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/Topology/SubsetProperties.lean | IsPreirreducible.interior | [] | [
1985,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1983,
1
] |
Mathlib/Order/WithBot.lean | WithBot.bot_lt_coe | [] | [
275,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithBot.coe_le_one | [] | [
515,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.coe_fst_eventuallyEq_proj | [] | [
432,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.nsmul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.90191\nf g : α → β\nc c₁ c₂ x : α\ninst✝ : AddMonoid α\nh : Periodic f c\nn : ℕ\n⊢ Periodic f (n • c)",
"tactic": "induction n <;> simp_all [Nat.succ_eq_add_one, add_nsmul, ← add_assoc, zero_nsmul]"
}
] | [
202,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
src/lean/Init/SizeOfLemmas.lean | UInt32.sizeOf | [
{
"state_after": "case mk\nval✝ : Fin size\n⊢ SizeOf.sizeOf { val := val✝ } = toNat { val := val✝ } + 2",
"state_before": "a : UInt32\n⊢ SizeOf.sizeOf a = toNat a + 2",
"tactic": "cases a"
},
{
"state_after": "no goals",
"state_before": "case mk\nval✝ : Fin size\n⊢ SizeOf.sizeOf { val := val... | [
21,
37
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
20,
9
] |
Mathlib/Algebra/GeomSum.lean | one_geom_sum | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Semiring α\nn : ℕ\n⊢ ∑ i in range n, 1 ^ i = ↑n",
"tactic": "simp"
}
] | [
79,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Analysis/InnerProductSpace/Adjoint.lean | ContinuousLinearMap.eq_adjoint_iff | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.798041\ninst✝⁹ : IsROrC 𝕜\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedAddCommGroup G\ninst✝⁵ : InnerProductSpace 𝕜 E\ninst✝⁴ : InnerProductSpace 𝕜 F\ninst✝³ : InnerProductSpace 𝕜 G\ninst✝² : CompleteSp... | [
177,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Data/Nat/Factorial/DoubleFactorial.lean | Nat.doubleFactorial_eq_prod_even | [
{
"state_after": "n : ℕ\n⊢ (2 * n + 2)‼ = (2 * n + 2) * (2 * n)‼",
"state_before": "n : ℕ\n⊢ (2 * (n + 1))‼ = ∏ i in Finset.range (n + 1), 2 * (i + 1)",
"tactic": "rw [Finset.prod_range_succ, ← doubleFactorial_eq_prod_even _, mul_comm (2 * n)‼,\n (by ring : 2 * (n + 1) = 2 * n + 2)]"
},
{
"stat... | [
71,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean | Real.lt_sin_mul | [
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx : 0 < x\nhx' : x < 1\n⊢ x < sin (π / 2 * x)",
"tactic": "simpa [mul_comm x] using\n strictConcaveOn_sin_Icc.2 ⟨le_rfl, pi_pos.le⟩ ⟨pi_div_two_pos.le, half_le_self pi_pos.le⟩\n pi_div_two_pos.ne (sub_pos.2 hx') hx"
}
] | [
232,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.range_snd | [] | [
960,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
959,
1
] |
Mathlib/RingTheory/AlgebraicIndependent.lean | algebraicIndependent_iff_injective_aeval | [] | [
93,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Std/Data/String/Lemmas.lean | String.lt_iff | [] | [
32,
58
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
32,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | padicNormE.norm_p_lt_one | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\n⊢ (↑p)⁻¹ < 1",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\n⊢ ‖↑p‖ < 1",
"tactic": "rw [norm_p]"
},
{
"state_after": "case ha\np : ℕ\nhp : Fact (Nat.Prime p)\n⊢ 1 < ↑p",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\n⊢ (↑p)⁻¹ < 1",
... | [
850,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
847,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.atBot_neBot | [] | [
158,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.principal_add_iff_add_lt_ne_self | [
{
"state_after": "a : Ordinal\nH : ∀ ⦃b c : Ordinal⦄, b < a → c < a → b + c ≠ a\nha : ¬Principal (fun x x_1 => x + x_1) a\n⊢ False",
"state_before": "a : Ordinal\nH : ∀ ⦃b c : Ordinal⦄, b < a → c < a → b + c ≠ a\n⊢ Principal (fun x x_1 => x + x_1) a",
"tactic": "by_contra' ha"
},
{
"state_after"... | [
184,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Data/SetLike/Basic.lean | SetLike.coe_mono | [] | [
198,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.tail_ofSeq | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ns : Seq α\n⊢ Option.rec nil Prod.snd (Option.map (fun a => (a, ↑(Seq.tail s))) (Seq.head s)) = ↑(Seq.tail s)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : Seq α\n⊢ tail ↑s = ↑(Seq.tail s)",
"tactic": "simp [tail]"
},
{
"state_aft... | [
1368,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1366,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | eq_one_of_mul_le_one_left | [] | [
1162,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1161,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Ordered.lean | lineMap_lt_map_iff_slope_lt_slope_right | [] | [
273,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/CategoryTheory/Preadditive/Biproducts.lean | CategoryTheory.Limits.biprod.desc_eq | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝³ : Category C\ninst✝² : Preadditive C\nJ : Type\ninst✝¹ : Fintype J\nX Y : C\ninst✝ : HasBinaryBiproduct X Y\nT : C\nf : X ⟶ T\ng : Y ⟶ T\n⊢ desc f g = fst ≫ f + snd ≫ g",
"tactic": "ext <;> simp [add_comp]"
}
] | [
459,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.mapsTo_insertNth_face_Icc | [] | [
419,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/LinearAlgebra/TensorAlgebra/Basic.lean | TensorAlgebra.ι_inj | [] | [
255,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Data/List/Nodup.lean | List.nodup_cons | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nl✝ l₁ l₂ : List α\nr : α → α → Prop\na✝ b a : α\nl : List α\n⊢ Nodup (a :: l) ↔ ¬a ∈ l ∧ Nodup l",
"tactic": "simp only [Nodup, pairwise_cons, forall_mem_ne]"
}
] | [
44,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_eq_restrict_iUnion_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.563218\nγ : Type ?u.563221\nδ : Type u_3\nι : Type u_1\nR : Type ?u.563230\nR' : Type ?u.563233\nm0 : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t : Set α\ninst✝ :... | [
2772,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2770,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.div_one | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.244913\nβ : Type ?u.244916\nγ : Type ?u.244919\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na : Ordinal\n⊢ a / 1 = a",
"tactic": "simpa only [one_mul] using mul_div_cancel a Ordinal.one_ne_zero"
}
] | [
962,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
961,
1
] |
Mathlib/MeasureTheory/Function/UniformIntegrable.lean | MeasureTheory.Memℒp.snorm_indicator_le' | [
{
"state_after": "case intro.intro\nα : Type u_2\nβ : Type u_1\nι : Type ?u.128216\nm : MeasurableSpace α\nμ : Measure α\ninst✝ : NormedAddCommGroup β\np : ℝ≥0∞\nf : α → β\nhp_one : 1 ≤ p\nhp_top : p ≠ ⊤\nhf : Memℒp f p\nhmeas : StronglyMeasurable f\nε : ℝ\nhε : 0 < ε\nM : ℝ\nhMpos : 0 < M\nhM : snorm (Set.indi... | [
375,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableEquiv.measurableSet_preimage | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.782118\nδ : Type ?u.782121\nδ' : Type ?u.782124\nι : Sort uι\ns✝ t u : Set α\ninst✝³ : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\ninst✝ : MeasurableSpace δ\ne : α ≃ᵐ β\ns : Set β\nh : Measur... | [
1307,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1304,
1
] |
Mathlib/Topology/Sheaves/Stalks.lean | TopCat.Presheaf.app_isIso_of_stalkFunctor_map_iso | [
{
"state_after": "C : Type u\ninst✝⁷ : Category C\ninst✝⁶ : HasColimits C\nX Y Z : TopCat\ninst✝⁵ : ConcreteCategory C\ninst✝⁴ : PreservesFilteredColimits (forget C)\ninst✝³ : HasLimits C\ninst✝² : PreservesLimits (forget C)\ninst✝¹ : ReflectsIsomorphisms (forget C)\nF G : Sheaf C X\nf : F ⟶ G\nU : Opens ↑X\nin... | [
607,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | Valuation.map_eq_of_sub_lt | [
{
"state_after": "K : Type ?u.2296489\nF : Type ?u.2296492\nR : Type u_2\ninst✝³ : DivisionRing K\nΓ₀ : Type u_1\nΓ'₀ : Type ?u.2296504\nΓ''₀ : Type ?u.2296507\ninst✝² : LinearOrderedCommMonoidWithZero Γ''₀\ninst✝¹ : Ring R\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nv : Valuation R Γ₀\nx y z : R\nh : ↑v (y - x... | [
337,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Data/Polynomial/Mirror.lean | Polynomial.mirror_neg | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Ring R\np q : R[X]\n⊢ mirror (-p) = -mirror p",
"tactic": "rw [mirror, mirror, reverse_neg, natTrailingDegree_neg, neg_mul_eq_neg_mul]"
}
] | [
197,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Analysis/Complex/Circle.lean | expMapCircle_sub | [] | [
151,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.count_ne_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.359007\nγ : Type ?u.359010\ninst✝ : DecidableEq α\na : α\ns : Multiset α\n⊢ count a s ≠ 0 ↔ a ∈ s",
"tactic": "simp [Ne.def, count_eq_zero]"
}
] | [
2425,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2424,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.smul_bot | [] | [
983,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
982,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.all_iff_forall | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nP : α → Prop\n⊢ ∀ (x : α), Emem x nil → P x",
"tactic": "rintro _ ⟨⟩"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\nP : α → Prop\nsize✝ : ℕ\nl : Ordnode α\nx : α\nr : Ordnode α\n⊢ All P (node size✝ l x r) ↔ ∀ (x_1 :... | [
481,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderIso.toRelIsoLT_symm | [] | [
1026,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1025,
1
] |
Mathlib/Topology/Order/Hom/Esakia.lean | EsakiaHom.id_apply | [] | [
302,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.top_apply | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.124154\nR : Type ?u.124157\nR' : Type ?u.124160\nms : Set (OuterMeasure α)\nm : OuterMeasure α\ns : Set α\nh : Set.Nonempty s\na : α\nas : a ∈ s\n⊢ ⊤ ≤ ↑(⊤ • dirac a) s",
"tactic": "simp [smul_dirac_apply, as]"
}
] | [
627,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | reflection_map_apply | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_3\nE✝ : Type ?u.715379\nF : Type ?u.715382\ninst✝¹⁰ : IsROrC 𝕜\ninst✝⁹ : NormedAddCommGroup E✝\ninst✝⁸ : NormedAddCommGroup F\ninst✝⁷ : InnerProductSpace 𝕜 E✝\ninst✝⁶ : InnerProductSpace ℝ F\nK✝ : Submodule 𝕜 E✝\ninst✝⁵ : CompleteSpace { x // x ∈ ... | [
712,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
708,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsGreatest.lt_iff | [] | [
304,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/Order/Heyting/Basic.lean | inf_sdiff_sup_left | [] | [
739,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
738,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | CauchySeq.tendsto_limUnder | [] | [
444,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.coe_neg | [] | [
460,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/LinearAlgebra/BilinearMap.lean | LinearMap.compl₂_apply | [] | [
334,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Data/Finset/Prod.lean | Finset.product_empty | [] | [
186,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.coe_isIntegral_iff | [
{
"state_after": "case refine'_1\nK : Type u_2\nL : Type u_3\nL' : Type ?u.191604\ninst✝⁸ : Field K\ninst✝⁷ : Field L\ninst✝⁶ : Field L'\ninst✝⁵ : Algebra K L\ninst✝⁴ : Algebra K L'\nS : IntermediateField K L\nR : Type u_1\ninst✝³ : CommRing R\ninst✝² : Algebra R K\ninst✝¹ : Algebra R L\ninst✝ : IsScalarTower R... | [
542,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | CategoryTheory.Limits.IsInitial.to_self | [] | [
169,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Int.cast_multiset_prod | [] | [
2244,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2242,
1
] |
Mathlib/Data/Polynomial/Coeff.lean | Polynomial.mul_X_pow_eq_zero | [] | [
296,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.erase_def | [
{
"state_after": "case h\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝¹ : (i : ι) → Zero (β i)\ninst✝ : (i : ι) → (x : β i) → Decidable (x ≠ 0)\ni : ι\nf : Π₀ (i : ι), β i\nj : ι\n⊢ ↑(erase i f) j = ↑(mk (Finset.erase (support f) i) fun j => ↑f ↑j) j",
... | [
1218,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1216,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | TopologicalGroup.continuous_conj' | [] | [
480,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.image_source_inter_eq' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.31956\nδ : Type ?u.31959\ne : LocalEquiv α β\ne' : LocalEquiv β γ\ns : Set α\n⊢ ↑e '' (e.source ∩ s) = e.target ∩ ↑(LocalEquiv.symm e) ⁻¹' s",
"tactic": "rw [inter_comm, e.leftInvOn.image_inter', image_source_eq_target... | [
486,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | HasSum.unop | [] | [
1347,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1345,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.toFun_eq_coe | [] | [
163,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Topology/UrysohnsLemma.lean | Urysohns.CU.approx_le_one | [
{
"state_after": "case zero\nX : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : NormalSpace X\nc✝ : CU X\nx : X\nc : CU X\n⊢ approx Nat.zero c x ≤ 1\n\ncase succ\nX : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : NormalSpace X\nc✝ : CU X\nx : X\nn : ℕ\nihn : ∀ (c : CU X), approx n c x ≤ 1\nc : CU X\n⊢ approx (... | [
171,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.head_terminates_of_mem | [] | [
1071,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1069,
1
] |
Mathlib/Data/UnionFind.lean | UFModel.Models.parent_eq | [] | [
127,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/MeasureTheory/Function/AEEqOfIntegral.lean | MeasureTheory.ae_eq_of_forall_set_integral_eq_of_sigmaFinite | [
{
"state_after": "α : Type u_1\nE : Type u_2\nm m0 : MeasurableSpace α\nμ : Measure α\ns t : Set α\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : CompleteSpace E\np : ℝ≥0∞\ninst✝ : SigmaFinite μ\nf g : α → E\nhf_int_finite : ∀ (s : Set α), MeasurableSet s → ↑↑μ s < ⊤ → IntegrableOn f s\nhg_i... | [
437,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean | DifferentiableAt.fderiv_restrictScalars | [] | [
106,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Log.lean | Complex.log_one | [
{
"state_after": "no goals",
"state_before": "⊢ log 1 = 0",
"tactic": "simp [log]"
}
] | [
97,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | le_csInf_iff | [] | [
585,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
584,
1
] |
Mathlib/GroupTheory/GroupAction/Group.lean | eq_inv_smul_iff | [] | [
119,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/RingTheory/Derivation/ToSquareZero.lean | derivationToSquareZeroOfLift_apply | [] | [
81,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.zeroLocus_empty | [] | [
279,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | HomologicalComplex.Hom.isIso_of_components | [] | [
516,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.sigmaCurry_zero | [
{
"state_after": "case h.h\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\nκ : Type ?u.604100\nα : ι → Type u_1\nδ : (i : ι) → α i → Type v\ninst✝ : (i : ι) → (j : α i) → Zero (δ i j)\ni : ι\nj : α i\n⊢ ↑(↑(sigmaCurry 0) i) j = ↑(↑0 i) j",
"state_before": "ι... | [
1486,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1483,
1
] |
Mathlib/Analysis/Calculus/TangentCone.lean | uniqueDiffOn_Ioo | [] | [
448,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/GroupTheory/Perm/List.lean | List.formPerm_apply_head | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.668395\ninst✝ : DecidableEq α\nl : List α\nx✝ x y : α\nxs : List α\nh : Nodup (x :: y :: xs)\n⊢ ↑(formPerm (x :: y :: xs)) x = y",
"tactic": "simp [formPerm_apply_of_not_mem _ _ h.not_mem]"
}
] | [
149,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasFDerivWithinAt.ccos | [] | [
316,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.spanExt_hom_app_right | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nX Y Z X' Y' Z' : C\niX : X ≅ X'\niY : Y ≅ Y'\niZ : Z ≅ Z'\nf : X ⟶ Y\ng : X ⟶ Z\nf' : X' ⟶ Y'\ng' : X' ⟶ Z'\nwf : iX.hom ≫ f' = f ≫ iY.hom\nwg : iX.hom ≫ g' = g ≫ iZ.hom\n⊢ (spanExt iX iY iZ wf wg... | [
481,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
480,
1
] |
Mathlib/Analysis/Calculus/Deriv/Mul.lean | DifferentiableOn.div_const | [] | [
320,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Algebra/CharP/Basic.lean | Ring.neg_one_ne_one_of_char_ne_two | [] | [
630,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.exact | [] | [
701,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/Algebra/NeZero.lean | NeZero.ne | [] | [
33,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/Order/CompactlyGenerated.lean | CompleteLattice.isSupFiniteCompact_iff_all_elements_compact | [
{
"state_after": "case refine'_1\nι : Sort ?u.75433\nα : Type u_1\ninst✝ : CompleteLattice α\nf : ι → α\nh : IsSupFiniteCompact α\nk : α\ns : Set α\nhs : k ≤ sSup s\n⊢ ∃ t, ↑t ⊆ s ∧ k ≤ Finset.sup t id\n\ncase refine'_2\nι : Sort ?u.75433\nα : Type u_1\ninst✝ : CompleteLattice α\nf : ι → α\nh : ∀ (k : α), IsCom... | [
261,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Init/Data/Bool/Lemmas.lean | Bool.ite_eq_false_distrib | [
{
"state_after": "no goals",
"state_before": "c : Prop\ninst✝ : Decidable c\na b : Bool\n⊢ ((if c then a else b) = false) = if c then a = false else b = false",
"tactic": "by_cases c <;> simp [*]"
}
] | [
181,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.diagonal_mul_diagonal' | [] | [
1045,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1043,
1
] |
Mathlib/Topology/Algebra/Module/Multilinear.lean | ContinuousMultilinearMap.coe_restrictScalars | [] | [
411,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
Mathlib/Data/List/Intervals.lean | List.Ico.trichotomy | [
{
"state_after": "case pos\nn a b : ℕ\nh₁ : n < a\n⊢ n < a ∨ b ≤ n ∨ n ∈ Ico a b\n\ncase neg\nn a b : ℕ\nh₁ : ¬n < a\n⊢ n < a ∨ b ≤ n ∨ n ∈ Ico a b",
"state_before": "n a b : ℕ\n⊢ n < a ∨ b ≤ n ∨ n ∈ Ico a b",
"tactic": "by_cases h₁ : n < a"
},
{
"state_after": "case pos.h\nn a b : ℕ\nh₁ : n < a... | [
244,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurableSet_Ioi | [] | [
507,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.image_symm_image_of_subset_target | [] | [
534,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.inf_principal | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.114761\nι : Sort x\nf g : Filter α\ns✝ t✝ s t : Set α\n⊢ ∃ t₁, t₁ ∈ 𝓟 s ∧ ∃ t₂, t₂ ∈ 𝓟 t ∧ s ∩ t = t₁ ∩ t₂",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.114761\nι : Sort x\nf g : Filter α\ns✝ t✝ s t : Set α\n⊢ 𝓟 s ⊓ 𝓟... | [
967,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
964,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderHom.mono | [] | [
236,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
11
] |
Mathlib/Order/Lattice.lean | sup_le_sup_left | [] | [
234,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.ωSup_total | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type ?u.7512\ninst✝ : OmegaCompletePartialOrder α\nc : Chain α\nx : α\nh : ∀ (i : ℕ), ↑c i ≤ x ∨ x ≤ ↑c i\nthis : ∃ x_1, ¬↑c x_1 ≤ x\n⊢ ∃ i, ¬↑c i ≤ x",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.7512\ninst✝ : OmegaCompletePartialOrder α\nc : Chain α\n... | [
211,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.IsPartition.inf | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nI J J₁ J₂ : Box ι\nπ π₁ π₂ : Prepartition I\nx : ι → ℝ\nπi πi₁ πi₂ : (J : Box ι) → Prepartition J\nh₁ : IsPartition π₁\nh₂ : IsPartition π₂\n⊢ Prepartition.iUnion (π₁ ⊓ π₂) = ↑I",
"tactic": "simp [h₁.iUnion_eq, h₂.iUnion_eq]"
}
] | [
777,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
776,
11
] |
Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesOnBall.analyticAt_of_mem | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.2353891\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace 𝕜 F\ninst✝² : NormedAddCommGroup G\ninst✝¹ : NormedSpace 𝕜 G\ninst✝ : CompleteSpa... | [
1364,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1359,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesAt.isBigO_image_sub_norm_mul_norm_sub | [
{
"state_after": "case intro\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.942458\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✝ : NormedSpace 𝕜 G\nf g : E →... | [
804,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
798,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.coe_one | [] | [
203,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.Iic_iInf | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.121213\nγ : Type ?u.121216\nι : Sort u_2\nκ : ι → Sort ?u.121224\ninst✝ : CompleteLattice α\nf : ι → α\nc : α\n⊢ c ∈ Iic (⨅ (i : ι), f i) ↔ c ∈ ⨅ (i : ι), Iic (f i)",
"tactic": "simp only [mem_Iic_iff, mem_iInf_iff, le_iInf_iff]"
... | [
1242,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1241,
1
] |
Mathlib/CategoryTheory/Sites/DenseSubsite.lean | CategoryTheory.CoverDense.Types.appHom_valid_glue | [
{
"state_after": "case h\nC : Type u_4\ninst✝⁴ : Category C\nD : Type u_2\ninst✝³ : Category D\nE : Type ?u.66083\ninst✝² : Category E\nJ : GrothendieckTopology C\nK : GrothendieckTopology D\nL : GrothendieckTopology E\nA : Type ?u.66135\ninst✝¹ : Category A\nG : C ⥤ D\nH : CoverDense K G\ninst✝ : Full G\nℱ : D... | [
239,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Algebra/AddTorsor.lean | Equiv.coe_vaddConst | [] | [
374,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/Deprecated/Subfield.lean | Field.closure_subset_iff | [] | [
143,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/RingTheory/WittVector/WittPolynomial.lean | xInTermsOfW_eq | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nR : Type u_1\ninst✝² : CommRing R\ninst✝¹ : DecidableEq R\ninst✝ : Invertible ↑p\nn : ℕ\n⊢ xInTermsOfW p R n = (X n - ∑ i in range n, ↑C (↑p ^ i) * xInTermsOfW p R i ^ p ^ (n - i)) * ↑C (⅟↑p ^ n)",
"tactic": "rw [xInTermsOfW, ← Fin.sum_univ_eq_sum_ran... | [
222,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Algebra/Ring/CompTypeclasses.lean | RingHomInvPair.comp_apply_eq | [
{
"state_after": "R₁ : Type u_1\nR₂ : Type u_2\nR₃ : Type ?u.2678\ninst✝³ : Semiring R₁\ninst✝² : Semiring R₂\ninst✝¹ : Semiring R₃\nσ₁₂ : R₁ →+* R₂\nσ₂₃ : R₂ →+* R₃\nσ₁₃ : R₁ →+* R₃\nσ : R₁ →+* R₂\nσ' : R₂ →+* R₁\ninst✝ : RingHomInvPair σ σ'\nx : R₁\n⊢ ↑(RingHom.id R₁) x = x",
"state_before": "R₁ : Type u_... | [
94,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | limsup_eq_tendsto_sum_indicator_atTop | [
{
"state_after": "α : Type u\nβ : Type v\nR : Type u_1\ninst✝¹ : StrictOrderedSemiring R\ninst✝ : Archimedean R\ns : ℕ → Set α\n⊢ {ω | Tendsto (fun n => ∑ k in Finset.range n, Set.indicator (s (k + 1)) 1 ω) atTop atTop} =\n {ω | Tendsto (fun n => ∑ k in Finset.range n, Set.indicator (s (k + 1)) 1 ω) atTop at... | [
527,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.ofReal_rat_cast | [] | [
861,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
860,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_multiset_prod | [] | [
1126,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1125,
1
] |
Mathlib/Topology/SubsetProperties.lean | ContinuousOn.preimage_clopen_of_clopen | [] | [
1623,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1620,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.lt_cof_type | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nr : α → α → Prop\ninst✝ : IsWellOrder α r\nS : Set α\n⊢ (#↑S) < cof (type r) → Bounded r S",
"tactic": "simpa using not_imp_not.2 cof_type_le"
}
] | [
175,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.