reserve i,j,k for Element of NAT;
reserve a,b for Element of REAL;
reserve r,s,t for Element of RAT+;
reserve i,j,k for Element of omega;

theorem Th4:
  INT c< RAT
proof
  1,2 are_coprime
  by ORDINAL3:37;
  then
A1: [1,2] in RAT+ by ARYTM_3:33,Lm11;
  not 1 in {0} by TARSKI:def 1;
  then ( not [1,2] in NAT)& not [1,2] in [:{0},NAT:] by ARYTM_3:32,ZFMISC_1:87;
  then not [1,2] in NAT \/ [:{0},NAT:] by XBOOLE_0:def 3;
  then INT <> RAT by A1,Lm4,XBOOLE_0:def 5;
  hence thesis by Lm15;
end;
