reserve a,b,m,x,y,i1,i2,i3,i for Integer,
  k,p,q,n for Nat,
  c,c1,c2 for Element of NAT,
  z for set;
reserve fp,fp1 for FinSequence of NAT,

  b,c,d, n for Element of NAT,
  a for Nat;

theorem Th32:
  for a st a in dom fp holds fp.a divides Product fp
proof
  let a;
  assume a in dom fp;
  then fp.a in rng fp by FUNCT_1:3;
  hence thesis by NAT_3:7;
end;
