let p be the Instructions of SCM+FSA -valued ManySortedSet of NAT ; :: thesis: for s being State of SCM+FSA
for J being Program of SCM+FSA
for i being parahalting good Instruction of SCM+FSA
for f being FinSeq-Location st ( J is parahalting or ( J is_halting_on Exec (i,(Initialized s)),p & J is_closed_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 J being Program of SCM+FSA
for i being parahalting good Instruction of SCM+FSA
for f being FinSeq-Location st ( J is parahalting or ( J is_halting_on Exec (i,(Initialized s)),p & J is_closed_on Exec (i,(Initialized s)),p ) ) holds
(IExec ((i ';' J),p,s)) . f = (IExec (J,p,(Exec (i,(Initialized s))))) . f
let J be Program of SCM+FSA; :: thesis: for i being parahalting good Instruction of SCM+FSA
for f being FinSeq-Location st ( J is parahalting or ( J is_halting_on Exec (i,(Initialized s)),p & J is_closed_on Exec (i,(Initialized s)),p ) ) holds
(IExec ((i ';' J),p,s)) . f = (IExec (J,p,(Exec (i,(Initialized s))))) . f
let i be parahalting good Instruction of SCM+FSA; :: thesis: for f being FinSeq-Location st ( J is parahalting or ( J is_halting_on Exec (i,(Initialized s)),p & J is_closed_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: ( ( J is parahalting or ( J is_halting_on Exec (i,(Initialized s)),p & J is_closed_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:6;
assume ( J is parahalting or ( J is_halting_on Exec (i,(Initialized s)),p & J is_closed_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 & J is_closed_on Exec (i,(Initialized s)),p ) by SCMFSA7B:24, SCMFSA7B:25;
A3: J is_closed_on IExec ((Macro i),p,s),p by A2, A1;
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 A3, Th9
.= (IExec (J,p,(Exec (i,(Initialized s))))) . f by SCMFSA6C:6 ;
:: thesis: verum