theorem Th75:
  Sum(F1^F2) = Sum F1 + Sum F2
proof
  reconsider F3=F1,F4=F2 as FinSequence of REAL by Lm2;
  thus Sum(F1^F2) = Sum(F3^F4)
    .= addreal.(addreal $$ F3,addreal $$ F4) by FINSOP_1:5
    .= Sum F3 + Sum F4 by BINOP_2:def 9
    .= Sum F1 + Sum F2;
end;
