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 & Initialize I 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 & Initialize I c= s holds
P halts_on s
let P be the Instructions of SCM+FSA -valued ManySortedSet of NAT ; :: thesis: ( I c= P & Initialize I c= s implies P halts_on s )
assume A1: I c= P ; :: thesis: ( not Initialize I c= s or P halts_on s )
A2: ProgramPart (Initialize I) = I by COMPOS_1:144;
assume A3: Initialize I c= s ; :: thesis: P halts_on s
Initialize I is halting by Def3;
hence P halts_on s by A3, A1, EXTPRO_1:def 10, A2; :: thesis: verum