begin
:: deftheorem SCMNORM:def 1 :
canceled;
:: deftheorem SCMNORM:def 2 :
canceled;
:: deftheorem defines Stop SCMNORM:def 3 :
theorem
canceled;
theorem
theorem
theorem
canceled;
theorem
canceled;
theorem
canceled;
theorem
canceled;
definition
canceled;canceled;canceled;canceled;canceled;canceled;let N be non
empty with_non-empty_elements set ;
let S be non
empty stored-program halting IC-Ins-separated definite AMI-Struct of
N;
let f be
NAT -defined the
Instructions of
S -valued finite Function;
let s be
State of
S;
assume A1:
f halts_on s
;
func Result f,
s -> State of
S means :
Def10:
ex
k being
Nat st
(
it = Comput f,
s,
k &
CurInstr f,
it = halt S );
uniqueness
for b1, b2 being State of S st ex k being Nat st
( b1 = Comput f,s,k & CurInstr f,b1 = halt S ) & ex k being Nat st
( b2 = Comput f,s,k & CurInstr f,b2 = halt S ) holds
b1 = b2
correctness
existence
ex b1 being State of S ex k being Nat st
( b1 = Comput f,s,k & CurInstr f,b1 = halt S );
end;
:: deftheorem SCMNORM:def 4 :
canceled;
:: deftheorem SCMNORM:def 5 :
canceled;
:: deftheorem SCMNORM:def 6 :
canceled;
:: deftheorem SCMNORM:def 7 :
canceled;
:: deftheorem SCMNORM:def 8 :
canceled;
:: deftheorem SCMNORM:def 9 :
canceled;
:: deftheorem Def10 defines Result SCMNORM:def 10 :
theorem
theorem
theorem
:: deftheorem SCMNORM:def 11 :
canceled;
:: deftheorem SCMNORM:def 12 :
canceled;
:: deftheorem defines IncrIC SCMNORM:def 13 :
theorem
canceled;
theorem
theorem Th13:
theorem
theorem Th15:
theorem
canceled;
theorem Th17:
theorem Th18:
theorem Th19:
theorem
theorem Th21:
theorem Th22:
theorem Th23:
theorem Th24:
theorem
theorem
theorem
theorem
theorem
theorem Th85:
theorem Th87:
theorem Th88:
theorem
theorem Th51:
theorem Th56:
theorem Th57:
theorem
theorem
theorem