proposition: Lemma bigO0_subproof F (g : T -> W) : Filter F -> bigO_def F (0 : T -> V) g.
proof: Proof. by move=> FF; near do [apply: filterE => x; rewrite normr0 pmulr_rge0 ?normr_ge0//]; exists 0. Unshelve. all: by end_near. Qed.
imports: HB(structures) mathcomp(all_ssreflect ssralg ssrnum) mathcomp(mathcomp_extra boolp classical_sets functions) ereal reals signed topology normedtype prodnormedzmodule