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 Th19:
  a,b '||' c,d implies c,d '||' a,b
proof
  assume
A1: a,b '||' c,d;
  a,b '||' a,b by Th18;
  then a<>b implies c,d '||' a,b by A1,Def11;
  hence thesis by Def11;
end;
