let I be Program of SCM+FSA; :: thesis: ( I is paraclosed implies I is InitClosed )
assume A1: I is paraclosed ; :: thesis: I is InitClosed
let s be State of SCM+FSA; :: according to SCM_HALT:def 1 :: thesis: for P being the Instructions of SCM+FSA -valued ManySortedSet of NAT st I c= P holds
for n being Element of NAT st Initialized I c= s holds
IC (Comput (P,s,n)) in dom I
let P be the Instructions of SCM+FSA -valued ManySortedSet of NAT ; :: thesis: ( I c= P implies for n being Element of NAT st Initialized I c= s holds
IC (Comput (P,s,n)) in dom I )
assume A2: I c= P ; :: thesis: for n being Element of NAT st Initialized I c= s holds
IC (Comput (P,s,n)) in dom I
let n be Element of NAT ; :: thesis: ( Initialized I c= s implies IC (Comput (P,s,n)) in dom I )
assume A3: Initialized I c= s ; :: thesis: IC (Comput (P,s,n)) in dom I
Initialize I c= Initialized I by Th6;
then Initialize I c= s by A3, XBOOLE_1:1;
hence IC (Comput (P,s,n)) in dom I by A1, SCMFSA6B:def 2, A2; :: thesis: verum