begin
theorem Th1:
theorem Th2:
theorem Th3:
:: deftheorem defines max_diff_index EUCLID_9:def 1 :
theorem
theorem Th5:
theorem Th6:
theorem
:: deftheorem defines @ EUCLID_9:def 2 :
theorem Th8:
theorem Th9:
theorem Th10:
:: deftheorem Def3 defines Intervals EUCLID_9:def 3 :
:: deftheorem defines OpenHypercube EUCLID_9:def 4 :
theorem Th11:
theorem Th12:
theorem Th13:
theorem Th14:
theorem Th15:
theorem Th16:
theorem Th17:
theorem
theorem Th19:
theorem Th20:
theorem Th21:
theorem Th22:
theorem
theorem
deffunc H1( Nat, Point of (Euclid $1)) -> set = { (OpenHypercube $2,(1 / m)) where m is non zero Element of NAT : verum } ;
:: deftheorem defines OpenHypercubes EUCLID_9:def 5 :
theorem Th25:
theorem Th26:
theorem Th27:
theorem