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Lemma: Composition of Relations (Sometimes) Preserves Their LeftTotal Property
Let \(A,B,C\) be sets and let let \(R_1\subseteq A\times B\) and \(R_2\subseteq B\times C\) be two lefttotal relations. Then the composition of the relations \((R_2\circ R_1)\subseteq A\times C\) is also lefttotal.
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References
Bibliography
 Knauer Ulrich: "Diskrete Strukturen  kurz gefasst", Spektrum Akademischer Verlag, 2001