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/Order/Filter/Basic.lean | Filter.EventuallyLE.mul_le_mul' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.213025\nι : Sort x\ninst✝³ : Mul β\ninst✝² : Preorder β\ninst✝¹ : CovariantClass β β (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\ninst✝ : CovariantClass β β (swap fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\nl : Fil... | [
1762,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1759,
1
] |
Mathlib/Analysis/InnerProductSpace/Adjoint.lean | ContinuousLinearMap.adjoint_inner_right | [] | [
130,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.seq_zero | [] | [
303,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | HasFDerivWithinAt.add | [] | [
138,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
8
] |
Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.pos_le_one_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝¹ : Lattice α\ninst✝ : CommGroup α\na : α\n⊢ a⁺ ≤ 1 ↔ a ≤ 1",
"tactic": "rw [m_pos_part_def, sup_le_iff, and_iff_left le_rfl]"
}
] | [
214,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.coe_singletonMonoidHom | [] | [
917,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
916,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.sub_lt_self | [
{
"state_after": "a b : Nat\nh₀ : 0 < a\nh₁ : a ≤ b\n⊢ 0 < b",
"state_before": "a b : Nat\nh₀ : 0 < a\nh₁ : a ≤ b\n⊢ b - a < b",
"tactic": "apply sub_lt _ h₀"
},
{
"state_after": "no goals",
"state_before": "a b : Nat\nh₀ : 0 < a\nh₁ : a ≤ b\n⊢ 0 < b",
"tactic": "apply Nat.lt_of_lt_of_le... | [
452,
33
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
450,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.eq_right_or_mem_Ioo_of_mem_Ioc | [] | [
944,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
943,
1
] |
Mathlib/Data/Finset/Interval.lean | Finset.Ico_eq_filter_ssubsets | [] | [
57,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Data/Real/Sqrt.lean | Real.sqrt_le_sqrt_iff | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\nhy : 0 ≤ y\n⊢ sqrt x ≤ sqrt y ↔ x ≤ y",
"tactic": "rw [sqrt, sqrt, NNReal.coe_le_coe, NNReal.sqrt_le_sqrt_iff, Real.toNNReal_le_toNNReal_iff hy]"
}
] | [
263,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Geometry/Manifold/ChartedSpace.lean | StructureGroupoid.le_iff | [] | [
216,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/CategoryTheory/Extensive.lean | CategoryTheory.IsInitial.isVanKampenColimit | [
{
"state_after": "J : Type v'\ninst✝² : Category J\nC : Type u\ninst✝¹ : Category C\ninst✝ : HasStrictInitialObjects C\nX : C\nh : IsInitial X\nF' : Discrete PEmpty ⥤ C\nc' : Cocone F'\nα : F' ⟶ Functor.empty C\nf : c'.pt ⟶ (asEmptyCocone X).pt\nhf : α ≫ (asEmptyCocone X).ι = c'.ι ≫ (Functor.const (Discrete PEm... | [
120,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Analysis/NormedSpace/ContinuousAffineMap.lean | ContinuousAffineMap.norm_image_zero_le | [] | [
181,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.nsmul_mem | [] | [
149,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
11
] |
Mathlib/Data/Finset/Basic.lean | Finset.union_distrib_right | [] | [
1753,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1752,
1
] |
Mathlib/Algebra/Module/Opposites.lean | MulOpposite.opLinearEquiv_symm_toAddEquiv | [] | [
72,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/RingTheory/SimpleModule.lean | LinearMap.isCoatom_ker_of_surjective | [
{
"state_after": "R : Type u_1\ninst✝⁵ : Ring R\nM : Type u_3\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\nm : Submodule R M\nN : Type u_2\ninst✝² : AddCommGroup N\ninst✝¹ : Module R N\ninst✝ : IsSimpleModule R N\nf : M →ₗ[R] N\nhf : Function.Surjective ↑f\n⊢ IsSimpleModule R (M ⧸ ker f)",
"state_before":... | [
171,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/CategoryTheory/Filtered.lean | CategoryTheory.IsFiltered.tulip | [
{
"state_after": "case intro.intro.intro\nC : Type u\ninst✝¹ : Category C\ninst✝ : IsFilteredOrEmpty C\nj₁ j₂ j₃ k₁ k₂ l : C\nf₁ : j₁ ⟶ k₁\nf₂ : j₂ ⟶ k₁\nf₃ : j₂ ⟶ k₂\nf₄ : j₃ ⟶ k₂\ng₁ : j₁ ⟶ l\ng₂ : j₃ ⟶ l\nl' : C\nk₁l : k₁ ⟶ l'\nk₂l : k₂ ⟶ l'\nhl : f₂ ≫ k₁l = f₃ ≫ k₂l\n⊢ ∃ s α β γ, f₁ ≫ α = g₁ ≫ β ∧ f₂ ≫ α = ... | [
459,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.get_eq_of_promises | [] | [
499,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.sign_prodCongrRight | [
{
"state_after": "case intro.intro\nα : Type u\nβ : Type v\ninst✝³ : DecidableEq α\ninst✝² : Fintype α\ninst✝¹ : DecidableEq β\ninst✝ : Fintype β\nσ : α → Perm β\nl : List α\nhl : List.Nodup l\nmem_l : ∀ (x : α), x ∈ l\n⊢ ↑sign (prodCongrRight σ) = ∏ k : α, ↑sign (σ k)",
"state_before": "α : Type u\nβ : Typ... | [
756,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
748,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.diag_apply | [] | [
613,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
612,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.equivFunOnFintype_symm_coe | [] | [
626,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
1
] |
Mathlib/Order/SymmDiff.lean | bihimp_right_injective | [] | [
669,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
668,
1
] |
Mathlib/CategoryTheory/Subobject/MonoOver.lean | CategoryTheory.MonoOver.lift_obj_arrow | [] | [
189,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | UniformOnFun.tendsto_iff_tendstoUniformlyOn | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.103872\nι : Type u_3\ns s' : Set α\nx : α\np : Filter ι\ng : ι → α\ninst✝ : UniformSpace β\n𝔖 : Set (Set α)\nF : ι → α →ᵤ[𝔖] β\nf : α →ᵤ[𝔖] β\n⊢ (∀ (i : Set α), Tendsto F p (𝓝 f)) ↔ ∀ (s : Set α), s ∈ 𝔖 → TendstoUniformlyOn F f p s",
"state_befo... | [
879,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
871,
11
] |
Mathlib/LinearAlgebra/BilinearMap.lean | LinearMap.mk₂'_apply | [] | [
115,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Topology/Algebra/Ring/Ideal.lean | Ideal.closure_eq_of_isClosed | [] | [
43,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalMaxOn.sub | [] | [
437,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
8
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | NonarchAddGroupSeminorm.toZeroHom_eq_coe | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.127014\nR : Type ?u.127017\nR' : Type ?u.127020\nE : Type u_1\nF : Type ?u.127026\nG : Type ?u.127029\ninst✝² : AddGroup E\ninst✝¹ : AddGroup F\ninst✝ : AddGroup G\np q : NonarchAddGroupSeminorm E\n⊢ ↑p.toZeroHom = ↑p",
"tactic": "rfl"
}
] | [
526,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.succ_lt_succ | [] | [
210,
15
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
209,
1
] |
Mathlib/Algebra/Group/Basic.lean | inv_eq_iff_mul_eq_one | [] | [
687,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
686,
1
] |
Mathlib/Order/SuccPred/IntervalSucc.lean | Monotone.pairwise_disjoint_on_Ioo_succ | [] | [
75,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean | Real.differentiableAt_tan_of_mem_Ioo | [] | [
84,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Data/List/Basic.lean | List.nthLe_cons | [
{
"state_after": "case inl\nι : Type ?u.48326\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l : List α\na : α\nn : ℕ\nhl : n < length (a :: l)\nh : n = 0\n⊢ nthLe (a :: l) n hl = a\n\ncase inr\nι : Type ?u.48326\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l : List α\na : α\nn : ℕ\nhl : n < l... | [
971,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
962,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.le_log2 | [
{
"state_after": "no goals",
"state_before": "n k : Nat\nh : n ≠ 0\n⊢ 0 ≤ log2 n ↔ 2 ^ 0 ≤ n",
"tactic": "simp [show 1 ≤ n from Nat.pos_of_ne_zero h]"
},
{
"state_after": "n k✝ : Nat\nh : n ≠ 0\nk : Nat\n⊢ (k + 1 ≤ if n ≥ 2 then log2 (n / 2) + 1 else 0) ↔ 2 ^ (k + 1) ≤ n",
"state_before": "n... | [
820,
78
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
811,
1
] |
Mathlib/FieldTheory/IsAlgClosed/Spectrum.lean | spectrum.exists_mem_of_not_isUnit_aeval_prod | [
{
"state_after": "R : Type u\nA : Type v\ninst✝³ : CommRing R\ninst✝² : Ring A\ninst✝¹ : Algebra R A\ninst✝ : IsDomain R\np : R[X]\na : A\nh : ¬IsUnit (List.prod (List.map (↑(aeval a)) (Multiset.toList (Multiset.map (fun x => X - ↑C x) (roots p)))))\n⊢ ∃ k, k ∈ σ a ∧ eval k p = 0",
"state_before": "R : Type... | [
69,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Topology/SubsetProperties.lean | isIrreducible_singleton | [] | [
1715,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1714,
1
] |
Mathlib/Data/Nat/Hyperoperation.lean | hyperoperation_ge_two_eq_self | [
{
"state_after": "case zero\nm : ℕ\n⊢ hyperoperation (Nat.zero + 2) m 1 = m\n\ncase succ\nm nn : ℕ\nnih : hyperoperation (nn + 2) m 1 = m\n⊢ hyperoperation (Nat.succ nn + 2) m 1 = m",
"state_before": "n m : ℕ\n⊢ hyperoperation (n + 2) m 1 = m",
"tactic": "induction' n with nn nih"
},
{
"state_af... | [
100,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Data/FinEnum.lean | FinEnum.mem_toList | [
{
"state_after": "α : Type u\nβ : α → Type v\ninst✝ : FinEnum α\nx : α\n⊢ ∃ a, ↑Equiv.symm a = x",
"state_before": "α : Type u\nβ : α → Type v\ninst✝ : FinEnum α\nx : α\n⊢ x ∈ toList α",
"tactic": "simp [toList]"
},
{
"state_after": "α : Type u\nβ : α → Type v\ninst✝ : FinEnum α\nx : α\n⊢ ↑Equiv... | [
77,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Data/List/Duplicate.lean | List.Duplicate.ne_singleton | [
{
"state_after": "case cons_mem\nα : Type u_1\nl : List α\nx y : α\nl' : List α\nh : x ∈ l'\n⊢ x :: l' ≠ [y]\n\ncase cons_duplicate\nα : Type u_1\nl : List α\nx y z : α\nl' : List α\nh : x ∈+ l'\na_ih✝ : l' ≠ [y]\n⊢ z :: l' ≠ [y]",
"state_before": "α : Type u_1\nl : List α\nx : α\nh : x ∈+ l\ny : α\n⊢ l ≠ [... | [
77,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.SimpleFunc.setToL1S_mono_left | [] | [
836,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
834,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.coprodComparison_inv_natural | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁷ : Category C\nX Y : C\nD : Type u₂\ninst✝⁶ : Category D\nF : C ⥤ D\nA A' B B' : C\ninst✝⁵ : HasBinaryCoproduct A B\ninst✝⁴ : HasBinaryCoproduct A' B'\ninst✝³ : HasBinaryCoproduct (F.obj A) (F.obj B)\ninst✝² : HasBinaryCoproduct (F.obj A') (F.o... | [
1388,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1384,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | Padic.coe_sub | [] | [
556,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/Data/List/AList.lean | AList.insertRec_insert_mk | [] | [
394,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/Algebra/Lie/Abelian.lean | LieModule.maxTrivEquiv_of_equiv_symm_eq_symm | [] | [
211,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/NumberTheory/ModularForms/CongruenceSubgroups.lean | Gamma1_in_Gamma0 | [
{
"state_after": "N✝ N : ℕ\nx : SL(2, ℤ)\nHA : x ∈ Gamma1 N\n⊢ x ∈ Gamma0 N",
"state_before": "N✝ N : ℕ\n⊢ Gamma1 N ≤ Gamma0 N",
"tactic": "intro x HA"
},
{
"state_after": "N✝ N : ℕ\nx : SL(2, ℤ)\nHA : ↑(↑x 0 0) = 1 ∧ ↑(↑x 1 1) = 1 ∧ ↑(↑x 1 0) = 0\n⊢ ↑(↑x 1 0) = 0",
"state_before": "N✝ N : ℕ... | [
203,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConvexOn.sub | [] | [
888,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
887,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.to_global_factors | [
{
"state_after": "R : Type u\ninst✝ : CommRing R\n⊢ toOpen R ⊤ =\n (CommRingCat.ofHom (algebraMap R (Localization.Away 1)) ≫ toBasicOpen R 1) ≫\n (structureSheaf R).val.map (eqToHom (_ : ⊤ = PrimeSpectrum.basicOpen 1)).op",
"state_before": "R : Type u\ninst✝ : CommRing R\n⊢ toOpen R ⊤ =\n CommRin... | [
996,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
986,
1
] |
Mathlib/Order/Lattice.lean | ofDual_inf | [] | [
953,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
952,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.map_le_iff_le_comap | [] | [
245,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.get?_cons_zero | [] | [
94,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Finset.lean | Finset.Nonempty.cSup_mem | [
{
"state_after": "α : Type u_1\nβ : Type ?u.8944\nγ : Type ?u.8947\ninst✝ : ConditionallyCompleteLinearOrder α\ns✝ t : Set α\na b : α\ns : Finset α\nh : Finset.Nonempty s\n⊢ max' s h ∈ s",
"state_before": "α : Type u_1\nβ : Type ?u.8944\nγ : Type ?u.8947\ninst✝ : ConditionallyCompleteLinearOrder α\ns✝ t : S... | [
54,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Order/CompleteLattice.lean | biSup_prod | [
{
"state_after": "α : Type u_3\nβ : Type u_1\nβ₂ : Type ?u.166426\nγ : Type u_2\nι : Sort ?u.166432\nι' : Sort ?u.166435\nκ : ι → Sort ?u.166440\nκ' : ι' → Sort ?u.166445\ninst✝ : CompleteLattice α\nf✝ g s✝ t✝ : ι → α\na b : α\nf : β × γ → α\ns : Set β\nt : Set γ\n⊢ (⨆ (i : β) (j : γ) (_ : i ∈ s) (_ : j ∈ t), f... | [
1559,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1556,
1
] |
Mathlib/Algebra/Order/Group/Abs.lean | abs_pos | [
{
"state_after": "case inl\nα : Type u_1\ninst✝² : AddGroup α\ninst✝¹ : LinearOrder α\ninst✝ : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1\na b c : α\nha : a < 0\n⊢ 0 < abs a ↔ a ≠ 0\n\ncase inr.inl\nα : Type u_1\ninst✝² : AddGroup α\ninst✝¹ : LinearOrder α\ninst✝ : CovariantClass α α (fun x ... | [
140,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | expSeries_hasSum_exp_of_mem_ball | [] | [
231,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Combinatorics/HalesJewett.lean | Combinatorics.Line.map_apply | [
{
"state_after": "α : Type u_1\nα' : Type u_2\nι : Type u_3\nf : α → α'\nl : Line α ι\nx : α\n⊢ (fun i => f (Option.getD (idxFun l i) x)) = f ∘ fun i => Option.getD (idxFun l i) x",
"state_before": "α : Type u_1\nα' : Type u_2\nι : Type u_3\nf : α → α'\nl : Line α ι\nx : α\n⊢ (fun x i => Option.getD (idxFun... | [
196,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Algebra/Ring/BooleanRing.lean | BooleanRing.le_sup_inf | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.18933\nγ : Type ?u.18936\ninst✝² : BooleanRing α\ninst✝¹ : BooleanRing β\ninst✝ : BooleanRing γ\na b c : α\n⊢ (a + b + a * b) * (a + c + a * c) + (a + b * c + a * (b * c)) +\n (a + b + a * b) * (a + c + a * c) * (a + b * c + a * (b... | [
240,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Data/Option/NAry.lean | Option.map₂_some_some | [] | [
54,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.map_algebraMap | [
{
"state_after": "l : Type ?u.584026\nm : Type ?u.584029\nn : Type u_2\no : Type ?u.584035\nm' : o → Type ?u.584040\nn' : o → Type ?u.584045\nR : Type u_1\nS : Type ?u.584051\nα : Type v\nβ : Type w\nγ : Type ?u.584058\ninst✝⁶ : Fintype n\ninst✝⁵ : DecidableEq n\ninst✝⁴ : CommSemiring R\ninst✝³ : Semiring α\nin... | [
1346,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1334,
1
] |
Mathlib/Analysis/Calculus/Deriv/Comp.lean | derivWithin.scomp | [] | [
115,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Data/Set/Image.lean | Set.preimage_inter_range | [] | [
842,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.eval₂Hom_map_hom | [] | [
1334,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1332,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.coe_clamp | [] | [
2496,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2495,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.lt_of_lt_of_equiv | [] | [
841,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
840,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.uIcc_injective_left | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.193752\nα : Type u_1\ninst✝¹ : DistribLattice α\ninst✝ : LocallyFiniteOrder α\na✝ a₁ a₂ b b₁ b₂ c x a : α\n⊢ Injective (uIcc a)",
"tactic": "simpa only [uIcc_comm] using uIcc_injective_right a"
}
] | [
982,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
981,
1
] |
Mathlib/Data/Polynomial/Coeff.lean | Polynomial.coeff_mul_X_pow' | [
{
"state_after": "case inl\nR : Type u\nS : Type v\na b : R\nn✝ m : ℕ\ninst✝ : Semiring R\np✝ q r p : R[X]\nn d : ℕ\nh : n ≤ d\n⊢ coeff (p * X ^ n) d = coeff p (d - n)\n\ncase inr\nR : Type u\nS : Type v\na b : R\nn✝ m : ℕ\ninst✝ : Semiring R\np✝ q r p : R[X]\nn d : ℕ\nh : ¬n ≤ d\n⊢ coeff (p * X ^ n) d = 0",
... | [
255,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.bot_or_nontrivial | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\nN : Type ?u.166126\nP : Type ?u.166129\ninst✝³ : MulOneClass M\ninst✝² : MulOneClass N\ninst✝¹ : MulOneClass P\nS✝ : Submonoid M\nA : Type ?u.166150\ninst✝ : SetLike A M\nhA : SubmonoidClass A M\nS' : A\nS : Submonoid M\n⊢ S = ⊥ ∨ Nontrivial { x //... | [
1380,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1379,
1
] |
Mathlib/Algebra/Hom/GroupInstances.lean | AddMonoidHom.coe_mul | [] | [
317,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/Algebra/Associated.lean | associated_one_iff_isUnit | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.150247\nγ : Type ?u.150250\nδ : Type ?u.150253\ninst✝ : Monoid α\na : α\nx✝ : IsUnit a\nc : αˣ\nh : ↑c = a\n⊢ 1 * ↑c = a",
"tactic": "simp [h]"
}
] | [
433,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/Algebra/Order/Group/MinMax.lean | min_div_div_left' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedCommGroup α\na✝ b✝ c✝ a b c : α\n⊢ min (a / b) (a / c) = a / max b c",
"tactic": "simp only [div_eq_mul_inv, min_mul_mul_left, min_inv_inv']"
}
] | [
68,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.const_injective | [] | [
55,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Algebra/Module/LocalizedModule.lean | IsLocalizedModule.mk'_add | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁷ : CommRing R\nS : Submonoid R\nM : Type u_3\nM' : Type u_2\nM'' : Type ?u.847575\ninst✝⁶ : AddCommMonoid M\ninst✝⁵ : AddCommMonoid M'\ninst✝⁴ : AddCommMonoid M''\ninst✝³ : Module R M\ninst✝² : Module R M'\ninst✝¹ : Module R M''\nf : M →ₗ[R] ... | [
973,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
972,
1
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.untop_one | [] | [
53,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.succ_ne_succ_iff | [] | [
487,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | IsClosed.rightCoset | [] | [
146,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Std/Data/RBMap/Alter.lean | Std.RBNode.Path.insertNew_eq_insert | [] | [
70,
41
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
68,
1
] |
Mathlib/RingTheory/Finiteness.lean | Module.Finite.equiv | [] | [
612,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
611,
1
] |
Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.CompactOpens.coe_compl | [] | [
569,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | Submodule.rank_sup_add_rank_inf_eq | [
{
"state_after": "no goals",
"state_before": "K : Type u\nV V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.1002876\ninst✝¹⁰ : DivisionRing K\ninst✝⁹ : AddCommGroup V\ninst✝⁸ : Module K V\ninst✝⁷ : AddCommGroup V'\ninst✝⁶ : Module K V'\ninst✝⁵ : A... | [
1152,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1140,
1
] |
Mathlib/Analysis/Normed/Field/UnitBall.lean | coe_one_unitSphere | [] | [
161,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Algebra/Hom/GroupInstances.lean | MonoidHom.compr₂_apply | [] | [
279,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Algebra/Order/Positive/Ring.lean | Positive.val_one | [] | [
130,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Analysis/InnerProductSpace/EuclideanDist.lean | Euclidean.isCompact_closedBall | [
{
"state_after": "E : Type u_1\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : TopologicalAddGroup E\ninst✝³ : T2Space E\ninst✝² : Module ℝ E\ninst✝¹ : ContinuousSMul ℝ E\ninst✝ : FiniteDimensional ℝ E\nx : E\nr : ℝ\n⊢ IsCompact (↑(ContinuousLinearEquiv.symm toEuclidean) '' Metric.closedBall (↑t... | [
92,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
8
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_map_complex | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.4079769\nE : Type ?u.4079772\nF : Type ?u.4079775\ninst✝⁶ : IsROrC 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : InnerProductSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nG : Type u_1\ninst✝¹ : Norme... | [
2241,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2240,
1
] |
Mathlib/Algebra/IsPrimePow.lean | IsPrimePow.one_lt | [] | [
128,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coe_mk | [] | [
187,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | LinearIsometryEquiv.contDiff | [] | [
168,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | lt_of_mul_lt_of_one_le_of_nonneg_left | [] | [
915,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
913,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_nonpos | [] | [
393,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
11
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.choose_le_succ_of_lt_half_left | [
{
"state_after": "r n : ℕ\nh : r < n / 2\n⊢ choose n r * (n - r) ≤ choose n (r + 1) * (n - r)",
"state_before": "r n : ℕ\nh : r < n / 2\n⊢ choose n r ≤ choose n (r + 1)",
"tactic": "refine' le_of_mul_le_mul_right _ (lt_tsub_iff_left.mpr (lt_of_lt_of_le h (n.div_le_self 2)))"
},
{
"state_after": ... | [
286,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/GroupTheory/Sylow.lean | card_sylow_modEq_one | [
{
"state_after": "p : ℕ\nG : Type u_1\ninst✝² : Group G\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : Fintype (Sylow p G)\nP : Sylow p G\n⊢ card (Sylow p G) ≡ 1 [MOD p]",
"state_before": "p : ℕ\nG : Type u_1\ninst✝² : Group G\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : Fintype (Sylow p G)\n⊢ card (Sylow p G) ≡ 1 [MOD p]"... | [
341,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Data/Int/Cast/Lemmas.lean | Pi.coe_int | [] | [
361,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/CategoryTheory/ConcreteCategory/Basic.lean | CategoryTheory.coe_comp | [] | [
136,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Std/Data/Int/Lemmas.lean | Int.ofNat_mul_negSucc | [] | [
373,
91
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
373,
9
] |
Mathlib/Analysis/Calculus/Series.lean | iteratedFDeriv_tsum_apply | [
{
"state_after": "no goals",
"state_before": "α : Type u_4\nβ : Type ?u.117040\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : CompleteSpace F\nu : α → ℝ\ninst✝ : NormedSpace 𝕜 F\nf : α → E → F... | [
225,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Analysis/Convex/Cone/Dual.lean | pointed_innerDualCone | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.9011\nE : Type ?u.9014\nF : Type ?u.9017\nG : Type ?u.9020\nH : Type u_1\ninst✝¹ : NormedAddCommGroup H\ninst✝ : InnerProductSpace ℝ H\ns t : Set H\nx : H\nx✝ : x ∈ s\n⊢ 0 ≤ inner x 0",
"tactic": "rw [inner_zero_right]"
}
] | [
85,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Data/Dfinsupp/NeLocus.lean | Dfinsupp.neLocus_self_add_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nN : α → Type u_2\ninst✝² : DecidableEq α\ninst✝¹ : (a : α) → DecidableEq (N a)\ninst✝ : (a : α) → AddGroup (N a)\nf f₁ f₂ g g₁ g₂ : Π₀ (a : α), N a\n⊢ neLocus f (f + g) = support g",
"tactic": "rw [← neLocus_zero_left, ← @neLocus_add_left α N _... | [
164,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Order/BoundedOrder.lean | exists_le_and_iff_exists | [] | [
615,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.pmul_apply | [] | [
513,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
1
] |
Mathlib/AlgebraicTopology/AlternatingFaceMapComplex.lean | AlgebraicTopology.AlternatingFaceMapComplex.obj_d_eq | [
{
"state_after": "no goals",
"state_before": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX✝ Y X : SimplicialObject C\nn : ℕ\n⊢ HomologicalComplex.d (obj X) (n + 1) n = ∑ i : Fin (n + 2), (-1) ^ ↑i • SimplicialObject.δ X i",
"tactic": "apply ChainComplex.of_d"
}
] | [
141,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.