sub — Mathlib

English

If h1 = OWith c1 l f1 g and h2 = o_l f2 g with c1 < c2, then f1 - f2 is OWith c2 l g.

Русский

Если h1 = OWith c1 l f1 g и h2 = o_l f2 g при c1 < c2, то f1 - f2 ∈ OWith c2 l g.

LaTeX

$$$ (h_1 : IsBigOWith c_1 l f_1 g) \\land (h_2 : f_2 =o[l] g) \\land (c_1 < c_2) \\Rightarrow IsBigOWith c_2 l (f_1 - f_2) g $$$

Lean4

theorem sub (h₁ : IsBigOWith c₁ l f₁ g) (h₂ : IsBigOWith c₂ l f₂ g) : IsBigOWith (c₁ + c₂) l (fun x => f₁ x - f₂ x) g :=
  by simpa only [sub_eq_add_neg] using h₁.add h₂.neg_left

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