begin
Lm1:
for A, B, C being set st C c= B holds
A \ C = (A \ B) \/ (A /\ (B \ C))
theorem Th1:
theorem Th2:
theorem
canceled;
theorem Th4:
theorem Th5:
theorem Th6:
theorem Th7:
theorem Th8:
theorem Th9:
theorem Th10:
theorem Th11:
theorem Th12:
theorem Th13:
theorem Th14:
:: deftheorem defines P2M PROB_4:def 1 :
theorem Th15:
:: deftheorem defines M2P PROB_4:def 2 :
Lm2:
for X being set
for A1 being SetSequence of X st A1 is non-descending holds
for n being Element of NAT holds (Partial_Union A1) . n = A1 . n
theorem Th16:
theorem Th17:
theorem
theorem Th19:
theorem
theorem
theorem
:: deftheorem Def3 defines is_complete PROB_4:def 3 :
theorem
:: deftheorem Def4 defines thin PROB_4:def 4 :
theorem Th24:
theorem Th25:
theorem Th26:
:: deftheorem Def5 defines COM PROB_4:def 5 :
theorem Th27:
theorem Th28:
:: deftheorem defines P_COM2M_COM PROB_4:def 6 :
theorem Th29:
:: deftheorem Def7 defines ProbPart PROB_4:def 7 :
theorem
theorem
theorem Th32:
theorem Th33:
theorem Th34:
theorem Th35:
theorem Th36:
theorem
:: deftheorem Def8 defines COM PROB_4:def 8 :
theorem
theorem
theorem Th40:
theorem Th41:
theorem