theorem
  <*r1*> + <*r2*> = <*r1+r2*>
proof
  reconsider s1=r1, s2=r2 as Element of REAL by XREAL_0:def 1;
  <*s1*> + <*s2*> = <*addreal.(s1,s2)*> by FINSEQ_2:74
    .= <*r1+r2*> by BINOP_2:def 9;
  hence thesis;
end;
