reserve V for RealLinearSpace;
reserve x,y for VECTOR of V;
reserve AS for Oriented_Orthogonality_Space;
reserve u,u1,u2,u3,v,v1,v2,v3,w,w1 for Element of AS;

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