begin
theorem Th1:
theorem Th2:
theorem Th3:
theorem Th4:
theorem Th5:
theorem Th6:
theorem
theorem
:: deftheorem Def1 defines |^ NAT_3:def 1 :
theorem Th9:
theorem
theorem Th11:
theorem Th12:
theorem Th13:
theorem Th14:
theorem
begin
:: deftheorem Def2 defines * NAT_3:def 2 :
theorem Th16:
:: deftheorem Def3 defines min NAT_3:def 3 :
theorem Th17:
:: deftheorem Def4 defines max NAT_3:def 4 :
theorem Th18:
:: deftheorem Def5 defines Product NAT_3:def 5 :
theorem Th19:
:: deftheorem Def6 defines |^ NAT_3:def 6 :
theorem Th20:
begin
:: deftheorem Def7 defines |-count NAT_3:def 7 :
theorem Th21:
theorem
theorem Th23:
theorem
theorem Th25:
theorem Th26:
theorem Th27:
theorem Th28:
theorem Th29:
theorem Th30:
theorem Th31:
theorem Th32:
begin
:: deftheorem Def8 defines prime_exponents NAT_3:def 8 :
theorem Th33:
theorem Th34:
theorem Th35:
theorem
theorem Th37:
theorem Th38:
theorem Th39:
theorem Th40:
theorem
theorem Th42:
theorem Th43:
theorem Th44:
theorem Th45:
theorem Th46:
theorem
theorem
theorem
theorem
theorem
theorem Th52:
theorem
theorem
begin
:: deftheorem Def9 defines prime_factorization NAT_3:def 9 :
theorem Th55:
theorem Th56:
theorem
theorem Th58:
theorem Th59:
theorem
theorem