begin
:: deftheorem Def1 defines are_separated CONNSP_1:def 1 :
theorem
canceled;
theorem Th2:
theorem Th3:
theorem Th4:
theorem Th5:
theorem Th6:
theorem Th7:
theorem Th8:
theorem Th9:
theorem Th10:
:: deftheorem Def2 defines connected CONNSP_1:def 2 :
theorem Th11:
theorem
theorem Th13:
theorem
theorem
:: deftheorem Def3 defines connected CONNSP_1:def 3 :
theorem Th16:
theorem Th17:
theorem Th18:
theorem Th19:
theorem Th20:
theorem Th21:
theorem
theorem
theorem Th24:
theorem
theorem Th26:
theorem Th27:
theorem Th28:
theorem Th29:
:: deftheorem Def4 defines are_joined CONNSP_1:def 4 :
theorem Th30:
theorem Th31:
theorem
theorem Th33:
:: deftheorem Def5 defines is_a_component_of CONNSP_1:def 5 :
theorem Th34:
theorem
theorem Th36:
theorem
theorem
:: deftheorem Def6 defines is_a_component_of CONNSP_1:def 6 :
theorem
:: deftheorem Def7 defines Component_of CONNSP_1:def 7 :
theorem Th40:
theorem Th41:
theorem Th42:
theorem Th43:
theorem
theorem
theorem
begin
theorem Th47:
theorem