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Found 184 definitions mentioning Differentiable. Of these, 115 match your pattern(s).
- differentiable_id Mathlib.Analysis.Calculus.FDeriv.Basic
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E], Differentiable π id - differentiable_id' Mathlib.Analysis.Calculus.FDeriv.Basic
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E], Differentiable π fun x => x - differentiable_const Mathlib.Analysis.Calculus.FDeriv.Basic
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace π F] (c : F), Differentiable π fun x => c - IsBoundedLinearMap.differentiable Mathlib.Analysis.Calculus.FDeriv.Linear
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace π F] {f : E β F}, IsBoundedLinearMap π f β Differentiable π f - ContinuousLinearMap.differentiable Mathlib.Analysis.Calculus.FDeriv.Linear
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace π F] (e : E βL[π] F), Differentiable π βe - Differentiable.iterate Mathlib.Analysis.Calculus.FDeriv.Comp
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {f : E β E}, Differentiable π f β β (n : β), Differentiable π f^[n] - Differentiable.comp Mathlib.Analysis.Calculus.FDeriv.Comp
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace π F] {G : Type u_4} [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace π G] {f : E β F} {g : F β G}, Differentiable π g β Differentiable π f β Differentiable π (g β f) - differentiable_fst Mathlib.Analysis.Calculus.FDeriv.Prod
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace π F], Differentiable π Prod.fst - differentiable_snd Mathlib.Analysis.Calculus.FDeriv.Prod
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace π F], Differentiable π Prod.snd - differentiable_apply Mathlib.Analysis.Calculus.FDeriv.Prod
β {π : Type u_1} [inst : NontriviallyNormedField π] {ΞΉ : Type u_6} [inst_1 : Fintype ΞΉ] {F' : ΞΉ β Type u_7} [inst_2 : (i : ΞΉ) β NormedAddCommGroup (F' i)] [inst_3 : (i : ΞΉ) β NormedSpace π (F' i)] (i : ΞΉ), Differentiable π fun f => f i - Differentiable.fst Mathlib.Analysis.Calculus.FDeriv.Prod
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace π F] {G : Type u_4} [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace π G] {fβ : E β F Γ G}, Differentiable π fβ β Differentiable π fun x => (fβ x).1 - Differentiable.snd Mathlib.Analysis.Calculus.FDeriv.Prod
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace π F] {G : Type u_4} [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace π G] {fβ : E β F Γ G}, Differentiable π fβ β Differentiable π fun x => (fβ x).2 - differentiable_pi'' Mathlib.Analysis.Calculus.FDeriv.Prod
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {ΞΉ : Type u_6} [inst_3 : Fintype ΞΉ] {F' : ΞΉ β Type u_7} [inst_4 : (i : ΞΉ) β NormedAddCommGroup (F' i)] [inst_5 : (i : ΞΉ) β NormedSpace π (F' i)] {Ξ¦ : E β (i : ΞΉ) β F' i}, (β (i : ΞΉ), Differentiable π fun x => Ξ¦ x i) β Differentiable π Ξ¦ - Differentiable.prod Mathlib.Analysis.Calculus.FDeriv.Prod
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace π F] {G : Type u_4} [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace π G] {fβ : E β F} {fβ : E β G}, Differentiable π fβ β Differentiable π fβ β Differentiable π fun x => (fβ x, fβ x) - LinearIsometryEquiv.differentiable Mathlib.Analysis.Calculus.FDeriv.Equiv
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace π F] (iso : E ββα΅’[π] F), Differentiable π βiso - ContinuousLinearEquiv.differentiable Mathlib.Analysis.Calculus.FDeriv.Equiv
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace π F] (iso : E βL[π] F), Differentiable π βiso - IsBoundedBilinearMap.differentiable Mathlib.Analysis.Calculus.FDeriv.Bilinear
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace π F] {G : Type u_4} [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace π G] {b : E Γ F β G}, IsBoundedBilinearMap π b β Differentiable π b - Differentiable.const_mul Mathlib.Analysis.Calculus.FDeriv.Mul
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {πΈ : Type u_6} [inst_3 : NormedRing πΈ] [inst_4 : NormedAlgebra π πΈ] {a : E β πΈ}, Differentiable π a β β (b : πΈ), Differentiable π fun y => b * a y - Differentiable.mul_const Mathlib.Analysis.Calculus.FDeriv.Mul
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {πΈ : Type u_6} [inst_3 : NormedRing πΈ] [inst_4 : NormedAlgebra π πΈ] {a : E β πΈ}, Differentiable π a β β (b : πΈ), Differentiable π fun y => a y * b - Differentiable.pow Mathlib.Analysis.Calculus.FDeriv.Mul
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {πΈ : Type u_6} [inst_3 : NormedRing πΈ] [inst_4 : NormedAlgebra π πΈ] {a : E β πΈ}, Differentiable π a β β (n : β), Differentiable π fun x => a x ^ n - Differentiable.inverse Mathlib.Analysis.Calculus.FDeriv.Mul
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {R : Type u_6} [inst_3 : NormedRing R] [inst_4 : NormedAlgebra π R] [inst_5 : CompleteSpace R] {h : E β R}, Differentiable π h β (β (x : E), IsUnit (h x)) β Differentiable π fun x => Ring.inverse (h x) - Differentiable.mul Mathlib.Analysis.Calculus.FDeriv.Mul
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {πΈ : Type u_6} [inst_3 : NormedRing πΈ] [inst_4 : NormedAlgebra π πΈ] {a b : E β πΈ}, Differentiable π a β Differentiable π b β Differentiable π fun y => a y * b y - Differentiable.inv' Mathlib.Analysis.Calculus.FDeriv.Mul
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {R : Type u_6} [inst_3 : NormedDivisionRing R] [inst_4 : NormedAlgebra π R] [inst_5 : CompleteSpace R] {h : E β R}, Differentiable π h β (β (x : E), h x β 0) β Differentiable π fun x => (h x)β»ΒΉ - Differentiable.smul_const Mathlib.Analysis.Calculus.FDeriv.Mul
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace π F] {π' : Type u_6} [inst_5 : NontriviallyNormedField π'] [inst_6 : NormedAlgebra π π'] [inst_7 : NormedSpace π' F] [inst_8 : IsScalarTower π π' F] {c : E β π'}, Differentiable π c β β (f : F), Differentiable π fun y => c y β’ f - Differentiable.smul Mathlib.Analysis.Calculus.FDeriv.Mul
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace π F] {f : E β F} {π' : Type u_6} [inst_5 : NontriviallyNormedField π'] [inst_6 : NormedAlgebra π π'] [inst_7 : NormedSpace π' F] [inst_8 : IsScalarTower π π' F] {c : E β π'}, Differentiable π c β Differentiable π f β Differentiable π fun y => c y β’ f y - Differentiable.continuousMultilinear_apply_const Mathlib.Analysis.Calculus.FDeriv.Mul
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {ΞΉ : Type u_6} [inst_3 : Fintype ΞΉ] {M : ΞΉ β Type u_7} [inst_4 : (i : ΞΉ) β NormedAddCommGroup (M i)] [inst_5 : (i : ΞΉ) β NormedSpace π (M i)] {H : Type u_8} [inst_6 : NormedAddCommGroup H] [inst_7 : NormedSpace π H] {c : E β ContinuousMultilinearMap π M H}, Differentiable π c β β (u : (i : ΞΉ) β M i), Differentiable π fun y => (c y) u - Differentiable.clm_apply Mathlib.Analysis.Calculus.FDeriv.Mul
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {G : Type u_4} [inst_3 : NormedAddCommGroup G] [inst_4 : NormedSpace π G] {H : Type u_6} [inst_5 : NormedAddCommGroup H] [inst_6 : NormedSpace π H] {c : E β G βL[π] H} {u : E β G}, Differentiable π c β Differentiable π u β Differentiable π fun y => (c y) (u y) - Differentiable.clm_comp Mathlib.Analysis.Calculus.FDeriv.Mul
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace π F] {G : Type u_4} [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace π G] {H : Type u_6} [inst_7 : NormedAddCommGroup H] [inst_8 : NormedSpace π H] {c : E β G βL[π] H} {d : E β F βL[π] G}, Differentiable π c β Differentiable π d β Differentiable π fun y => (c y).comp (d y) - Differentiable.neg Mathlib.Analysis.Calculus.FDeriv.Add
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace π F] {f : E β F}, Differentiable π f β Differentiable π fun y => -f y - Differentiable.const_sub Mathlib.Analysis.Calculus.FDeriv.Add
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace π F] {f : E β F}, Differentiable π f β β (c : F), Differentiable π fun y => c - f y - Differentiable.sub_const Mathlib.Analysis.Calculus.FDeriv.Add
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace π F] {f : E β F}, Differentiable π f β β (c : F), Differentiable π fun y => f y - c - Differentiable.add_const Mathlib.Analysis.Calculus.FDeriv.Add
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace π F] {f : E β F}, Differentiable π f β β (c : F), Differentiable π fun y => f y + c - Differentiable.const_add Mathlib.Analysis.Calculus.FDeriv.Add
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace π F] {f : E β F}, Differentiable π f β β (c : F), Differentiable π fun y => c + f y - Differentiable.sum Mathlib.Analysis.Calculus.FDeriv.Add
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace π F] {ΞΉ : Type u_6} {u : Finset ΞΉ} {A : ΞΉ β E β F}, (β i β u, Differentiable π (A i)) β Differentiable π fun y => u.sum fun i => A i y - Differentiable.sub Mathlib.Analysis.Calculus.FDeriv.Add
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace π F] {f g : E β F}, Differentiable π f β Differentiable π g β Differentiable π fun y => f y - g y - Differentiable.add Mathlib.Analysis.Calculus.FDeriv.Add
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace π F] {f g : E β F}, Differentiable π f β Differentiable π g β Differentiable π fun y => f y + g y - Differentiable.const_smul Mathlib.Analysis.Calculus.FDeriv.Add
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace π F] {f : E β F} {R : Type u_6} [inst_5 : Semiring R] [inst_6 : Module R F] [inst_7 : SMulCommClass π R F] [inst_8 : ContinuousConstSMul R F], Differentiable π f β β (c : R), Differentiable π fun y => c β’ f y - Differentiable.div_const Mathlib.Analysis.Calculus.Deriv.Mul
β {π : Type u} [inst : NontriviallyNormedField π] {π' : Type u_2} [inst_1 : NontriviallyNormedField π'] [inst_2 : NormedAlgebra π π'] {c : π β π'}, Differentiable π c β β (d : π'), Differentiable π fun x => c x / d - Differentiable.restrictScalars Mathlib.Analysis.Calculus.FDeriv.RestrictScalars
β (π : Type u_1) [inst : NontriviallyNormedField π] {π' : Type u_2} [inst_1 : NontriviallyNormedField π'] [inst_2 : NormedAlgebra π π'] {E : Type u_3} [inst_3 : NormedAddCommGroup E] [inst_4 : NormedSpace π E] [inst_5 : NormedSpace π' E] [inst_6 : IsScalarTower π π' E] {F : Type u_4} [inst_7 : NormedAddCommGroup F] [inst_8 : NormedSpace π F] [inst_9 : NormedSpace π' F] [inst_10 : IsScalarTower π π' F] {f : E β F}, Differentiable π' f β Differentiable π f - differentiable_pow Mathlib.Analysis.Calculus.Deriv.Pow
β {π : Type u} [inst : NontriviallyNormedField π] (n : β), Differentiable π fun x => x ^ n - Differentiable.inv Mathlib.Analysis.Calculus.Deriv.Inv
β {π : Type u} [inst : NontriviallyNormedField π] {E : Type w} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {h : E β π}, Differentiable π h β (β (x : E), h x β 0) β Differentiable π fun x => (h x)β»ΒΉ - Differentiable.div Mathlib.Analysis.Calculus.Deriv.Inv
β {π : Type u} [inst : NontriviallyNormedField π] {π' : Type u_1} [inst_1 : NontriviallyNormedField π'] [inst_2 : NormedAlgebra π π'] {c d : π β π'}, Differentiable π c β Differentiable π d β (β (x : π), d x β 0) β Differentiable π fun x => c x / d x - Differentiable.zpow Mathlib.Analysis.Calculus.Deriv.ZPow
β {π : Type u} [inst : NontriviallyNormedField π] {E : Type v} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {m : β€} {f : E β π}, Differentiable π f β (β (x : E), f x β 0) β¨ 0 β€ m β Differentiable π fun x => f x ^ m - ContDiff.differentiable Mathlib.Analysis.Calculus.ContDiff.Defs
β {π : Type u} [inst : NontriviallyNormedField π] {E : Type uE} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {F : Type uF} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace π F] {f : E β F} {n : ββ}, ContDiff π n f β 1 β€ n β Differentiable π f - ContDiff.differentiable_iteratedFDeriv Mathlib.Analysis.Calculus.ContDiff.Defs
β {π : Type u} [inst : NontriviallyNormedField π] {E : Type uE} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {F : Type uF} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace π F] {f : E β F} {n : ββ} {m : β}, βm < n β ContDiff π n f β Differentiable π fun x => iteratedFDeriv π m f x - HasFTaylorSeriesUpTo.differentiable Mathlib.Analysis.Calculus.ContDiff.Defs
β {π : Type u} [inst : NontriviallyNormedField π] {E : Type uE} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {F : Type uF} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace π F] {f : E β F} {n : ββ} {p : E β FormalMultilinearSeries π E F}, HasFTaylorSeriesUpTo n f p β 1 β€ n β Differentiable π f - Conformal.differentiable Mathlib.Analysis.Calculus.Conformal.NormedSpace
β {X : Type u_1} {Y : Type u_2} [inst : NormedAddCommGroup X] [inst_1 : NormedAddCommGroup Y] [inst_2 : NormedSpace β X] [inst_3 : NormedSpace β Y] {f : X β Y}, Conformal f β Differentiable β f - differentiable_neg Mathlib.Analysis.Calculus.Deriv.Add
β {π : Type u} [inst : NontriviallyNormedField π], Differentiable π Neg.neg - AffineMap.differentiable Mathlib.Analysis.Calculus.Deriv.AffineMap
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] (f : π βα΅[π] E), Differentiable π βf - ContDiff.differentiable_iteratedDeriv Mathlib.Analysis.Calculus.IteratedDeriv.Defs
β {π : Type u_1} [inst : NontriviallyNormedField π] {F : Type u_2} [inst_1 : NormedAddCommGroup F] [inst_2 : NormedSpace π F] {f : π β F} {n : ββ} (m : β), ContDiff π n f β βm < n β Differentiable π (iteratedDeriv m f) - Real.differentiable_exp Mathlib.Analysis.SpecialFunctions.ExpDeriv
Differentiable β Real.exp - Complex.differentiable_exp Mathlib.Analysis.SpecialFunctions.ExpDeriv
β {π : Type u_1} [inst : NontriviallyNormedField π] [inst_1 : NormedAlgebra π β], Differentiable π Complex.exp - Differentiable.exp Mathlib.Analysis.SpecialFunctions.ExpDeriv
β {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace β E] {f : E β β}, Differentiable β f β Differentiable β fun x => (f x).exp - Differentiable.cexp Mathlib.Analysis.SpecialFunctions.ExpDeriv
β {π : Type u_1} [inst : NontriviallyNormedField π] [inst_1 : NormedAlgebra π β] {E : Type u_2} [inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace π E] {f : E β β}, Differentiable π f β Differentiable π fun x => (f x).exp - Differentiable.log Mathlib.Analysis.SpecialFunctions.Log.Deriv
β {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace β E] {f : E β β}, Differentiable β f β (β (x : E), f x β 0) β Differentiable β fun x => (f x).log - differentiable_circleMap Mathlib.MeasureTheory.Integral.CircleIntegral
β (c : β) (R : β), Differentiable β (circleMap c R) - Polynomial.differentiable Mathlib.Analysis.Calculus.Deriv.Polynomial
β {π : Type u} [inst : NontriviallyNormedField π] (p : Polynomial π), Differentiable π fun x => Polynomial.eval x p - Polynomial.differentiable_aeval Mathlib.Analysis.Calculus.Deriv.Polynomial
β {π : Type u} [inst : NontriviallyNormedField π] {R : Type u_1} [inst_1 : CommSemiring R] [inst_2 : Algebra R π] (q : Polynomial R), Differentiable π fun x => (Polynomial.aeval x) q - differentiable_tsum' Mathlib.Analysis.Calculus.SmoothSeries
β {Ξ± : Type u_1} {π : Type u_3} {F : Type u_5} [inst : RCLike π] [inst_1 : NormedAddCommGroup F] [inst_2 : CompleteSpace F] {u : Ξ± β β} [inst_3 : NormedSpace π F] {g g' : Ξ± β π β F}, Summable u β (β (n : Ξ±) (y : π), HasDerivAt (g n) (g' n y) y) β (β (n : Ξ±) (y : π), βg' n yβ β€ u n) β Differentiable π fun z => β' (n : Ξ±), g n z - differentiable_tsum Mathlib.Analysis.Calculus.SmoothSeries
β {Ξ± : Type u_1} {π : Type u_3} {E : Type u_4} {F : Type u_5} [inst : RCLike π] [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] [inst_3 : NormedAddCommGroup F] [inst_4 : CompleteSpace F] {u : Ξ± β β} [inst_5 : NormedSpace π F] {f : Ξ± β E β F} {f' : Ξ± β E β E βL[π] F}, Summable u β (β (n : Ξ±) (x : E), HasFDerivAt (f n) (f' n x) x) β (β (n : Ξ±) (x : E), βf' n xβ β€ u n) β Differentiable π fun y => β' (n : Ξ±), f n y - Differentiable.sqrt Mathlib.Analysis.SpecialFunctions.Sqrt
β {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace β E] {f : E β β}, Differentiable β f β (β (x : E), f x β 0) β Differentiable β fun y => (f y).sqrt - Differentiable.norm_sq Mathlib.Analysis.InnerProductSpace.Calculus
β (π : Type u_1) {E : Type u_2} [inst : RCLike π] [inst_1 : NormedAddCommGroup E] [inst : InnerProductSpace π E] [inst : NormedSpace β E] {G : Type u_4} [inst_2 : NormedAddCommGroup G] [inst_3 : NormedSpace β G] {f : G β E}, Differentiable β f β Differentiable β fun y => βf yβ ^ 2 - Differentiable.norm Mathlib.Analysis.InnerProductSpace.Calculus
β (π : Type u_1) {E : Type u_2} [inst : RCLike π] [inst_1 : NormedAddCommGroup E] [inst : InnerProductSpace π E] [inst : NormedSpace β E] {G : Type u_4} [inst_2 : NormedAddCommGroup G] [inst_3 : NormedSpace β G] {f : G β E}, Differentiable β f β (β (x : G), f x β 0) β Differentiable β fun y => βf yβ - Differentiable.dist Mathlib.Analysis.InnerProductSpace.Calculus
β (π : Type u_1) {E : Type u_2} [inst : RCLike π] [inst_1 : NormedAddCommGroup E] [inst : InnerProductSpace π E] [inst : NormedSpace β E] {G : Type u_4} [inst_2 : NormedAddCommGroup G] [inst_3 : NormedSpace β G] {f g : G β E}, Differentiable β f β Differentiable β g β (β (x : G), f x β g x) β Differentiable β fun y => dist (f y) (g y) - differentiable_inner Mathlib.Analysis.InnerProductSpace.Calculus
β {π : Type u_1} {E : Type u_2} [inst : RCLike π] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace π E] [inst_3 : NormedSpace β E], Differentiable β fun p => βͺp.1, p.2β«_π - Differentiable.inner Mathlib.Analysis.InnerProductSpace.Calculus
β (π : Type u_1) {E : Type u_2} [inst : RCLike π] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace π E] [inst_3 : NormedSpace β E] {G : Type u_4} [inst_4 : NormedAddCommGroup G] [inst_5 : NormedSpace β G] {f g : G β E}, Differentiable β f β Differentiable β g β Differentiable β fun x => βͺf x, g xβ«_π - expNegInvGlue.differentiable_polynomial_eval_inv_mul Mathlib.Analysis.SpecialFunctions.SmoothTransition
β (p : Polynomial β), Differentiable β fun x => Polynomial.eval xβ»ΒΉ p * expNegInvGlue x - Differentiable.star Mathlib.Analysis.Calculus.FDeriv.Star
β {π : Type u_1} [inst : NontriviallyNormedField π] [inst_1 : StarRing π] [inst_2 : TrivialStar π] {E : Type u_2} [inst_3 : NormedAddCommGroup E] [inst_4 : NormedSpace π E] {F : Type u_3} [inst_5 : NormedAddCommGroup F] [inst_6 : StarAddMonoid F] [inst_7 : NormedSpace π F] [inst_8 : StarModule π F] [inst_9 : ContinuousStar F] {f : E β F}, Differentiable π f β Differentiable π fun y => star (f y) - Differentiable.clog Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv
β {E : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace β E] {f : E β β}, Differentiable β f β (β (x : E), f x β Complex.slitPlane) β Differentiable β fun t => (f t).log - Complex.differentiable_cos Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv
Differentiable β Complex.cos - Complex.differentiable_cosh Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv
Differentiable β Complex.cosh - Complex.differentiable_sin Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv
Differentiable β Complex.sin - Complex.differentiable_sinh Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv
Differentiable β Complex.sinh - Real.differentiable_cos Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv
Differentiable β Real.cos - Real.differentiable_cosh Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv
Differentiable β Real.cosh - Real.differentiable_sin Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv
Differentiable β Real.sin - Real.differentiable_sinh Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv
Differentiable β Real.sinh - Differentiable.ccos Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv
β {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace β E] {f : E β β}, Differentiable β f β Differentiable β fun x => (f x).cos - Differentiable.ccosh Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv
β {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace β E] {f : E β β}, Differentiable β f β Differentiable β fun x => (f x).cosh - Differentiable.cos Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv
β {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace β E] {f : E β β}, Differentiable β f β Differentiable β fun x => (f x).cos - Differentiable.cosh Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv
β {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace β E] {f : E β β}, Differentiable β f β Differentiable β fun x => (f x).cosh - Differentiable.csin Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv
β {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace β E] {f : E β β}, Differentiable β f β Differentiable β fun x => (f x).sin - Differentiable.csinh Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv
β {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace β E] {f : E β β}, Differentiable β f β Differentiable β fun x => (f x).sinh - Differentiable.sin Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv
β {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace β E] {f : E β β}, Differentiable β f β Differentiable β fun x => (f x).sin - Differentiable.sinh Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv
β {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace β E] {f : E β β}, Differentiable β f β Differentiable β fun x => (f x).sinh - Real.differentiable_rpow_const Mathlib.Analysis.SpecialFunctions.Pow.Deriv
β {p : β}, 1 β€ p β Differentiable β fun x => x ^ p - Differentiable.const_cpow Mathlib.Analysis.SpecialFunctions.Pow.Deriv
β {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace β E] {f : E β β} {c : β}, Differentiable β f β (c β 0 β¨ β (x : E), f x β 0) β Differentiable β fun x => c ^ f x - Differentiable.rpow_const Mathlib.Analysis.SpecialFunctions.Pow.Deriv
β {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace β E] {f : E β β} {p : β}, Differentiable β f β (β (x : E), f x β 0 β¨ 1 β€ p) β Differentiable β fun x => f x ^ p - Differentiable.cpow Mathlib.Analysis.SpecialFunctions.Pow.Deriv
β {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace β E] {f g : E β β}, Differentiable β f β Differentiable β g β (β (x : E), f x β Complex.slitPlane) β Differentiable β fun x => f x ^ g x - Differentiable.rpow Mathlib.Analysis.SpecialFunctions.Pow.Deriv
β {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace β E] {f g : E β β}, Differentiable β f β Differentiable β g β (β (x : E), f x β 0) β Differentiable β fun x => f x ^ g x - Real.differentiable_arctan Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv
Differentiable β Real.arctan - Differentiable.arctan Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv
β {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace β E] {f : E β β}, Differentiable β f β Differentiable β fun x => (f x).arctan - Real.differentiable_arsinh Mathlib.Analysis.SpecialFunctions.Arsinh
Differentiable β Real.arsinh - Differentiable.arsinh Mathlib.Analysis.SpecialFunctions.Arsinh
β {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace β E] {f : E β β}, Differentiable β f β Differentiable β fun x => (f x).arsinh - SchwartzMap.differentiable Mathlib.Analysis.Distribution.SchwartzSpace
β {E : Type u_4} {F : Type u_5} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace β E] [inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace β F] (f : SchwartzMap E F), Differentiable β βf - Real.differentiable_fourierIntegral Mathlib.Analysis.Fourier.FourierTransformDeriv
β {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace β E] {V : Type u_2} [inst_2 : NormedAddCommGroup V] [inst_3 : InnerProductSpace β V] [inst_4 : FiniteDimensional β V] [inst_5 : MeasurableSpace V] [inst_6 : BorelSpace V] {f : V β E}, MeasureTheory.Integrable f MeasureTheory.volume β MeasureTheory.Integrable (fun v => βvβ * βf vβ) MeasureTheory.volume β Differentiable β (Real.fourierIntegral f) - VectorFourier.differentiable_fourierIntegral Mathlib.Analysis.Fourier.FourierTransformDeriv
β {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace β E] {V : Type u_2} {W : Type u_3} [inst_2 : NormedAddCommGroup V] [inst_3 : NormedSpace β V] [inst_4 : NormedAddCommGroup W] [inst_5 : NormedSpace β W] (L : V βL[β] W βL[β] β) {f : V β E} [inst_6 : MeasurableSpace V] [inst_7 : BorelSpace V] [inst_8 : SecondCountableTopology V] {ΞΌ : MeasureTheory.Measure V}, MeasureTheory.Integrable f ΞΌ β MeasureTheory.Integrable (fun v => βvβ * βf vβ) ΞΌ β Differentiable β (VectorFourier.fourierIntegral Real.fourierChar ΞΌ L.toLinearMapβ f) - Complex.differentiable_one_div_Gamma Mathlib.Analysis.SpecialFunctions.Gamma.Beta
Differentiable β fun s => s.Gammaβ»ΒΉ - Complex.differentiable_Gammaβ_inv Mathlib.Analysis.SpecialFunctions.Gamma.Deligne
Differentiable β fun s => s.Gammaββ»ΒΉ - Differentiable.inversion Mathlib.Geometry.Euclidean.Inversion.Calculus
β {E : Type u_1} {F : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace β E] [inst_2 : NormedAddCommGroup F] [inst_3 : InnerProductSpace β F] {c x : E β F} {R : E β β}, Differentiable β c β Differentiable β R β Differentiable β x β (β (a : E), x a β c a) β Differentiable β fun a => EuclideanGeometry.inversion (c a) (R a) (x a) - MDifferentiable.differentiable Mathlib.Geometry.Manifold.MFDeriv.FDeriv
β {π : Type u_1} [inst : NontriviallyNormedField π] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace π E] {E' : Type u_3} [inst_3 : NormedAddCommGroup E'] [inst_4 : NormedSpace π E'] {f : E β E'}, MDifferentiable (modelWithCornersSelf π E) (modelWithCornersSelf π E') f β Differentiable π f - differentiable_completed_zetaβ Mathlib.NumberTheory.ZetaFunction
Differentiable β riemannCompletedZetaβ - differentiable_mellin_zetaKernelβ Mathlib.NumberTheory.ZetaFunction
Differentiable β (mellin zetaKernelβ) - StrongFEPair.differentiable_Ξ Mathlib.NumberTheory.LSeries.AbstractFuncEq
β {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace β E] (P : StrongFEPair E), Differentiable β P.Ξ - WeakFEPair.differentiable_Ξβ Mathlib.NumberTheory.LSeries.AbstractFuncEq
β {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace β E] (P : WeakFEPair E), Differentiable β P.Ξβ - differentiable_completedCosZetaβ Mathlib.NumberTheory.LSeries.HurwitzZetaEven
β (a : UnitAddCircle), Differentiable β (completedCosZetaβ a) - differentiable_completedHurwitzZetaEvenβ Mathlib.NumberTheory.LSeries.HurwitzZetaEven
β (a : UnitAddCircle), Differentiable β (completedHurwitzZetaEvenβ a) - differentiable_hurwitzZetaEven_sub_hurwitzZetaEven Mathlib.NumberTheory.LSeries.HurwitzZetaEven
β (a b : UnitAddCircle), Differentiable β fun s => hurwitzZetaEven a s - hurwitzZetaEven b s - differentiable_cosZeta_of_ne_zero Mathlib.NumberTheory.LSeries.HurwitzZetaEven
β {a : UnitAddCircle}, a β 0 β Differentiable β (cosZeta a) - differentiableAt_sinZeta Mathlib.NumberTheory.LSeries.HurwitzZetaOdd
β (a : UnitAddCircle), Differentiable β (sinZeta a) - differentiable_completedHurwitzZetaOdd Mathlib.NumberTheory.LSeries.HurwitzZetaOdd
β (a : UnitAddCircle), Differentiable β (completedHurwitzZetaOdd a) - differentiable_completedSinZeta Mathlib.NumberTheory.LSeries.HurwitzZetaOdd
β (a : UnitAddCircle), Differentiable β (completedSinZeta a) - differentiable_hurwitzZetaOdd Mathlib.NumberTheory.LSeries.HurwitzZetaOdd
β (a : UnitAddCircle), Differentiable β (hurwitzZetaOdd a) - Differentiable.comp' Mathlib.Tactic.FunProp.Differentiable
β {K : Type u_1} [inst : NontriviallyNormedField K] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace K E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace K F] {G : Type u_4} [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace K G] {f : E β F} {g : F β G}, Differentiable K g β Differentiable K f β Differentiable K fun x => g (f x) - ContDiff.differentiable_iteratedDeriv' Mathlib.Tactic.FunProp.ContDiff
β {K : Type u_1} [inst : NontriviallyNormedField K] {F : Type u_3} [inst_1 : NormedAddCommGroup F] [inst_2 : NormedSpace K F] {m : β} {f : K β F}, ContDiff K (βm + 1) f β Differentiable K (iteratedDeriv m f)
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About
Loogle searches of Lean and Mathlib definitions and theorems.
You may also want to try the CLI version, the VS
Code extension, the lean.nvim
integration or the Zulip bot.
Usage
Loogle finds definitions and lemmas in various ways:
By constant:
πReal.sin
finds all lemmas whose statement somehow mentions the sine function.By lemma name substring:
π"differ"
finds all lemmas that have"differ"
somewhere in their lemma name.By subexpression:
π_ * (_ ^ _)
finds all lemmas whose statements somewhere include a product where the second argument is raised to some power.The pattern can also be non-linear, as in
πReal.sqrt ?a * Real.sqrt ?a
If the pattern has parameters, they are matched in any order. Both of these will find
List.map
:
π(?a -> ?b) -> List ?a -> List ?b
πList ?a -> (?a -> ?b) -> List ?b
By main conclusion:
π|- tsum _ = _ * tsum _
finds all lemmas where the conclusion (the subexpression to the right of allβ
andβ
) has the given shape.As before, if the pattern has parameters, they are matched against the hypotheses of the lemma in any order; for example,
π|- _ < _ β tsum _ < tsum _
will findtsum_lt_tsum
even though the hypothesisf i < g i
is not the last.
If you pass more than one such search filter, separated by commas
Loogle will return lemmas which match all of them. The
search
π Real.sin, "two", tsum, _ * _, _ ^ _, |- _ < _ β _
woould find all lemmas which mention the constants Real.sin
and tsum
, have "two"
as a substring of the
lemma name, include a product and a power somewhere in the type,
and have a hypothesis of the form _ < _
(if
there were any such lemmas). Metavariables (?a
) are
assigned independently in each filter.
The #lucky
button will directly send you to the
documentation of the first hit.
Source code
You can find the source code for this service at https://github.com/nomeata/loogle. The https://loogle.lean-lang.org/ service is currently provided by Joachim Breitner <mail@joachim-breitner.de>.
This is Loogle revision fa2ddf5
serving mathlib revision c44d42e