let s be State of SCM+FSA; :: thesis: for f being FinSeq-Location

for p being Instruction-Sequence of SCM+FSA

for I being really-closed InitHalting keepInt0_1 Program of SCM+FSA

for J being really-closed InitHalting Program of SCM+FSA holds (IExec ((I ";" J),p,s)) . f = (IExec (J,p,(IExec (I,p,s)))) . f

let f be FinSeq-Location ; :: thesis: for p being Instruction-Sequence of SCM+FSA

for I being really-closed InitHalting keepInt0_1 Program of SCM+FSA

for J being really-closed InitHalting Program of SCM+FSA holds (IExec ((I ";" J),p,s)) . f = (IExec (J,p,(IExec (I,p,s)))) . f

let p be Instruction-Sequence of SCM+FSA; :: thesis: for I being really-closed InitHalting keepInt0_1 Program of SCM+FSA

for J being really-closed InitHalting Program of SCM+FSA holds (IExec ((I ";" J),p,s)) . f = (IExec (J,p,(IExec (I,p,s)))) . f

let I be really-closed InitHalting keepInt0_1 Program of SCM+FSA; :: thesis: for J being really-closed InitHalting Program of SCM+FSA holds (IExec ((I ";" J),p,s)) . f = (IExec (J,p,(IExec (I,p,s)))) . f

let J be really-closed InitHalting Program of SCM+FSA; :: thesis: (IExec ((I ";" J),p,s)) . f = (IExec (J,p,(IExec (I,p,s)))) . f

( IExec ((I ";" J),p,s) = IncIC ((IExec (J,p,(IExec (I,p,s)))),(card I)) & not f in dom (Start-At (((IC (IExec (J,p,(IExec (I,p,s))))) + (card I)),SCM+FSA)) ) by Th17, SCMFSA_2:103;

hence (IExec ((I ";" J),p,s)) . f = (IExec (J,p,(IExec (I,p,s)))) . f by FUNCT_4:11; :: thesis: verum

for p being Instruction-Sequence of SCM+FSA

for I being really-closed InitHalting keepInt0_1 Program of SCM+FSA

for J being really-closed InitHalting Program of SCM+FSA holds (IExec ((I ";" J),p,s)) . f = (IExec (J,p,(IExec (I,p,s)))) . f

let f be FinSeq-Location ; :: thesis: for p being Instruction-Sequence of SCM+FSA

for I being really-closed InitHalting keepInt0_1 Program of SCM+FSA

for J being really-closed InitHalting Program of SCM+FSA holds (IExec ((I ";" J),p,s)) . f = (IExec (J,p,(IExec (I,p,s)))) . f

let p be Instruction-Sequence of SCM+FSA; :: thesis: for I being really-closed InitHalting keepInt0_1 Program of SCM+FSA

for J being really-closed InitHalting Program of SCM+FSA holds (IExec ((I ";" J),p,s)) . f = (IExec (J,p,(IExec (I,p,s)))) . f

let I be really-closed InitHalting keepInt0_1 Program of SCM+FSA; :: thesis: for J being really-closed InitHalting Program of SCM+FSA holds (IExec ((I ";" J),p,s)) . f = (IExec (J,p,(IExec (I,p,s)))) . f

let J be really-closed InitHalting Program of SCM+FSA; :: thesis: (IExec ((I ";" J),p,s)) . f = (IExec (J,p,(IExec (I,p,s)))) . f

( IExec ((I ";" J),p,s) = IncIC ((IExec (J,p,(IExec (I,p,s)))),(card I)) & not f in dom (Start-At (((IC (IExec (J,p,(IExec (I,p,s))))) + (card I)),SCM+FSA)) ) by Th17, SCMFSA_2:103;

hence (IExec ((I ";" J),p,s)) . f = (IExec (J,p,(IExec (I,p,s)))) . f by FUNCT_4:11; :: thesis: verum