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;
reserve a, b, c, d, e, f for object;

theorem
 for x, y being object st x in dom <*y*> holds x = 1
proof
  let x, y be object;
  assume x in dom <*y*>;
  then x in Seg 1 by Th38;
  hence thesis by Th2,TARSKI:def 1;
end;
