let p be Instruction-Sequence of SCM+FSA; :: thesis: for s being State of SCM+FSA
for i being sequential good Instruction of SCM+FSA
for f being FinSeq-Location
for J being really-closed Program of SCM+FSA st ( J is parahalting or J is_halting_on Exec (i,(Initialized s)),p ) holds
(IExec ((i ";" J),p,s)) . f = (IExec (J,p,(Exec (i,(Initialized s))))) . f
let s be State of SCM+FSA; :: thesis: for i being sequential good Instruction of SCM+FSA
for f being FinSeq-Location
for J being really-closed Program of SCM+FSA st ( J is parahalting or J is_halting_on Exec (i,(Initialized s)),p ) holds
(IExec ((i ";" J),p,s)) . f = (IExec (J,p,(Exec (i,(Initialized s))))) . f
let i be sequential good Instruction of SCM+FSA; :: thesis: for f being FinSeq-Location
for J being really-closed Program of SCM+FSA st ( J is parahalting or J is_halting_on Exec (i,(Initialized s)),p ) holds
(IExec ((i ";" J),p,s)) . f = (IExec (J,p,(Exec (i,(Initialized s))))) . f
let f be FinSeq-Location ; :: thesis: for J being really-closed Program of SCM+FSA st ( J is parahalting or J is_halting_on Exec (i,(Initialized s)),p ) holds
(IExec ((i ";" J),p,s)) . f = (IExec (J,p,(Exec (i,(Initialized s))))) . f
let J be really-closed Program of SCM+FSA; :: thesis: ( ( J is parahalting or J is_halting_on Exec (i,(Initialized s)),p ) implies (IExec ((i ";" J),p,s)) . f = (IExec (J,p,(Exec (i,(Initialized s))))) . f )
set Mi = Macro i;
A1: IExec ((Macro i),p,s) = Exec (i,(Initialized s)) by SCMFSA6C:5;
assume ( J is parahalting or J is_halting_on Exec (i,(Initialized s)),p ) ; :: thesis: (IExec ((i ";" J),p,s)) . f = (IExec (J,p,(Exec (i,(Initialized s))))) . f
then A2: J is_halting_on Exec (i,(Initialized s)),p by SCMFSA7B:19;
J is_halting_on IExec ((Macro i),p,s),p by A2, A1;
hence (IExec ((i ";" J),p,s)) . f = (IExec (J,p,(IExec ((Macro i),p,s)))) . f by Th7
.= (IExec (J,p,(IExec ((Macro i),p,s)))) . f
.= (IExec (J,p,(Exec (i,(Initialized s))))) . f by A1
.= (IExec (J,p,(Exec (i,(Initialized s))))) . f ;
:: thesis: verum