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
a is not Instruction-Location of SCM+FSA by SCMFSA_2:84;
then not a in NAT by AMI_1:def 4;
then not a in dom (s | NAT ) by RELAT_1:86;
then A2: (IExec I,s) . a = (Result (s +* (Initialized I))) . a by FUNCT_4:12;
s +* (Initialized I) is halting by Th19, FUNCT_4:26;
then consider n being Element of NAT such that
A3: ( Result (s +* (Initialized I)) = Computation (s +* (Initialized I)),n & CurInstr (Result (s +* (Initialized I))) = halt SCM+FSA ) by AMI_1:def 22;
A4: I +* (Start-At (insloc 0 )) c= s +* (Initialized I) by Th8, FUNCT_4:26;
then A5: for m being Element of NAT st m < n holds
IC (Computation (s +* (Initialized I)),m) in dom I by Def2;
A6: ( not a in dom (Initialized I) & a in dom s ) by SCMFSA6A:48, SCMFSA_2:66;
thus (IExec I,s) . a = (s +* (Initialized I)) . a by A1, A2, A3, A4, A5, SF_MASTR:69
.= s . a by A6, FUNCT_4:12 ; :: thesis: verum