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/Data/Fintype/Card.lean | Fintype.card_le_of_embedding | [] | [
468,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
1
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.ExprCnstr.eq_true_of_isValid | [
{
"state_after": "ctx : Context\nc : ExprCnstr\nh : PolyCnstr.isValid (toNormPoly c) = true\nthis : PolyCnstr.denote ctx (toNormPoly c) = True\n⊢ denote ctx c = True",
"state_before": "ctx : Context\nc : ExprCnstr\nh : PolyCnstr.isValid (toNormPoly c) = true\n⊢ denote ctx c = True",
"tactic": "have := P... | [
669,
13
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
666,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_congr | [] | [
634,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
633,
1
] |
Mathlib/Control/EquivFunctor.lean | EquivFunctor.mapEquiv.injective | [
{
"state_after": "no goals",
"state_before": "f : Type u₀ → Type u₁\ninst✝¹ : Applicative f\ninst✝ : LawfulApplicative f\nα β : Type u₀\nh : ∀ (γ : Type u₀), Injective pure\ne₁ e₂ : α ≃ β\nH : mapEquiv f e₁ = mapEquiv f e₂\nx : α\n⊢ pure (↑e₁ x) = pure (↑e₂ x)",
"tactic": "simpa [EquivFunctor.map] using... | [
109,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/RingTheory/Polynomial/Vieta.lean | MvPolynomial.prod_C_add_X_eq_sum_esymm | [
{
"state_after": "R : Type u_2\nσ : Type u_1\ninst✝¹ : CommSemiring R\ninst✝ : Fintype σ\ns : Multiset (MvPolynomial σ R) := Multiset.map (fun i => X i) univ.val\n⊢ ∏ i : σ, (Polynomial.X + ↑Polynomial.C (X i)) =\n ∑ j in range (Fintype.card σ + 1), ↑Polynomial.C (esymm σ R j) * Polynomial.X ^ (Fintype.card ... | [
180,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | UniformSpace.Completion.Continuous.inner | [] | [
2345,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2343,
11
] |
Mathlib/Algebra/CharP/CharAndCard.lean | isUnit_iff_not_dvd_char | [] | [
56,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Computability/PartrecCode.lean | Nat.Partrec.Code.smn | [] | [
698,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
] |
Mathlib/Data/Option/Defs.lean | Option.mem_some_iff | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.1536\nβ : Type ?u.1539\nα : Type u_1\na b : α\n⊢ a ∈ some b ↔ b = a",
"tactic": "simp"
}
] | [
73,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.mem_support_ofFintype_iff | [] | [
218,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.ncard_mono | [] | [
83,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.RightInverse.injective | [] | [
366,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Analysis/Calculus/Deriv/Inv.lean | derivWithin_inv | [
{
"state_after": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type w\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL : Filter 𝕜\nx_ne_zero : x ≠ 0\nhxs : Uniq... | [
110,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_natCast | [
{
"state_after": "no goals",
"state_before": "α β : Type u\nn : ℕ\n⊢ lift ↑n = ↑n",
"tactic": "induction n <;> simp [*]"
}
] | [
1282,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1282,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.parallelPair_map_right | [] | [
239,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Data/List/Prime.lean | perm_of_prod_eq_prod | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝¹ : CancelCommMonoidWithZero M\ninst✝ : Unique Mˣ\na : M\nl₁ : List M\nb : M\nl₂ : List M\nh : prod (a :: l₁) = prod (b :: l₂)\nhl₁ : ∀ (p : M), p ∈ a :: l₁ → Prime p\nhl₂ : ∀ (p : M), p ∈ b :: l₂ → Prime p\n⊢ a :: l₁ ~ b :: l₂",
"tactic":... | [
81,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.map_filter | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.274085\np : α → Prop\ninst✝ : DecidablePred p\nf : β → α\ns : Multiset β\nl : List β\n⊢ List.map f (List.filter ((fun b => decide (p b)) ∘ f) l) ~ List.map f (List.filter (fun b => decide (p (f b))) l)",
"state_before": "α : Type u_2\nβ : Type u_1\nγ... | [
2093,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2092,
1
] |
Mathlib/Data/Finsupp/Order.lean | Finsupp.sub_single_one_add | [] | [
257,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.add_le_add_iff_right | [] | [
267,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
11
] |
Mathlib/Logic/Unique.lean | eq_const_of_unique | [
{
"state_after": "case h\nα : Sort u_1\nβ : Sort u_2\ninst✝ : Unique α\nf : α → β\nx : α\n⊢ f x = Function.const α (f default) x",
"state_before": "α : Sort u_1\nβ : Sort u_2\ninst✝ : Unique α\nf : α → β\n⊢ f = Function.const α (f default)",
"tactic": "ext x"
},
{
"state_after": "case h\nα : Sor... | [
212,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Data/List/Range.lean | List.pairwise_gt_iota | [
{
"state_after": "no goals",
"state_before": "α : Type u\nn : ℕ\n⊢ Pairwise (fun x x_1 => x > x_1) (iota n)",
"tactic": "simpa only [iota_eq_reverse_range', pairwise_reverse] using pairwise_lt_range' 1 n"
}
] | [
118,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Control/Bifunctor.lean | Bifunctor.comp_fst | [
{
"state_after": "no goals",
"state_before": "F : Type u₀ → Type u₁ → Type u₂\ninst✝¹ : Bifunctor F\ninst✝ : LawfulBifunctor F\nα₀ α₁ α₂ : Type u₀\nβ : Type u₁\nf : α₀ → α₁\nf' : α₁ → α₂\nx : F α₀ β\n⊢ fst f' (fst f x) = fst (f' ∘ f) x",
"tactic": "simp [fst, bimap_bimap]"
}
] | [
93,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.toNatOrdinal_cast_nat | [
{
"state_after": "n : ℕ\n⊢ ↑toNatOrdinal (↑toOrdinal ↑n) = ↑n",
"state_before": "n : ℕ\n⊢ ↑toNatOrdinal ↑n = ↑n",
"tactic": "rw [← toOrdinal_cast_nat n]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ ↑toNatOrdinal (↑toOrdinal ↑n) = ↑n",
"tactic": "rfl"
}
] | [
399,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/Data/Set/Pairwise/Basic.lean | Set.pairwise_pair_of_symmetric | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.14609\nγ : Type ?u.14612\nι : Type ?u.14615\nι' : Type ?u.14618\nr p q : α → α → Prop\nf g : ι → α\ns t u : Set α\na b : α\nhr : Symmetric r\n⊢ Set.Pairwise {a, b} r ↔ a ≠ b → r a b",
"tactic": "simp [pairwise_insert_of_symmetric hr... | [
200,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.comp₂Measurable_toGerm | [
{
"state_after": "no goals",
"state_before": "α : Type u_4\nβ : Type u_1\nγ : Type u_2\nδ : Type u_3\ninst✝¹⁵ : MeasurableSpace α\nμ ν : Measure α\ninst✝¹⁴ : TopologicalSpace β\ninst✝¹³ : TopologicalSpace γ\ninst✝¹² : TopologicalSpace δ\ninst✝¹¹ : PseudoMetrizableSpace β\ninst✝¹⁰ : SecondCountableTopology β... | [
413,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mem_map_iff_mem | [] | [
1466,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1464,
1
] |
Mathlib/Algebra/Group/Prod.lean | MulEquiv.coe_prodComm | [] | [
696,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
695,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.ext | [] | [
81,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.InfiniteNeg.not_infinitesimal | [] | [
494,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/Algebra/Group/WithOne/Defs.lean | WithZero.coe_zpow | [] | [
327,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Mathlib/Data/Polynomial/UnitTrinomial.lean | Polynomial.trinomial_leading_coeff' | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nk m n : ℕ\nu v w : R\nhkm : k < m\nhmn : m < n\n⊢ coeff (trinomial k m n u v w) n = w",
"tactic": "rw [trinomial_def, coeff_add, coeff_add, coeff_C_mul_X_pow, coeff_C_mul_X_pow, coeff_C_mul_X_pow,\n if_neg (hkm.trans hmn).n... | [
55,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Algebra/Order/WithZero.lean | inv_le_inv₀ | [] | [
221,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Algebra/Field/Basic.lean | one_div_add_one_div | [] | [
214,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.continuous_cos | [] | [
102,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Topology/UniformSpace/Separation.lean | UniformSpace.uniformContinuous_quotient_lift₂ | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : UniformSpace α\ninst✝¹ : UniformSpace β\ninst✝ : UniformSpace γ\nf : α → β → γ\nh : ∀ (a : α) (c : β) (b : α) (d : β), (a, b) ∈ 𝓢 α → (c, d) ∈ 𝓢 β → f a c = f b d\nhf : UniformContinuous fun p => f p.fst p.snd\n⊢ Tendsto\n (((fun x => (Quotient... | [
313,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Reflexive.lean | CategoryTheory.IsCoreflexivePair.common_retraction | [] | [
64,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.inv_eq_iff_mul_eq_one | [] | [
2179,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2177,
1
] |
Mathlib/RingTheory/ClassGroup.lean | ClassGroup.induction | [
{
"state_after": "R : Type u_1\nK : Type u_2\nL : Type ?u.669485\ninst✝¹⁰ : CommRing R\ninst✝⁹ : Field K\ninst✝⁸ : Field L\ninst✝⁷ : DecidableEq L\ninst✝⁶ : Algebra R K\ninst✝⁵ : IsFractionRing R K\ninst✝⁴ : Algebra K L\ninst✝³ : FiniteDimensional K L\ninst✝² : Algebra R L\ninst✝¹ : IsScalarTower R K L\ninst✝ :... | [
176,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.nat_lt_aleph0 | [
{
"state_after": "α β : Type u\nn : ℕ\n⊢ Nonempty (Fin (Nat.succ n) ↪ ℕ)",
"state_before": "α β : Type u\nn : ℕ\n⊢ succ ↑n ≤ ℵ₀",
"tactic": "rw [← nat_succ, ← lift_mk_fin, aleph0, lift_mk_le.{0, 0, u}]"
},
{
"state_after": "no goals",
"state_before": "α β : Type u\nn : ℕ\n⊢ Nonempty (Fin (Na... | [
1410,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1406,
1
] |
Mathlib/Order/BoundedOrder.lean | inf_eq_top_iff | [] | [
502,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/Data/Part.lean | Part.ret_eq_some | [] | [
608,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
1
] |
Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.range_coe_inter_infty | [] | [
131,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/RingTheory/WittVector/Defs.lean | WittVector.mul_coeff_zero | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nR : Type u_1\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\nx y : 𝕎 R\n⊢ coeff (x * y) 0 = coeff x 0 * coeff y 0",
"tactic": "simp [mul_coeff, peval]"
}
] | [
394,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
Std/Data/List/Lemmas.lean | List.exists_of_mem_map | [] | [
162,
82
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
162,
1
] |
Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.HomotopicRel.equivalence | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.344889\nX : Type u\nY : Type v\nZ : Type w\nZ' : Type x\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace Y\ninst✝¹ : TopologicalSpace Z\ninst✝ : TopologicalSpace Z'\nS : Set X\n⊢ ∀ {x y : C(X, Y)}, HomotopicRel x y S → HomotopicRel y x S",
... | [
701,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.coe_symm_trans | [] | [
585,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
] |
Mathlib/Combinatorics/SetFamily/LYM.lean | Finset.card_mul_le_card_shadow_mul | [
{
"state_after": "𝕜 : Type ?u.38\nα : Type u_1\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\n𝒜 : Finset (Finset α)\nr : ℕ\nh𝒜 : Set.Sized r ↑𝒜\ni : DecidableRel fun x x_1 => x ⊆ x_1 := fun x x_1 => Classical.dec ((fun x x_2 => x ⊆ x_2) x x_1)\n⊢ card 𝒜 * r ≤ card ((∂ ) 𝒜) * (... | [
89,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.onFinset_prod | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nι : Type ?u.133454\nγ : Type ?u.133457\nA : Type ?u.133460\nB : Type ?u.133463\nC : Type ?u.133466\ninst✝⁵ : AddCommMonoid A\ninst✝⁴ : AddCommMonoid B\ninst✝³ : AddCommMonoid C\nt : ι → A → C\nh0 : ∀ (i : ι), t i 0 = 0\nh1 : ∀ (i : ι) (x y : A), t ... | [
167,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.ofFn_get | [
{
"state_after": "case mk\nα : Type u_1\nl : List α\n⊢ ofFn (get { val := l, property := (_ : List.length l = List.length l) }) =\n { val := l, property := (_ : List.length l = List.length l) }",
"state_before": "n : ℕ\nα : Type u_1\nv : Vector α n\n⊢ ofFn (get v) = v",
"tactic": "rcases v with ⟨l, r... | [
152,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.ContinuousHom.monotone | [] | [
614,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
11
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.sup | [] | [
734,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
733,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.mul_single_apply | [] | [
1657,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1655,
1
] |
Mathlib/Analysis/NormedSpace/HahnBanach/Separation.lean | geometric_hahn_banach_closed_compact | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.97824\nE : Type u_1\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : AddCommGroup E\ninst✝³ : TopologicalAddGroup E\ninst✝² : Module ℝ E\ninst✝¹ : ContinuousSMul ℝ E\ns✝ t✝ : Set E\nx y : E\ninst✝ : LocallyConvexSpace ℝ E\nhs₁ : Convex ℝ s✝\nhs₂ : IsClosed s✝... | [
179,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Std/Data/Int/DivMod.lean | Int.zero_dvd | [
{
"state_after": "no goals",
"state_before": "n : Int\nx✝ : 0 ∣ n\nk : Int\ne : n = 0 * k\n⊢ n = 0",
"tactic": "rw [e, Int.zero_mul]"
}
] | [
601,
76
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
600,
11
] |
Mathlib/Algebra/CharP/CharAndCard.lean | isUnit_iff_not_dvd_char_of_ringChar_ne_zero | [
{
"state_after": "R : Type u_1\ninst✝¹ : CommRing R\np : ℕ\ninst✝ : Fact (Nat.Prime p)\nhR : ringChar R ≠ 0\nhch : ↑(ringChar R) = 0\n⊢ IsUnit ↑p ↔ ¬p ∣ ringChar R",
"state_before": "R : Type u_1\ninst✝¹ : CommRing R\np : ℕ\ninst✝ : Fact (Nat.Prime p)\nhR : ringChar R ≠ 0\n⊢ IsUnit ↑p ↔ ¬p ∣ ringChar R",
... | [
49,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
26,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Measurable.edist | [] | [
1665,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1663,
1
] |
Mathlib/Combinatorics/Additive/SalemSpencer.lean | rothNumberNat_zero | [] | [
501,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
500,
1
] |
Mathlib/Analysis/Convex/PartitionOfUnity.lean | PartitionOfUnity.finsum_smul_mem_convex | [] | [
42,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.Disjoint.zpow_disjoint_zpow | [] | [
194,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Algebra/Free.lean | FreeMagma.map_pure | [] | [
175,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.sin_eq_zero_iff_angle_eq_zero_or_angle_eq_pi | [
{
"state_after": "no goals",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\n⊢ sin (angle x y) = 0 ↔ angle x y = 0 ∨ angle x y = π",
"tactic": "rw [sin_eq_zero_iff_cos_eq, cos_eq_one_iff_angle_eq_zero, cos_eq_neg_one_iff_angle_eq_pi]"
}
] | [
367,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | UniformSpace.ball_mem_nhds | [
{
"state_after": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.59981\ninst✝ : UniformSpace α\nx : α\nV : Set (α × α)\nV_in : V ∈ 𝓤 α\n⊢ ∃ V_1, V_1 ∈ 𝓤 α ∧ ball x V_1 ⊆ ball x V",
"state_before": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.59981\ninst✝ : UniformSpace... | [
747,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
745,
1
] |
Mathlib/Data/Finmap.lean | Finmap.union_assoc | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\ns₁✝ s₂✝ s₃✝ : Finmap β\ns₁ s₂ s₃ : AList β\n⊢ ⟦s₁⟧ ∪ ⟦s₂⟧ ∪ ⟦s₃⟧ = ⟦s₁⟧ ∪ (⟦s₂⟧ ∪ ⟦s₃⟧)",
"tactic": "simp only [AList.toFinmap_eq, union_toFinmap, AList.union_assoc]"
}
] | [
619,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
617,
1
] |
Mathlib/Algebra/Jordan/Basic.lean | two_nsmul_lie_lmul_lmul_add_add_eq_zero | [
{
"state_after": "A : Type u_1\ninst✝¹ : NonUnitalNonAssocRing A\ninst✝ : IsCommJordan A\na b c : A\n⊢ 0 = 2 • (⁅↑L a, ↑L (b * c)⁆ + ⁅↑L b, ↑L (c * a)⁆ + ⁅↑L c, ↑L (a * b)⁆)",
"state_before": "A : Type u_1\ninst✝¹ : NonUnitalNonAssocRing A\ninst✝ : IsCommJordan A\na b c : A\n⊢ 2 • (⁅↑L a, ↑L (b * c)⁆ + ⁅↑L ... | [
254,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Data/Set/Function.lean | Set.EqOn.injOn_iff | [] | [
625,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
624,
1
] |
src/lean/Init/Core.lean | PUnit.eq_punit | [] | [
1064,
26
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1063,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | TotallyBounded.closure | [] | [
514,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/MeasureTheory/Covering/Differentiation.lean | VitaliFamily.ae_tendsto_lintegral_nnnorm_sub_div | [
{
"state_after": "α : Type u_2\ninst✝⁵ : MetricSpace α\nm0 : MeasurableSpace α\nμ : MeasureTheory.Measure α\nv : VitaliFamily μ\nE : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : SecondCountableTopology α\ninst✝² : BorelSpace α\ninst✝¹ : IsLocallyFiniteMeasure μ\nρ : MeasureTheory.Measure α\ninst✝ : IsLocal... | [
892,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
881,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPolynomial.coe_def | [] | [
1071,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1070,
1
] |
Std/Logic.lean | imp_congr_right | [] | [
134,
69
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
133,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.div_eq_one_iff | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.311957\nβ : Type ?u.311960\na✝ b✝ c d : ℝ≥0∞\nr p q : ℝ≥0\na b : ℝ≥0∞\nhb₀ : b ≠ 0\nhb₁ : b ≠ ⊤\nh : a / b = 1\n⊢ a = b",
"tactic": "rw [← (eq_div_iff hb₀ hb₁).mp h.symm, mul_one]"
}
] | [
1716,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1714,
1
] |
Mathlib/GroupTheory/GroupAction/FixingSubgroup.lean | fixedPoints_subgroup_antitone | [] | [
140,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.iterate_derivative_X_add_pow | [
{
"state_after": "case zero\nR : Type u\nS : Type v\nT : Type w\nι : Type y\nA : Type z\na b : R\nn✝ : ℕ\ninst✝ : CommSemiring R\nn : ℕ\nc : R\n⊢ (↑derivative^[Nat.zero]) ((X + ↑C c) ^ n) = ↑(∏ i in range Nat.zero, (n - i)) * (X + ↑C c) ^ (n - Nat.zero)\n\ncase succ\nR : Type u\nS : Type v\nT : Type w\nι : Type... | [
542,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/Data/List/Card.lean | List.card_append_disjoint | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Sort ?u.49007\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\nx✝¹ : List α\nx✝ : Disjoint [] x✝¹\n⊢ card ([] ++ x✝¹) = card [] + card x✝¹",
"tactic": "simp"
},
{
"state_after": "α : Type u_1\nβ : Sort ?u.49007\ninst✝¹ : DecidableEq ... | [
186,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/MeasureTheory/Function/L2Space.lean | MeasureTheory.Integrable.inner_const | [
{
"state_after": "α : Type u_2\nm : MeasurableSpace α\np : ℝ≥0∞\nμ : Measure α\nE : Type u_1\n𝕜 : Type u_3\ninst✝² : IsROrC 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : InnerProductSpace 𝕜 E\nf : α → E\nhf : Memℒp f 1\nc : E\n⊢ Memℒp (fun x => inner (f x) c) 1",
"state_before": "α : Type u_2\nm : Measurable... | [
93,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_lt_integral_of_ae_le_of_measure_setOf_lt_ne_zero | [
{
"state_after": "ι : Type ?u.20041361\n𝕜 : Type ?u.20041364\nE : Type ?u.20041367\nF : Type ?u.20041370\nA : Type ?u.20041373\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\nf g : ℝ → ℝ\na b : ℝ\nμ : MeasureTheory.Measure ℝ\nhab : a ≤ b\nhfi : IntervalIntegrable f μ a b\nhgi... | [
1334,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1326,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.mem_sup_iff | [] | [
733,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
732,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Adj.reachable | [] | [
1865,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1864,
11
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.comp_id | [] | [
797,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
] |
Mathlib/Topology/Sheaves/SheafCondition/PairwiseIntersections.lean | TopCat.Sheaf.interUnionPullbackCone_fst | [] | [
334,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/MeasureTheory/Function/Egorov.lean | MeasureTheory.Egorov.iUnionNotConvergentSeq_measurableSet | [] | [
147,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/MeasureTheory/Function/SpecialFunctions/IsROrC.lean | IsROrC.measurable_im | [] | [
35,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | AddValuation.IsEquiv.symm | [] | [
833,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
832,
1
] |
src/lean/Init/Core.lean | Iff.symm | [] | [
672,
35
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
671,
1
] |
Mathlib/Data/Set/Basic.lean | Set.union_right_comm | [] | [
795,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.diff_null | [
{
"state_after": "α : Type u_1\nβ : Type ?u.20498\nR : Type ?u.20501\nR' : Type ?u.20504\nms : Set (OuterMeasure α)\nm✝ m : OuterMeasure α\ns t : Set α\nht : ↑m t = 0\n⊢ ↑m s ≤ ↑m (s \\ t)",
"state_before": "α : Type u_1\nβ : Type ?u.20498\nR : Type ?u.20501\nR' : Type ?u.20504\nms : Set (OuterMeasure α)\nm... | [
232,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Data/PFun.lean | PFun.prodMap_comp_comp | [] | [
710,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
705,
1
] |
Mathlib/GroupTheory/Torsion.lean | isTorsion_of_finite | [] | [
154,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Algebra/Group/Basic.lean | eq_one_div_of_mul_eq_one_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.22415\nG : Type ?u.22418\ninst✝ : DivisionMonoid α\na b c : α\nh : a * b = 1\n⊢ b = 1 / a",
"tactic": "rw [eq_inv_of_mul_eq_one_right h, one_div]"
}
] | [
385,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
1
] |
Std/Data/Int/Lemmas.lean | Int.mul_eq_zero | [
{
"state_after": "no goals",
"state_before": "a b : Int\nh : a * b = 0\n⊢ a = 0 ∨ b = 0",
"tactic": "exact match Int.lt_trichotomy a 0, Int.lt_trichotomy b 0 with\n| .inr (.inl heq₁), _ => .inl heq₁\n| _, .inr (.inl heq₂) => .inr heq₂\n| .inl hlt₁, .inl hlt₂ => absurd h <| Int.ne_of_gt <| Int.mul_pos_of... | [
1304,
92
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1296,
11
] |
Mathlib/Data/Setoid/Partition.lean | Setoid.IsPartition.sUnion_eq_univ | [
{
"state_after": "α : Type u_1\nc : Set (Set α)\nhc : IsPartition c\nx : α\nt : Set α\nht : (∃ x_1, x ∈ t) ∧ ∀ (y : Set α), (∃ x_1, x ∈ y) → y = t\n⊢ t ∈ c ∧ x ∈ t",
"state_before": "α : Type u_1\nc : Set (Set α)\nhc : IsPartition c\nx : α\nt : Set α\nht : (fun b => ∃! x_1, x ∈ b) t ∧ ∀ (y : Set α), (fun b ... | [
234,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.Principal.iterate_lt | [
{
"state_after": "case zero\nop : Ordinal → Ordinal → Ordinal\na o : Ordinal\nhao : a < o\nho : Principal op o\n⊢ (op a^[Nat.zero]) a < o\n\ncase succ\nop : Ordinal → Ordinal → Ordinal\na o : Ordinal\nhao : a < o\nho : Principal op o\nn : ℕ\nhn : (op a^[n]) a < o\n⊢ (op a^[Nat.succ n]) a < o",
"state_before... | [
77,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Data/Dfinsupp/Multiset.lean | Multiset.toDfinsupp_le_toDfinsupp | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : α → Type ?u.75810\ninst✝ : DecidableEq α\ns t : Multiset α\n⊢ ↑toDfinsupp s ≤ ↑toDfinsupp t ↔ s ≤ t",
"tactic": "simp [Multiset.le_iff_count, Dfinsupp.le_def]"
}
] | [
107,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.comp_continuousOn_iff | [] | [
681,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
1
] |
Mathlib/Algebra/Lie/Basic.lean | lie_skew | [
{
"state_after": "R : Type u\nL : Type v\nM : Type w\nN : Type w₁\ninst✝¹⁰ : CommRing R\ninst✝⁹ : LieRing L\ninst✝⁸ : LieAlgebra R L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\ninst✝¹ : LieRingModule L N\ninst... | [
161,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | norm_fst_le | [] | [
2381,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2380,
1
] |
Mathlib/Data/Fintype/Card.lean | Infinite.nonempty | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.67178\nβ : Type ?u.67181\nγ : Type ?u.67184\nα : Type u_1\ninst✝ : Infinite α\n⊢ Nonempty α",
"tactic": "infer_instance"
}
] | [
1010,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1010,
11
] |
Mathlib/Data/Option/Defs.lean | Option.mem_toList | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.3576\na : α\no : Option α\n⊢ a ∈ toList o ↔ a ∈ o",
"tactic": "cases o <;> simp [toList, eq_comm]"
}
] | [
110,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Algebra/Hom/Equiv/Units/Basic.lean | Equiv.divRight_eq_mulRight_inv | [] | [
225,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | Ideal.Quotient.algHom_ext | [] | [
193,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
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