let I be Program of SCM+FSA ; :: thesis: for s being State of SCM+FSA st Initialized I c= s holds
I c= s
let s be State of SCM+FSA ; :: thesis: ( Initialized I c= s implies I c= s )
assume A1: Initialized I c= s ; :: thesis: I c= s
A2: Initialized I = I +* (((intloc 0 ) .--> 1) +* (Start-At (insloc 0 ))) by FUNCT_4:15;
dom I misses dom (((intloc 0 ) .--> 1) +* (Start-At (insloc 0 ))) by Th2;
then I +* (((intloc 0 ) .--> 1) +* (Start-At (insloc 0 ))) = I \/ (((intloc 0 ) .--> 1) +* (Start-At (insloc 0 ))) by FUNCT_4:32;
hence I c= s by A1, A2, XBOOLE_1:11; :: thesis: verum