The indefinable term 'prokaryote' and the polyphyletic origin of genes

An analysis has been performed on implications existing between the presence/absence of the evolutionary stage of the prokaryote, that is to say, the presence/absence of common characteristics between archaea and bacteria, and the monophyletic/polyphyletic origin of genes of proteins. Thereafter, a theorem stating that: 'the polyphyletic origin of proteins would imply the absence of common characteristics between bacteria and archaea and therefore the lack of the evolutionary stage of the prokaryote, and vice versa that the indefinable prokaryote stage implies a polyphyletic origin of proteins', has been made and validated. The conclusion is that given the absence of truth in common characteristics between archaea and bacteria, the origin of genes of proteins should have been polyphyletic.