begin
theorem Th1:
theorem Th2:
begin
:: deftheorem Def1 defines union HALLMAR1:def 1 :
theorem Th3:
theorem
theorem Th5:
theorem Th6:
theorem Th7:
theorem Th8:
theorem Th9:
theorem Th10:
begin
:: deftheorem Def2 defines Cut HALLMAR1:def 2 :
theorem Th11:
theorem Th12:
theorem Th13:
theorem Th14:
begin
:: deftheorem Def3 defines is_a_system_of_different_representatives_of HALLMAR1:def 3 :
:: deftheorem Def4 defines Hall HALLMAR1:def 4 :
theorem Th15:
theorem Th16:
theorem Th17:
theorem Th18:
begin
:: deftheorem Def5 defines Reduction HALLMAR1:def 5 :
:: deftheorem Def6 defines Reduction HALLMAR1:def 6 :
:: deftheorem Def7 defines Singlification HALLMAR1:def 7 :
theorem Th19:
theorem Th20:
theorem Th21:
theorem Th22:
theorem
theorem Th24:
theorem
theorem Th26:
:: deftheorem Def8 defines Singlification HALLMAR1:def 8 :
theorem Th27:
begin
theorem Th28:
theorem Th29:
theorem Th30:
theorem Th31:
theorem