let s be State of SCM+FSA ; :: thesis: for I being parahalting Program of SCM+FSA
for a being read-write Int-Location st not a in UsedIntLoc I holds
(IExec I,s) . a = s . a
let I be parahalting Program of SCM+FSA ; :: thesis: for a being read-write Int-Location st not a in UsedIntLoc I holds
(IExec I,s) . a = s . a
let a be read-write Int-Location ; :: thesis: ( not a in UsedIntLoc I implies (IExec I,s) . a = s . a )
assume A1: not a in UsedIntLoc I ; :: thesis: (IExec I,s) . a = s . a
ProgramPart (s +* (Initialized I)) halts_on s +* (Initialized I) by Th19, FUNCT_4:26;
then consider n being Element of NAT such that
A2: Result (s +* (Initialized I)) = Comput (ProgramPart (s +* (Initialized I))),(s +* (Initialized I)),n and
CurInstr (ProgramPart (Result (s +* (Initialized I)))),(Result (s +* (Initialized I))) = halt SCM+FSA by AMI_1:def 22;
A3: not a in dom (Initialized I) by SCMFSA6A:48;
a is not Element of NAT by SCMFSA_2:84;
then not a in NAT ;
then not a in dom (s | NAT ) by RELAT_1:86;
then A4: (IExec I,s) . a = (Result (s +* (Initialized I))) . a by FUNCT_4:12;
A5: I +* (Start-At 0 ,SCM+FSA ) c= s +* (Initialized I) by Th8, FUNCT_4:26;
then for m being Element of NAT st m < n holds
IC (Comput (ProgramPart (s +* (Initialized I))),(s +* (Initialized I)),m) in dom I by Def2;
hence (IExec I,s) . a = (s +* (Initialized I)) . a by A1, A4, A2, A5, SF_MASTR:69
.= s . a by A3, FUNCT_4:12 ;
:: thesis: verum