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 Th6:
  x,y // x,z iff x,y // y,z or x,z // z,y
proof
  now
    assume x,y // y,z or x,z // z,y;
    then x,y // x,z or x,z // x,y by ANALOAF:def 5;
    hence x,y // x,z by Th2;
  end;
  hence thesis by ANALOAF:def 5;
end;
