let p be Instruction-Sequence of SCM+FSA; :: 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 a being Int-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)) . a = (IExec (J,p,(Exec (i,(Initialized s))))) . a
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)),p & J is_closed_on Exec (i,(Initialized s)),p ) ) holds
(IExec ((i ";" J),p,s)) . a = (IExec (J,p,(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)),p & J is_closed_on Exec (i,(Initialized s)),p ) ) holds
(IExec ((i ";" J),p,s)) . a = (IExec (J,p,(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)),p & J is_closed_on Exec (i,(Initialized s)),p ) ) holds
(IExec ((i ";" J),p,s)) . a = (IExec (J,p,(Exec (i,(Initialized s))))) . a
let a be Int-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)) . a = (IExec (J,p,(Exec (i,(Initialized s))))) . a )
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 & J is_closed_on Exec (i,(Initialized s)),p ) ) ; :: thesis: (IExec ((i ";" J),p,s)) . a = (IExec (J,p,(Exec (i,(Initialized s))))) . a
then A2: ( J is_halting_on Exec (i,(Initialized s)),p & J is_closed_on Exec (i,(Initialized s)),p ) by SCMFSA7B:18, SCMFSA7B:19;
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)) . a = (IExec (J,p,(IExec ((Macro i),p,s)))) . a by A3, Th7
.= (IExec (J,p,(IExec ((Macro i),p,s)))) . a
.= (IExec (J,p,(Exec (i,(Initialized s))))) . a by A1
.= (IExec (J,p,(Exec (i,(Initialized s))))) . a ;
:: thesis: verum