theorem Th62:
  len RFin = 0 implies Sum RFin = 0
proof
  assume
A1: len RFin=0;
   0 in REAL by XREAL_0:def 1;
   then
A2: addreal is having_a_unity by RVSUM_1:1,SETWISEO:def 2;
  reconsider RFin as FinSequence of REAL by FINSEQ_1:106;
  Sum(RFin) = addreal $$ RFin by RVSUM_1:def 12
    .= 0 by A1,A2,BINOP_2:2,FINSOP_1:def 1;
  hence thesis;
end;
