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 Th3:
  for f,g being FinSequence holds
  f^g is X-valued implies f is X-valued & g is X-valued
  proof
    let f,g be FinSequence;
    set h = f^g;
    assume h is X-valued;
    then
A1: rng h c= X by RELAT_1:def 19;
    rng f c= rng h & rng g c= rng h by FINSEQ_1:29,30;
    then rng f c= X & rng g c= X by A1;
    hence thesis by RELAT_1:def 19;
  end;
