reserve x,y for object,
        i,j,k,m,n for Nat;

theorem Th2:
  n in OddNAT iff n is odd
proof
  thus n in OddNAT implies n is odd
  proof
    assume n in OddNAT;
    then ex i be Element of NAT st
    n=2*i+1 by FIB_NUM2:def 4;
    hence thesis;
  end;
  assume n is odd;
  then consider i such that
  A1:n=2*i+1 by ABIAN:9;
  i in NAT by ORDINAL1:def 12;
  hence thesis by A1,FIB_NUM2:def 4;
end;
