reserve x,y,z for Real,
  x3,y3 for Real,
  p for Point of TOP-REAL 3;

theorem Th1:
  ex x, y, z st p = <* x, y, z *>
proof
  the carrier of TOP-REAL 3 = REAL 3 by EUCLID:22;
  then p is Element of 3-tuples_on REAL by EUCLID:def 1;
  then p in 3-tuples_on REAL;
  then reconsider p as Tuple of 3,REAL by FINSEQ_2:131;
  ex x,y,z being Element of REAL st p=<*x,y,z*> by FINSEQ_2:103;
  hence thesis;
end;
