theorem
  (i|->r1) + (i|->r2) = i|->(r1+r2)
proof
  reconsider s1=r1, s2=r2 as Element of REAL by XREAL_0:def 1;
  (i|->s1) + (i|->s2) = i|->(addreal.(s1,s2)) by FINSEQOP:17
    .= i|->(r1+r2) by BINOP_2:def 9;
  hence thesis;
end;
