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 Th32:
  not a,b '||' a,c & a,c '||' p,r & b,c '||' p,r implies p=r
proof
  assume that
A1: ( not a,b '||' a,c)& a,c '||' p,r and
A2: b,c '||' p,r;
A3: p,r '||' b,c by A2,Th23;
  ( not a,c '||' b,c)& p,r '||' a,c by A1,Th23,Th29;
  hence thesis by A3,Def11;
end;
