let a be Int-Location; :: thesis: for s being State of SCM+FSA
for P being Instruction-Sequence of SCM+FSA
for I being keeping_0 really-closed parahalting Program of SCM+FSA
for J being really-closed 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 Instruction-Sequence of SCM+FSA
for I being keeping_0 really-closed parahalting Program of SCM+FSA
for J being really-closed parahalting Program of SCM+FSA holds (IExec ((I ";" J),P,s)) . a = (IExec (J,P,(IExec (I,P,s)))) . a
let P be Instruction-Sequence of SCM+FSA; :: thesis: for I being keeping_0 really-closed parahalting Program of SCM+FSA
for J being really-closed parahalting Program of SCM+FSA holds (IExec ((I ";" J),P,s)) . a = (IExec (J,P,(IExec (I,P,s)))) . a
let I be keeping_0 really-closed parahalting Program of SCM+FSA; :: thesis: for J being really-closed parahalting Program of SCM+FSA holds (IExec ((I ";" J),P,s)) . a = (IExec (J,P,(IExec (I,P,s)))) . a
let J be really-closed 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 SCMFSA_2:102;
IExec ((I ";" J),P,s) = IncIC ((IExec (J,P,(IExec (I,P,s)))),(card I)) by SCMFSA6B:20;
hence (IExec ((I ";" J),P,s)) . a = (IExec (J,P,(IExec (I,P,s)))) . a by A1, FUNCT_4:11; :: thesis: verum