reserve a,b,k,m,n,s for Nat;
reserve c,c1,c2,c3 for Complex;
reserve i,j,z for Integer;
reserve p for Prime;
reserve x for object;

theorem Th45:
  for k,s being Nat st k < s holds
  Product PrimeNumbersFS(s) / primenumber(k) is Nat
  proof
    let k,s be Nat;
    assume k < s;
    then PrimeNumbersFS(s).(k+1) = primenumber(k) by Th43;
    hence thesis;
  end;
