:: Joining of Decorated Trees
:: by Grzegorz Bancerek
::
:: Received October 8, 1993
:: Copyright (c) 1993 Association of Mizar Users
:: deftheorem defines = TREES_4:def 1 :
theorem Th1: :: TREES_4:1
theorem Th2: :: TREES_4:2
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: :: TREES_4:3
theorem :: TREES_4:4
theorem Th5: :: TREES_4:5
theorem :: TREES_4:6
:: deftheorem Def3 defines -flat_tree TREES_4:def 3 :
theorem :: TREES_4:7
theorem Th8: :: TREES_4:8
theorem Th9: :: TREES_4:9
:: deftheorem Def4 defines -tree TREES_4:def 4 :
:: deftheorem defines -tree TREES_4:def 5 :
:: deftheorem defines -tree TREES_4:def 6 :
theorem Th10: :: TREES_4:10
theorem Th11: :: TREES_4:11
theorem Th12: :: TREES_4:12
theorem :: TREES_4:13
theorem :: TREES_4:14
theorem :: TREES_4:15
theorem :: TREES_4:16
theorem :: TREES_4:17
theorem :: TREES_4:18
theorem :: TREES_4:19
theorem :: TREES_4:20
theorem :: TREES_4:21
theorem :: TREES_4:22
:: deftheorem Def7 defines <- TREES_4:def 7 :
theorem :: TREES_4:23
theorem Th24: :: TREES_4:24
theorem Th25: :: TREES_4:25
theorem :: TREES_4:26
theorem Th27: :: TREES_4:27
theorem Th28: :: TREES_4:28
theorem Th29: :: TREES_4:29
theorem Th30: :: TREES_4:30
theorem :: TREES_4:31
theorem :: TREES_4:32