let f be FinSeq-Location ; :: thesis: for s being State of SCM+FSA
for P being the Instructions of SCM+FSA -valued ManySortedSet of NAT
for i being parahalting keeping_0 Instruction of SCM+FSA
for j being parahalting Instruction of SCM+FSA holds (IExec ((i ';' j),P,s)) . f = (Exec (j,(Exec (i,(Initialized s))))) . f
let s be State of SCM+FSA; :: thesis: for P being the Instructions of SCM+FSA -valued ManySortedSet of NAT
for i being parahalting keeping_0 Instruction of SCM+FSA
for j being parahalting Instruction of SCM+FSA holds (IExec ((i ';' j),P,s)) . f = (Exec (j,(Exec (i,(Initialized s))))) . f
let P be the Instructions of SCM+FSA -valued ManySortedSet of NAT ; :: thesis: for i being parahalting keeping_0 Instruction of SCM+FSA
for j being parahalting Instruction of SCM+FSA holds (IExec ((i ';' j),P,s)) . f = (Exec (j,(Exec (i,(Initialized s))))) . f
let i be parahalting keeping_0 Instruction of SCM+FSA; :: thesis: for j being parahalting Instruction of SCM+FSA holds (IExec ((i ';' j),P,s)) . f = (Exec (j,(Exec (i,(Initialized s))))) . f
let j be parahalting Instruction of SCM+FSA; :: thesis: (IExec ((i ';' j),P,s)) . f = (Exec (j,(Exec (i,(Initialized s))))) . f
set Mi = Macro i;
A: NPP (IExec ((Macro i),P,s)) = NPP (Exec (i,(Initialized s))) by Th6;
thus (IExec ((i ';' j),P,s)) . f = (IExec (((Macro i) ';' j),P,s)) . f
.= (Exec (j,(IExec ((Macro i),P,s)))) . f by Th8
.= (NPP (Exec (j,(IExec ((Macro i),P,s))))) . f by Lm5
.= (NPP (Exec (j,(Exec (i,(Initialized s)))))) . f by A, AMISTD_2:def 20
.= (Exec (j,(Exec (i,(Initialized s))))) . f by Lm5 ; :: thesis: verum