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 a being Int-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)) . a = (IExec (J,(Exec (i,(Initialized s))))) . a
let J be Program of SCM+FSA; :: thesis: for i being parahalting good Instruction of SCM+FSA
for a being Int-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)) . a = (IExec (J,(Exec (i,(Initialized s))))) . a
let i be parahalting good Instruction of SCM+FSA; :: thesis: for a being Int-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)) . a = (IExec (J,(Exec (i,(Initialized s))))) . a
let a be Int-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)) . a = (IExec (J,(Exec (i,(Initialized s))))) . a )
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)) . a = (IExec (J,(Exec (i,(Initialized s))))) . a
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)) . a = (IExec (J,(IExec ((Macro i),s)))) . a by A2, Th8
.= (IExec (J,(Exec (i,(Initialized s))))) . a by SCMFSA6C:6 ;
:: thesis: verum