theorem Th74:
  Sum(F^<*r*>) = Sum F + r
proof
  reconsider s=r as Element of REAL by XREAL_0:def 1;
  reconsider F1=F as FinSequence of REAL by Lm2;
  thus Sum(F^<*r*>) = Sum(F1^<*s*>) .= addreal.(addreal $$ F1,s) by FINSOP_1:4
    .= Sum F1 + r by BINOP_2:def 9
    .= Sum F + r;
end;
