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/RingTheory/FractionalIdeal.lean | FractionalIdeal.le_spanSingleton_mul_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁷ : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝⁶ : CommRing P\ninst✝⁵ : Algebra R P\nloc : IsLocalization S P\nR₁ : Type ?u.1730977\ninst✝⁴ : CommRing R₁\nK : Type ?u.1730983\ninst✝³ : Field K\ninst✝² : Algebra R₁ K\ninst✝¹ : IsFractionRi... | [
1527,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1524,
1
] |
Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.imageSubobjectMap_arrow | [
{
"state_after": "C : Type u\ninst✝⁴ : Category C\nX✝ Y✝ Z✝ : C\nf✝ : X✝ ⟶ Y✝\ninst✝³ : HasImage f✝\nW X Y Z : C\nf : W ⟶ X\ninst✝² : HasImage f\ng : Y ⟶ Z\ninst✝¹ : HasImage g\nsq : Arrow.mk f ⟶ Arrow.mk g\ninst✝ : HasImageMap sq\n⊢ (imageSubobjectIso f).hom ≫ image.map sq ≫ image.ι g = arrow (imageSubobject f... | [
470,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | lt_div_iff_mul_lt | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Group α\ninst✝¹ : LT α\ninst✝ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x < x_1\na b c d : α\n⊢ a < c / b ↔ a * b < c",
"tactic": "rw [← mul_lt_mul_iff_right b, div_eq_mul_inv, inv_mul_cancel_right]"
}
] | [
914,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
913,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | aestronglyMeasurable_const_smul_iff₀ | [] | [
1771,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1769,
1
] |
Mathlib/MeasureTheory/Function/L2Space.lean | MeasureTheory.Memℒp.inner_const | [
{
"state_after": "α : Type u_2\nm : MeasurableSpace α\np : ℝ≥0∞\nμ : Measure α\nE : Type u_1\n𝕜 : Type u_3\ninst✝² : IsROrC 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : InnerProductSpace 𝕜 E\nf : α → E\nhf : Memℒp f p\nc : E\nx : α\n⊢ ‖inner (f x) c‖ ≤ ‖f x‖ * ?m.29976 hf c\n\nα : Type u_2\nm : MeasurableSpace ... | [
83,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
src/lean/Init/SimpLemmas.lean | Bool.false_or | [
{
"state_after": "no goals",
"state_before": "b : Bool\n⊢ (false || b) = b",
"tactic": "cases b <;> rfl"
}
] | [
104,
83
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
104,
9
] |
Mathlib/Topology/UniformSpace/Matrix.lean | Matrix.uniformContinuous | [
{
"state_after": "m : Type u_2\nn : Type u_3\n𝕜 : Type u_4\ninst✝¹ : UniformSpace 𝕜\nβ : Type u_1\ninst✝ : UniformSpace β\nf : β → Matrix m n 𝕜\n⊢ (∀ (i : m) (i_1 : n),\n Filter.Tendsto ((fun a => (Prod.fst a i i_1, Prod.snd a i i_1)) ∘ fun x => (f x.fst, f x.snd)) (𝓤 β) (𝓤 𝕜)) ↔\n ∀ (i : m) (j : ... | [
38,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/Analysis/SpecialFunctions/Polynomials.lean | Polynomial.div_tendsto_leadingCoeff_div_of_degree_eq | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹ : NormedLinearOrderedField 𝕜\nP Q : 𝕜[X]\ninst✝ : OrderTopology 𝕜\nhdeg : degree P = degree Q\n⊢ Tendsto (fun x => leadingCoeff P / leadingCoeff Q * x ^ (↑(natDegree P) - ↑(natDegree Q))) atTop\n (𝓝 (leadingCoeff P / leadingCoeff Q))",
"state_before": "𝕜 : Typ... | [
172,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | posMulMono_iff_posMulReflectLT | [] | [
320,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.image_mul_right | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.619432\nα : Type u_1\nβ : Type ?u.619438\nγ : Type ?u.619441\ninst✝⁴ : DecidableEq α\ninst✝³ : DecidableEq β\ninst✝² : Group α\ninst✝¹ : DivisionMonoid β\ninst✝ : MonoidHomClass F α β\nf : F\ns t : Finset α\na b : α\n⊢ ↑(image (fun x => x * b) t) =\n... | [
1162,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1161,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | Submodule.toConvexCone_inf | [] | [
544,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
1
] |
Mathlib/Analysis/Calculus/Deriv/Polynomial.lean | Polynomial.hasDerivWithinAt_aeval | [] | [
100,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
11
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.tendsto_translationNumber_aux | [] | [
683,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
1
] |
Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.principal_add_omega | [] | [
195,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.reverse_concat | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v w : V\np : Walk G u v\nh : Adj G v w\n⊢ reverse (concat p h) = cons (_ : Adj G w v) (reverse p)",
"tactic": "simp [concat_eq_append]"
}
] | [
374,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | hasDerivAt_iff_isLittleO | [] | [
281,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Slope.lean | LinearMap.slope_comp | [] | [
92,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Combinatorics/SetFamily/Compression/UV.lean | UV.sup_sdiff_mem_of_mem_compression_of_not_mem | [
{
"state_after": "α : Type u_1\ninst✝² : GeneralizedBooleanAlgebra α\ninst✝¹ : DecidableRel Disjoint\ninst✝ : DecidableRel fun x x_1 => x ≤ x_1\ns : Finset α\nu v a b : α\nh : a ∈ s ∧ compress u v a ∈ s ∨ ¬a ∈ s ∧ ∃ b, b ∈ s ∧ compress u v b = a\nha : ¬a ∈ s\n⊢ (a ⊔ v) \\ u ∈ s",
"state_before": "α : Type u... | [
256,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/LinearAlgebra/Matrix/ZPow.lean | Matrix.Commute.zpow_right | [
{
"state_after": "case inl.intro\nn' : Type u_1\ninst✝² : DecidableEq n'\ninst✝¹ : Fintype n'\nR : Type u_2\ninst✝ : CommRing R\nA B : M\nh : Commute A B\nm : ℤ\nhB : B⁻¹ ⬝ B = 1\nright✝ : B ⬝ B⁻¹ = 1\n⊢ Commute A (B ^ m)\n\ncase inr\nn' : Type u_1\ninst✝² : DecidableEq n'\ninst✝¹ : Fintype n'\nR : Type u_2\nin... | [
221,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Complex.abs_cpow_eq_rpow_re_of_pos | [
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx : 0 < x\ny : ℂ\n⊢ ↑abs (↑x ^ y) = x ^ y.re",
"tactic": "rw [abs_cpow_of_ne_zero (ofReal_ne_zero.mpr hx.ne'), arg_ofReal_of_nonneg hx.le,\n MulZeroClass.zero_mul, Real.exp_zero, div_one, abs_of_nonneg hx.le]"
}
] | [
296,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Data/List/Card.lean | List.union_equiv_append | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\nas bs : List α\nx : α\n⊢ x ∈ List.union as bs ↔ x ∈ as ++ bs",
"tactic": "simp"
}
] | [
30,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
29,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.map_le_map_iff_of_injective | [] | [
426,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.ext_ring_iff | [] | [
531,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
1
] |
Mathlib/RingTheory/SimpleModule.lean | JordanHolderModule.iso_symm | [] | [
219,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Data/List/AList.lean | AList.insertRec_empty | [
{
"state_after": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\nC : AList β → Sort u_1\nH0 : C ∅\nIH : (a : α) → (b : β a) → (l : AList β) → ¬a ∈ l → C l → C (insert a b l)\n⊢ insertRec H0 IH { entries := [], nodupKeys := (_ : NodupKeys []) } = H0",
"state_before": "α : Type u\nβ : α → Type v\ninst✝ : ... | [
373,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Data/Set/Countable.lean | Set.countable_univ | [] | [
116,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/GroupTheory/GroupAction/ConjAct.lean | ConjAct.ofConjAct_mul | [] | [
139,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.equiv_symm_zero | [] | [
775,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
774,
1
] |
Mathlib/Algebra/Category/ModuleCat/Adjunctions.lean | ModuleCat.Free.right_unitality | [
{
"state_after": "R : Type u\ninst✝ : CommRing R\nX : Type u\n⊢ (ρ_ ((free R).obj X)).hom =\n (𝟙 ((free R).obj X) ⊗ ε R) ≫ (μ R X (𝟙_ (Type u))).hom ≫ map (free R).toPrefunctor.obj (ρ_ X).hom",
"state_before": "R : Type u\ninst✝ : CommRing R\nX : Type u\n⊢ (ρ_ ((free R).obj X)).hom =\n (𝟙 ((free R)... | [
152,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Data/PNat/Interval.lean | PNat.card_Ioc | [
{
"state_after": "a b : ℕ+\n⊢ card (Ioc a b) = card (Ioc ↑a ↑b)",
"state_before": "a b : ℕ+\n⊢ card (Ioc a b) = ↑b - ↑a",
"tactic": "rw [← Nat.card_Ioc]"
},
{
"state_after": "a b : ℕ+\n⊢ card (Ioc a b) = card (map (Function.Embedding.subtype fun n => 0 < n) (Ioc a b))",
"state_before": "a b ... | [
84,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Data/Nat/Totient.lean | Nat.totient_even | [
{
"state_after": "n : ℕ\nhn : 2 < n\nthis : Fact (1 < n)\n⊢ Even (φ n)",
"state_before": "n : ℕ\nhn : 2 < n\n⊢ Even (φ n)",
"tactic": "haveI : Fact (1 < n) := ⟨one_lt_two.trans hn⟩"
},
{
"state_after": "n : ℕ\nhn : 2 < n\nthis✝ : Fact (1 < n)\nthis : NeZero n\n⊢ Even (φ n)",
"state_before": ... | [
136,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | HomogeneousIdeal.toIdeal_mul | [] | [
469,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
1
] |
Mathlib/Order/Concept.lean | intentClosure_swap | [] | [
78,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Data/Int/Parity.lean | Int.ediv_two_mul_two_of_even | [] | [
257,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.zpow_apply_eq_self_of_apply_eq_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nf g h : Perm α\nx : α\nhfx : ↑f x = x\nn : ℕ\n⊢ ↑(f ^ Int.negSucc n) x = x",
"tactic": "rw [zpow_negSucc, inv_eq_iff_eq, pow_apply_eq_self_of_apply_eq_self hfx]"
}
] | [
158,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.Lp.simpleFunc.toSimpleFunc_indicatorConst | [] | [
716,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
713,
1
] |
Mathlib/CategoryTheory/GlueData.lean | CategoryTheory.GlueData.diagramIso_inv_app_right | [] | [
336,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.exists_le_of_prod_le' | [
{
"state_after": "ι : Type u_2\nα : Type ?u.101039\nM : Type u_1\nN : Type ?u.101045\nP : Type ?u.101048\nM₀ : Type ?u.101051\nG : Type ?u.101054\nR : Type ?u.101057\ninst✝⁷ : Monoid M\ninst✝⁶ : Monoid N\ninst✝⁵ : Monoid P\nl✝ l₁ l₂ : List M\na : M\ninst✝⁴ : LinearOrder M\ninst✝³ : CovariantClass M M (fun x x_1... | [
359,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.chain_dartAdj_darts | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nd : Dart G\nv w : V\nh : d.snd = v\np : Walk G v w\n⊢ List.Chain (DartAdj G) d (darts p)",
"tactic": "induction p generalizing d with\n| nil => exact List.C... | [
661,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
1
] |
src/lean/Init/SimpLemmas.lean | true_or | [] | [
89,
81
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
89,
9
] |
Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean | ModularGroup.T_mul_apply_one | [
{
"state_after": "no goals",
"state_before": "g : SL(2, ℤ)\n⊢ ↑(T * g) 1 = ↑g 1",
"tactic": "simpa using T_pow_mul_apply_one 1 g"
}
] | [
385,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
1
] |
Mathlib/Combinatorics/SimpleGraph/DegreeSum.lean | SimpleGraph.even_card_odd_degree_vertices | [
{
"state_after": "V : Type u\nG : SimpleGraph V\ninst✝¹ : Fintype V\ninst✝ : DecidableRel G.Adj\nh : (fun n => ↑n) (∑ v : V, degree G v) = (fun n => ↑n) (2 * card (edgeFinset G))\n⊢ Even (card (filter (fun v => Odd (degree G v)) univ))",
"state_before": "V : Type u\nG : SimpleGraph V\ninst✝¹ : Fintype V\nin... | [
136,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_norm_mul_le | [] | [
1122,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1121,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | SubgroupClass.coe_pow | [] | [
300,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Order/SymmDiff.lean | symmDiff_left_involutive | [] | [
510,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.ofReal_add | [] | [
209,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Order/Grade.lean | IsMax.grade | [] | [
150,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
11
] |
Mathlib/Order/SymmDiff.lean | le_symmDiff_iff_right | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.67558\nα : Type u_1\nβ : Type ?u.67564\nπ : ι → Type ?u.67569\ninst✝ : GeneralizedBooleanAlgebra α\na b c d : α\n⊢ b ≤ a ∆ b ↔ Disjoint a b",
"tactic": "rw [symmDiff_comm, le_symmDiff_iff_left, disjoint_comm]"
}
] | [
456,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
] |
Mathlib/Algebra/Field/Basic.lean | ofDual_rat_cast | [] | [
387,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.blockDiagonal'_one | [
{
"state_after": "no goals",
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714,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
711,
1
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Mathlib/Order/Filter/Extr.lean | isExtrFilter_const | [] | [
189,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Data/Set/Constructions.lean | FiniteInter.finiteInterClosure_insert | [
{
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84,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
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Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingIso.self_trans_symm | [] | [
500,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
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Mathlib/Logic/Equiv/Basic.lean | Equiv.uniqueProd_apply | [] | [
208,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.angle_comm | [] | [
130,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
8
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Mathlib/Data/Dfinsupp/NeLocus.lean | Dfinsupp.neLocus_neg | [
{
"state_after": "no goals",
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"tactic": "rw [← neLocus_neg_neg, neg_neg]"
}
] | [
145,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
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Mathlib/Analysis/NormedSpace/Dual.lean | NormedSpace.inclusionInDoubleDual_norm_eq | [] | [
102,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
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Mathlib/Algebra/Group/Commute.lean | Commute.semiconjBy | [] | [
71,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
11
] |
Mathlib/RingTheory/JacobsonIdeal.lean | Ideal.isRadical_of_eq_jacobson | [] | [
251,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
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Mathlib/Order/CompleteLattice.lean | le_sInf_iff | [] | [
233,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
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Mathlib/Data/Fin/Tuple/Basic.lean | Fin.insertNth_sub_same | [
{
"state_after": "no goals",
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"tactic": "simp_rw [← insertNth_sub, ← ... | [
797,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
795,
1
] |
Mathlib/Data/Set/Prod.lean | Set.diag_preimage_prod | [] | [
511,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
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Mathlib/MeasureTheory/Covering/Differentiation.lean | VitaliFamily.ae_tendsto_measure_inter_div_of_measurableSet | [
{
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748,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
742,
1
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Mathlib/RingTheory/DedekindDomain/Factorization.lean | Ideal.finprod_heightOneSpectrum_factorization_coe | [
{
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179,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
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Mathlib/Analysis/Normed/Group/Quotient.lean | AddSubgroup.norm_trivial_quotient_mk | [
{
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338,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
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Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiff_succ_iff_has_fderiv | [
{
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1489,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1485,
1
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Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.isDomain | [
{
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878,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
874,
11
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Mathlib/Combinatorics/SimpleGraph/Clique.lean | SimpleGraph.cliqueFree_bot | [
{
"state_after": "α : Type u_1\nG H : SimpleGraph α\nm n : ℕ\ns : Finset α\nh : 2 ≤ n\nt : Finset α\nht : IsNClique ⊥ n t\n⊢ False",
"state_before": "α : Type u_1\nG H : SimpleGraph α\nm n : ℕ\ns : Finset α\nh : 2 ≤ n\n⊢ CliqueFree ⊥ n",
"tactic": "intro t ht"
},
{
"state_after": "α : Type u_1\n... | [
213,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
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Mathlib/Data/Finsupp/AList.lean | AList.lookupFinsupp_surjective | [] | [
142,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
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Mathlib/RingTheory/Ideal/LocalRing.lean | LocalRing.of_surjective | [
{
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"state_before": "R : Ty... | [
333,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Data/List/Rdrop.lean | List.rtakeWhile_concat_neg | [
{
"state_after": "no goals",
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"tactic": "rw [rtakeWhile_concat, if_neg h]"
}
] | [
213,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiffOn_fst | [] | [
758,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
757,
1
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.factorial_zero | [] | [
46,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.ExprCnstr.denote_toNormPoly | [
{
"state_after": "case mk\nctx : Context\neq✝ : Bool\nlhs✝ rhs✝ : Expr\n⊢ PolyCnstr.denote ctx (toNormPoly { eq := eq✝, lhs := lhs✝, rhs := rhs✝ }) =\n denote ctx { eq := eq✝, lhs := lhs✝, rhs := rhs✝ }",
"state_before": "ctx : Context\nc : ExprCnstr\n⊢ PolyCnstr.denote ctx (toNormPoly c) = denote ctx c"... | [
573,
85
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
568,
1
] |
Std/Data/List/Init/Lemmas.lean | List.append_inj | [
{
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"state_before": "α : Type u_1\na : α\ns₁ : List α\nb : α\ns₂ t₁ t₂ : List α\nh : a :: s₁ ++ t₁ = b :: s₂ ++ t₂\nhl : length (a :: s₁) = length (b :: s₂)\n⊢ a :: s₁ = b... | [
60,
71
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
56,
1
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Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidHom.toMonoidHom_eq_coe | [] | [
548,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
1
] |
Mathlib/Algebra/EuclideanDomain/Defs.lean | EuclideanDomain.mod_lt | [] | [
149,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/MeasureTheory/Function/UniformIntegrable.lean | MeasureTheory.Memℒp.integral_indicator_norm_ge_nonneg_le | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nι : Type ?u.89388\nm : MeasurableSpace α\nμ : Measure α\ninst✝ : NormedAddCommGroup β\np : ℝ≥0∞\nf : α → β\nhf : Memℒp f 1\nε : ℝ\nhε : 0 < ε\nhf_mk : Memℒp (AEStronglyMeasurable.mk f (_ : AEStronglyMeasurable f μ)) 1\n⊢ ∃ M, 0 ≤ M ∧ (∫⁻ (x : α), ↑‖Set.indicator {x ... | [
231,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/NumberTheory/PythagoreanTriples.lean | PythagoreanTriple.normalize | [
{
"state_after": "case pos\nx y z : ℤ\nh : PythagoreanTriple x y z\nh0 : Int.gcd x y = 0\n⊢ PythagoreanTriple (x / ↑(Int.gcd x y)) (y / ↑(Int.gcd x y)) (z / ↑(Int.gcd x y))\n\ncase neg\nx y z : ℤ\nh : PythagoreanTriple x y z\nh0 : ¬Int.gcd x y = 0\n⊢ PythagoreanTriple (x / ↑(Int.gcd x y)) (y / ↑(Int.gcd x y)) (... | [
207,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | hasFTaylorSeriesUpToOn_top_iff' | [] | [
262,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | iteratedFDerivWithin_one_apply | [
{
"state_after": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nX : Type uX\ninst✝¹ : NormedAdd... | [
876,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
871,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableEquiv.coe_mk | [] | [
1194,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1192,
1
] |
Mathlib/Topology/LocallyConstant/Basic.lean | IsLocallyConstant.of_constant | [] | [
124,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.map_codRestrict | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nR₁ : Type ?u.1010618\nR₂ : Type u_1\nR₃ : Type ?u.1010624\nR₄ : Type ?u.1010627\nS : Type ?u.1010630\nK : Type ?u.1010633\nK₂ : Type ?u.1010636\nM : Type u_3\nM' : Type ?u.1010642\nM₁ : Type ?u.1010645\nM₂ : Type u_4\nM₃ : Type ?u.1010651\nM₄ : Typ... | [
1183,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1181,
1
] |
Mathlib/Data/Finset/Prod.lean | Finset.singleton_product | [
{
"state_after": "case a.mk\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.68532\ns s' : Finset α\nt t' : Finset β\na✝ : α\nb : β\na x : α\ny : β\n⊢ (x, y) ∈ {a} ×ˢ t ↔ (x, y) ∈ map { toFun := Prod.mk a, inj' := (_ : Function.Injective (Prod.mk a)) } t",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.68... | [
220,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/CategoryTheory/Sites/Subsheaf.lean | CategoryTheory.GrothendieckTopology.Subpresheaf.nat_trans_naturality | [] | [
180,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Order/Interval.lean | Interval.coe_coe | [] | [
493,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_nonempty | [] | [
129,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Data/Part.lean | Part.append_def | [] | [
704,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
704,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.sum_cond | [] | [
2101,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2100,
1
] |
Mathlib/Analysis/InnerProductSpace/GramSchmidtOrtho.lean | gramSchmidt_def | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\nE : Type u_1\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace 𝕜 E\nι : Type u_3\ninst✝² : LinearOrder ι\ninst✝¹ : LocallyFiniteOrderBot ι\ninst✝ : IsWellOrder ι fun x x_1 => x < x_1\nf : ι → E\nn : ι\n⊢ gramSchmidt �... | [
66,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.le_radical | [] | [
860,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
860,
1
] |
Mathlib/Algebra/Lie/Nilpotent.lean | LieSubmodule.ucs_succ | [] | [
369,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.digits_lt_base | [
{
"state_after": "case succ.succ\nn m d b : ℕ\nhd : d ∈ digits (succ (succ b)) m\n⊢ d < succ (succ b)",
"state_before": "n b m d : ℕ\nhb : 1 < b\nhd : d ∈ digits b m\n⊢ d < b",
"tactic": "rcases b with (_ | _ | b) <;> try simp_all"
},
{
"state_after": "no goals",
"state_before": "case succ.s... | [
391,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/Data/Polynomial/Mirror.lean | Polynomial.mirror_involutive | [] | [
134,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.BoundedFormula.realize_exs | [
{
"state_after": "case zero\nL : Language\nL' : Language\nM : Type w\nN : Type ?u.637329\nP : Type ?u.637332\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nn : ℕ\nT : Theory L\nφ✝ : BoundedFormula L α n\nv : α → M\nφ : BoundedFormula L α Nat.zero\n⊢ Formula.Rea... | [
912,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
902,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Concrete.lean | Equiv.Perm.toList_eq_nil_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np✝ : Perm α\nx✝ : α\np : Perm α\nx : α\n⊢ toList p x = [] ↔ ¬x ∈ support p",
"tactic": "simp [toList]"
}
] | [
229,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.mem_toAddSubgroup | [] | [
441,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | measurableSet_insert | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.13146\nγ : Type ?u.13149\nδ : Type ?u.13152\nδ' : Type ?u.13155\nι : Sort ?u.13158\ns✝ t u : Set α\ninst✝¹ : MeasurableSpace α\ninst✝ : MeasurableSingletonClass α\na : α\ns : Set α\nh : MeasurableSet (insert a s)\nha : a ∈ s\n⊢ Measurab... | [
302,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/CategoryTheory/PEmpty.lean | CategoryTheory.Functor.empty_ext' | [] | [
68,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
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