theorem Th87:
  Sum(r*F) = r*(Sum F)
proof
  reconsider F1=F as FinSequence of REAL by Lm2;
  reconsider s=r as Element of REAL by XREAL_0:def 1;
  set rM = multreal[;](s,id REAL);
  thus Sum (r*F) = rM.(addreal $$ F1) by Th3,Th8,SETWOP_2:30
    .= r*(Sum F1) by Lm1
    .= r*(Sum F);
end;
