let s be State of SCM+FSA; :: thesis: for P being the Instructions of SCM+FSA -valued ManySortedSet of NAT
for I being parahalting Program of SCM+FSA holds IC (IExec (I,P,s)) = IC (Result ((P +* I),(s +* (Initialized I))))
let P be the Instructions of SCM+FSA -valued ManySortedSet of NAT ; :: thesis: for I being parahalting Program of SCM+FSA holds IC (IExec (I,P,s)) = IC (Result ((P +* I),(s +* (Initialized I))))
let I be parahalting Program of SCM+FSA; :: thesis: IC (IExec (I,P,s)) = IC (Result ((P +* I),(s +* (Initialized I))))
dom (ProgramPart s) = NAT by COMPOS_1:34;
hence IC (IExec (I,P,s)) = IC (Result ((P +* I),(s +* (Initialized I)))) by Lm1, FUNCT_4:12; :: thesis: verum