let x be _Graph; :: according to GLPACY00:def 5 :: thesis: ( x in X \/ Y implies x is Path-like )
assume x in X \/ Y ; :: thesis: x is Path-like

per cases then ( x in X or x in Y ) by XBOOLE_0:def 3;

suppose x in X ; :: thesis: x is Path-like

hence x is Path-like by Def5; :: thesis: verum

end;

suppose x in Y ; :: thesis: x is Path-like

hence x is Path-like by Def5; :: thesis: verum

end;

end;