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 Th50:
  x+{} = x
proof
A1: (numerator x)*^1 = numerator x & {}*^(denominator x) = {} by ORDINAL2:35,39
;
A2: (denominator x)*^1 = denominator x & (numerator x)+^{} = numerator x by
ORDINAL2:27,39;
  denominator {} = 1 & numerator {} = {} by Def8,Def9,Lm1;
  hence thesis by A1,A2,Th39;
end;
