theorem
  for u,v,w being Element of AS holds ex u1 being Element of AS st u1,w
  '//' u,v & u1<>w
proof
  let u,v,w;
  consider u1 such that
A1: u1<>w and
A2: w,u1 '//' v,u by Def1;
  u1,w '//' u,v by A2,Def1;
  hence thesis by A1;
end;
