let p be Instruction-Sequence of SCM+FSA; :: thesis: for s being State of SCM+FSA

for I being really-closed InitHalting Program of SCM+FSA

for a being Int-Location st not I destroys a holds

(IExec (I,p,s)) . a = (Initialized s) . a

let s be State of SCM+FSA; :: thesis: for I being really-closed InitHalting Program of SCM+FSA

for a being Int-Location st not I destroys a holds

(IExec (I,p,s)) . a = (Initialized s) . a

let I be really-closed InitHalting Program of SCM+FSA; :: thesis: for a being Int-Location st not I destroys a holds

(IExec (I,p,s)) . a = (Initialized s) . a

let a be Int-Location; :: thesis: ( not I destroys a implies (IExec (I,p,s)) . a = (Initialized s) . a )

A1: Initialized s = s +* ((Initialize ((intloc 0) .--> 1)) +* (Start-At (0,SCM+FSA)))

.= (Initialized s) +* (Start-At (0,SCM+FSA)) by FUNCT_4:14 ;

assume not I destroys a ; :: thesis: (IExec (I,p,s)) . a = (Initialized s) . a

hence (IExec (I,p,s)) . a = (Comput ((p +* I),(Initialize (Initialized s)),0)) . a by Th43

.= (Initialized s) . a by A1 ;

:: thesis: verum

for I being really-closed InitHalting Program of SCM+FSA

for a being Int-Location st not I destroys a holds

(IExec (I,p,s)) . a = (Initialized s) . a

let s be State of SCM+FSA; :: thesis: for I being really-closed InitHalting Program of SCM+FSA

for a being Int-Location st not I destroys a holds

(IExec (I,p,s)) . a = (Initialized s) . a

let I be really-closed InitHalting Program of SCM+FSA; :: thesis: for a being Int-Location st not I destroys a holds

(IExec (I,p,s)) . a = (Initialized s) . a

let a be Int-Location; :: thesis: ( not I destroys a implies (IExec (I,p,s)) . a = (Initialized s) . a )

A1: Initialized s = s +* ((Initialize ((intloc 0) .--> 1)) +* (Start-At (0,SCM+FSA)))

.= (Initialized s) +* (Start-At (0,SCM+FSA)) by FUNCT_4:14 ;

assume not I destroys a ; :: thesis: (IExec (I,p,s)) . a = (Initialized s) . a

hence (IExec (I,p,s)) . a = (Comput ((p +* I),(Initialize (Initialized s)),0)) . a by Th43

.= (Initialized s) . a by A1 ;

:: thesis: verum