file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Algebra/ModEq.lean | AddCommGroup.not_modEq_iff_ne_add_zsmul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddCommGroup α\np a a₁ a₂ b b₁ b₂ c : α\nn : ℕ\nz : ℤ\n⊢ ¬a ≡ b [PMOD p] ↔ ∀ (z : ℤ), b ≠ a + z • p",
"tactic": "rw [modEq_iff_eq_add_zsmul, not_exists]"
}
] | [
297,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.limNthHom_zero | [
{
"state_after": "p : ℕ\nhp_prime : Fact (Nat.Prime p)\nR : Type u_1\ninst✝ : NonAssocSemiring R\nf : (k : ℕ) → R →+* ZMod (p ^ k)\nf_compat : ∀ (k1 k2 : ℕ) (hk : k1 ≤ k2), RingHom.comp (ZMod.castHom (_ : p ^ k1 ∣ p ^ k2) (ZMod (p ^ k1))) (f k2) = f k1\n⊢ ofIntSeq 0 (_ : IsCauSeq (padicNorm p) fun n => ↑(OfNat.... | [
592,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
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Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.coe_toNonUnitalRingHom | [] | [
619,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
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Mathlib/Data/Set/Pointwise/BigOperators.lean | Set.image_multiset_prod | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.19659\nα : Type u_1\nβ : Type u_2\nF : Type u_3\ninst✝² : CommMonoid α\ninst✝¹ : CommMonoid β\ninst✝ : MonoidHomClass F α β\nf : F\n⊢ ∀ (a : List (Set α)),\n ↑f '' Multiset.prod (Quotient.mk (List.isSetoid (Set α)) a) =\n Multiset.prod (Multi... | [
50,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
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Mathlib/Data/Nat/Factorization/Basic.lean | Nat.ord_compl_of_not_prime | [
{
"state_after": "no goals",
"state_before": "n p : ℕ\nhp : ¬Prime p\n⊢ n / p ^ ↑(factorization n) p = n",
"tactic": "simp [factorization_eq_zero_of_non_prime n hp]"
}
] | [
365,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
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Mathlib/Data/Multiset/Basic.lean | Multiset.attach_map_val' | [] | [
1535,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1534,
1
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Mathlib/GroupTheory/PGroup.lean | IsPGroup.iff_orderOf | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nG : Type u_1\ninst✝ : Group G\nhp : Fact (Nat.Prime p)\ng : G\nk : ℕ\nhk : orderOf g = p ^ k\n⊢ g ^ p ^ k = 1",
"tactic": "rw [← hk, pow_orderOf_eq_one]"
}
] | [
48,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Std/Logic.lean | or_or_or_comm | [
{
"state_after": "no goals",
"state_before": "a b c d : Prop\n⊢ (a ∨ b) ∨ c ∨ d ↔ (a ∨ c) ∨ b ∨ d",
"tactic": "rw [← or_assoc, @or_right_comm a, or_assoc]"
}
] | [
281,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
280,
1
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Mathlib/GroupTheory/NielsenSchreier.lean | IsFreeGroupoid.SpanningTree.loopOfHom_eq_id | [
{
"state_after": "G : Type u\ninst✝² : Groupoid G\ninst✝¹ : IsFreeGroupoid G\nT : WideSubquiver (Symmetrify (Generators G))\ninst✝ : Arborescence (WideSubquiver.toType (Symmetrify (Generators G)) T)\na b : Generators G\ne : a ⟶ b\nH : e ∈ wideSubquiverSymmetrify T a b\n⊢ treeHom T\n (let_fun this := a;\n... | [
205,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
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Mathlib/Analysis/Calculus/UniformLimitsDeriv.lean | uniformCauchySeqOn_ball_of_fderiv | [
{
"state_after": "ι : Type u_3\nl : Filter ι\nE : Type u_1\ninst✝⁴ : NormedAddCommGroup E\n𝕜 : Type u_4\ninst✝³ : IsROrC 𝕜\ninst✝² : NormedSpace 𝕜 E\nG : Type u_2\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : ι → E → G\ng : E → G\nf' : ι → E → E →L[𝕜] G\ng' : E → E →L[𝕜] G\nx : E\nr : ℝ\nhf... | [
225,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
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Mathlib/Order/Bounds/Basic.lean | BddBelow.image2_bddAbove | [
{
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1481,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1479,
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Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.sub_self_im | [] | [
303,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.insertNth_zero' | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\nα : Fin (n + 1) → Type u\nβ : Type v\nx : β\np : Fin n → β\n⊢ insertNth 0 x p = cons x p",
"tactic": "simp [insertNth_zero]"
}
] | [
732,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
731,
1
] |
Mathlib/Logic/Equiv/List.lean | Encodable.mem_sortedUniv | [] | [
208,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.NormNoninc.id | [] | [
838,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
838,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_nat_gt_zero_eq | [] | [
1682,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1681,
1
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Mathlib/Topology/Order/Basic.lean | csSup_mem_closure | [] | [
2776,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2775,
1
] |
Mathlib/Topology/CompactOpen.lean | ContinuousMap.continuous_comp_left | [
{
"state_after": "α : Type u_3\nβ : Type u_1\nγ : Type u_2\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\ng : C(β, γ)\nf : C(α, β)\nm : Set C(α, γ)\nx✝ : m ∈ {m | ∃ s x u x, m = CompactOpen.gen s u}\ns : Set α\nhs : IsCompact s\nu : Set γ\nhu : IsOpen u\nhm : m = CompactO... | [
125,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.Ioo_succ_right_eq_insert_of_not_isMax | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : SuccOrder α\na b : α\nh₁ : a < b\nh₂ : ¬IsMax b\n⊢ Ioo a (succ b) = insert b (Ioo a b)",
"tactic": "simp_rw [← Iio_inter_Ioi, Iio_succ_eq_insert_of_not_isMax h₂, insert_inter_of_mem (mem_Ioi.2 h₁)]"
}
] | [
471,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
469,
1
] |
Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.closure_iUnion | [] | [
536,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iio_subset_Iio_union_Ico | [] | [
1374,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1373,
1
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Mathlib/Topology/Algebra/Nonarchimedean/Basic.lean | NonarchimedeanRing.left_mul_subset | [] | [
143,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/CategoryTheory/Category/Basic.lean | CategoryTheory.ite_comp | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\nX✝ Y✝ Z✝ : C\nP : Prop\ninst✝ : Decidable P\nX Y Z : C\nf f' : X ⟶ Y\ng : Y ⟶ Z\n⊢ (if P then f else f') ≫ g = if P then f ≫ g else f' ≫ g",
"tactic": "aesop"
}
] | [
247,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
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Mathlib/Algebra/Order/Floor.lean | Nat.le_floor_iff | [] | [
134,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.cast_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Ring α\nm n : ZNum\n⊢ ↑(m * n) = ↑m * ↑n",
"tactic": "rw [← cast_to_int, mul_to_int, Int.cast_mul, cast_to_int, cast_to_int]"
}
] | [
1355,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1354,
1
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Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.top_prod | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\ninst✝² : NonAssocSemiring R\nM : Submonoid R\ninst✝¹ : NonAssocSemiring S\ninst✝ : NonAssocSemiring T\ns : Subsemiring S\nx : R × S\n⊢ x ∈ prod ⊤ s ↔ x ∈ comap (RingHom.snd R S) s",
"tactic": "simp [mem_prod, MonoidHom.coe... | [
1074,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1073,
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Mathlib/Topology/Connected.lean | connectedComponent_nonempty | [] | [
605,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
604,
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Mathlib/Analysis/Calculus/Inverse.lean | HasStrictFDerivAt.map_nhds_eq_of_surj | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Parity.lean | IsSquare.pow | [
{
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"state_before": "F : Type ?u.8146\nα : Type u_1\nβ : Type ?u.8152\nR : Type ?u.8155\ninst✝ : Monoid α\nn✝ : ℕ\na : α\nn : ℕ\n⊢ IsSquare a → IsSquare... | [
108,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Data/Set/Image.lean | Set.mem_range_self | [] | [
657,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
1
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Mathlib/Algebra/Group/Units.lean | IsUnit.mul_right_cancel | [] | [
788,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
787,
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] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.lift_left_inverse | [
{
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1079,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1064,
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Mathlib/FieldTheory/Fixed.lean | finrank_algHom | [] | [
342,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | LinearMap.restrictScalars_inj | [] | [
476,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
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Mathlib/Data/PFunctor/Multivariate/M.lean | MvPFunctor.M.dest_corec | [
{
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262,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
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Mathlib/Topology/Category/TopCat/Limits/Cofiltered.lean | TopCat.isTopologicalBasis_cofiltered_limit | [
{
"state_after": "J : Type v\ninst✝¹ : SmallCategory J\ninst✝ : IsCofiltered J\nF : J ⥤ TopCatMax\nC : Cone F\nhC : IsLimit C\nT : (j : J) → Set (Set ↑(F.obj j))\nhT : ∀ (j : J), IsTopologicalBasis (T j)\nuniv : ∀ (i : J), Set.univ ∈ T i\ninter : ∀ (i : J) (U1 U2 : Set ↑(F.obj i)), U1 ∈ T i → U2 ∈ T i → U1 ∩ U2... | [
129,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
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Mathlib/Analysis/Convex/Hull.lean | convexHull_subset_affineSpan | [] | [
218,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
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Mathlib/Algebra/Associated.lean | associated_unit_mul_left_iff | [] | [
504,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
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] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.Measure.pi_pi | [
{
"state_after": "ι : Type u_2\nι' : Type ?u.3051144\nα : ι → Type u_1\ninst✝² : Fintype ι\nm : (i : ι) → OuterMeasure (α i)\ninst✝¹ : (i : ι) → MeasurableSpace (α i)\nμ : (i : ι) → Measure (α i)\ninst✝ : ∀ (i : ι), SigmaFinite (μ i)\ns : (i : ι) → Set (α i)\nthis : Encodable ι\n⊢ ↑↑(Measure.pi μ) (Set.pi univ ... | [
400,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
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] |
Mathlib/Topology/UniformSpace/Separation.lean | separated_def' | [
{
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"state_before": "α✝ : Type u\nβ : T... | [
144,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
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Mathlib/Topology/Constructions.lean | continuousAt_fst | [] | [
341,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
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Mathlib/CategoryTheory/Preadditive/Injective.lean | CategoryTheory.Adjunction.map_injective | [
{
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"state_before": "C : Type u₁\ninst✝² : Categor... | [
324,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.support_nonempty_iff | [
{
"state_after": "no goals",
"state_before": "Γ : Type u_1\nR : Type u_2\ninst✝¹ : PartialOrder Γ\ninst✝ : Zero R\nx : HahnSeries Γ R\n⊢ Set.Nonempty (support x) ↔ x ≠ 0",
"tactic": "rw [support, support_nonempty_iff, Ne.def, coeff_fun_eq_zero_iff]"
}
] | [
141,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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8
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Mathlib/Topology/ContinuousOn.lean | continuousOn_open_iff | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.342559\nδ : Type ?u.342562\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α → β\ns : Set α\nhs : IsOpen s\n⊢ (∀ (t : Set β), IsOpen t → ∃ u, IsOpen u ∧ f ⁻¹' t ∩ s = u ∩ s) ↔ ∀ (t :... | [
1004,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
994,
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Mathlib/Topology/Instances/Real.lean | Real.continuous_inv | [] | [
116,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
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Mathlib/Topology/ContinuousFunction/Basic.lean | ContinuousMap.restrict_apply | [] | [
372,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.dom_natCast | [] | [
121,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Analysis/Calculus/Deriv/Mul.lean | derivWithin_mul_const | [] | [
226,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.inf_subgroupOf_inf_normal_of_left | [] | [
3584,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3579,
1
] |
Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | ContDiffAt.cexp | [] | [
164,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Analysis/InnerProductSpace/Calculus.lean | DifferentiableWithinAt.norm_sq | [] | [
262,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Data/List/Perm.lean | List.Subperm.countp_le | [] | [
479,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/Data/Fintype/Sum.lean | Finset.exists_equiv_extend_of_card_eq | [
{
"state_after": "case empty\nα : Type u_1\nβ : Type u_2\ninst✝¹ : Fintype α\ninst✝ : DecidableEq β\nt : Finset β\nhαt : Fintype.card α = card t\ns : Finset α\nf✝ : α → β\nhfst✝ : image f✝ s ⊆ t\nhfs✝ : Set.InjOn f✝ ↑s\nf : α → β\nhfst : image f ∅ ⊆ t\nhfs : Set.InjOn f ↑∅\n⊢ ∃ g, ∀ (i : α), i ∈ ∅ → ↑(↑g i) = f... | [
103,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Data/List/Sort.lean | List.Sorted.merge | [
{
"state_after": "no goals",
"state_before": "α : Type uu\nr : α → α → Prop\ninst✝² : DecidableRel r\ninst✝¹ : IsTotal α r\ninst✝ : IsTrans α r\nx✝¹ x✝ : Sorted r []\n⊢ Sorted r (List.merge r [] [])",
"tactic": "simp [List.merge]"
},
{
"state_after": "no goals",
"state_before": "α : Type uu\... | [
437,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/GroupTheory/SpecificGroups/Cyclic.lean | IsCyclic.card_orderOf_eq_totient | [
{
"state_after": "no goals",
"state_before": "α : Type u\na : α\ninst✝² : Group α\ninst✝¹ : IsCyclic α\ninst✝ : Fintype α\nd : ℕ\nhd : d ∣ Fintype.card α\n⊢ card (filter (fun a => orderOf a = d) univ) = φ d",
"tactic": "classical apply card_orderOf_eq_totient_aux₂ (fun n => IsCyclic.card_pow_eq_one_le) ... | [
419,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/Data/Dfinsupp/Interval.lean | Dfinsupp.support_rangeIcc_subset | [
{
"state_after": "ι : Type u_1\nα : ι → Type u_2\ninst✝⁴ : (i : ι) → Zero (α i)\ninst✝³ : (i : ι) → PartialOrder (α i)\ninst✝² : (i : ι) → LocallyFiniteOrder (α i)\nf g : Π₀ (i : ι), α i\ni : ι\na : α i\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → DecidableEq (α i)\nx : ι\nhx : x ∈ support (rangeIcc f g)\n⊢ x ∈ s... | [
135,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/FieldTheory/IsAlgClosed/Basic.lean | IsAlgClosure.equivOfEquiv_symm_comp_algebraMap | [] | [
530,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | neg_of_mul_pos_left | [] | [
576,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
575,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Ideal.isPrime_map_C_of_isPrime | [] | [
728,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
726,
1
] |
Mathlib/Analysis/NormedSpace/MazurUlam.lean | IsometryEquiv.coeFn_toRealAffineIsometryEquiv | [] | [
159,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiffOn_succ_iff_hasFDerivWithinAt | [
{
"state_after": "case mp\n𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nX : Type uX\ninst✝¹ : ... | [
755,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.power_ne_zero | [] | [
585,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
582,
1
] |
Mathlib/Data/Finset/Interval.lean | Finset.card_Ico_finset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\nh : s ⊆ t\n⊢ card (Ico s t) = 2 ^ (card t - card s) - 1",
"tactic": "rw [card_Ico_eq_card_Icc_sub_one, card_Icc_finset h]"
}
] | [
109,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Data/List/Chain.lean | List.Chain'.take | [] | [
331,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.or_inr | [
{
"state_after": "no goals",
"state_before": "a b : Bool\nH : b = true\n⊢ (a || b) = true",
"tactic": "cases a <;> simp [H]"
}
] | [
162,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Algebra/AddTorsor.lean | vsub_self | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nP : Type u_2\ninst✝ : AddGroup G\nT : AddTorsor G P\np : P\n⊢ p -ᵥ p = 0",
"tactic": "rw [← zero_add (p -ᵥ p), ← vadd_vsub_assoc, vadd_vsub]"
}
] | [
128,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Analysis/Asymptotics/AsymptoticEquivalent.lean | Asymptotics.IsLittleO.add_isEquivalent | [] | [
177,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_lt_coe_iff | [] | [
108,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
11
] |
Mathlib/Data/Finite/Card.lean | Finite.card_le_of_injective | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.2279\ninst✝ : Finite β\nf : α → β\nhf : Function.Injective f\nthis : Fintype β\n⊢ Nat.card α ≤ Nat.card β",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.2279\ninst✝ : Finite β\nf : α → β\nhf : Function.Injective f\n⊢ Nat.card α ≤ Nat.card... | [
105,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Data/Set/Pointwise/Finite.lean | Set.infinite_smul_set | [] | [
155,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.count_injective_image' | [
{
"state_after": "case pos\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.386958\nδ : Type ?u.386961\nι : Type ?u.386964\nR : Type ?u.386967\nR' : Type ?u.386970\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✝ : MeasurableSpace... | [
2330,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2321,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.weightedVSubOfPoint_eq_of_sum_eq_zero | [
{
"state_after": "case h\nk : Type u_1\nV : Type u_3\nP : Type u_4\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nS : AffineSpace V P\nι : Type u_2\ns : Finset ι\nι₂ : Type ?u.31556\ns₂ : Finset ι₂\nw : ι → k\np : ι → P\nh : ∑ i in s, w i = 0\nb₁ b₂ : P\n⊢ ↑(weightedVSubOfPoint s p b₁) w - ↑(wei... | [
127,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | orthogonalProjectionFn_eq | [] | [
476,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
1
] |
Mathlib/Algebra/Parity.lean | Even.mul_left | [] | [
282,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Data/List/Basic.lean | List.take_cons | [] | [
1926,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1925,
1
] |
Mathlib/Analysis/InnerProductSpace/PiL2.lean | EuclideanSpace.edist_eq | [] | [
143,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Data/Set/Finite.lean | Finset.bddBelow | [] | [
1646,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1645,
11
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.to_ring_inverse | [
{
"state_after": "case pos\nR : Type u_1\nM : Type u_2\nM₂ : Type u_3\ninst✝⁷ : TopologicalSpace M\ninst✝⁶ : TopologicalSpace M₂\ninst✝⁵ : Ring R\ninst✝⁴ : AddCommGroup M\ninst✝³ : TopologicalAddGroup M\ninst✝² : Module R M\ninst✝¹ : AddCommGroup M₂\ninst✝ : Module R M₂\ne : M ≃L[R] M₂\nf : M →L[R] M₂\nh₁ : ∃ e... | [
2545,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2530,
1
] |
Mathlib/Algebra/Algebra/Operations.lean | Submodule.pow_toAddSubmonoid | [
{
"state_after": "case zero\nι : Sort uι\nR : Type u\ninst✝² : CommSemiring R\nA : Type v\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\nS T : Set A\nM N P Q : Submodule R A\nm n✝ : A\nn : ℕ\nh✝ : n ≠ 0\nh : Nat.zero ≠ 0\n⊢ (M ^ Nat.zero).toAddSubmonoid = M.toAddSubmonoid ^ Nat.zero\n\ncase succ\nι : Sort uι\nR : T... | [
425,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.toSet_subset_iff | [
{
"state_after": "no goals",
"state_before": "x y : ZFSet\n⊢ toSet x ⊆ toSet y ↔ x ⊆ y",
"tactic": "simp [subset_def, Set.subset_def]"
}
] | [
792,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
791,
1
] |
Mathlib/Algebra/Group/Pi.lean | Pi.mulSingle_inf | [] | [
486,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/Combinatorics/Hindman.lean | Hindman.FP.singleton | [
{
"state_after": "case zero\nM : Type u_1\ninst✝ : Semigroup M\na✝ a : Stream' M\n⊢ Stream'.nth a Nat.zero ∈ FP a\n\ncase succ\nM : Type u_1\ninst✝ : Semigroup M\na✝ : Stream' M\ni : ℕ\nih : ∀ (a : Stream' M), Stream'.nth a i ∈ FP a\na : Stream' M\n⊢ Stream'.nth a (Nat.succ i) ∈ FP a",
"state_before": "M : ... | [
262,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/CategoryTheory/Monoidal/Rigid/Basic.lean | CategoryTheory.rightAdjointMate_comp_evaluation | [
{
"state_after": "C : Type u₁\ninst✝³ : Category C\ninst✝² : MonoidalCategory C\nX Y : C\ninst✝¹ : HasRightDual X\ninst✝ : HasRightDual Y\nf : X ⟶ Y\n⊢ ↑(tensorRightHomEquiv Yᘁ X Xᘁ (𝟙_ C)) ((fᘁ ⊗ 𝟙 X) ≫ ε_ X Xᘁ) =\n ↑(tensorRightHomEquiv Yᘁ X Xᘁ (𝟙_ C)) ((𝟙 Yᘁ ⊗ f) ≫ ε_ Y Yᘁ)",
"state_before": "C : ... | [
566,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
563,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroObjects.lean | CategoryTheory.Limits.IsZero.unop | [] | [
138,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Topology/Separation.lean | t0Space_of_injective_of_continuous | [] | [
326,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/NumberTheory/Padics/PadicVal.lean | range_pow_padicValNat_subset_divisors | [
{
"state_after": "p n : ℕ\nhn : n ≠ 0\nt : ℕ\nht : t ∈ Finset.image (fun x => p ^ x) (Finset.range (padicValNat p n + 1))\n⊢ t ∈ divisors n",
"state_before": "p n : ℕ\nhn : n ≠ 0\n⊢ Finset.image (fun x => p ^ x) (Finset.range (padicValNat p n + 1)) ⊆ divisors n",
"tactic": "intro t ht"
},
{
"sta... | [
495,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_C | [
{
"state_after": "case pos\nR : Type u\nS : Type v\na✝ b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q r : R[X]\na : R\nha : a = 0\n⊢ natDegree (↑C a) = 0\n\ncase neg\nR : Type u\nS : Type v\na✝ b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q r : R[X]\na : R\nha : ¬a = 0\n⊢ natDegree (↑C a) = 0",
"state_before": "R... | [
275,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Data/Multiset/Lattice.lean | Multiset.sup_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : SemilatticeSup α\ninst✝ : OrderBot α\ns : Multiset α\na : α\n⊢ sup 0 ≤ a ↔ ∀ (b : α), b ∈ 0 → b ≤ a",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : SemilatticeSup α\ninst✝ : OrderB... | [
63,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.lt_base_pow_length_digits | [
{
"state_after": "case succ.succ\nn m b : ℕ\n⊢ m < succ (succ b) ^ List.length (digits (succ (succ b)) m)",
"state_before": "n b m : ℕ\nhb : 1 < b\n⊢ m < b ^ List.length (digits b m)",
"tactic": "rcases b with (_ | _ | b) <;> try simp_all"
},
{
"state_after": "no goals",
"state_before": "cas... | [
424,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_C_mul_X_pow_le | [
{
"state_after": "R : Type u\nS : Type v\na✝ b c d : R\nn✝ m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nn : ℕ\na : R\n⊢ degree (↑(monomial n) a) ≤ ↑n",
"state_before": "R : Type u\nS : Type v\na✝ b c d : R\nn✝ m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nn : ℕ\na : R\n⊢ degree (↑C a * X ^ n) ≤ ↑n",
"tactic": "r... | [
309,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/AlgebraicTopology/SimplexCategory.lean | SimplexCategory.skeletalFunctor.coe_map | [] | [
365,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
src/lean/Init/Data/Char/Basic.lean | Char.isValidUInt32 | [
{
"state_after": "no goals",
"state_before": "n : Nat\nh : isValidCharNat n\n⊢ n < UInt32.size",
"tactic": "match h with\n| Or.inl h =>\n apply Nat.lt_trans h\n decide\n| Or.inr ⟨_, h₂⟩ =>\n apply Nat.lt_trans h₂\n decide"
},
{
"state_after": "n : Nat\nh✝ : isValidCharNat n\nh : n < ... | [
41,
11
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
34,
1
] |
Mathlib/Analysis/Convex/Function.lean | LinearMap.concaveOn | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.183332\nα : Type ?u.183335\nβ : Type u_3\nι : Type ?u.183341\ninst✝⁶ : OrderedSemiring 𝕜\ninst✝⁵ : AddCommMonoid E\ninst✝⁴ : AddCommMonoid F\ninst✝³ : OrderedAddCommMonoid α\ninst✝² : OrderedAddCommMonoid β\ninst✝¹ : Mod... | [
366,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Std/Data/List/Init/Lemmas.lean | List.drop_length_le | [] | [
141,
62
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
140,
1
] |
Mathlib/Analysis/NormedSpace/Basic.lean | frontier_closedBall | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.89099\nβ : Type ?u.89102\nγ : Type ?u.89105\nι : Type ?u.89108\ninst✝⁶ : NormedField α\ninst✝⁵ : SeminormedAddCommGroup β\nE : Type u_1\ninst✝⁴ : SeminormedAddCommGroup E\ninst✝³ : NormedSpace α E\nF : Type ?u.89139\ninst✝² : SeminormedAddCommGroup F... | [
155,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.IsLimit.pos | [] | [
288,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.dvd_iff_normalizedFactors_le_normalizedFactors | [
{
"state_after": "case mp\nα : Type u_1\ninst✝³ : CancelCommMonoidWithZero α\ninst✝² : DecidableEq α\ninst✝¹ : NormalizationMonoid α\ninst✝ : UniqueFactorizationMonoid α\nx y : α\nhx : x ≠ 0\nhy : y ≠ 0\n⊢ x ∣ y → normalizedFactors x ≤ normalizedFactors y\n\ncase mpr\nα : Type u_1\ninst✝³ : CancelCommMonoidWith... | [
728,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
721,
1
] |
Mathlib/Analysis/NormedSpace/ContinuousLinearMap.lean | ContinuousLinearEquiv.toSpanNonzeroSingleton_homothety | [] | [
276,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/RingTheory/Polynomial/Bernstein.lean | bernsteinPolynomial.iterate_derivative_at_1 | [
{
"state_after": "R : Type u_1\ninst✝ : CommRing R\nn ν : ℕ\nh : ν ≤ n\n⊢ eval 1 ((↑derivative^[n - ν]) (comp (bernsteinPolynomial R n (n - ν)) (1 - X))) =\n (-1) ^ (n - ν) * eval (↑ν + 1) (pochhammer R (n - ν))",
"state_before": "R : Type u_1\ninst✝ : CommRing R\nn ν : ℕ\nh : ν ≤ n\n⊢ eval 1 ((↑derivati... | [
238,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/LinearAlgebra/StdBasis.lean | Pi.basis_repr | [] | [
268,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
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