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
  u,u1 // w,w & w,w // u,u1
proof
  set v = the Element of AS;
  consider v1 such that
A1: v1<>v and
A2: v,v1 '//' u,u1 by Def1;
  v,v1 '//' w,w by Def1;
  hence thesis by A1,A2;
end;
