let s be State of SCM+FSA; :: thesis: for a being Int-Location
for p being the Instructions of SCM+FSA -valued ManySortedSet of NAT
for I being InitHalting keepInt0_1 Program of SCM+FSA
for J being InitHalting Program of SCM+FSA holds (IExec ((I ';' J),p,s)) . a = (IExec (J,p,(IExec (I,p,s)))) . a
let a be Int-Location ; :: thesis: for p being the Instructions of SCM+FSA -valued ManySortedSet of NAT
for I being InitHalting keepInt0_1 Program of SCM+FSA
for J being InitHalting 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 InitHalting keepInt0_1 Program of SCM+FSA
for J being InitHalting Program of SCM+FSA holds (IExec ((I ';' J),p,s)) . a = (IExec (J,p,(IExec (I,p,s)))) . a
let I be InitHalting keepInt0_1 Program of SCM+FSA; :: thesis: for J being InitHalting Program of SCM+FSA holds (IExec ((I ';' J),p,s)) . a = (IExec (J,p,(IExec (I,p,s)))) . a
let J be InitHalting Program of SCM+FSA; :: thesis: (IExec ((I ';' J),p,s)) . a = (IExec (J,p,(IExec (I,p,s)))) . a
( IExec ((I ';' J),p,s) = IncIC ((IExec (J,p,(IExec (I,p,s)))),(card I)) & not a in dom (Start-At (((IC (IExec (J,p,(IExec (I,p,s))))) + (card I)),SCM+FSA)) ) by Th29, SCMFSA6B:9;
hence (IExec ((I ';' J),p,s)) . a = (IExec (J,p,(IExec (I,p,s)))) . a by FUNCT_4:12; :: thesis: verum