reserve X for set;
reserve a,b,c,k,m,n for Nat;
reserve i,j for Integer;
reserve r,s for Real;
reserve p,p1,p2,p3 for Prime;
reserve z for Complex;

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;
