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: not I destroys 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)
thus (Comput ((ProgramPart s),s,k)) . (intloc 0) = s . (intloc 0) by A2, A3, Th27, A1, Th24; :: thesis: verum

end;

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