begin
:: deftheorem Def1 defines Component_of CONNSP_3:def 1 :
theorem Th1:
theorem
theorem Th3:
theorem
theorem Th5:
theorem Th6:
theorem Th7:
theorem Th8:
theorem
theorem
theorem Th11:
theorem Th12:
theorem Th13:
theorem Th14:
theorem Th15:
theorem
theorem
theorem
begin
:: deftheorem Def2 defines a_union_of_components CONNSP_3:def 2 :
theorem Th19:
theorem Th20:
theorem Th21:
theorem
theorem
theorem
theorem
begin
:: deftheorem Def3 defines Down CONNSP_3:def 3 :
:: deftheorem defines Up CONNSP_3:def 4 :
:: deftheorem defines Down CONNSP_3:def 5 :
:: deftheorem defines Up CONNSP_3:def 6 :
:: deftheorem Def7 defines Component_of CONNSP_3:def 7 :
theorem
theorem Th27:
theorem
canceled;
theorem
theorem Th30:
theorem
theorem
theorem
theorem
canceled;
theorem
theorem