reserve A,B,C for Ordinal;
reserve a,b,c,d for natural Ordinal;
reserve l,m,n for natural Ordinal;
reserve i,j,k for Element of omega;
reserve x,y,z for Element of RAT+;
reserve i,j,k for natural Ordinal;

theorem Th55:
  x <> {} implies ex z st y = x*'z
proof
  reconsider o = one as Element of RAT+;
  assume x <> {};
  then consider z such that
A1: x*'z = 1 by Th54;
  take z*'y;
  thus y = y*'o by Th53
    .= x*'(z*'y) by A1,Th52;
end;
