let S be Subset of (Vertices G); :: thesis: ( S is trivial implies S is stable )
assume A1: S is trivial ; :: thesis: S is stable

per cases ( S is empty or ex c being object st S = {c} ) by A1, ZFMISC_1:131;

suppose S is empty ; :: thesis: S is stable

then S = {} (Vertices G) ;
hence S is stable ; :: thesis: verum

end;

suppose ex c being object st S = {c} ; :: thesis: S is stable

then consider c being object such that
A2: S = {c} ;
thus S is stable by A2, Th61; :: thesis: verum

end;

end;