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/List/Lemmas.lean | List.length_insert_of_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\na : α\nl : List α\nh : a ∈ l\n⊢ length (List.insert a l) = length l",
"tactic": "rw [insert_of_mem h]"
}
] | [
917,
62
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
916,
9
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.Measure.ext | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.9977\nγ : Type ?u.9980\nδ : Type ?u.9983\nι : Type ?u.9986\ninst✝ : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns s₁ s₂ t : Set α\nh : ∀ (s : Set α), MeasurableSet s → ↑↑μ₁ s = ↑↑μ₂ s\n⊢ ↑μ₁ = ↑μ₂",
"tactic": "rw [← trimmed, OuterMeasur... | [
140,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | NNReal.coe_natAbs | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.1112225\n𝕜 : Type ?u.1112228\nα : Type ?u.1112231\nι : Type ?u.1112234\nκ : Type ?u.1112237\nE : Type ?u.1112240\nF : Type ?u.1112243\nG : Type ?u.1112246\ninst✝¹ : SeminormedCommGroup E\ninst✝ : SeminormedCommGroup F\na a₁ a₂ b b₁ b₂ : E\nr r₁ r₂ ... | [
1804,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1799,
1
] |
Mathlib/Control/Basic.lean | map_bind | [
{
"state_after": "no goals",
"state_before": "α β γ : Type u\nm : Type u → Type v\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nx : m α\ng : α → m β\nf : β → γ\n⊢ f <$> (x >>= g) = do\n let a ← x\n f <$> g a",
"tactic": "rw [← bind_pure_comp, bind_assoc] <;> simp [bind_pure_comp]"
}
] | [
103,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.kernel.ι_of_mono | [] | [
475,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
1
] |
Mathlib/Data/Nat/Fib.lean | Nat.fib_add | [
{
"state_after": "case zero\nm✝ m : ℕ\n⊢ fib (m + zero + 1) = fib m * fib zero + fib (m + 1) * fib (zero + 1)\n\ncase succ\nm✝ n : ℕ\nih : ∀ (m : ℕ), fib (m + n + 1) = fib m * fib n + fib (m + 1) * fib (n + 1)\nm : ℕ\n⊢ fib (m + succ n + 1) = fib m * fib (succ n) + fib (m + 1) * fib (succ n + 1)",
"state_be... | [
157,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.order_C | [
{
"state_after": "case pos\nΓ : Type u_1\nR : Type u_2\ninst✝¹ : OrderedCancelAddCommMonoid Γ\ninst✝ : NonAssocSemiring R\nr : R\nh : r = 0\n⊢ order (↑C r) = 0\n\ncase neg\nΓ : Type u_1\nR : Type u_2\ninst✝¹ : OrderedCancelAddCommMonoid Γ\ninst✝ : NonAssocSemiring R\nr : R\nh : ¬r = 0\n⊢ order (↑C r) = 0",
... | [
992,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
989,
1
] |
Mathlib/Data/Finset/MulAntidiagonal.lean | Set.IsPwo.mul | [
{
"state_after": "α : Type u_1\ns t : Set α\ninst✝ : OrderedCancelCommMonoid α\nhs : IsPwo s\nht : IsPwo t\n⊢ IsPwo ((fun x => x.fst * x.snd) '' s ×ˢ t)",
"state_before": "α : Type u_1\ns t : Set α\ninst✝ : OrderedCancelCommMonoid α\nhs : IsPwo s\nht : IsPwo t\n⊢ IsPwo (s * t)",
"tactic": "rw [← image_m... | [
30,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
28,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.card_biUnion | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.860588\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf g : α → β\ninst✝ : DecidableEq β\ns : Finset α\nt : α → Finset β\nh : ∀ (x : α), x ∈ s → ∀ (y : α), y ∈ s → x ≠ y → Disjoint (t x) (t y)\n⊢ ∑ a in s, ∑ _i in t a, 1 = ∑ u in s,... | [
1870,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1864,
1
] |
Mathlib/Analysis/Calculus/FDerivMeasurable.lean | RightDerivMeasurableAux.le_of_mem_a | [
{
"state_after": "case intro.intro\nF : Type u_1\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : ℝ → F\nK : Set F\nr ε : ℝ\nL : F\nx y z : ℝ\nhy : y ∈ Icc x (x + r / 2)\nhz : z ∈ Icc x (x + r / 2)\nr' : ℝ\nr'mem : r' ∈ Ioc (r / 2) r\nhr' : ∀ (y : ℝ), y ∈ Icc x (x + r') → ∀ (z : ℝ), z ∈ Icc x (x + r... | [
524,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Summable.congr | [] | [
111,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.X_pow_sub_C_ne_zero | [
{
"state_after": "R : Type u\nS : Type v\na✝ b c d : R\nn✝ m : ℕ\ninst✝¹ : Ring R\ninst✝ : Nontrivial R\nn : ℕ\nhn : 0 < n\na : R\n⊢ X ^ n + ↑C (-a) ≠ 0",
"state_before": "R : Type u\nS : Type v\na✝ b c d : R\nn✝ m : ℕ\ninst✝¹ : Ring R\ninst✝ : Nontrivial R\nn : ℕ\nhn : 0 < n\na : R\n⊢ X ^ n - ↑C a ≠ 0",
... | [
1487,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1485,
1
] |
Mathlib/Topology/Instances/AddCircle.lean | AddCircle.card_addOrderOf_eq_totient | [
{
"state_after": "case inl\n𝕜 : Type u_1\nB : Type ?u.287307\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\np q : 𝕜\nhp : Fact (0 < p)\n⊢ Nat.card { u // addOrderOf u = 0 } = Nat.totient 0\n\ncase inr\n𝕜 : Type u_1\nB : Type ?u.287307\ninst✝² : LinearOrderedField 𝕜\... | [
495,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
] |
Mathlib/Data/List/Basic.lean | List.map_bind | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.2509\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\ng : β → List γ\nf : α → β\na : α\nl : List α\n⊢ List.bind (map f (a :: l)) g = List.bind (a :: l) fun a => g (f a)",
"tactic": "simp only [cons_bind, map_cons, map_bind _ _ l]"... | [
168,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Data/List/Basic.lean | List.get_enum | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.455762\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l : List α\ni : Fin (length (enum l))\n⊢ ↑i < length l",
"tactic": "simpa [length_enum] using i.2"
},
{
"state_after": "case h.e'_3.h.e'_3\nι : Type ?u.455762\nα : Type u\nβ : ... | [
3961,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3957,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.zero_mem_smul_set | [] | [
823,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
822,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.range_map_nonempty | [] | [
751,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
749,
1
] |
Mathlib/Algebra/Category/ModuleCat/Products.lean | ModuleCat.piIsoPi_inv_kernel_ι | [] | [
65,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Algebra.mem_sup_right | [] | [
823,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
822,
1
] |
Mathlib/Analysis/Normed/Field/Basic.lean | norm_mul_le | [] | [
196,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Order/Monotone/Monovary.lean | MonovaryOn.comp_antitone_on_left | [] | [
184,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Algebra/Lie/Solvable.lean | LieAlgebra.derivedLength_eq_derivedLengthOfIdeal | [
{
"state_after": "R : Type u\nL : Type v\nM : Type w\nL' : Type w₁\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\ninst✝¹ : LieRing L'\ninst✝ : LieAlgebra R L'\nI✝ J : LieIdeal R L\nf : L' →ₗ⁅R⁆ L\nI : LieIdeal R L\ns₁ : Set ℕ := {k | derivedSeries R { x // x ∈ ↑I } k = ⊥}\n⊢ derivedLength R ... | [
331,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | MeasureTheory.Measure.add_haar_preimage_smul | [
{
"state_after": "E : Type u_1\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : MeasurableSpace E\ninst✝⁵ : BorelSpace E\ninst✝⁴ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝³ : IsAddHaarMeasure μ\nF : Type ?u.1915974\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\ninst✝ : CompleteSp... | [
343,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.aeval_subalgebra_coe | [] | [
317,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.lt_of_eq_of_lt | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedField α\nf g h : CauSeq α abs\nfg : f ≈ g\ngh : g < h\nthis : Pos (h - g + -(f - g))\n⊢ f < h",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\nf g h : CauSeq α abs\nfg : f ≈ g\ngh : g < h\n⊢ f < h",
"tactic": "have := pos_add_limZero gh ... | [
735,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
733,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.comp_id | [] | [
429,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.findGreatest_mono_right | [
{
"state_after": "m n✝ k l : ℕ\nP✝ Q : ℕ → Prop\ninst✝¹ : DecidablePred P✝\nP : ℕ → Prop\ninst✝ : DecidablePred P\nn : ℕ\n⊢ Nat.findGreatest P n ≤ Nat.findGreatest P (n + 1)",
"state_before": "m n k l : ℕ\nP✝ Q : ℕ → Prop\ninst✝¹ : DecidablePred P✝\nP : ℕ → Prop\ninst✝ : DecidablePred P\n⊢ Monotone (Nat.fin... | [
653,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
647,
1
] |
Mathlib/Order/Max.lean | not_isMax_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.12549\ninst✝ : Preorder α\na b : α\n⊢ ¬IsMax a ↔ ∃ b, a < b",
"tactic": "simp [lt_iff_le_not_le, IsMax, not_forall, exists_prop]"
}
] | [
346,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.floor_eq_on_Ico | [] | [
251,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Analysis/NormedSpace/Units.lean | NormedRing.inverse_one_sub | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹ : NormedRing R\ninst✝ : CompleteSpace R\nt : R\nh : ‖t‖ < 1\n⊢ inverse (1 - t) = ↑(Units.oneSub t h)⁻¹",
"tactic": "rw [← inverse_unit (Units.oneSub t h), Units.oneSub_val]"
}
] | [
117,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Topology/SubsetProperties.lean | CompactExhaustion.subset | [] | [
1460,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1459,
11
] |
Mathlib/Data/Nat/Bits.lean | Nat.zero_bits | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ bits 0 = []",
"tactic": "simp [Nat.bits]"
}
] | [
213,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | AddCommGroup.tfae_modEq | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na b c : α\nn : ℤ\n⊢ TFAE\n [toIcoMod hp a b = a, ∀ (z : ℤ), ¬b - z • p ∈ Set.Ioo a (a + p), toIcoMod hp a b ≠ toIocMod hp a b,\n toIcoMod hp a b + p = toIocMod hp a b]",
"state_before": "α : T... | [
640,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
1
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.HasIntegral.integral_eq | [] | [
261,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Analysis/Normed/Group/HomCompletion.lean | NormedAddGroupHom.completion_coe_to_fun | [] | [
77,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | Filter.Tendsto.tendstoUniformlyOnFilter_const | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝ : UniformSpace β\nF : ι → α → β\nf : α → β\ns s' : Set α\nx : α\np : Filter ι\np'✝ : Filter α\ng✝ : ι → α\ng : ι → β\nb : β\nhg : Tendsto g p (𝓝 b)\np' : Filter α\n⊢ TendstoUniformlyOnFilter (fun n x => g n)... | [
362,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.finset_sup_factors | [
{
"state_after": "C : Type u₁\ninst✝⁵ : Category C\nX Y Z : C\nD : Type u₂\ninst✝⁴ : Category D\ninst✝³ : HasImages C\ninst✝² : HasBinaryCoproducts C\ninst✝¹ : HasInitial C\ninst✝ : InitialMonoClass C\nI : Type u_1\nA B : C\ns : Finset I\nP : I → Subobject B\nf : A ⟶ B\n⊢ (∃ i, i ∈ s ∧ Factors (P i) f) → Factor... | [
551,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
1
] |
Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | HasFDerivAt.cexp | [] | [
135,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Topology/Algebra/Polynomial.lean | Polynomial.continuous_eval₂ | [
{
"state_after": "R : Type u_2\nS : Type u_1\ninst✝³ : Semiring R\ninst✝² : TopologicalSpace R\ninst✝¹ : TopologicalSemiring R\np✝ : R[X]\ninst✝ : Semiring S\np : S[X]\nf : S →+* R\n⊢ Continuous fun x => sum p fun e a => ↑f a * x ^ e",
"state_before": "R : Type u_2\nS : Type u_1\ninst✝³ : Semiring R\ninst✝²... | [
55,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
11
] |
Mathlib/Algebra/Homology/QuasiIso.lean | HomotopyEquiv.toQuasiIso_inv | [
{
"state_after": "ι : Type u_3\nV : Type u\ninst✝¹³ : Category V\ninst✝¹² : HasZeroMorphisms V\ninst✝¹¹ : HasZeroObject V\ninst✝¹⁰ : HasEqualizers V\ninst✝⁹ : HasImages V\ninst✝⁸ : HasImageMaps V\ninst✝⁷ : HasCokernels V\nc : ComplexShape ι\nC✝ D✝ E : HomologicalComplex V c\nW : Type u_2\ninst✝⁶ : Category W\ni... | [
90,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.ofLinear_symm_apply | [] | [
2130,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2129,
1
] |
Mathlib/RingTheory/IsTensorProduct.lean | Algebra.IsPushout.symm | [
{
"state_after": "R : Type u_1\nM : Type v₁\nN : Type v₂\nS : Type v₃\ninst✝³¹ : AddCommMonoid M\ninst✝³⁰ : AddCommMonoid N\ninst✝²⁹ : CommRing R\ninst✝²⁸ : CommRing S\ninst✝²⁷ : Algebra R S\ninst✝²⁶ : Module R M\ninst✝²⁵ : Module R N\ninst✝²⁴ : Module S N\ninst✝²³ : IsScalarTower R S N\nf : M →ₗ[R] N\nh✝ : IsB... | [
408,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Algebra/Group/Conj.lean | isConj_iff_eq | [
{
"state_after": "α✝ : Type u\nβ : Type v\ninst✝² : Monoid α✝\ninst✝¹ : Monoid β\nα : Type u_1\ninst✝ : CommMonoid α\na b : α\nx✝ : IsConj a b\nc : αˣ\nhc : a = b\n⊢ a = b",
"state_before": "α✝ : Type u\nβ : Type v\ninst✝² : Monoid α✝\ninst✝¹ : Monoid β\nα : Type u_1\ninst✝ : CommMonoid α\na b : α\nx✝ : IsC... | [
58,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Std/Data/Int/Lemmas.lean | Int.sub_pos_of_lt | [
{
"state_after": "a b : Int\nh✝ : b < a\nh : b + -b < a + -b\n⊢ 0 < a - b",
"state_before": "a b : Int\nh : b < a\n⊢ 0 < a - b",
"tactic": "have h := Int.add_lt_add_right h (-b)"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nh✝ : b < a\nh : b + -b < a + -b\n⊢ 0 < a - b",
"t... | [
936,
31
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
934,
11
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Poly.denote_toExpr | [
{
"state_after": "no goals",
"state_before": "ctx : Context\np : Poly\n⊢ Expr.denote ctx (toExpr p) = denote ctx p",
"tactic": "match p with\n| [] => simp [toExpr, Expr.denote, Poly.denote]\n| (k, v) :: p => simp [toExpr, Expr.denote, Poly.denote]"
},
{
"state_after": "no goals",
"state_befo... | [
713,
59
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
710,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.IsPath.toDeleteEdges | [] | [
1816,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1814,
11
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iic_union_Icc | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type ?u.109826\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\nhcd : c ≤ d\nh : c ≤ b\n⊢ Iic b ∪ Icc c d = Iic (max b d)\n\ncase inr\nα : Type u_1\nβ : Type ?u.109826\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\nhcd : d < c\nh : c ≤ b ∨ d ≤ b\n⊢ Iic b ∪ Icc c d... | [
1475,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1469,
1
] |
Std/Data/String/Lemmas.lean | String.utf8Len_append | [
{
"state_after": "no goals",
"state_before": "cs₁ cs₂ : List Char\n⊢ utf8Len (cs₁ ++ cs₂) = utf8Len cs₁ + utf8Len cs₂",
"tactic": "induction cs₁ <;> simp [*, Nat.add_right_comm]"
}
] | [
52,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
51,
9
] |
Mathlib/Algebra/Lie/Basic.lean | LieModuleHom.coe_linearMap_comp | [] | [
853,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
851,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesAt.sub | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.553210\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedS... | [
582,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
1
] |
Mathlib/Data/Set/Basic.lean | Set.inter_union_distrib_right | [] | [
1070,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1069,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.le_toOuterMeasure_caratheodory | [] | [
656,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
1
] |
Mathlib/Deprecated/Group.lean | IsGroupHom.map_inv | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : Group α\ninst✝ : Group β\nf : α → β\nhf✝ hf : IsGroupHom f\na : α\n⊢ f a⁻¹ * f a = 1",
"tactic": "rw [← hf.map_mul, inv_mul_self, hf.map_one]"
}
] | [
302,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Data/Set/Basic.lean | Set.antitone_setOf | [] | [
2934,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2933,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.coe_imJ | [] | [
838,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
838,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mul_mk'_eq_mk'_of_mul | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type u_2\ninst✝¹ : CommMonoid N\nP : Type ?u.915559\ninst✝ : CommMonoid P\nf : LocalizationMap S N\nx₁ x₂ : M\ny : { x // x ∈ S }\n⊢ ↑(toMap f) x₁ * mk' f x₂ y = mk' f (x₁ * x₂) y",
"tactic": "rw [← m... | [
851,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
850,
1
] |
Mathlib/Combinatorics/SimpleGraph/Regularity/Uniform.lean | SimpleGraph.nonuniformWitness_subset | [
{
"state_after": "α : Type u_1\n𝕜 : Type u_2\ninst✝¹ : LinearOrderedField 𝕜\nG : SimpleGraph α\ninst✝ : DecidableRel G.Adj\nε : 𝕜\ns t : Finset α\na b : α\nh : ¬IsUniform G ε s t\n⊢ (if WellOrderingRel s t then (nonuniformWitnesses G ε s t).fst else (nonuniformWitnesses G ε t s).snd) ⊆ s",
"state_before"... | [
171,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.cast_refl | [] | [
318,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
9
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.mk'_mul_mk'_eq_one | [
{
"state_after": "R : Type u_1\ninst✝⁴ : CommSemiring R\nM : Submonoid R\nS : Type u_2\ninst✝³ : CommSemiring S\ninst✝² : Algebra R S\nP : Type ?u.817480\ninst✝¹ : CommSemiring P\ninst✝ : IsLocalization M S\nx y : { x // x ∈ M }\n⊢ mk' S (↑y * ↑x) (y * x) = 1",
"state_before": "R : Type u_1\ninst✝⁴ : CommSe... | [
423,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/RingTheory/LaurentSeries.lean | PowerSeries.coe_mul | [] | [
214,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Topology/Instances/NNReal.lean | NNReal.nhds_zero_basis | [] | [
141,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.lf_congr_left | [] | [
822,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
821,
1
] |
Mathlib/Order/BooleanAlgebra.lean | compl_comp_compl | [] | [
641,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
640,
1
] |
Mathlib/Topology/Order/Basic.lean | IsClosed.csSup_mem | [] | [
2785,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2783,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | Class.toSet_of_ZFSet | [
{
"state_after": "no goals",
"state_before": "A : Class\nx : ZFSet\nx✝ : ToSet A ↑x\ny : ZFSet\nyx : ↑y = ↑x\npy : A y\n⊢ A x",
"tactic": "rwa [ofSet.inj yx] at py"
}
] | [
1618,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1617,
1
] |
Mathlib/Algebra/Order/Monoid/Canonical/Defs.lean | self_le_mul_left | [] | [
176,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Topology/Semicontinuous.lean | Continuous.comp_upperSemicontinuous | [] | [
856,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
854,
1
] |
Mathlib/Logic/Basic.lean | dite_apply | [
{
"state_after": "no goals",
"state_before": "α : Sort u_2\nβ : Sort ?u.39434\nσ : α → Sort u_1\nf✝ : α → β\nP Q : Prop\ninst✝¹ : Decidable P\ninst✝ : Decidable Q\na✝ b c : α\nA : P → α\nB : ¬P → α\nf : P → (a : α) → σ a\ng : ¬P → (a : α) → σ a\na : α\n⊢ dite P f g a = if h : P then f h a else g h a",
"... | [
1240,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1239,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLinearEquiv.lean | Matrix.exists_mulVec_eq_zero_iff_aux | [
{
"state_after": "case mp\nR : Type ?u.157867\nM✝ : Type ?u.157870\ninst✝⁵ : CommRing R\ninst✝⁴ : AddCommGroup M✝\ninst✝³ : Module R M✝\nn : Type u_2\ninst✝² : Fintype n\nK : Type u_1\ninst✝¹ : DecidableEq n\ninst✝ : Field K\nM : Matrix n n K\n⊢ (∃ v x, mulVec M v = 0) → det M = 0\n\ncase mpr\nR : Type ?u.15786... | [
135,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Topology/PathConnected.lean | IsPathConnected.mem_pathComponent | [] | [
990,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
988,
1
] |
Mathlib/RingTheory/Localization/FractionRing.lean | IsFractionRing.injective | [] | [
89,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
11
] |
Mathlib/Order/BoundedOrder.lean | isMax_iff_eq_top | [] | [
135,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
src/lean/Init/Control/Lawful.lean | ReaderT.run_map | [] | [
193,
49
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
192,
9
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | ContDiffBump.tendsto_support_normed_smallSets | [
{
"state_after": "E : Type u_2\nX : Type ?u.2328028\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace ℝ E\ninst✝⁷ : NormedAddCommGroup X\ninst✝⁶ : NormedSpace ℝ X\ninst✝⁵ : HasContDiffBump E\nc : E\nf : ContDiffBump c\nx : E\nn : ℕ∞\ninst✝⁴ : MeasurableSpace E\nμ : MeasureTheory.Measure E\ninst✝³ : BorelSpac... | [
556,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | one_lt_div_iff | [
{
"state_after": "case inl\nι : Type ?u.160788\nα : Type u_1\nβ : Type ?u.160794\ninst✝ : LinearOrderedField α\na b c d : α\nn : ℤ\nhb : b < 0\n⊢ 1 < a / b ↔ 0 < b ∧ b < a ∨ b < 0 ∧ a < b\n\ncase inr.inl\nι : Type ?u.160788\nα : Type u_1\nβ : Type ?u.160794\ninst✝ : LinearOrderedField α\na c d : α\nn : ℤ\n⊢ 1 <... | [
839,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
835,
1
] |
Mathlib/Analysis/Calculus/Deriv/Slope.lean | HasDerivWithinAt.limsup_slope_norm_le | [
{
"state_after": "E : Type u\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : ℝ → E\nf' : E\ns : Set ℝ\nx r : ℝ\nhf : HasDerivWithinAt f f' s x\nhr : ‖f'‖ < r\n⊢ ∀ (x_1 : ℝ), ‖x_1 - x‖⁻¹ * ‖f x_1 - f x‖ < r → ‖x_1 - x‖⁻¹ * (‖f x_1‖ - ‖f x‖) < r",
"state_before": "E : Type u\ninst✝¹ : NormedAddCo... | [
153,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Order/Disjoint.lean | Codisjoint.eq_top_of_le | [] | [
279,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Std/Logic.lean | and_comm | [] | [
159,
45
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
159,
1
] |
Mathlib/Data/Real/Pi/Bounds.lean | Real.pi_gt_3141592 | [
{
"state_after": "no goals",
"state_before": "⊢ 3.141592 < π",
"tactic": "pi_lower_bound\n [11482 / 8119, 7792 / 4217, 54055 / 27557, 949247 / 476920, 3310126 / 1657059,\n 2635492 / 1318143, 1580265 / 790192, 1221775 / 610899, 3612247 / 1806132, 849943 / 424972]"
}
] | [
195,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.normSq_def' | [
{
"state_after": "no goals",
"state_before": "S : Type ?u.539505\nT : Type ?u.539508\nR : Type u_1\ninst✝ : CommRing R\nr x y z : R\na b c : ℍ[R]\n⊢ ↑normSq a = a.re ^ 2 + a.imI ^ 2 + a.imJ ^ 2 + a.imK ^ 2",
"tactic": "simp only [normSq_def, sq, mul_neg, sub_neg_eq_add, mul_re, star_re, star_imI, star_i... | [
1203,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1201,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_const_mul_Ico | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\na✝ a b c : α\nh : 0 < c\n⊢ (fun x x_1 => x * x_1) c ⁻¹' Ico a b = Ico (a / c) (b / c)",
"tactic": "simp [← Ici_inter_Iio, h]"
}
] | [
632,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
631,
1
] |
Mathlib/Topology/Basic.lean | Filter.Frequently.mem_of_closed | [] | [
1444,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1442,
1
] |
Mathlib/Algebra/Order/Group/Abs.lean | abs_of_pos | [] | [
115,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.tmul_add | [] | [
156,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Tactic/LinearCombination.lean | Mathlib.Tactic.LinearCombination.eq_of_add | [
{
"state_after": "α : Type u_1\na b a' b' : α\ninst✝ : AddGroup α\np✝ : a = b\np : a - b = 0\nH : a' - b' - (a - b) = 0\n⊢ a' - b' = 0",
"state_before": "α : Type u_1\na b a' b' : α\ninst✝ : AddGroup α\np : a = b\nH : a' - b' - (a - b) = 0\n⊢ a' = b'",
"tactic": "rw [← sub_eq_zero] at p ⊢"
},
{
... | [
124,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.get_eq_of_mem | [] | [
469,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/InverseDeriv.lean | Real.deriv_arcsin | [
{
"state_after": "case h\nx : ℝ\n⊢ deriv arcsin x = 1 / sqrt (1 - x ^ 2)",
"state_before": "⊢ deriv arcsin = fun x => 1 / sqrt (1 - x ^ 2)",
"tactic": "funext x"
},
{
"state_after": "case pos\nx : ℝ\nh : x ≠ -1 ∧ x ≠ 1\n⊢ deriv arcsin x = 1 / sqrt (1 - x ^ 2)\n\ncase neg\nx : ℝ\nh : ¬(x ≠ -1 ∧ x... | [
117,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.Tendsto.nsmul_atBot | [] | [
672,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
670,
1
] |
Mathlib/Data/List/Perm.lean | List.perm_append_left_iff | [] | [
655,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
653,
1
] |
Mathlib/Data/Fintype/Basic.lean | Set.toFinset_range | [
{
"state_after": "case a\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.95007\ns t : Set α\ninst✝² : DecidableEq α\ninst✝¹ : Fintype β\nf : β → α\ninst✝ : Fintype ↑(range f)\na✝ : α\n⊢ a✝ ∈ toFinset (range f) ↔ a✝ ∈ Finset.image f Finset.univ",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.95007\ns t :... | [
778,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
775,
1
] |
Mathlib/Topology/List.lean | Filter.Tendsto.cons | [] | [
85,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.smul_toOuterMeasure | [] | [
827,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
825,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.infEdist_union | [] | [
71,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieEquiv.surjective | [] | [
671,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
669,
11
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.eq_of_factors_eq_factors | [
{
"state_after": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ndec_irr : (p : Associates α) → Decidable (Irreducible p)\ninst✝ : UniqueFactorizationMonoid α\ndec : DecidableEq α\ndec' : DecidableEq (Associates α)\na b : Associates α\nh : factors a = factors b\nthis : FactorSet.prod (factors a) = FactorSet... | [
1480,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1478,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | mul_self_pos | [
{
"state_after": "case mp\nα : Type u\nβ : Type ?u.211359\ninst✝ : LinearOrderedRing α\na✝ b c a : α\n⊢ 0 < a * a → a ≠ 0\n\ncase mpr\nα : Type u\nβ : Type ?u.211359\ninst✝ : LinearOrderedRing α\na✝ b c a : α\n⊢ a ≠ 0 → 0 < a * a",
"state_before": "α : Type u\nβ : Type ?u.211359\ninst✝ : LinearOrderedRing α... | [
1178,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1171,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | ChainComplex.mk_X_0 | [] | [
719,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
718,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.lf_iff_sub_zero_lf | [] | [
1815,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1807,
1
] |
Mathlib/Analysis/Calculus/FormalMultilinearSeries.lean | FormalMultilinearSeries.removeZero_of_pos | [
{
"state_after": "𝕜 : Type u\n𝕜' : Type u'\nE : Type v\nF : Type w\nG : Type x\ninst✝¹⁵ : CommRing 𝕜\ninst✝¹⁴ : AddCommGroup E\ninst✝¹³ : Module 𝕜 E\ninst✝¹² : TopologicalSpace E\ninst✝¹¹ : TopologicalAddGroup E\ninst✝¹⁰ : ContinuousConstSMul 𝕜 E\ninst✝⁹ : AddCommGroup F\ninst✝⁸ : Module 𝕜 F\ninst✝⁷ : Top... | [
113,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.properDivisors.not_self_mem | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ ¬n ∈ properDivisors n",
"tactic": "simp [properDivisors]"
}
] | [
77,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.