begin
:: deftheorem defines Del PENCIL_2:def 1 :
theorem Th1:
theorem Th2:
theorem Th3:
theorem Th4:
theorem Th5:
theorem Th6:
begin
theorem Th7:
:: deftheorem Def2 defines Segre-Coset PENCIL_2:def 2 :
theorem Th8:
:: deftheorem Def3 defines are_joinable PENCIL_2:def 3 :
theorem
theorem Th10:
theorem Th11:
begin
theorem
:: deftheorem Def4 defines isomorphic PENCIL_2:def 4 :
theorem Th13:
theorem Th14:
theorem
theorem Th16:
theorem
theorem Th18:
theorem
theorem Th20:
theorem
theorem Th22:
theorem Th23:
theorem Th24:
theorem