let s be State of SCM+FSA ; :: thesis: for I, J being Program of SCM+FSA
for l being Element of NAT holds
( I is_closed_on s & I is_halting_on s iff ( I is_closed_on s +* (I +* (Start-At l,SCM+FSA )) & I is_halting_on s +* (I +* (Start-At l,SCM+FSA )) ) )
let I, J be Program of SCM+FSA ; :: thesis: for l being Element of NAT holds
( I is_closed_on s & I is_halting_on s iff ( I is_closed_on s +* (I +* (Start-At l,SCM+FSA )) & I is_halting_on s +* (I +* (Start-At l,SCM+FSA )) ) )
let l be Element of NAT ; :: thesis: ( I is_closed_on s & I is_halting_on s iff ( I is_closed_on s +* (I +* (Start-At l,SCM+FSA )) & I is_halting_on s +* (I +* (Start-At l,SCM+FSA )) ) )
DataPart s = DataPart (s +* (I +* (Start-At l,SCM+FSA ))) by SCMFSA8A:11;
hence ( I is_closed_on s & I is_halting_on s iff ( I is_closed_on s +* (I +* (Start-At l,SCM+FSA )) & I is_halting_on s +* (I +* (Start-At l,SCM+FSA )) ) ) by Th8; :: thesis: verum