consider t1 being Element of T;
consider s1, s2 being Element of S such that
A1: s1 <> s2 by YELLOW_8:def 1;

per cases ( s1 = t1 or s1 <> t1 ) ;

suppose s1 = t1 ; :: thesis: not DiffElems (S,T) is empty

then [s2,t1] in DiffElems (S,T) by A1;
hence not DiffElems (S,T) is empty ; :: thesis: verum

end;

suppose s1 <> t1 ; :: thesis: not DiffElems (S,T) is empty

then [s1,t1] in DiffElems (S,T) ;
hence not DiffElems (S,T) is empty ; :: thesis: verum

end;

end;