reserve F for Field,
  a,b,c,d,e,f,g,h for Element of F;
reserve x,y for Element of [:the carrier of F,the carrier of F,the carrier of
  F:];
reserve F for Field;
reserve PS for non empty ParStr;
reserve x for set,
  a,b,c,d,e,f,g,h,i,j,k,l for Element of [:the carrier of F,
  the carrier of F,the carrier of F:];
reserve a,b,c,d,p,q,r,s for Element of MPS(F);
reserve PS for ParSp,
  a,b,c,d,p,q,r,s for Element of PS;

theorem Th30:
  not a,b '||' c,d & a,b '||' p,q & c,d '||' r,s & p<>q & r<>s
  implies not p,q '||' r,s
proof
  assume that
A1: not a,b '||' c,d and
A2: a,b '||' p,q and
A3: c,d '||' r,s and
A4: p<>q and
A5: r<>s;
  assume p,q '||' r,s;
  then a,b '||' r,s by A2,A4,Th26;
  then
A6: r,s '||' a,b by Th23;
  r,s '||' c,d by A3,Th23;
  hence contradiction by A1,A5,A6,Def11;
end;
