let a be Int-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 Program of SCM+FSA
for J being parahalting Program of SCM+FSA holds (IExec ((I ';' J),P,s)) . a = (IExec (J,P,(IExec (I,P,s)))) . a
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 Program of SCM+FSA
for J being parahalting Program of SCM+FSA holds (IExec ((I ';' J),P,s)) . a = (IExec (J,P,(IExec (I,P,s)))) . a
let P be the Instructions of SCM+FSA -valued ManySortedSet of NAT ; :: thesis: for I being parahalting keeping_0 Program of SCM+FSA
for J being parahalting Program of SCM+FSA holds (IExec ((I ';' J),P,s)) . a = (IExec (J,P,(IExec (I,P,s)))) . a
let I be parahalting keeping_0 Program of SCM+FSA; :: thesis: for J being parahalting Program of SCM+FSA holds (IExec ((I ';' J),P,s)) . a = (IExec (J,P,(IExec (I,P,s)))) . a
let J be parahalting Program of SCM+FSA; :: thesis: (IExec ((I ';' J),P,s)) . a = (IExec (J,P,(IExec (I,P,s)))) . a
A1: not a in dom (Start-At (((IC (IExec (J,P,(IExec (I,P,s))))) + (card I)),SCM+FSA)) by SCMFSA6B:9;
IExec ((I ';' J),P,s) = (IExec (J,P,(IExec (I,P,s)))) +* (Start-At (((IC (IExec (J,P,(IExec (I,P,s))))) + (card I)),SCM+FSA)) by SCMFSA6B:44;
hence (IExec ((I ';' J),P,s)) . a = (IExec (J,P,(IExec (I,P,s)))) . a by A1, FUNCT_4:12; :: thesis: verum