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
  for x being object holds (<*x*>^p).1 = x
proof let x be object;
  1 in Seg 1;
  then 1 in dom <*x*> by Def8;
  then (<*x*>^p).1 = <*x*>.1 by Def7;
  hence thesis;
end;
