let P be the Instructions of SCM+FSA -valued ManySortedSet of NAT ; :: thesis: for s being State of SCM+FSA
for I being Program of SCM+FSA holds IExec (I,P,s) = IExec (I,P,(Initialized s))
let s be State of SCM+FSA; :: thesis: for I being Program of SCM+FSA holds IExec (I,P,s) = IExec (I,P,(Initialized s))
set A = NAT ;
set D = Data-Locations SCM+FSA;
let I be Program of SCM+FSA; :: thesis: IExec (I,P,s) = IExec (I,P,(Initialized s))
A1: for x being set st x in NAT holds
s . x = (Initialized s) . x by SCMFSA6C:3;
dom (Initialized s) = ((Data-Locations SCM+FSA) \/ {(IC )}) \/ NAT by COMPOS_1:172;
then A2: NAT c= dom (Initialized s) by XBOOLE_1:7;
dom s = ((Data-Locations SCM+FSA) \/ {(IC )}) \/ NAT by COMPOS_1:172;
then NAT c= dom s by XBOOLE_1:7;
then A3: s | NAT = (Initialized s) | NAT by A2, A1, FUNCT_1:165;
A4: (Initialized s) +* (Initialized I) = s +* (Initialized I) by SCMFSA8A:8;
thus IExec (I,P,s) = (Result ((P +* I),(s +* (Initialized I)))) +* (s | NAT)
.= IExec (I,P,(Initialized s)) by A3, A4 ; :: thesis: verum