reserve n,m,k,i for Nat,
  g,s,t,p for Real,
  x,y,z for object, X,Y,Z for set,
  A1 for SetSequence of X,
  F1 for FinSequence of bool X,
  RFin for real-valued FinSequence,
  Si for SigmaField of X,
  XSeq,YSeq for SetSequence of Si,
  Omega for non empty set,
  Sigma for SigmaField of Omega,
  ASeq,BSeq for SetSequence of Sigma,
  P for Probability of Sigma;
reserve FSeq for FinSequence of Sigma;

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;
