| {"name":"Asymptotics.isLittleO_const_id_atTop2","declaration":"theorem Asymptotics.isLittleO_const_id_atTop2 {E'' : Type u_9} {F'' : Type u_10} [NormedAddCommGroup E''] [NormedAddCommGroup F''] [LinearOrder F''] [NoMaxOrder F''] [ClosedIciTopology F''] [ProperSpace F''] (c : E'') : (fun _x => c) =o[Filter.atTop] id"} |
| {"name":"Filter.Eventually.natCast","declaration":"theorem Filter.Eventually.natCast {f : ℝ → Prop} (hf : ∀ᶠ (x : ℝ) in Filter.atTop, f x) : ∀ᶠ (n : ℕ) in Filter.atTop, f ↑n"} |
| {"name":"Asymptotics.isLittleO_const_id_atBot2","declaration":"theorem Asymptotics.isLittleO_const_id_atBot2 {E'' : Type u_9} {F'' : Type u_10} [NormedAddCommGroup E''] [NormedAddCommGroup F''] [LinearOrder F''] [NoMinOrder F''] [ClosedIicTopology F''] [ProperSpace F''] (c : E'') : (fun _x => c) =o[Filter.atBot] id"} |
| {"name":"Asymptotics.isLittleO_const_id_cocompact","declaration":"theorem Asymptotics.isLittleO_const_id_cocompact {E'' : Type u_9} {F'' : Type u_10} [NormedAddCommGroup E''] [NormedAddCommGroup F''] [ProperSpace F''] (c : E'') : (fun _x => c) =o[Filter.cocompact F''] id"} |
| {"name":"Asymptotics.IsBigO.natCast","declaration":"theorem Asymptotics.IsBigO.natCast {E : Type u_3} [Norm E] {f : ℝ → E} {g : ℝ → E} (h : f =O[Filter.atTop] g) : (fun n => f ↑n) =O[Filter.atTop] fun n => g ↑n"} |
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