let p be PartState of SCM+FSA; :: thesis: intloc 0 in dom (Initialized p)
A1: ( dom ((intloc 0) .--> 1) = {(intloc 0)} & dom (Start-At (0,SCM+FSA)) = {(IC )} ) ;
intloc 0 in {(intloc 0)} by TARSKI:def 1;
then A2: intloc 0 in (dom p) \/ {(intloc 0)} by XBOOLE_0:def 3;
Initialized p = Initialize (p +* ((intloc 0) .--> 1)) by FUNCT_4:14;
then dom (Initialized p) = (dom (p +* ((intloc 0) .--> 1))) \/ (dom (Start-At (0,SCM+FSA))) by FUNCT_4:def 1
.= ((dom p) \/ {(intloc 0)}) \/ {(IC )} by A1, FUNCT_4:def 1 ;
hence intloc 0 in dom (Initialized p) by A2, XBOOLE_0:def 3; :: thesis: verum