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
  a in dom fp & p divides fp.a implies p divides Product fp
proof
  assume that
A1: a in dom fp and
A2: p divides fp.a;
  fp.a divides Product fp by A1,Th32;
  hence thesis by A2,NAT_D:4;
end;
