theorem Th12:
  for X being included_in_Seg set st
  X c= SetPrimes & p divides Product Sgm X holds p in X
  proof
    let X be included_in_Seg set such that
A1: X c= SetPrimes;
A2: rng Sgm X = X by FINSEQ_1:def 14;
    then Sgm X is FinSequence of SetPrimes by A1,FINSEQ_1:def 4;
    hence thesis by A2,NAT_3:8;
  end;
