:: AMI_1 semantic presentation
definition
let N be
set ;
canceled;func Trivial-AMI N -> strict AMI-Struct of
N means :
Def2:
:: AMI_1:def 2
( the
carrier of
it = {0,1} & the
Instruction-Counter of
it = 0 & the
Instruction-Locations of
it = {1} & the
Instructions of
it = {[0,{} ]} & the
Object-Kind of
it = 0,1
--> {1},
{[0,{} ]} & the
Execution of
it = [0,{} ] .--> (id (product (0,1 --> {1},{[0,{} ]}))) );
existence
ex b1 being strict AMI-Struct of N st
( the carrier of b1 = {0,1} & the Instruction-Counter of b1 = 0 & the Instruction-Locations of b1 = {1} & the Instructions of b1 = {[0,{} ]} & the Object-Kind of b1 = 0,1 --> {1},{[0,{} ]} & the Execution of b1 = [0,{} ] .--> (id (product (0,1 --> {1},{[0,{} ]}))) )
uniqueness
for b1, b2 being strict AMI-Struct of N st the carrier of b1 = {0,1} & the Instruction-Counter of b1 = 0 & the Instruction-Locations of b1 = {1} & the Instructions of b1 = {[0,{} ]} & the Object-Kind of b1 = 0,1 --> {1},{[0,{} ]} & the Execution of b1 = [0,{} ] .--> (id (product (0,1 --> {1},{[0,{} ]}))) & the carrier of b2 = {0,1} & the Instruction-Counter of b2 = 0 & the Instruction-Locations of b2 = {1} & the Instructions of b2 = {[0,{} ]} & the Object-Kind of b2 = 0,1 --> {1},{[0,{} ]} & the Execution of b2 = [0,{} ] .--> (id (product (0,1 --> {1},{[0,{} ]}))) holds
b1 = b2
;
end;
:: deftheorem AMI_1:def 1 :
canceled;
:: deftheorem Def2 defines Trivial-AMI AMI_1:def 2 :
:: deftheorem Def3 defines void AMI_1:def 3 :
:: deftheorem Def4 defines Instruction-Location AMI_1:def 4 :
:: deftheorem defines IC AMI_1:def 5 :
:: deftheorem defines ObjectKind AMI_1:def 6 :
:: deftheorem defines Exec AMI_1:def 7 :
:: deftheorem Def8 defines halting AMI_1:def 8 :
:: deftheorem Def9 defines halting AMI_1:def 9 :
theorem :: AMI_1:1
canceled;
theorem :: AMI_1:2
canceled;
theorem :: AMI_1:3
canceled;
theorem :: AMI_1:4
canceled;
theorem :: AMI_1:5
canceled;
theorem Th6: :: AMI_1:6
:: deftheorem defines halt AMI_1:def 10 :
:: deftheorem Def11 defines IC-Ins-separated AMI_1:def 11 :
:: deftheorem AMI_1:def 12 :
canceled;
:: deftheorem Def13 defines steady-programmed AMI_1:def 13 :
:: deftheorem Def14 defines definite AMI_1:def 14 :
theorem Th7: :: AMI_1:7
theorem :: AMI_1:8
canceled;
theorem Th9: :: AMI_1:9
theorem Th10: :: AMI_1:10
theorem Th11: :: AMI_1:11
:: deftheorem defines IC AMI_1:def 15 :
theorem :: AMI_1:12
canceled;
theorem :: AMI_1:13
canceled;
theorem :: AMI_1:14
theorem :: AMI_1:15
definition
canceled;
end;
:: deftheorem AMI_1:def 16 :
canceled;
theorem :: AMI_1:16
canceled;
theorem :: AMI_1:17
canceled;
theorem :: AMI_1:18
canceled;
theorem :: AMI_1:19
canceled;
theorem :: AMI_1:20
canceled;
theorem :: AMI_1:21
canceled;
theorem :: AMI_1:22
canceled;
theorem :: AMI_1:23
canceled;
theorem :: AMI_1:24
canceled;
theorem :: AMI_1:25
theorem :: AMI_1:26
theorem :: AMI_1:27
theorem :: AMI_1:28
theorem :: AMI_1:29
theorem :: AMI_1:30
theorem :: AMI_1:31
theorem :: AMI_1:32
theorem :: AMI_1:33
theorem :: AMI_1:34
theorem :: AMI_1:35
theorem :: AMI_1:36
theorem :: AMI_1:37
theorem :: AMI_1:38
theorem :: AMI_1:39
theorem :: AMI_1:40
theorem :: AMI_1:41
theorem :: AMI_1:42
theorem :: AMI_1:43
theorem :: AMI_1:44
theorem :: AMI_1:45
theorem :: AMI_1:46
theorem :: AMI_1:47
:: deftheorem defines CurInstr AMI_1:def 17 :
:: deftheorem defines Following AMI_1:def 18 :
:: deftheorem Def19 defines Computation AMI_1:def 19 :
:: deftheorem Def20 defines halting AMI_1:def 20 :
:: deftheorem Def21 defines realistic AMI_1:def 21 :
theorem :: AMI_1:48
theorem :: AMI_1:49
canceled;
theorem :: AMI_1:50
canceled;
theorem Th51: :: AMI_1:51
theorem Th52: :: AMI_1:52
:: deftheorem Def22 defines Result AMI_1:def 22 :
theorem :: AMI_1:53
theorem Th54: :: AMI_1:54
theorem :: AMI_1:55
theorem Th56: :: AMI_1:56
theorem :: AMI_1:57
:: deftheorem defines FinPartSt AMI_1:def 23 :
Lem:
for N being set
for S being AMI-Struct of N
for x being finite Element of sproduct the Object-Kind of S holds x in FinPartSt S
;
:: deftheorem AMI_1:def 24 :
canceled;
:: deftheorem Def25 defines autonomic AMI_1:def 25 :
:: deftheorem Def26 defines halting AMI_1:def 26 :
:: deftheorem Def27 defines programmable AMI_1:def 27 :
theorem Th58: :: AMI_1:58
theorem Th59: :: AMI_1:59
theorem Th60: :: AMI_1:60
theorem Th61: :: AMI_1:61
theorem Th62: :: AMI_1:62
theorem :: AMI_1:63
theorem Th64: :: AMI_1:64
theorem Th65: :: AMI_1:65
theorem Th66: :: AMI_1:66
theorem Th67: :: AMI_1:67
:: deftheorem defines Result AMI_1:def 28 :
:: deftheorem Def29 defines computes AMI_1:def 29 :
theorem Th68: :: AMI_1:68
theorem Th69: :: AMI_1:69
theorem Th70: :: AMI_1:70
:: deftheorem Def30 defines computable AMI_1:def 30 :
theorem Th71: :: AMI_1:71
theorem Th72: :: AMI_1:72
theorem Th73: :: AMI_1:73
:: deftheorem defines Program AMI_1:def 31 :
theorem :: AMI_1:74
theorem :: AMI_1:75
theorem :: AMI_1:76
:: deftheorem Def32 defines standard-ins AMI_1:def 32 :
:: deftheorem defines InsCodes AMI_1:def 33 :
theorem :: AMI_1:77
:: deftheorem Defx defines IL-FinSequence AMI_1:def 34 :
:: deftheorem defines /. AMI_1:def 35 :
:: deftheorem defines IL-Function AMI_1:def 36 :
:: deftheorem defines IL-DecoratedTree AMI_1:def 37 :
:: deftheorem defines . AMI_1:def 38 :