theorem
  u,u1 // v,v1 implies u1,u // v1,v
proof
  assume u,u1 // v,v1;
  then consider w,w1 such that
A1: w<>w1 and
A2: w,w1 '//' u,u1 and
A3: w,w1 '//' v,v1;
A4: w1,w '//' v1,v by A3,Def1;
  w1,w '//' u1,u by A2,Def1;
  hence thesis by A1,A4;
end;
