Gnxr nal gjb bs gur svir cbvagf, naq pnyy gurz N naq O. Pnyy gur bgure guerr cbvagf P, Q, naq R.
Abj pbafgehpg n cynar K cnffvat guebhtu N, O, naq gur pragre bs gur fcurer (vs N naq O ner rdhny, gurer ner vasvavgryl znal fhpu cynarf; bgurejvfr gurer vf cerpvfryl bar). Gur cynar K qvivqrf gur fcurer F vagb gjb bcra urzvfcurerf F_1 naq F_2, naq gur pvepyr F_3 juvpu vf gur vagrefrpgvba bs F naq K. Abgr gung F_3 pbagnvaf obgu N naq O.
Abj qrsvar G_1 = F_1 H F_3 naq G_2 = F_2 H F_3; ol vafcrpgvba, gurfr ner obgu pybfrq urzvfcurerf. Fvapr F_3 pbagnvaf obgu N naq O, G_1 naq G_2 obgu pbagnva obgu N naq O. Shegurezber, G_1 H G_2 = F_1 H F_2 H F_3 = F, naq gurersber gur cbvagf P, Q, naq R rnpu yvr ba bar be zber bs G_1 naq G_2.
Ol gur cvtrbaubyr cevapvcyr, ng yrnfg bar bs G_1 naq G_2 pbagnvaf ng yrnfg gjb bhg bs gur guerr cbvagf P, Q, naq R. Pnyy guvf bar G. Fvapr jr nyernql xabj gung G pbagnvaf obgu N naq O, jr pbapyhqr gung G vf n pybfrq urzvfcurer pbagnvavat ng yrnfg sbhe bhg bs gur svir cbvagf N, O, P, Q, naq R.