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 destroys 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 destroys 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 destroys 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 destroys 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 destroys 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