begin
:: deftheorem Def1 defines symmetrical FUNCT_8:def 1 :
:: deftheorem Def2 defines with_symmetrical_domain FUNCT_8:def 2 :
:: deftheorem Def3 defines quasi_even FUNCT_8:def 3 :
:: deftheorem Def4 defines even FUNCT_8:def 4 :
:: deftheorem Def5 defines is_even_on FUNCT_8:def 5 :
:: deftheorem Def6 defines quasi_odd FUNCT_8:def 6 :
:: deftheorem Def7 defines odd FUNCT_8:def 7 :
:: deftheorem Def8 defines is_odd_on FUNCT_8:def 8 :
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem Th16:
theorem Th17:
theorem Th18:
theorem Th19:
theorem Th20:
theorem Th21:
theorem Th22:
theorem Th23:
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
begin
:: deftheorem Def9 defines signum FUNCT_8:def 9 :
theorem Th56:
theorem Th57:
theorem Th58:
theorem Th59:
theorem
theorem Th61:
theorem Th62:
theorem Th63:
theorem
theorem Th65:
theorem Th66:
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem Th81:
theorem
theorem Th83:
theorem