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
  rng p c= dom f implies f*p is FinSequence
proof
  assume rng p c= dom f;
  then dom(f*p) = dom p by RELAT_1:27
    .= Seg len p by Def3;
  hence thesis by Def2;
end;
