let s be State of SCM+FSA; :: thesis: for I, J being Program of SCM+FSA holds
( I is_closed_on Initialized s iff I is_closed_on s +* (Initialized J) )
let I, J be Program of SCM+FSA; :: thesis: ( I is_closed_on Initialized s iff I is_closed_on s +* (Initialized J) )
DataPart (Initialized s) = DataPart (s +* (Initialized J)) by Th5;
hence ( I is_closed_on Initialized s iff I is_closed_on s +* (Initialized J) ) by Th6; :: thesis: verum