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/LinearAlgebra/AffineSpace/MidpointZero.lean | homothety_inv_two | [] | [
45,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/GroupTheory/Abelianization.lean | card_commutatorSet_closureCommutatorRepresentatives | [
{
"state_after": "G : Type u\ninst✝ : Group G\n⊢ Nat.card ↑(commutatorSet { x // x ∈ closureCommutatorRepresentatives G }) =\n Nat.card\n ↑(↑(Subgroup.subtype (closureCommutatorRepresentatives G)) ''\n commutatorSet { x // x ∈ closureCommutatorRepresentatives G })",
"state_before": "G : Typ... | [
310,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Analysis/Calculus/Conformal/InnerProduct.lean | conformalFactorAt_pos | [] | [
53,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Data/Set/Intervals/WithBotTop.lean | WithBot.image_coe_Iio | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : PartialOrder α\na b : α\n⊢ some '' Iio a = Ioo ⊥ ↑a",
"tactic": "rw [← preimage_coe_Iio, image_preimage_eq_inter_range, range_coe, inter_comm, Ioi_inter_Iio]"
}
] | [
199,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Algebra/Group/Conj.lean | ConjClasses.mk_bijective | [] | [
265,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Aesop/BuiltinRules.lean | Aesop.BuiltinRules.empty_false | [] | [
46,
53
] | ca73109cc40837bc61df8024c9016da4b4f99d4c | https://github.com/JLimperg/aesop | [
46,
1
] |
Mathlib/GroupTheory/Complement.lean | Subgroup.IsComplement'.card_mul | [] | [
525,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_int_mul_two_pi | [] | [
351,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/Data/Polynomial/IntegralNormalization.lean | Polynomial.integralNormalization_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝ : Semiring R\n⊢ integralNormalization 0 = 0",
"tactic": "simp [integralNormalization]"
}
] | [
48,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Algebra/Tropical/BigOperators.lean | List.trop_minimum | [
{
"state_after": "case nil\nR : Type u_1\nS : Type ?u.18757\ninst✝ : LinearOrder R\n⊢ trop (minimum []) = sum (map (trop ∘ WithTop.some) [])\n\ncase cons\nR : Type u_1\nS : Type ?u.18757\ninst✝ : LinearOrder R\nhd : R\ntl : List R\nIH : trop (minimum tl) = sum (map (trop ∘ WithTop.some) tl)\n⊢ trop (minimum (hd... | [
87,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Order/SymmDiff.lean | symmDiff_eq_top | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.89407\nα : Type u_1\nβ : Type ?u.89413\nπ : ι → Type ?u.89418\ninst✝ : BooleanAlgebra α\na b c d : α\n⊢ a ∆ b = ⊤ ↔ IsCompl a b",
"tactic": "rw [symmDiff_eq', ← compl_inf, inf_eq_top_iff, compl_eq_top, isCompl_iff, disjoint_iff,\n codisjoint_iff... | [
759,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
757,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_smul_real_right | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1390293\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx y : E\nr : ℝ\n⊢ ↑r * inner x y = ↑(algebraMap ℝ 𝕜) r * inner x y",
"... | [
498,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.map_congr | [] | [
1878,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1877,
1
] |
Mathlib/Data/Option/Basic.lean | Option.liftOrGet_choice | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.17342\nγ : Type ?u.17345\nδ : Type ?u.17348\nf : α → α → α\nh : ∀ (a b : α), f a b = a ∨ f a b = b\na b : α\n⊢ liftOrGet f (some a) (some b) = some a ∨ liftOrGet f (some a) (some b) = some b",
"tactic": "simpa [liftOrGet] using h a ... | [
327,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/Topology/Algebra/Order/MonotoneContinuity.lean | OrderIso.coe_toHomeomorph | [] | [
327,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Mathlib/Algebra/Group/Basic.lean | bit0_add | [] | [
134,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.rank_eq_rank_subalgebra | [] | [
684,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
683,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.node4L_lemma₂ | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.281928\ninst✝ : Preorder α\nb c d : ℕ\nmr₂ : b + c + 1 ≤ 3 * d\n⊢ c ≤ 3 * d",
"tactic": "linarith"
}
] | [
1146,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1146,
1
] |
Mathlib/Data/Set/Image.lean | Set.mem_image_iff_bex | [] | [
208,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.norm_const_le | [] | [
867,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
866,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.integral_Ioi_of_hasDerivAt_of_tendsto' | [
{
"state_after": "E : Type u_1\nf f' : ℝ → E\ng g' : ℝ → ℝ\na b l : ℝ\nm : E\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nhderiv : ∀ (x : ℝ), x ∈ Ici a → HasDerivAt f (f' x) x\nf'int : IntegrableOn f' (Ioi a)\nhf : Tendsto f atTop (𝓝 m)\nx : ℝ\nhx : x ∈ Ici a\n⊢ Continuous... | [
696,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/Data/Int/ConditionallyCompleteOrder.lean | Int.csInf_mem | [
{
"state_after": "case h.e'_4\ns : Set ℤ\nh1 : Set.Nonempty s\nh2 : BddBelow s\n⊢ sInf s = ↑(leastOfBdd (choose h2) (_ : choose h2 ∈ lowerBounds s) h1)",
"state_before": "s : Set ℤ\nh1 : Set.Nonempty s\nh2 : BddBelow s\n⊢ sInf s ∈ s",
"tactic": "convert (leastOfBdd _ (Classical.choose_spec h2) h1).2.1"
... | [
106,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Topology/MetricSpace/MetricSeparated.lean | IsMetricSeparated.union_left | [
{
"state_after": "case intro.intro.intro.intro\nX : Type u_1\ninst✝ : EMetricSpace X\ns t : Set X\nx y : X\ns' : Set X\nr : ENNReal\nr0 : r ≠ 0\nhr : ∀ (x : X), x ∈ s → ∀ (y : X), y ∈ t → r ≤ edist x y\nr' : ENNReal\nr0' : r' ≠ 0\nhr' : ∀ (x : X), x ∈ s' → ∀ (y : X), y ∈ t → r' ≤ edist x y\n⊢ IsMetricSeparated ... | [
88,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConvexOn.translate_left | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.131601\nα : Type ?u.131604\nβ : Type u_3\nι : Type ?u.131610\ninst✝⁶ : OrderedSemiring 𝕜\ninst✝⁵ : AddCommMonoid E\ninst✝⁴ : AddCommMonoid F\ninst✝³ : OrderedAddCommMonoid α\ninst✝² : OrderedAddCommMonoid β\ninst✝¹ : Mod... | [
298,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Data/Set/Image.lean | Set.Nonempty.image_const | [] | [
351,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/CategoryTheory/Generator.lean | CategoryTheory.thin_of_isCoseparating_empty | [] | [
232,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Data/List/Basic.lean | List.mem_map_of_injective | [] | [
131,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean | SimpleGraph.ComponentCompl.pairwise_disjoint | [
{
"state_after": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nC D : ComponentCompl G K\nne : C ≠ D\n⊢ Disjoint ↑C ↑D",
"state_before": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\n⊢ Pairwise fun C D => Disjoint ↑C ↑D",
"tactic": "rintro C D ne"
},
{
"state_after": "V : Type u\nG : Simp... | [
138,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
11
] |
Mathlib/Data/Set/Basic.lean | Set.insert_union_distrib | [] | [
1212,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1211,
1
] |
Mathlib/Algebra/Hom/Units.lean | IsUnit.inv_mul_cancel_left | [] | [
297,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
11
] |
Mathlib/Data/Real/Sign.lean | Real.sign_inv | [
{
"state_after": "case inl\nr : ℝ\nhn : r < 0\n⊢ sign r⁻¹ = sign r\n\ncase inr.inl\n\n⊢ sign 0⁻¹ = sign 0\n\ncase inr.inr\nr : ℝ\nhp : 0 < r\n⊢ sign r⁻¹ = sign r",
"state_before": "r : ℝ\n⊢ sign r⁻¹ = sign r",
"tactic": "obtain hn | rfl | hp := lt_trichotomy r (0 : ℝ)"
},
{
"state_after": "no go... | [
123,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Order/Antichain.lean | IsAntichain.to_dual | [] | [
189,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Analysis/Calculus/Deriv/Add.lean | HasDerivWithinAt.add_const | [] | [
98,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
8
] |
Mathlib/Computability/Reduce.lean | manyOneReducible_toNat_toNat | [] | [
353,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/Data/Complex/Determinant.lean | Complex.linearEquiv_det_conjAe | [
{
"state_after": "no goals",
"state_before": "⊢ ↑LinearEquiv.det (AlgEquiv.toLinearEquiv conjAe) = -1",
"tactic": "rw [← Units.eq_iff, LinearEquiv.coe_det, AlgEquiv.toLinearEquiv_toLinearMap, det_conjAe,\n Units.coe_neg_one]"
}
] | [
36,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Std/Data/List/Lemmas.lean | List.cons_diff_of_not_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\na : α\nl₂ : List α\nh : ¬a ∈ l₂\nl₁ : List α\n⊢ List.diff (a :: l₁) l₂ = a :: List.diff l₁ l₂",
"tactic": "rw [cons_diff, if_neg h]"
}
] | [
1516,
71
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1515,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.image_mul_left | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.121388\nα : Type u_1\nβ : Type ?u.121394\nγ : Type ?u.121397\ninst✝ : Group α\ns t : Set α\na b : α\n⊢ (fun x x_1 => x * x_1) a '' t = (fun x x_1 => x * x_1) a⁻¹ ⁻¹' t",
"tactic": "rw [image_eq_preimage_of_inverse] <;> intro c <;> simp"
}
] | [
1200,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1199,
1
] |
Mathlib/Topology/Instances/RealVectorSpace.lean | AddMonoidHom.coe_toRealLinearMap | [] | [
45,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/Data/Real/Basic.lean | Real.ind_mk | [
{
"state_after": "case ofCauchy\nx✝ y : ℝ\nC : ℝ → Prop\nh : ∀ (y : CauSeq ℚ abs), C (mk y)\nx : Cauchy abs\n⊢ C { cauchy := x }",
"state_before": "x✝ y : ℝ\nC : ℝ → Prop\nx : ℝ\nh : ∀ (y : CauSeq ℚ abs), C (mk y)\n⊢ C x",
"tactic": "cases' x with x"
},
{
"state_after": "case ofCauchy.h\nx✝ y : ... | [
366,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
11
] |
Mathlib/Algebra/MonoidAlgebra/Degree.lean | AddMonoidAlgebra.le_inf_support_add | [] | [
57,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Data/Part.lean | Part.left_dom_of_div_dom | [] | [
763,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
763,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.exists_of_lt_mex | [
{
"state_after": "α : Type ?u.376990\nβ : Type ?u.376993\nγ : Type ?u.376996\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nι : Type u_1\nf : ι → Ordinal\na : Ordinal\nha : a < mex f\nha' : ∀ (i : ι), f i ≠ a\n⊢ False",
"state_before": "α : Type ?u.376990\nβ : Type ?u.376993\nγ : Type ?u.376996\nr :... | [
2031,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2029,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.prod.leftUnitor_hom_naturality | [] | [
1077,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1075,
1
] |
Mathlib/CategoryTheory/Arrow.lean | CategoryTheory.Arrow.hom.congr_left | [
{
"state_after": "no goals",
"state_before": "T : Type u\ninst✝ : Category T\nf g : Arrow T\nφ₁ φ₂ : f ⟶ g\nh : φ₁ = φ₂\n⊢ φ₁.left = φ₂.left",
"tactic": "rw [h]"
}
] | [
166,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiff_top_iff_fderiv | [
{
"state_after": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nX : Type uX\ninst✝¹ : NormedAdd... | [
1686,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1683,
1
] |
Mathlib/RingTheory/Polynomial/Pochhammer.lean | pochhammer_nat_eq_descFactorial | [
{
"state_after": "case zero\nS : Type u\ninst✝ : Semiring S\na : ℕ\n⊢ eval a (pochhammer ℕ Nat.zero) = Nat.descFactorial (a + Nat.zero - 1) Nat.zero\n\ncase succ\nS : Type u\ninst✝ : Semiring S\na b : ℕ\n⊢ eval a (pochhammer ℕ (Nat.succ b)) = Nat.descFactorial (a + Nat.succ b - 1) (Nat.succ b)",
"state_befo... | [
164,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.type_subrel_lt | [
{
"state_after": "α : Type ?u.105581\nβ : Type ?u.105584\nγ : Type ?u.105587\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no : Ordinal\n⊢ ∀ (a : WellOrder),\n type (Subrel (fun x x_1 => x < x_1) {o' | o' < Quotient.mk isEquivalent a}) = lift (Quotient.mk isEquivalent a)",
"state_before": "α : Ty... | [
385,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/CategoryTheory/Subobject/FactorThru.lean | CategoryTheory.Subobject.factors_iff | [] | [
89,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | HasDerivWithinAt.mono | [] | [
367,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.subset_iff | [] | [
375,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Logic/Function/Iterate.lean | Function.Commute.comp_iterate | [
{
"state_after": "case zero\nα : Type u\nβ : Type v\nf g : α → α\nh : Commute f g\n⊢ (f ∘ g)^[Nat.zero] = f^[Nat.zero] ∘ g^[Nat.zero]\n\ncase succ\nα : Type u\nβ : Type v\nf g : α → α\nh : Commute f g\nn : ℕ\nihn : (f ∘ g)^[n] = f^[n] ∘ g^[n]\n⊢ (f ∘ g)^[Nat.succ n] = f^[Nat.succ n] ∘ g^[Nat.succ n]",
"stat... | [
149,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean | isLittleO_log_rpow_atTop | [] | [
290,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.choose_succ_self_right | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ choose (n + 1 + 1) (n + 1) = n + 1 + 1",
"tactic": "rw [choose_succ_succ, choose_succ_self_right n, choose_self]"
}
] | [
224,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Algebra/Star/Unitary.lean | unitary.star_mem | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹ : Monoid R\ninst✝ : StarSemigroup R\nU : R\nhU : U ∈ unitary R\n⊢ star (star U) * star U = 1",
"tactic": "rw [star_star, mul_star_self_of_mem hU]"
},
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹ : Monoid... | [
70,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.isRight_inl | [] | [
106,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
9
] |
Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | ContDiffWithinAt.exp | [] | [
274,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | LinearMap.rank_comp_le_right | [
{
"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.1132953\ninst✝¹⁰ : Ring K\ninst✝⁹ : AddCommGroup V\ninst✝⁸ : Module K V\ninst✝⁷ : AddCommGroup V₁\ninst✝⁶ : Module K V₁\ninst✝⁵ : AddCommGr... | [
1354,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1353,
1
] |
Mathlib/Analysis/Calculus/Dslope.lean | dslope_eventuallyEq_slope_of_ne | [] | [
63,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | padicNormE.eq_of_norm_add_lt_right | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nz1 z2 : ℚ_[p]\nh : ‖z1 + z2‖ < ‖z2‖\nhne : ¬‖z1‖ = ‖z2‖\n⊢ max ‖z1‖ ‖z2‖ ≥ ‖z2‖",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nz1 z2 : ℚ_[p]\nh : ‖z1 + z2‖ < ‖z2‖\nhne : ¬‖z1‖ = ‖z2‖\n⊢ ‖z1 + z2‖ ≥ ‖z2‖",
"tactic": "rw [padicNormE.add_eq_max_of_ne hn... | [
952,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
950,
1
] |
Mathlib/Topology/Basic.lean | Continuous.comp | [] | [
1638,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1636,
1
] |
Mathlib/CategoryTheory/Abelian/LeftDerived.lean | CategoryTheory.Abelian.Functor.exact_of_map_projectiveResolution | [
{
"state_after": "C : Type u\ninst✝⁵ : Category C\nD : Type u\ninst✝⁴ : Category D\nF : C ⥤ D\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\ninst✝³ : Abelian C\ninst✝² : Abelian D\ninst✝¹ : Functor.Additive F\nP : ProjectiveResolution X\ninst✝ : PreservesFiniteColimits F\n⊢ HomologicalComplex.d ((mapHomologicalComplex F (Co... | [
68,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Std/Data/String/Lemmas.lean | String.extract.go₂_add_right_cancel | [
{
"state_after": "case ind\ns : List Char\ni e n : Nat\n⊢ ∀ (c : Char) (cs : List Char) (i : Pos),\n ¬i = { byteIdx := e } →\n go₂ cs { byteIdx := i.byteIdx + csize c + n } { byteIdx := e + n } = go₂ cs (i + c) { byteIdx := e } →\n (if { byteIdx := i.byteIdx + n } = { byteIdx := e + n } then []\n... | [
395,
11
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
387,
1
] |
Mathlib/MeasureTheory/Category/MeasCat.lean | MeasCat.coe_of | [] | [
65,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSpace.generateFrom_singleton_univ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.21280\nγ : Type ?u.21283\nδ : Type ?u.21286\nδ' : Type ?u.21289\nι : Sort ?u.21292\ns t u : Set α\n⊢ ∀ (t : Set α), t ∈ {univ} → MeasurableSet t",
"tactic": "simp"
}
] | [
448,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsGreatest.isGreatest_image2_of_isLeast | [] | [
1442,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1439,
1
] |
Mathlib/Algebra/Order/Archimedean.lean | archimedean_iff_int_le | [] | [
357,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.toNat_le_iff_le_of_lt_aleph0 | [
{
"state_after": "no goals",
"state_before": "α β : Type u\nc d : Cardinal\nhc : c < ℵ₀\nhd : d < ℵ₀\n⊢ ↑toNat c ≤ ↑toNat d ↔ c ≤ d",
"tactic": "rw [← natCast_le, cast_toNat_of_lt_aleph0 hc, cast_toNat_of_lt_aleph0 hd]"
}
] | [
1695,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1693,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.seq_destruct_cons | [] | [
649,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
1
] |
Mathlib/Data/Nat/Choose/Central.lean | Nat.four_pow_lt_mul_centralBinom | [
{
"state_after": "case h\nn✝ : ℕ\nn_big✝ : 4 ≤ n✝\nn : ℕ\nIH : ∀ (m : ℕ), m < n → 4 ≤ m → 4 ^ m < m * centralBinom m\nn_big : 4 ≤ n\n⊢ 4 ^ n < n * centralBinom n",
"state_before": "n : ℕ\nn_big : 4 ≤ n\n⊢ 4 ^ n < n * centralBinom n",
"tactic": "induction' n using Nat.strong_induction_on with n IH"
},
... | [
100,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Topology/ContinuousOn.lean | eventually_mem_of_tendsto_nhdsWithin | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.188629\nδ : Type ?u.188632\ninst✝ : TopologicalSpace α\nf : β → α\na : α\ns : Set α\nl : Filter β\nh : ∀ (i : Set α), a ∈ i ∧ IsOpen i → (∀ᶠ (x : β) in l, f x ∈ i) ∧ ∀ᶠ (x : β) in l, f x ∈ s\n⊢ ∀ᶠ (i : β) in l, f i ∈ s",
"state_before": "α : Type u_1... | [
385,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.nat_cast_mul | [
{
"state_after": "no goals",
"state_before": "m : ℕ\n⊢ ↑(m * 0) = ↑m * ↑0",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "m n : ℕ\n⊢ ↑(m * (n + 1)) = ↑m * ↑(n + 1)",
"tactic": "rw [Nat.mul_succ, Nat.cast_add, nat_cast_mul m n, Nat.cast_succ, mul_add_one]"
}
] | [
2301,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2299,
1
] |
Mathlib/Topology/Algebra/WithZeroTopology.lean | WithZeroTopology.tendsto_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nγ γ₁ γ₂ : Γ₀\nl : Filter α\nf : α → Γ₀\n⊢ Tendsto f l (𝓝 0) ↔ ∀ (γ₀ : Γ₀), γ₀ ≠ 0 → ∀ᶠ (x : α) in l, f x < γ₀",
"tactic": "simp [nhds_zero]"
}
] | [
82,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Data/Rat/NNRat.lean | NNRat.bddBelow_coe | [] | [
309,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/Init/Propext.lean | imp_congr_ctx_eq | [] | [
23,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
22,
1
] |
Std/Data/List/Lemmas.lean | List.isSuffix.sublist | [] | [
1613,
20
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1612,
11
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.C_inv | [
{
"state_after": "case inl\nσ : Type u_1\nR : Type ?u.1971115\nk : Type u_2\ninst✝ : Field k\n⊢ (↑(C σ k) 0)⁻¹ = ↑(C σ k) 0⁻¹\n\ncase inr\nσ : Type u_1\nR : Type ?u.1971115\nk : Type u_2\ninst✝ : Field k\nr : k\nhr : r ≠ 0\n⊢ (↑(C σ k) r)⁻¹ = ↑(C σ k) r⁻¹",
"state_before": "σ : Type u_1\nR : Type ?u.1971115... | [
1034,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1030,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Group.lean | le_ciInf_mul_ciInf | [] | [
58,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/NumberTheory/Padics/PadicNorm.lean | padicNorm.of_int | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nz : ℤ\nhz : z = 0\n⊢ padicNorm p ↑z ≤ 1",
"tactic": "simp [hz, zero_le_one]"
},
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nz : ℤ\nhz : ¬z = 0\n⊢ (if ↑z = 0 then 0 else ↑p ^ (-padicValRat p ↑z)) ≤ 1",
"state_... | [
181,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
11
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | ContDiffAt.rpow_const_of_le | [
{
"state_after": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf g : E → ℝ\nf' g' : E →L[ℝ] ℝ\nx : E\ns : Set E\nc p : ℝ\nn : ℕ∞\nm : ℕ\nhf : ContDiffWithinAt ℝ (↑m) f Set.univ x\nh : ↑m ≤ p\n⊢ ContDiffWithinAt ℝ (↑m) (fun x => f x ^ p) Set.univ x",
"state_before": "E : Type u_1\nin... | [
548,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
] |
Mathlib/Analysis/InnerProductSpace/Dual.lean | InnerProductSpace.toDualMap_apply | [] | [
75,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.one_nadd | [
{
"state_after": "no goals",
"state_before": "a b c : Ordinal\n⊢ 1 ♯ a = succ a",
"tactic": "rw [nadd_comm, nadd_one]"
}
] | [
306,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Topology/Algebra/GroupCompletion.lean | AddMonoidHom.extension_coe | [] | [
259,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.Bounded.isCompact_closure | [] | [
2522,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2521,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisInsertion.isGLB_of_u_image | [] | [
610,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
1
] |
Mathlib/MeasureTheory/Measure/MutuallySingular.lean | MeasureTheory.Measure.MutuallySingular.sum_left | [
{
"state_after": "α : Type u_2\nm0 : MeasurableSpace α\nμ✝ μ₁ μ₂ ν ν₁ ν₂ : Measure α\nι : Type u_1\ninst✝ : Countable ι\nμ : ι → Measure α\nH : ∀ (i : ι), μ i ⟂ₘ ν\n⊢ sum μ ⟂ₘ ν",
"state_before": "α : Type u_2\nm0 : MeasurableSpace α\nμ✝ μ₁ μ₂ ν ν₁ ν₂ : Measure α\nι : Type u_1\ninst✝ : Countable ι\nμ : ι → ... | [
95,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Topology/Algebra/Order/Field.lean | tendsto_inv_atTop_zero' | [
{
"state_after": "𝕜 : Type u_1\nα : Type ?u.26472\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf g : α → 𝕜\n⊢ ∀ (ib : 𝕜), ib ∈ Ioi 0 → ∃ ia, True ∧ ∀ (x : 𝕜), x ∈ Ici ia → x⁻¹ ∈ Ioc 0 ib",
"state_before": "𝕜 : Type u_1\nα : Type ?u.26472\ninst✝²... | [
136,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
src/lean/Init/SimpLemmas.lean | dite_true | [] | [
79,
111
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
79,
9
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_iUnion_toMeasurable | [] | [
364,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_pow_le | [
{
"state_after": "case zero\nR : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np✝ q : R[X]\nι : Type ?u.695996\np : R[X]\n⊢ natDegree (p ^ Nat.zero) ≤ Nat.zero * natDegree p\n\ncase succ\nR : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np✝ q : R[X]\nι : Type ?u.695996\np : R[X]\... | [
1042,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1037,
1
] |
Mathlib/Topology/Instances/AddCircle.lean | AddCircle.coe_sub | [] | [
167,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.not_dvd_of_natDegree_lt | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : Semiring R\ninst✝ : NoZeroDivisors R\np✝ q✝ p q : R[X]\nh0 : q ≠ 0\nhl : natDegree q < natDegree p\nhcontra : p ∣ q\n⊢ False",
"state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : Semiring R\ninst✝ : NoZe... | [
199,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | MeasureTheory.Measure.add_haar_preimage_continuousLinearEquiv | [] | [
286,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | one_div_le_neg_one | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.182424\nα : Type u_1\nβ : Type ?u.182430\ninst✝ : LinearOrderedField α\na b c d : α\nn : ℤ\nh1 : a < 0\nh2 : -1 ≤ a\nthis : 1 / a ≤ 1 / -1\n⊢ 1 / a ≤ -1",
"tactic": "rwa [one_div_neg_one_eq_neg_one] at this"
}
] | [
901,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
899,
1
] |
Mathlib/Topology/Homotopy/Path.lean | Path.Homotopy.symm_symm | [] | [
120,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Data/Finsupp/Interval.lean | Finsupp.card_Ioc | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : Type u_2\ninst✝² : PartialOrder α\ninst✝¹ : Zero α\ninst✝ : LocallyFiniteOrder α\nf g : ι →₀ α\n⊢ card (Ioc f g) = ∏ i in f.support ∪ g.support, card (Icc (↑f i) (↑g i)) - 1",
"tactic": "rw [card_Ioc_eq_card_Icc_sub_one, card_Icc]"
}
] | [
121,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Term.realize_functions_apply₁ | [
{
"state_after": "L : Language\nL' : Language\nM : Type w\nN : Type ?u.5630\nP : Type ?u.5633\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nf : Functions L 1\nt : Term L α\nv : α → M\n⊢ (funMap f fun i => realize v (Matrix.vecCons t ![] i)) = funMap f ![realiz... | [
117,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/GroupTheory/GroupAction/Defs.lean | smul_inv' | [] | [
1059,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1058,
1
] |
Mathlib/Data/Polynomial/Div.lean | Polynomial.divByMonic_mul_pow_rootMultiplicity_eq | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na✝ b : R\nn : ℕ\ninst✝ : CommRing R\np✝ q p : R[X]\na : R\nthis : Monic ((X - ↑C a) ^ rootMultiplicity a p)\n⊢ p /ₘ (X - ↑C a) ^ rootMultiplicity a p * (X - ↑C a) ^ rootMultiplicity a p = p",
"state_before": "R : Type u\nS : Type v\nT : Type ... | [
600,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
594,
1
] |
Mathlib/Order/Bounds/Basic.lean | isGLB_empty_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ns t : Set α\na b : α\n⊢ IsGLB ∅ a ↔ IsTop a",
"tactic": "simp [IsGLB]"
}
] | [
884,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
883,
9
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.set_index_subset | [] | [
313,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.