reserve x,y for set;
reserve X for non empty set;
reserve a,b,c,d for Element of X;
reserve S for OAffinSpace;
reserve a,b,c,d,p,q,r,x,y,z,t,u,w for Element of S;

theorem Th25:
  ex t st x,z '||' y,t & y<>t
proof
  consider t such that
  x,y // z,t and
A1: x,z // y,t and
A2: y<>t by ANALOAF:def 5;
  x,z '||' y,t by A1;
  hence thesis by A2;
end;
