let s be State of SCM+FSA ; :: thesis: for I being parahalting Program of SCM+FSA
for a being Int-Location
for k being Element of NAT st not I destroysdestroy a holds
(IExec I,s) . a = (Comput (ProgramPart ((Initialized s) +* (I +* (Start-At 0 ,SCM+FSA )))),((Initialized s) +* (I +* (Start-At 0 ,SCM+FSA ))),k) . a
let I be parahalting Program of SCM+FSA ; :: thesis: for a being Int-Location
for k being Element of NAT st not I destroysdestroy a holds
(IExec I,s) . a = (Comput (ProgramPart ((Initialized s) +* (I +* (Start-At 0 ,SCM+FSA )))),((Initialized s) +* (I +* (Start-At 0 ,SCM+FSA ))),k) . a
let a be Int-Location ; :: thesis: for k being Element of NAT st not I destroysdestroy a holds
(IExec I,s) . a = (Comput (ProgramPart ((Initialized s) +* (I +* (Start-At 0 ,SCM+FSA )))),((Initialized s) +* (I +* (Start-At 0 ,SCM+FSA ))),k) . a
let k be Element of NAT ; :: thesis: ( not I destroysdestroy a implies (IExec I,s) . a = (Comput (ProgramPart ((Initialized s) +* (I +* (Start-At 0 ,SCM+FSA )))),((Initialized s) +* (I +* (Start-At 0 ,SCM+FSA ))),k) . a )
set s0 = Initialized s;
set s1 = (Initialized s) +* (I +* (Start-At 0 ,SCM+FSA ));
A1: I is_closed_on Initialized s by SCMFSA7B:24;
ProgramPart ((Initialized s) +* (I +* (Start-At 0 ,SCM+FSA ))) halts_on (Initialized s) +* (I +* (Start-At 0 ,SCM+FSA )) by FUNCT_4:26, SCMFSA6B:18;
then A2: I is_halting_on Initialized s by SCMFSA7B:def 8;
assume not I destroysdestroy a ; :: thesis: (IExec I,s) . a = (Comput (ProgramPart ((Initialized s) +* (I +* (Start-At 0 ,SCM+FSA )))),((Initialized s) +* (I +* (Start-At 0 ,SCM+FSA ))),k) . a
hence (IExec I,s) . a = (Comput (ProgramPart ((Initialized s) +* (I +* (Start-At 0 ,SCM+FSA )))),((Initialized s) +* (I +* (Start-At 0 ,SCM+FSA ))),k) . a by A1, A2, Th89; :: thesis: verum