:: MSATERM semantic presentation
Lemma22:
for n being set
for p being FinSequence st n in dom p holds
ex k being Element of NAT st
( n = k + 1 & k < len p )
:: deftheorem Def1 defines -Terms MSATERM:def 1 :
:: deftheorem Def2 defines ArgumentSeq MSATERM:def 2 :
theorem Th1: :: MSATERM:1
theorem Th2: :: MSATERM:2
theorem Th3: :: MSATERM:3
theorem Th4: :: MSATERM:4
theorem Th5: :: MSATERM:5
theorem Th6: :: MSATERM:6
theorem Th7: :: MSATERM:7
theorem Th8: :: MSATERM:8
theorem Th9: :: MSATERM:9
theorem Th10: :: MSATERM:10
:: deftheorem Def3 defines -term MSATERM:def 3 :
:: deftheorem Def4 defines -term MSATERM:def 4 :
theorem Th11: :: MSATERM:11
theorem Th12: :: MSATERM:12
theorem Th13: :: MSATERM:13
Lemma78:
for x being set holds not x in x
;
:: deftheorem Def5 defines the_sort_of MSATERM:def 5 :
theorem Th14: :: MSATERM:14
theorem Th15: :: MSATERM:15
theorem Th16: :: MSATERM:16
theorem Th17: :: MSATERM:17
theorem Th18: :: MSATERM:18
theorem Th19: :: MSATERM:19
theorem Th20: :: MSATERM:20
theorem Th21: :: MSATERM:21
Lemma97:
for S being non empty non void ManySortedSign
for V being V5 ManySortedSet of the carrier of S
for o being OperSymbol of S
for a being ArgumentSeq of Sym o,V holds
( len a = len (the_arity_of o) & dom a = dom (the_arity_of o) & ( for i being Nat st i in dom a holds
ex t being Term of S,V st
( t = a . i & t = a /. i & the_sort_of t = (the_arity_of o) . i & the_sort_of t = (the_arity_of o) /. i ) ) )
theorem Th22: :: MSATERM:22
theorem Th23: :: MSATERM:23
theorem Th24: :: MSATERM:24
theorem Th25: :: MSATERM:25
theorem Th26: :: MSATERM:26
theorem Th27: :: MSATERM:27
:: deftheorem Def6 defines CompoundTerm MSATERM:def 6 :
:: deftheorem Def7 defines SetWithCompoundTerm MSATERM:def 7 :
theorem Th28: :: MSATERM:28
Lemma103:
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 )
theorem Th29: :: MSATERM:29
:: deftheorem Def8 defines Variables MSATERM:def 8 :
theorem Th30: :: MSATERM:30
:: deftheorem Def9 defines is_an_evaluation_of MSATERM:def 9 :
theorem Th31: :: MSATERM:31
theorem Th32: :: MSATERM:32
theorem Th33: :: MSATERM:33
theorem Th34: :: MSATERM:34
theorem Th35: :: MSATERM:35
theorem Th36: :: MSATERM:36
theorem Th37: :: MSATERM:37
theorem Th38: :: MSATERM:38
:: deftheorem Def10 defines @ MSATERM:def 10 :
theorem Th39: :: MSATERM:39
theorem Th40: :: MSATERM:40
theorem Th41: :: MSATERM:41
theorem Th42: :: MSATERM:42
theorem Th43: :: MSATERM:43