file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.pow_mem_of_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\na b : α\ninst✝ : CommSemiring α\nI : Ideal α\nha : a ∈ I\nn : ℕ\nhn : 0 < n\n⊢ ¬0 < Nat.zero",
"tactic": "decide"
}
] | [
573,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.dotProduct_add | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.138074\nm : Type u_1\nn : Type ?u.138080\no : Type ?u.138083\nm' : o → Type ?u.138088\nn' : o → Type ?u.138093\nR : Type ?u.138096\nS : Type ?u.138099\nα : Type v\nβ : Type w\nγ : Type ?u.138106\ninst✝² : Fintype m\ninst✝¹ : Fintype n\ninst✝ : NonUni... | [
773,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
772,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | le_mul_of_one_le_left' | [] | [
355,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_C_X | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝¹ : Semiring R\np✝ q✝ r : R[X]\ninst✝ : Semiring S\nf : R →+* S\nx : S\np q : R[X]\nhp : eval₂ C X p = p\nhq : eval₂ C X q = q\n⊢ eval₂ C X (p + q) = p + q",
"tactic": "simp [hp, hq]"
}... | [
125,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Data/Finset/Finsupp.lean | Finset.mem_finsupp_iff | [
{
"state_after": "case refine'_1\nι : Type u_2\nα : Type u_1\ninst✝ : Zero α\ns : Finset ι\nf : ι →₀ α\nt : ι → Finset α\n⊢ (∃ a, a ∈ pi s t ∧ ↑{ toFun := indicator s, inj' := (_ : Function.Injective fun f => indicator s f) } a = f) →\n f.support ⊆ s ∧ ∀ (i : ι), i ∈ s → ↑f i ∈ t i\n\ncase refine'_2\nι : Typ... | [
59,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Data/Fintype/Card.lean | Fintype.card_congr' | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.5163\nβ✝ : Type ?u.5166\nγ : Type ?u.5169\nα β : Type u_1\ninst✝¹ : Fintype α\ninst✝ : Fintype β\nh : α = β\n⊢ α ≃ β",
"tactic": "rw [h]"
}
] | [
158,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinitesimal_iff_infinite_inv | [
{
"state_after": "no goals",
"state_before": "x : ℝ*\nh : x ≠ 0\n⊢ Infinitesimal x ↔ Infinitesimal x⁻¹⁻¹",
"tactic": "rw [inv_inv]"
}
] | [
781,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
780,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.equivSubtype_symm_trans_valEmbedding | [] | [
358,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Data/Finset/Interval.lean | Finset.Ioc_eq_filter_powerset | [] | [
61,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Computability/NFA.lean | NFA.mem_accepts | [
{
"state_after": "no goals",
"state_before": "α : Type u\nσ σ' : Type v\nM : NFA α σ\nx : List α\n⊢ x ∈ accepts M ↔ ∃ S, S ∈ M.accept ∧ S ∈ evalFrom M M.start x",
"tactic": "rfl"
}
] | [
112,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/LinearAlgebra/Ray.lean | Module.Ray.map_symm | [] | [
308,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/LinearAlgebra/TensorAlgebra/Basic.lean | TensorAlgebra.tprod_apply | [] | [
304,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.self_trans_inv | [] | [
177,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Data/Fintype/Basic.lean | Set.toFinset_empty | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.91377\nγ : Type ?u.91380\ns t : Set α\ninst✝ : Fintype ↑∅\na✝ : α\n⊢ a✝ ∈ toFinset ∅ ↔ a✝ ∈ ∅",
"state_before": "α : Type u_1\nβ : Type ?u.91377\nγ : Type ?u.91380\ns t : Set α\ninst✝ : Fintype ↑∅\n⊢ toFinset ∅ = ∅",
"tactic": "ext"
},
{
"state... | [
733,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
731,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoDiv_sub_eq_toIcoDiv_add' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c✝ : α\nn : ℤ\na b c : α\n⊢ toIcoDiv hp (a - c) b = toIcoDiv hp a (b + c)",
"tactic": "rw [← sub_neg_eq_add, toIcoDiv_sub_eq_toIcoDiv_add, sub_eq_add_neg]"
}
] | [
373,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | RingHom.eq_liftOfRightInverse | [
{
"state_after": "A : Type u_1\nB : Type u_2\nC : Type u_3\ninst✝² : Ring A\ninst✝¹ : Ring B\ninst✝ : Ring C\nf : A →+* B\nf_inv : B → A\nhf : Function.RightInverse f_inv ↑f\ng : A →+* C\nhg : ker f ≤ ker g\nh : B →+* C\nhh : comp h f = g\n⊢ h = ↑(liftOfRightInverse f f_inv hf) { val := comp h f, property := (_... | [
2293,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2289,
1
] |
Mathlib/Algebra/Algebra/Bilinear.lean | LinearMap.mulLeft_zero_eq_zero | [] | [
102,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.mul_subset_mul | [] | [
418,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.set_integral_nonpos_of_ae | [] | [
759,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
758,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.restrict_trim | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.698391\nm : MeasurableSpace α\nL : Type ?u.698397\nM : Type u_2\nN : Type ?u.698403\ninst✝⁵ : AddCommMonoid L\ninst✝⁴ : TopologicalSpace L\ninst✝³ : AddCommMonoid M\ninst✝² : TopologicalSpace M\ninst✝¹ : AddCommMonoid N\ninst✝ : TopologicalSpace N\nn : Measura... | [
1315,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1310,
1
] |
Mathlib/Analysis/Convex/Complex.lean | convex_halfspace_re_le | [] | [
27,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
26,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_union_Ioc_symm | [
{
"state_after": "α : Type u_1\nβ : Type ?u.212353\ninst✝¹ : LinearOrder α\ninst✝ : LinearOrder β\nf : α → β\na a₁ a₂ b b₁ b₂ c d : α\n⊢ Ioc a b ∪ Ioc b a = Ioc (min a b) (max b a)",
"state_before": "α : Type u_1\nβ : Type ?u.212353\ninst✝¹ : LinearOrder α\ninst✝ : LinearOrder β\nf : α → β\na a₁ a₂ b b₁ b₂ ... | [
1853,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1851,
1
] |
Mathlib/CategoryTheory/Over.lean | CategoryTheory.Over.forget_map | [] | [
152,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Topology/PartitionOfUnity.lean | PartitionOfUnity.continuous_finsum_smul | [] | [
196,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/MeasureTheory/Function/SpecialFunctions/IsROrC.lean | measurable_of_re_im | [
{
"state_after": "case h.e'_5.h\nα : Type u_1\n𝕜 : Type u_2\ninst✝¹ : IsROrC 𝕜\ninst✝ : MeasurableSpace α\nf : α → 𝕜\nμ : MeasureTheory.Measure α\nhre : Measurable fun x => ↑IsROrC.re (f x)\nhim : Measurable fun x => ↑IsROrC.im (f x)\nx✝ : α\n⊢ f x✝ = (IsROrC.ofReal ∘ fun x => ↑IsROrC.re (f x)) x✝ + (IsROrC.... | [
79,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | mem_posSubmonoid | [] | [
1442,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1440,
1
] |
Std/Data/List/Lemmas.lean | List.getElem?_eq_get? | [
{
"state_after": "α : Type u_1\nl : List α\ni : Nat\n⊢ (if h : (fun as i => i < length as) l i then some l[i] else none) = get? l i",
"state_before": "α : Type u_1\nl : List α\ni : Nat\n⊢ l[i]? = get? l i",
"tactic": "unfold getElem?"
},
{
"state_after": "case inl\nα : Type u_1\nl : List α\ni : ... | [
549,
52
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
546,
9
] |
Mathlib/Data/Rat/Defs.lean | Rat.zero_of_num_zero | [
{
"state_after": "a b c q : ℚ\nhq : q.num = 0\nthis : q = q.num /. ↑q.den\n⊢ q = 0",
"state_before": "a b c q : ℚ\nhq : q.num = 0\n⊢ q = 0",
"tactic": "have : q = q.num /. q.den := num_den.symm"
},
{
"state_after": "no goals",
"state_before": "a b c q : ℚ\nhq : q.num = 0\nthis : q = q.num /.... | [
418,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.one_shiftLeft | [
{
"state_after": "no goals",
"state_before": "n : Nat\n⊢ 1 <<< n = 2 ^ n",
"tactic": "rw [shiftLeft_eq, Nat.one_mul]"
}
] | [
805,
87
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
805,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.dual_node4R | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : Ordnode α\nx : α\nm : Ordnode α\ny : α\nr : Ordnode α\n⊢ dual (node4R l x m y r) = node4L (dual r) y (dual m) x (dual l)",
"tactic": "cases m <;> simp [node4L, node4R, node3L, dual_node3R, dual_node', add_comm]"
}
] | [
332,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.card_erase_le | [] | [
1119,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1118,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_neg | [] | [
1350,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1349,
1
] |
Mathlib/Algebra/Algebra/Hom.lean | AlgHom.map_sub | [] | [
489,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
11
] |
Mathlib/Algebra/AddTorsor.lean | vadd_vsub_vadd_cancel_right | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nP : Type u_2\ninst✝ : AddGroup G\nT : AddTorsor G P\nv₁ v₂ : G\np : P\n⊢ v₁ +ᵥ p -ᵥ (v₂ +ᵥ p) = v₁ - v₂",
"tactic": "rw [vsub_vadd_eq_vsub_sub, vadd_vsub_assoc, vsub_self, add_zero]"
}
] | [
205,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.abs_sinh | [
{
"state_after": "no goals",
"state_before": "x✝ y z x : ℝ\n⊢ abs (sinh x) = sinh (abs x)",
"tactic": "cases le_total x 0 <;> simp [abs_of_nonneg, abs_of_nonpos, *]"
}
] | [
721,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
720,
1
] |
Mathlib/Algebra/Order/Sub/Defs.lean | add_tsub_add_eq_tsub_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.55470\ninst✝⁵ : PartialOrder α\ninst✝⁴ : AddCommSemigroup α\ninst✝³ : Sub α\ninst✝² : OrderedSub α\na✝ b✝ c✝ d : α\ninst✝¹ : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1\ninst✝ : ContravariantClass α α (fun x x_1 => x ... | [
399,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/RingTheory/Localization/Submodule.lean | IsLocalization.mem_coeSubmodule | [] | [
44,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/Data/PFun.lean | PFun.preimage_comp | [
{
"state_after": "case h\nα : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.55840\nε : Type ?u.55843\nι : Type ?u.55846\nf✝ : α →. β\nf : β →. γ\ng : α →. β\ns : Set γ\nx✝ : α\n⊢ x✝ ∈ preimage (comp f g) s ↔ x✝ ∈ preimage g (preimage f s)",
"state_before": "α : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ : ... | [
610,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
605,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | IsROrC.inner_apply | [] | [
1936,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1935,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.Reaches.to₀ | [] | [
814,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
813,
1
] |
Mathlib/Data/Set/Function.lean | StrictAntiOn.injOn | [] | [
1550,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1548,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.liminf_le_of_frequently_le | [] | [
1151,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1147,
1
] |
Mathlib/Order/SymmDiff.lean | Codisjoint.bihimp_left | [] | [
704,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
702,
11
] |
Mathlib/Probability/ProbabilityMassFunction/Uniform.lean | Pmf.uniformOfFinset_apply_of_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.4518\nγ : Type ?u.4521\ns : Finset α\nhs : Finset.Nonempty s\na : α\nha : a ∈ s\n⊢ ↑(uniformOfFinset s hs) a = (↑(Finset.card s))⁻¹",
"tactic": "simp [ha]"
}
] | [
60,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/CategoryTheory/Limits/Types.lean | CategoryTheory.Limits.Types.FilteredColimit.rel_equiv | [
{
"state_after": "no goals",
"state_before": "J : Type v\ninst✝¹ : SmallCategory J\nF : J ⥤ TypeMax\ninst✝ : IsFilteredOrEmpty J\nx y z : (j : J) × F.obj j\nx✝¹ : FilteredColimit.Rel F x y\nx✝ : FilteredColimit.Rel F y z\nk : J\nf : x.fst ⟶ k\ng : y.fst ⟶ k\nh : F.map f x.snd = F.map g y.snd\nk' : J\nf' : y... | [
461,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
11
] |
Mathlib/Data/Set/Intervals/OrdConnected.lean | Set.ordConnected_Ioo | [] | [
171,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.le_ncard_of_inj_on_range | [
{
"state_after": "α : Type u_1\nβ : Type ?u.90617\ns t : Set α\na b x y : α\nf✝ : α → β\nn : ℕ\nf : ℕ → α\nhf : ∀ (i : ℕ), i < n → f i ∈ s\nf_inj : ∀ (i : ℕ), i < n → ∀ (j : ℕ), j < n → f i = f j → i = j\nhs : autoParam (Set.Finite s) _auto✝\n⊢ n ≤ Finset.card (Finite.toFinset hs)",
"state_before": "α : Typ... | [
408,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/CategoryTheory/Monad/Basic.lean | CategoryTheory.monadToFunctor_mapIso_monad_iso_mk | [
{
"state_after": "case w.w.h\nC : Type u₁\ninst✝ : Category C\nT : Monad C\nG : Comonad C\nM N : Monad C\nf : M.toFunctor ≅ N.toFunctor\nf_η : ∀ (X : C), (Monad.η M).app X ≫ f.hom.app X = (Monad.η N).app X\nf_μ : ∀ (X : C), (Monad.μ M).app X ≫ f.hom.app X = (M.map (f.hom.app X) ≫ f.hom.app (N.obj X)) ≫ (Monad.μ... | [
323,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieHom.coe_injective | [
{
"state_after": "case mk.mk.mk.mk.mk.mk\nR : Type u\nL₁ : Type v\nL₂ : Type w\nL₃ : Type w₁\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L₁\ninst✝⁴ : LieAlgebra R L₁\ninst✝³ : LieRing L₂\ninst✝² : LieAlgebra R L₂\ninst✝¹ : LieRing L₃\ninst✝ : LieAlgebra R L₃\nf : L₁ → L₂\nmap_add'✝¹ : ∀ (x y : L₁), f (x + y) = f x +... | [
380,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Deriv.lean | DifferentiableWithinAt.log | [] | [
156,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Order/Ideal.lean | Order.Ideal.bot_mem | [] | [
260,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/CategoryTheory/Yoneda.lean | CategoryTheory.Yoneda.isIso | [] | [
112,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | LinearMap.leftInverse_splittingOfFinsuppSurjective | [] | [
1234,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1232,
1
] |
Mathlib/Order/WellFounded.lean | WellFounded.induction_bot' | [] | [
269,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.ldiff'_to_nat | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.612393\n⊢ ∀ (m n : Num), ↑(ldiff m n) = Nat.ldiff' ↑m ↑n",
"tactic": "apply bitwise'_to_nat PosNum.ldiff <;> intros <;> cases_type* Bool <;> rfl"
}
] | [
948,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
947,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.bind_promises | [
{
"state_after": "case intro.intro\nα : Type u\nβ : Type v\nγ : Type w\ns : Computation α\nf : α → Computation β\na : α\nb : β\nh1 : s ~> a\nh2 : f a ~> b\nb' : β\nbB : b' ∈ bind s f\na' : α\na's : a' ∈ s\nba' : b' ∈ f a'\n⊢ b = b'",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : Computation α\nf ... | [
858,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
855,
1
] |
Mathlib/Algebra/Homology/QuasiIso.lean | quasiIso_of_comp_left | [] | [
61,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Data/List/Infix.lean | List.map_reverse_tails | [
{
"state_after": "α : Type u_1\nβ : Type ?u.48141\nl✝ l₁ l₂ l₃ : List α\na b : α\nm n : ℕ\nl : List α\n⊢ map reverse (reverse (map reverse (inits (reverse l)))) = reverse (inits (reverse l))",
"state_before": "α : Type u_1\nβ : Type ?u.48141\nl✝ l₁ l₂ l₃ : List α\na b : α\nm n : ℕ\nl : List α\n⊢ map reverse... | [
422,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.mul_le_mul | [] | [
587,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
586,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | mul_mem_cancel_left | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nG' : Type ?u.14819\ninst✝⁶ : Group G\ninst✝⁵ : Group G'\nA : Type ?u.14828\ninst✝⁴ : AddGroup A\nM : Type ?u.14834\nS : Type u_2\ninst✝³ : DivInvMonoid M\ninst✝² : SetLike S M\nhSM : SubgroupClass S M\nH K : S\ninst✝¹ : SetLike S G\ninst✝ : Subgrou... | [
192,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Data/Set/NAry.lean | Set.Nonempty.of_image2_left | [] | [
167,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | Ideal.prime_of_isPrime | [
{
"state_after": "R : Type ?u.797297\nA : Type u_1\nK : Type ?u.797303\ninst✝⁶ : CommRing R\ninst✝⁵ : CommRing A\ninst✝⁴ : Field K\ninst✝³ : IsDomain A\ninst✝² : IsDedekindDomain A\ninst✝¹ : Algebra A K\ninst✝ : IsFractionRing A K\nP : Ideal A\nhP : P ≠ ⊥\nh : IsPrime P\nI J : Ideal A\nhIJ : P ∣ I * J\n⊢ P ∣ I ... | [
717,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
715,
1
] |
Mathlib/CategoryTheory/Monoidal/Braided.lean | CategoryTheory.braiding_leftUnitor_aux₁ | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\ninst✝¹ : MonoidalCategory C\ninst✝ : BraidedCategory C\nX : C\n⊢ (α_ (𝟙_ C) (𝟙_ C) X).hom ≫ (λ_ (𝟙_ C ⊗ X)).hom ≫ (β_ X (𝟙_ C)).inv = ((λ_ (𝟙_ C)).hom ⊗ 𝟙 X) ≫ (β_ X (𝟙_ C)).inv",
"state_before": "C : Type u₁\ninst✝² : Category C\ninst✝¹ : MonoidalC... | [
147,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Logic/Basic.lean | exists_prop_of_true | [] | [
875,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
874,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.pow | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝² : PseudoEMetricSpace α\ninst✝¹ : PseudoEMetricSpace β\ninst✝ : PseudoEMetricSpace γ\nK✝ : ℝ≥0\nf✝ : α → β\nx y : α\nr : ℝ≥0∞\nf : Function.End α\nK : ℝ≥0\nh : LipschitzWith K f\n⊢ LipschitzWith (K ^ 0) (f ^ ... | [
303,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
11
] |
Mathlib/Algebra/Ring/BooleanRing.lean | ofBoolAlg_mul_ofBoolAlg_eq_left_iff | [] | [
327,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesOnBall.sum | [] | [
904,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
902,
1
] |
Mathlib/Data/Polynomial/HasseDeriv.lean | Polynomial.hasseDeriv_one' | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nk : ℕ\nf : R[X]\n⊢ ↑(hasseDeriv 1) f = ↑derivative f",
"tactic": "simp only [hasseDeriv_apply, derivative_apply, ← C_mul_X_pow_eq_monomial, Nat.choose_one_right,\n (Nat.cast_commute _ _).eq]"
}
] | [
107,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Algebra/GroupPower/Identities.lean | sum_eight_sq_mul_sum_eight_sq | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : CommRing R\na b x₁ x₂ x₃ x₄ x₅ x₆ x₇ x₈ y₁ y₂ y₃ y₄ y₅ y₆ y₇ y₈ n : R\n⊢ (x₁ ^ 2 + x₂ ^ 2 + x₃ ^ 2 + x₄ ^ 2 + x₅ ^ 2 + x₆ ^ 2 + x₇ ^ 2 + x₈ ^ 2) *\n (y₁ ^ 2 + y₂ ^ 2 + y₃ ^ 2 + y₄ ^ 2 + y₅ ^ 2 + y₆ ^ 2 + y₇ ^ 2 + y₈ ^ 2) =\n (x₁ * y... | [
81,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigOWith_zero' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.260515\nE : Type ?u.260518\nF : Type u_3\nG : Type ?u.260524\nE' : Type u_2\nF' : Type ?u.260530\nG' : Type ?u.260533\nE'' : Type ?u.260536\nF'' : Type ?u.260539\nG'' : Type ?u.260542\nR : Type ?u.260545\nR' : Type ?u.260548\n𝕜 : Type ... | [
1204,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1203,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_biUnion_le | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.17016\nδ : Type ?u.17019\nι : Type ?u.17022\ninst✝ : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns✝ s₁ s₂ t : Set α\ns : Set β\nhs : Set.Countable s\nf : β → Set α\nthis : Countable ↑s\n⊢ ↑↑μ (⋃ (b : β) (_ : b ∈ s), f b) ≤ ∑' (p : ↑s), ↑↑μ (f ↑p)",
"stat... | [
244,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.dist_le_two_norm' | [] | [
830,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
825,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | nndist_pi_le_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.389587\nι : Type ?u.389590\ninst✝² : PseudoMetricSpace α\nπ : β → Type u_1\ninst✝¹ : Fintype β\ninst✝ : (b : β) → PseudoMetricSpace (π b)\nf g : (b : β) → π b\nr : ℝ≥0\n⊢ nndist f g ≤ r ↔ ∀ (b : β), nndist (f b) (g b) ≤ r",
... | [
1996,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1995,
1
] |
Mathlib/Order/Synonym.lean | OrderDual.le_toDual | [] | [
113,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.ofFractionRing_div | [
{
"state_after": "no goals",
"state_before": "K : Type u\ninst✝¹ : CommRing K\ninst✝ : IsDomain K\np q : FractionRing K[X]\n⊢ { toFractionRing := p / q } = { toFractionRing := p } / { toFractionRing := q }",
"tactic": "simp only [Div.div, HDiv.hDiv, RatFunc.div]"
}
] | [
404,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.add_lt_add_left | [] | [
766,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
765,
21
] |
Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsColimit.equivIsoColimit_apply | [] | [
709,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
707,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.Red.reduce_left | [] | [
1239,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1238,
1
] |
Mathlib/Data/Subtype.lean | Subtype.restrict_def | [] | [
164,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Data/Polynomial/Taylor.lean | Polynomial.taylor_coeff_one | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nr : R\nf : R[X]\n⊢ coeff (↑(taylor r) f) 1 = eval r (↑derivative f)",
"tactic": "rw [taylor_coeff, hasseDeriv_one]"
}
] | [
97,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Order/Monotone/Basic.lean | StrictAnti.comp_strictMono | [] | [
687,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
686,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigOWith_map | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nE : Type u_3\nF : Type u_4\nG : Type ?u.69939\nE' : Type ?u.69942\nF' : Type ?u.69945\nG' : Type ?u.69948\nE'' : Type ?u.69951\nF'' : Type ?u.69954\nG'' : Type ?u.69957\nR : Type ?u.69960\nR' : Type ?u.69963\n𝕜 : Type ?u.69966\n𝕜' : Type ?u.69969\ninst✝¹² : Norm E... | [
434,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.primPart_dvd | [] | [
313,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.mem_singleton | [] | [
920,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
918,
1
] |
Mathlib/Algebra/Divisibility/Basic.lean | dvd_mul_left | [] | [
168,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.le_floor | [] | [
138,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/SetTheory/Lists.lean | Lists'.mem_def | [] | [
160,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Algebra/Symmetrized.lean | SymAlg.sym_add | [] | [
175,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Init/Function.lean | Function.uncurry_curry | [] | [
147,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
9
] |
Mathlib/Analysis/SpecialFunctions/Complex/Log.lean | Complex.two_pi_I_ne_zero | [
{
"state_after": "⊢ ¬(π = 0 ∨ I = 0)",
"state_before": "⊢ 2 * ↑π * I ≠ 0",
"tactic": "norm_num"
},
{
"state_after": "no goals",
"state_before": "⊢ ¬(π = 0 ∨ I = 0)",
"tactic": "simp [Real.pi_ne_zero, I_ne_zero]"
}
] | [
139,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Order/Bounded.lean | Set.unbounded_ge_univ | [] | [
161,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.Injective.of_comp_iff' | [] | [
142,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.eval₂Hom_id_X_eq_join₂ | [] | [
141,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Algebra/Group/Prod.lean | Prod.mk_mul_mk | [] | [
62,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Analysis/Complex/RealDeriv.lean | HasDerivAt.comp_ofReal | [
{
"state_after": "no goals",
"state_before": "e : ℂ → ℂ\ne' : ℂ\nz : ℝ\nE : Type ?u.147902\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nhf : HasDerivAt e e' ↑z\n⊢ HasDerivAt (fun y => e ↑y) e' z",
"tactic": "simpa only [ofRealClm_apply, ofReal_one, mul_one] using hf.comp z ofRealClm.hasDeriv... | [
139,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesAt.coeff_zero | [] | [
619,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_iUnion_null_iff | [] | [
273,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Logic/Equiv/Set.lean | Equiv.image_compl | [] | [
103,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
11
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coe_nsmul | [] | [
505,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | UniformFun.precomp_uniformContinuous | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nι : Type ?u.43134\ns s' : Set α\nx : α\np : Filter ι\ng : ι → α\ninst✝ : UniformSpace β\nf : γ → α\n⊢ uniformSpace α β ≤ UniformSpace.comap (fun g => ↑ofFun (g ∘ f)) (uniformSpace γ β)",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nι ... | [
465,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
11
] |
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