reserve
  a for natural Number,
  k,l,m,n,k1,b,c,i for Nat,
  x,y,z,y1,y2 for object,
  X,Y for set,
  f,g for Function;
reserve p,q,r,s,t for FinSequence;
reserve D for set;

theorem Th18:
  for p being D-valued FinSequence holds p|(Seg a) is FinSequence of D
proof
  let p be D-valued FinSequence;
A1: p|(Seg a) is FinSequence by Th15;
  rng(p|(Seg a)) c= rng p & rng p c= D by RELAT_1:70,def 19;
  hence thesis by A1,Def4,XBOOLE_1:1;
end;
