proposition: Lemma eqadd_some_OP (F : filter_on T) (f g : T -> V) (e : T -> W) h : f = g + [O_F e of h] -> bigO_def F (f - g) e.
proof: Proof. rewrite /the_bigO /insubd=> ->. case: insubP => /= [u /asboolP fg_o_e ->|_]. by rewrite addrAC subrr add0r; apply: fg_o_e. by rewrite addrC addKr; apply: bigOP. Qed.
imports: HB(structures) mathcomp(all_ssreflect ssralg ssrnum) mathcomp(mathcomp_extra boolp classical_sets functions) ereal reals signed topology normedtype prodnormedzmodule