begin
:: deftheorem defines = TREES_4:def 1 :
theorem Th1:
theorem Th2:
Lm2:
for n being Element of NAT
for p being FinSequence st n < len p holds
( n + 1 in dom p & p . (n + 1) in rng p )
:: deftheorem defines root-tree TREES_4:def 2 :
theorem Th3:
theorem
theorem Th5:
theorem
:: deftheorem Def3 defines -flat_tree TREES_4:def 3 :
theorem
theorem Th8:
theorem Th9:
:: deftheorem Def4 defines -tree TREES_4:def 4 :
:: deftheorem defines -tree TREES_4:def 5 :
:: deftheorem defines -tree TREES_4:def 6 :
theorem Th10:
theorem Th11:
theorem Th12:
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
theorem
begin
:: deftheorem Def7 defines <- TREES_4:def 7 :
theorem
begin
theorem Th24:
theorem Th25:
theorem
theorem Th27:
theorem Th28:
theorem Th29:
theorem Th30:
theorem
theorem