let p be the Instructions of SCM+FSA -valued ManySortedSet of NAT ; :: thesis: for s being State of SCM+FSA
for I being Program of SCM+FSA st s . (intloc 0) = 1 holds
( I is_closed_on s,p & I is_halting_on s,p iff ( I is_closed_on Initialized s,p & I is_halting_on Initialized s,p ) )
let s be State of SCM+FSA; :: thesis: for I being Program of SCM+FSA st s . (intloc 0) = 1 holds
( I is_closed_on s,p & I is_halting_on s,p iff ( I is_closed_on Initialized s,p & I is_halting_on Initialized s,p ) )
let I be Program of SCM+FSA; :: thesis: ( s . (intloc 0) = 1 implies ( I is_closed_on s,p & I is_halting_on s,p iff ( I is_closed_on Initialized s,p & I is_halting_on Initialized s,p ) ) )
assume s . (intloc 0) = 1 ; :: thesis: ( I is_closed_on s,p & I is_halting_on s,p iff ( I is_closed_on Initialized s,p & I is_halting_on Initialized s,p ) )
then DataPart (Initialized s) = DataPart s by SCMFSA8C:27;
hence ( I is_closed_on s,p & I is_halting_on s,p iff ( I is_closed_on Initialized s,p & I is_halting_on Initialized s,p ) ) by SCMFSA8B:8; :: thesis: verum