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,(Initialize s) & J is_closed_on Exec i,(Initialize s) ) ) holds
(IExec (i ';' J),s) . f = (IExec J,(Exec i,(Initialize 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,(Initialize s) & J is_closed_on Exec i,(Initialize s) ) ) holds
(IExec (i ';' J),s) . f = (IExec J,(Exec i,(Initialize 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,(Initialize s) & J is_closed_on Exec i,(Initialize s) ) ) holds
(IExec (i ';' J),s) . f = (IExec J,(Exec i,(Initialize s))) . f
let f be FinSeq-Location ; :: thesis: ( ( J is parahalting or ( J is_halting_on Exec i,(Initialize s) & J is_closed_on Exec i,(Initialize s) ) ) implies (IExec (i ';' J),s) . f = (IExec J,(Exec i,(Initialize s))) . f )
assume A1: ( J is parahalting or ( J is_halting_on Exec i,(Initialize s) & J is_closed_on Exec i,(Initialize s) ) ) ; :: thesis: (IExec (i ';' J),s) . f = (IExec J,(Exec i,(Initialize s))) . f
set Mi = Macro i;
A3: ( J is_halting_on IExec (Macro i),s & J is_closed_on IExec (Macro i),s ) by A1, SCMFSA6C:6, SCMFSA7B:24, SCMFSA7B:25;
thus (IExec (i ';' J),s) . f = (IExec J,(IExec (Macro i),s)) . f by A3, Th9
.= (IExec J,(Exec i,(Initialize s))) . f by SCMFSA6C:6 ; :: thesis: verum