Summary: We present the original proof, based on the Doitchinov completion [\textit{D. Doitchinov}, C. R. Acad. Bulg. Sci. 41, No. 7, 5-8 (1988; Zbl 0649.54015); Topology Appl. 30, No. 2, 127-148 (1988; Zbl 0668.54019); 38, No. 3, 205-217 (1991; Zbl 0723.54030)], that a totally bounded quiet quasi-informity is a uniformity. The proof was obtained about ten years ago, but never published. In the meantime several stronger results have been obtained by more direct arguments [\textit{H. P. A. Künzi}, Topology Proc. 15, 113-115 (1990; Zbl 0767.54022); \textit{H. P. A. Künzi}, \textit{M. Mršević}, \textit{I. L. Reilly}, and \textit{M. K. Vamanamurthy}, Math. Jap. 38, No. 2, 239-253 (1993; Zbl 0783.54022); \textit{J. Deák}, Acta Math. Hung. 70, No. 4, 317-327 (1996; Zbl 0841.54024)]. In particular it follows from Künzi's [loc. cit.] proofs that each totally bounded locally quiet quasi-uniform space is uniform, and recently Deák [loc. cit.] observed that even each totally bounded Cauchy quasi-uniformity is a uniformity.