[see also: case
The possibility A=Ø is not excluded.
The only possibility for G not to be 1-1 is that there exists......
The remaining possibility is that v is labelled 2.
These two possibilities cannot arise simultaneously.
However, this still left open the possibility that the converse of Theorem 3 held for m=3.
The reader may wonder why we have apparently ignored the possibility of obtaining a better lower bound by considering...... [Not: “the possibility to obtain'']