let I be Program of SCM+FSA; :: thesis: ( I is parahalting implies I is InitHalting )
assume Z0: I is parahalting ; :: thesis: I is InitHalting
let s be State of SCM+FSA; :: according to SCM_HALT:def 2 :: 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 )
assume Z1: 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 Z2: I c= P ; :: thesis: P halts_on s
Start-At (0,SCM+FSA) c= Initialize ((intloc 0) .--> 1) by FUNCT_4:26;
then Start-At (0,SCM+FSA) c= s by Z1, XBOOLE_1:1;
hence P halts_on s by Z0, Z2, SCMFSA6B:def 3; :: thesis: verum