let s be State of SCM+FSA ; :: thesis: for I being InitHalting 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 InitHalting 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 )
assume A1: 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
( I is_halting_on Initialized s & I is_closed_on Initialized s ) by Th59, Th60;
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, SCMFSA8C:89; :: thesis: verum