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 iff I is_closed_on Initialize s )
let I be Program of SCM+FSA ; :: thesis: ( s . (intloc 0 ) = 1 implies ( I is_closed_on s iff I is_closed_on Initialize s ) )
assume s . (intloc 0 ) = 1 ; :: thesis: ( I is_closed_on s iff I is_closed_on Initialize s )
then DataPart (Initialize s) = DataPart s by SCMFSA8C:27;
hence ( I is_closed_on s iff I is_closed_on Initialize s ) by SCMFSA8B:6; :: thesis: verum