let x be _Graph; :: according to GLIB_014:def 3 :: thesis: ( x in X \/ Y implies x is loopless )
assume x in X \/ Y ; :: thesis: x is loopless

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

suppose x in X ; :: thesis: x is loopless

hence x is loopless by Def3; :: thesis: verum

end;

suppose x in Y ; :: thesis: x is loopless

hence x is loopless by Def3; :: thesis: verum

end;

end;