reserve X for set;
reserve n,i for Element of NAT;
reserve a,b,c,d,e,r,x0 for Real;
reserve A for non empty closed_interval Subset of REAL;
reserve f,g,h for PartFunc of REAL,REAL n;
reserve E for Element of REAL n;

theorem Th3:
  a <= b & c in ['a,b'] & d in ['a,b'] & ['a,b'] c= X
  implies ['min(c,d),max(c,d)'] c= X
  proof
    assume a <= b & c in ['a,b'] & d in ['a,b'];
    then ['min(c,d),max(c,d)'] c= ['a,b'] by Lm2;
    hence thesis;
  end;
