let I be Program of SCM+FSA ; :: thesis: ( I is paraclosed & I is good implies I is keeping_0 )
assume A1: ( I is paraclosed & I is good ) ; :: thesis: I is keeping_0
then A2: I does_not_destroy intloc 0 by Def5;

now

let s be State of SCM+FSA ; :: thesis: ( I +* (Start-At 0 ,SCM+FSA ) c= s implies for k being Element of NAT holds (Comput (ProgramPart s),s,k) . (intloc 0 ) = s . (intloc 0 ) )
assume I +* (Start-At 0 ,SCM+FSA ) c= s ; :: thesis: for k being Element of NAT holds (Comput (ProgramPart s),s,k) . (intloc 0 ) = s . (intloc 0 )
then A3: s +* (I +* (Start-At 0 ,SCM+FSA )) = s by FUNCT_4:79;
let k be Element of NAT ; :: thesis: (Comput (ProgramPart s),s,k) . (intloc 0 ) = s . (intloc 0 )
I is_closed_on s by A1, Th24;
hence (Comput (ProgramPart s),s,k) . (intloc 0 ) = s . (intloc 0 ) by A2, A3, Th27; :: thesis: verum

end;

hence I is keeping_0 by SCMFSA6B:def 4; :: thesis: verum