let I be Program of SCM+FSA; :: thesis: ( I is really-closed & I is good implies I is keepInt0_1 )
assume A1: ( I is really-closed & I is good ) ; :: thesis: I is keepInt0_1

now :: thesis: for s being State of SCM+FSA st Initialize ((intloc 0) .--> 1) c= s holds
for p being Instruction-Sequence of SCM+FSA st I c= p holds
for k being Nat holds (Comput (p,s,k)) . (intloc 0) = 1

let s be State of SCM+FSA; :: thesis: ( Initialize ((intloc 0) .--> 1) c= s implies for p being Instruction-Sequence of SCM+FSA st I c= p holds
for k being Nat holds (Comput (p,s,k)) . (intloc 0) = 1 )
assume A2: Initialize ((intloc 0) .--> 1) c= s ; :: thesis: for p being Instruction-Sequence of SCM+FSA st I c= p holds
for k being Nat holds (Comput (p,s,k)) . (intloc 0) = 1
let p be Instruction-Sequence of SCM+FSA; :: thesis: ( I c= p implies for k being Nat holds (Comput (p,s,k)) . (intloc 0) = 1 )
assume A3: I c= p ; :: thesis: for k being Nat holds (Comput (p,s,k)) . (intloc 0) = 1
let k be Nat; :: thesis: (Comput (p,s,k)) . (intloc 0) = 1
thus (Comput (p,s,k)) . (intloc 0) = s . (intloc 0) by A1, A2, Th24, A3
.= 1 by A2, SCMFSA_M:30 ; :: thesis: verum

end;

hence I is keepInt0_1 ; :: thesis: verum