theorem
  ex i st x = x.i
proof
  x in VAR;
  then consider j such that
A1: x = j and
A2: 5 <= j;
  consider i be Nat such that
A3: j = 5+i by A2,NAT_1:10;
  reconsider i as Element of NAT by ORDINAL1:def 12;
  take i;
  thus thesis by A1,A3;
end;
