theorem Th87:
  diff(a,b,o)=o iff a=b
proof
  diff(a,b,o)=o implies a=b
  proof
    assume diff(a,b,o)=o;
    then opposite(a,o)= opposite(b,o) by Def6;
    hence thesis by Th82;
  end;
  hence thesis by Def6;
end;
