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;

theorem Th15:
  p|(Seg a) is FinSequence
proof
A0: a is Nat by TARSKI:1;
A1: dom(p|Seg a) = dom p /\ Seg a by RELAT_1:61
    .= Seg len p /\ Seg a by Def3;
  len p <= a or a <= len p;
  then dom(p|Seg a) = Seg len p or dom(p|Seg a) = Seg a by A1,Th5,XBOOLE_1:28;
  hence thesis by A0,Def2;
end;
