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 Th33:
  not p,q '||' p,r & p,r '||' p,s & q,r '||' q,s implies r=s
proof
  assume that
A1: ( not p,q '||' p,r)& p,r '||' p,s and
A2: q,r '||' q,s;
A3: r,s '||' r,q by A2,Th29;
  ( not r,p '||' r,q)& r,s '||' r,p by A1,Th29;
  hence thesis by A3,Def11;
end;
