let s be State of SCM+FSA; :: thesis: for I being parahalting Program of SCM+FSA
for P being the Instructions of SCM+FSA -valued ManySortedSet of NAT st I c= P & Start-At (0,SCM+FSA) c= s holds
P halts_on s
let I be parahalting Program of SCM+FSA; :: thesis: for P being the Instructions of SCM+FSA -valued ManySortedSet of NAT st I c= P & Start-At (0,SCM+FSA) c= s holds
P halts_on s
let P be the Instructions of SCM+FSA -valued ManySortedSet of NAT ; :: thesis: ( I c= P & Start-At (0,SCM+FSA) c= s implies P halts_on s )
assume A1: I c= P ; :: thesis: ( not Start-At (0,SCM+FSA) c= s or P halts_on s )
assume Start-At (0,SCM+FSA) c= s ; :: thesis: P halts_on s
hence P halts_on s by A1, Def3; :: thesis: verum