let P be Instruction-Sequence of SCM+FSA; :: thesis: for s being State of SCM+FSA
for I, J being Program of SCM+FSA
for l being Element of NAT holds
( I is_closed_on s,P & I is_halting_on s,P iff ( I is_closed_on s +* (Start-At (l,SCM+FSA)),P +* I & I is_halting_on s +* (Start-At (l,SCM+FSA)),P +* I ) )
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,P & I is_halting_on s,P iff ( I is_closed_on s +* (Start-At (l,SCM+FSA)),P +* I & I is_halting_on s +* (Start-At (l,SCM+FSA)),P +* I ) )
let I, J be Program of SCM+FSA; :: thesis: for l being Element of NAT holds
( I is_closed_on s,P & I is_halting_on s,P iff ( I is_closed_on s +* (Start-At (l,SCM+FSA)),P +* I & I is_halting_on s +* (Start-At (l,SCM+FSA)),P +* I ) )
let l be Element of NAT ; :: thesis: ( I is_closed_on s,P & I is_halting_on s,P iff ( I is_closed_on s +* (Start-At (l,SCM+FSA)),P +* I & I is_halting_on s +* (Start-At (l,SCM+FSA)),P +* I ) )
DataPart s = DataPart (s +* (Start-At (l,SCM+FSA))) by MEMSTR_0:79;
hence ( I is_closed_on s,P & I is_halting_on s,P iff ( I is_closed_on s +* (Start-At (l,SCM+FSA)),P +* I & I is_halting_on s +* (Start-At (l,SCM+FSA)),P +* I ) ) by Th8; :: thesis: verum