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;

theorem Th24:
  for s,t being non zero Nat st s,t are_coprime holds
  dom Euler_factorization s misses dom Euler_factorization t
  proof
    let s,t be non zero Nat;
A1: dom Euler_factorization s = support ppf s by Def1;
A2: dom Euler_factorization t = support ppf t by Def1;
A3: support ppf s = support pfexp s by NAT_3:def 9;
    support ppf t = support pfexp t by NAT_3:def 9;
    hence thesis by A1,A2,A3,NAT_3:44;
  end;
