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)) & J is_closed_on Exec (i,(Initialized s)) ) ) holds
(IExec ((i ';' J),s)) . f = (IExec (J,(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)) & J is_closed_on Exec (i,(Initialized s)) ) ) holds
(IExec ((i ';' J),s)) . f = (IExec (J,(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)) & J is_closed_on Exec (i,(Initialized s)) ) ) holds
(IExec ((i ';' J),s)) . f = (IExec (J,(Exec (i,(Initialized s))))) . f
let f be FinSeq-Location ; :: thesis: ( ( J is parahalting or ( J is_halting_on Exec (i,(Initialized s)) & J is_closed_on Exec (i,(Initialized s)) ) ) implies (IExec ((i ';' J),s)) . f = (IExec (J,(Exec (i,(Initialized s))))) . f )
set Mi = Macro i;
assume A1: ( J is parahalting or ( J is_halting_on Exec (i,(Initialized s)) & J is_closed_on Exec (i,(Initialized s)) ) ) ; :: thesis: (IExec ((i ';' J),s)) . f = (IExec (J,(Exec (i,(Initialized s))))) . f
A2: J is_closed_on IExec ((Macro i),s) by A1, SCMFSA6C:6, SCMFSA7B:24;
J is_halting_on IExec ((Macro i),s) by A1, SCMFSA6C:6, SCMFSA7B:25;
hence (IExec ((i ';' J),s)) . f = (IExec (J,(IExec ((Macro i),s)))) . f by A2, Th9
.= (IExec (J,(Exec (i,(Initialized s))))) . f by SCMFSA6C:6 ;
:: thesis: verum