : Action V G\nf : M ≅ N\ng : ↑G\n⊢ ((forget V G).mapIso f).hom ≫ ↑N.ρ g = ↑M.ρ g ≫ ((forget V G).mapIso f).hom",
"state_before": "V : Type (u + 1)\ninst✝ : LargeCategory V\nG : MonCat\nM N : Action V G\nf : M ≅ N\ng : ↑G\n⊢ ↑N.ρ g ... | [
335,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
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] |
Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.isPrimitive_of_dvd | [] | [
70,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/LinearAlgebra/Matrix/Transvection.lean | Matrix.transvection_zero | [
{
"state_after": "no goals",
"state_before": "n : Type u_1\np : Type ?u.1470\nR : Type u₂\n𝕜 : Type ?u.1475\ninst✝³ : Field 𝕜\ninst✝² : DecidableEq n\ninst✝¹ : DecidableEq p\ninst✝ : CommRing R\ni j : n\n⊢ transvection i j 0 = 1",
"tactic": "simp [transvection]"
}
] | [
92,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean | SimpleGraph.ComponentCompl.mem_of_adj | [
{
"state_after": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nC : ComponentCompl G K\nc d : V\nx✝ : c ∈ C\ndnK : ¬d ∈ K\ncd : Adj G c d\ncnK : ¬c ∈ K\nh : componentComplMk G cnK = C\n⊢ Reachable (induce (Kᶜ) G) { val := d, property := dnK } { val := c, property := cnK }",
"state_before": "V : Type u\nG... | [
147,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.monic_denom | [
{
"state_after": "no goals",
"state_before": "K : Type u\ninst✝ : Field K\nx : RatFunc K\n⊢ Monic (denom x)",
"tactic": "induction x using RatFunc.induction_on with\n | f p q hq =>\n rw [denom_div p hq, mul_comm]\n exact Polynomial.monic_mul_leadingCoeff_inv (right_div_gcd_ne_zero hq)"
},
{
... | [
1203,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1199,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.spanSingleton_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\ninst✝⁶ : CommRing R\nS : Submonoid R\nP : Type u_1\ninst✝⁵ : CommRing P\ninst✝⁴ : Algebra R P\nloc : IsLocalization S P\nR₁ : Type ?u.1326146\ninst✝³ : CommRing R₁\nK : Type ?u.1326152\ninst✝² : Field K\ninst✝¹ : Algebra R₁ K\ninst✝ : IsFractionRin... | [
1351,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1348,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm'_const_of_isProbabilityMeasure | [
{
"state_after": "no goals",
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288,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Data/Polynomial/Div.lean | Polynomial.ker_evalRingHom | [
{
"state_after": "case h\nR : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\ninst✝ : CommRing R\np q : R[X]\nx : R\ny : R[X]\n⊢ y ∈ RingHom.ker (evalRingHom x) ↔ y ∈ Ideal.span {X - ↑C x}",
"state_before": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\ninst✝ : CommRing R\np q ... | [
507,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
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] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiff.comp | [] | [
669,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
667,
1
] |
Mathlib/Data/List/Sort.lean | List.perm_split | [
{
"state_after": "case mk\nα : Type uu\nr : α → α → Prop\ninst✝ : DecidableRel r\na : α\nl l₁' l₂' : List α\nh : split (a :: l) = (l₁', l₂')\nl₁ l₂ : List α\ne : split l = (l₁, l₂)\n⊢ a :: l ~ l₁' ++ l₂'",
"state_before": "α : Type uu\nr : α → α → Prop\ninst✝ : DecidableRel r\na : α\nl l₁' l₂' : List α\nh :... | [
341,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.map_mul | [] | [
930,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
929,
11
] |
Mathlib/Analysis/NormedSpace/Pointwise.lean | Metric.Bounded.smul | [
{
"state_after": "case intro\n𝕜 : Type u_2\nE : Type u_1\ninst✝² : NormedField 𝕜\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\ns : Set E\nhs : Bounded s\nc : 𝕜\nR : ℝ\nhR : ∀ (x : E), x ∈ s → ‖x‖ ≤ R\n⊢ Bounded (c • s)",
"state_before": "𝕜 : Type u_2\nE : Type u_1\ninst✝² : NormedField �... | [
121,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Data/Rat/Order.lean | Rat.add_le_add_left | [
{
"state_after": "no goals",
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"tactic": "rw [Rat.le_iff_Nonneg, add_sub_add_left_eq_sub, Rat.le_iff_Nonneg]"
}
] | [
249,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
11
] |
Mathlib/Order/Filter/Cofinite.lean | Filter.le_cofinite_iff_eventually_ne | [] | [
104,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.symm_comp | [] | [
559,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.mul_add_left_left_iff | [] | [
340,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | RingHom.Finite.to_isIntegral | [] | [
406,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.fract_one | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.158043\nα : Type u_1\nβ : Type ?u.158049\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na : α\n⊢ fract 1 = 0",
"tactic": "simp [fract]"
}
] | [
891,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
891,
1
] |
Mathlib/CategoryTheory/Filtered.lean | CategoryTheory.IsFiltered.coeq₃_condition₁ | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : IsFilteredOrEmpty C\nj₁ j₂ : C\nf g h : j₁ ⟶ j₂\n⊢ f ≫ coeq₃Hom f g h = g ≫ coeq₃Hom f g h",
"tactic": "simp only [coeq₃Hom, ← Category.assoc, coeq_condition f g]"
}
] | [
389,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.range_toProd | [
{
"state_after": "case intro\n𝕜 : Type u_2\nA : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NonUnitalNormedRing A\ninst✝² : NormedSpace 𝕜 A\ninst✝¹ : SMulCommClass 𝕜 A A\ninst✝ : IsScalarTower 𝕜 A A\na : 𝓜(𝕜, A)\n⊢ a.toProd ∈ {lr | ∀ (x y : A), ↑lr.snd x * y = x * ↑lr.fst y}",
"state_befor... | [
115,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasStrictFDerivAt.exists_lipschitzOnWith_of_nnnorm_lt | [
{
"state_after": "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.210344\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.210439\... | [
449,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
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] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.equalizer.lift_ι | [] | [
802,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
800,
1
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Mathlib/RingTheory/Subring/Basic.lean | Subring.toSubsemiring_mono | [] | [
266,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_C_mul_X | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na✝ b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q r : R[X]\na : R\nha : a ≠ 0\n⊢ natDegree (↑C a * X) = 1",
"tactic": "simpa only [pow_one] using natDegree_C_mul_X_pow 1 a ha"
}
] | [
323,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.contentRegular_exists_compact | [
{
"state_after": "G : Type w\ninst✝ : TopologicalSpace G\nμ : Content G\nH : ContentRegular μ\nK : Compacts G\nε : ℝ≥0\nhε : ε ≠ 0\nhc : ¬∃ K', K.carrier ⊆ interior K'.carrier ∧ (fun s => ↑(toFun μ s)) K' ≤ (fun s => ↑(toFun μ s)) K + ↑ε\n⊢ False",
"state_before": "G : Type w\ninst✝ : TopologicalSpace G\nμ ... | [
432,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_mul_le_Lp_mul_Lq_of_nonneg | [
{
"state_after": "α : Type u_1\nE : Type ?u.1686459\nF : Type ?u.1686462\n𝕜 : Type ?u.1686465\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace ℝ E\ninst✝⁸ : CompleteSpace E\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : SMulCommClass ℝ 𝕜 E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³... | [
1718,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1701,
1
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Mathlib/Data/Finset/Pointwise.lean | Finset.smul_univ₀ | [
{
"state_after": "F : Type ?u.897847\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.897856\ninst✝³ : DecidableEq β\ninst✝² : GroupWithZero α\ninst✝¹ : MulAction α β\ns✝ t : Finset β\na : α\nb : β\ninst✝ : Fintype β\ns : Finset α\nhs : ¬↑s ⊆ ↑0\n⊢ ↑(s • univ) = ↑univ",
"state_before": "F : Type ?u.897847\nα : Type... | [
2076,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2072,
1
] |
Std/Data/Int/Lemmas.lean | Int.ofNat_lt | [
{
"state_after": "n m : Nat\n⊢ succ n ≤ m ↔ n < m",
"state_before": "n m : Nat\n⊢ ↑n < ↑m ↔ n < m",
"tactic": "rw [lt_iff_add_one_le, ← ofNat_succ, ofNat_le]"
},
{
"state_after": "no goals",
"state_before": "n m : Nat\n⊢ succ n ≤ m ↔ n < m",
"tactic": "rfl"
}
] | [
600,
54
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
599,
20
] |
Std/Data/Rat/Lemmas.lean | Rat.sub_def | [
{
"state_after": "a b : Rat\n⊢ Rat.sub a b = normalize (a.num * ↑b.den - b.num * ↑a.den) (a.den * b.den)",
"state_before": "a b : Rat\n⊢ a - b = normalize (a.num * ↑b.den - b.num * ↑a.den) (a.den * b.den)",
"tactic": "show Rat.sub .. = _"
},
{
"state_after": "a b : Rat\n⊢ (let g := Nat.gcd a.den... | [
231,
72
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
218,
1
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Mathlib/Data/List/Basic.lean | List.eq_cons_of_length_one | [
{
"state_after": "ι : Type ?u.104743\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l : List α\nh : length l = 1\nn : ℕ\nh₁ : n < length l\nh₂ : n < length [nthLe l 0 (_ : 0 < length l)]\n⊢ get l { val := n, isLt := h₁ } = get [nthLe l 0 (_ : 0 < length l)] { val := n, isLt := h₂ }",
"state_before":... | [
1484,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1479,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Submodule.annihilator_iSup | [] | [
105,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Topology/MetricSpace/IsometricSMul.lean | dist_div_left | [
{
"state_after": "no goals",
"state_before": "M : Type u\nG : Type v\nX : Type w\ninst✝³ : Group G\ninst✝² : PseudoMetricSpace G\ninst✝¹ : IsometricSMul G G\ninst✝ : IsometricSMul Gᵐᵒᵖ G\na b c : G\n⊢ dist (a / b) (a / c) = dist b c",
"tactic": "simp [div_eq_mul_inv]"
}
] | [
415,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.continuousOn_iff_continuousOn_comp_right | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type u_3\nδ : Type ?u.99648\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ne : LocalHomeomorph α β\ne' : LocalHomeomorph β γ\nf : β → γ\ns : Set β\nh : s ⊆ e.target\n⊢ (∀ (x : β), x ∈ s → Conti... | [
1162,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1156,
1
] |
Mathlib/Analysis/NormedSpace/Units.lean | Units.isOpen | [
{
"state_after": "R : Type u_1\ninst✝¹ : NormedRing R\ninst✝ : CompleteSpace R\n✝ : Nontrivial R\n⊢ IsOpen {x | IsUnit x}",
"state_before": "R : Type u_1\ninst✝¹ : NormedRing R\ninst✝ : CompleteSpace R\n⊢ IsOpen {x | IsUnit x}",
"tactic": "nontriviality R"
},
{
"state_after": "R : Type u_1\ninst... | [
86,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
11
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | uniformity_basis_edist' | [] | [
227,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Logic/Equiv/Fin.lean | finSuccEquivLast_symm_none | [] | [
289,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
9
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableEquiv.symm_preimage_preimage | [] | [
1296,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1295,
1
] |
Mathlib/Analysis/Convex/Quasiconvex.lean | Monotone.quasiconvexOn | [] | [
209,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiffOn.ftaylorSeriesWithin | [
{
"state_after": "case zero_eq\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... | [
1042,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1003,
11
] |
Mathlib/Data/Sym/Sym2.lean | Sym2.toRel_fromRel | [] | [
545,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
544,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | exists_eq_pow_of_mul_eq_pow | [] | [
662,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
659,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.count_replicate_self | [
{
"state_after": "case h.e'_2\nα : Type u_1\nβ : Type ?u.362314\nγ : Type ?u.362317\ninst✝ : DecidableEq α\na : α\nn : ℕ\n⊢ count a (replicate n a) = List.count a (List.replicate n a)",
"state_before": "α : Type u_1\nβ : Type ?u.362314\nγ : Type ?u.362317\ninst✝ : DecidableEq α\na : α\nn : ℕ\n⊢ count a (rep... | [
2435,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2433,
1
] |
Mathlib/AlgebraicTopology/SimplexCategory.lean | SimplexCategory.Hom.ext | [] | [
163,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/RingTheory/PowerBasis.lean | PowerBasis.natDegree_minpoly | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.143265\nS : Type u_2\nT : Type ?u.143271\ninst✝⁹ : CommRing R\ninst✝⁸ : Ring S\ninst✝⁷ : Algebra R S\nA : Type u_1\nB : Type ?u.143577\ninst✝⁶ : CommRing A\ninst✝⁵ : CommRing B\ninst✝⁴ : IsDomain B\ninst✝³ : Algebra A B\nK : Type ?u.143999\ninst✝² : ... | [
222,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_comm' | [
{
"state_after": "α : Type ?u.360325\nβ : Type u_3\nγ : Type u_2\nδ : Type u_1\ninst✝⁷ : AddCommMonoid α\ninst✝⁶ : TopologicalSpace α\ninst✝⁵ : T2Space α\nf✝ g : β → α\na a₁ a₂ : α\ninst✝⁴ : ContinuousAdd α\ninst✝³ : AddCommMonoid δ\ninst✝² : TopologicalSpace δ\ninst✝¹ : T3Space δ\ninst✝ : ContinuousAdd δ\nf : ... | [
681,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
678,
1
] |
Mathlib/Topology/Basic.lean | mem_closure_image | [] | [
1723,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1720,
1
] |
Mathlib/Topology/Instances/Matrix.lean | Matrix.transpose_tsum | [
{
"state_after": "case pos\nX : Type u_4\nα : Type ?u.51831\nl : Type ?u.51834\nm : Type u_2\nn : Type u_3\np : Type ?u.51843\nS : Type ?u.51846\nR : Type u_1\nm' : l → Type ?u.51854\nn' : l → Type ?u.51859\ninst✝⁴ : Semiring α\ninst✝³ : AddCommMonoid R\ninst✝² : TopologicalSpace R\ninst✝¹ : Module α R\ninst✝ :... | [
315,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.isSymm_toMatrix' | [
{
"state_after": "case a.h\nS : Type ?u.554283\nR : Type ?u.554286\nR₁ : Type u_1\nM : Type ?u.554292\nn : Type w\ninst✝⁵ : Fintype n\ninst✝⁴ : DecidableEq n\ninst✝³ : CommRing R₁\ninst✝² : AddCommMonoid M\ninst✝¹ : Module R₁ M\ninst✝ : Invertible 2\nQ : QuadraticForm R₁ (n → R₁)\ni j : n\n⊢ Matrix.transpose (t... | [
1003,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1000,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | orthogonalProjection_eq_self_iff | [
{
"state_after": "case refine'_1\n𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.516714\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : InnerProductSpace ℝ F\nK : Submodule 𝕜 E\ninst✝ : CompleteSpace { x // x ∈ K }\nv : E\nh : ↑(↑(orthogona... | [
527,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/CategoryTheory/Monoidal/OfChosenFiniteProducts/Symmetric.lean | CategoryTheory.MonoidalOfChosenFiniteProducts.symmetry | [
{
"state_after": "C : Type u\ninst✝ : Category C\nX✝ Y✝ : C\n𝒯 : LimitCone (Functor.empty C)\nℬ : (X Y : C) → LimitCone (pair X Y)\nX Y : C\n⊢ (IsLimit.conePointUniqueUpToIso (ℬ X Y).isLimit (IsLimit.swapBinaryFan (ℬ Y X).isLimit)).hom ≫\n (IsLimit.conePointUniqueUpToIso (ℬ Y X).isLimit (IsLimit.swapBinar... | [
87,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.one_lt_coe_iff | [] | [
675,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
675,
1
] |
Mathlib/Topology/Algebra/UniformRing.lean | UniformSpace.Completion.algebraMap_def | [] | [
214,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | QuotientGroup.measurable_coe | [] | [
510,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
] |
src/lean/Init/Core.lean | HEq.subst | [] | [
622,
20
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
621,
1
] |
Mathlib/Analysis/Calculus/Deriv/AffineMap.lean | AffineMap.differentiableWithinAt | [] | [
53,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
11
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.RespectsIso.isomorphisms | [
{
"state_after": "case right\nC : Type u\ninst✝¹ : Category C\nD : Type ?u.61837\ninst✝ : Category D\nX Y Z : C\ne : Y ≅ Z\nf : X ⟶ Y\n⊢ MorphismProperty.isomorphisms C f → MorphismProperty.isomorphisms C (f ≫ e.hom)",
"state_before": "case right\nC : Type u\ninst✝¹ : Category C\nD : Type ?u.61837\ninst✝ : ... | [
450,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
Mathlib/Order/RelClasses.lean | IsLinearOrder.swap | [] | [
116,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Data/Finmap.lean | Finmap.mem_lookup_union | [] | [
605,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
] |
Mathlib/MeasureTheory/Integral/Average.lean | MeasureTheory.average_pair | [] | [
142,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | ENNReal.exists_pos_tsum_mul_lt_of_countable | [
{
"state_after": "case intro\nα : Type ?u.479540\nβ : Type ?u.479543\nι✝ : Type ?u.479546\nε : ℝ≥0∞\nhε : ε ≠ 0\nι : Type u_1\ninst✝ : Countable ι\nw : ι → ℝ≥0\n⊢ ∃ δ, (∀ (i : ι), 0 < δ i) ∧ (∑' (i : ι), (fun i => ↑(w i)) i * ↑(δ i)) < ε",
"state_before": "α : Type ?u.479540\nβ : Type ?u.479543\nι✝ : Type ?... | [
527,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.smul_finset_sdiff | [] | [
1998,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1997,
1
] |
Mathlib/Data/Multiset/FinsetOps.lean | Multiset.le_ndunion_right | [] | [
168,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Algebra/DirectSum/Internal.lean | DirectSum.coe_mul_of_apply_of_le | [] | [
260,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Order/Antichain.lean | IsAntichain.preimage_compl | [] | [
203,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.PointedMap.headI_map | [
{
"state_after": "no goals",
"state_before": "Γ : Type u_1\nΓ' : Type u_2\ninst✝¹ : Inhabited Γ\ninst✝ : Inhabited Γ'\nf : PointedMap Γ Γ'\nl : List Γ\n⊢ List.headI (List.map f.f l) = Turing.PointedMap.f f (List.headI l)",
"tactic": "cases l <;> [exact (PointedMap.map_pt f).symm; rfl]"
}
] | [
379,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_subset_Icc_self | [] | [
517,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/Combinatorics/SimpleGraph/Triangle/Basic.lean | SimpleGraph.CliqueFree.not_farFromTriangleFree | [] | [
78,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Topology/Semicontinuous.lean | lowerSemicontinuousOn_const | [] | [
188,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Combinatorics/SetFamily/Shadow.lean | Finset.mem_shadow_iff_insert_mem | [
{
"state_after": "case refine'_1\nα : Type u_1\ninst✝ : DecidableEq α\n𝒜 : Finset (Finset α)\ns t : Finset α\na : α\nk r : ℕ\n⊢ (∃ t, t ∈ 𝒜 ∧ ∃ a, a ∈ t ∧ erase t a = s) → ∃ a x, insert a s ∈ 𝒜\n\ncase refine'_2\nα : Type u_1\ninst✝ : DecidableEq α\n𝒜 : Finset (Finset α)\ns t : Finset α\na : α\nk r : ℕ\n⊢ (... | [
108,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Data/Part.lean | Part.mem_mk_iff | [] | [
113,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Data/Finset/NoncommProd.lean | Finset.noncommProd_empty | [] | [
274,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.eq_of_infinite_eval_eq | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np✝ q✝ p q : R[X]\nh : Set.Infinite {x | eval x p = eval x q}\n⊢ p - q = 0",
"state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np✝ q✝ p q :... | [
623,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
619,
1
] |
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