let s be State of SCM+FSA; :: thesis: for I being parahalting Program of SCM+FSA st Initialize ((intloc 0) .--> 1) c= s holds
for P being the Instructions of SCM+FSA -valued ManySortedSet of NAT st I c= P holds
P halts_on s
let I be parahalting Program of SCM+FSA; :: thesis: ( Initialize ((intloc 0) .--> 1) c= s implies for P being the Instructions of SCM+FSA -valued ManySortedSet of NAT st I c= P holds
P halts_on s )
B2: Start-At (0,SCM+FSA) c= Initialize ((intloc 0) .--> 1) by FUNCT_4:26;
assume A3: Initialize ((intloc 0) .--> 1) c= s ; :: thesis: for P being the Instructions of SCM+FSA -valued ManySortedSet of NAT st I c= P holds
P halts_on s
let P be the Instructions of SCM+FSA -valued ManySortedSet of NAT ; :: thesis: ( I c= P implies P halts_on s )
assume A4: I c= P ; :: thesis: P halts_on s
A5: Start-At (0,SCM+FSA) c= s by A3, B2, XBOOLE_1:1;
thus P halts_on s by A4, A5, Def3; :: thesis: verum