let s be State of SCMPDS ; :: thesis: for I, J being Program of SCMPDS holds
( I is_closed_on s iff I is_closed_on s +* (Initialized J) )
let I, J be Program of SCMPDS ; :: thesis: ( I is_closed_on s iff I is_closed_on s +* (Initialized J) )
DataPart s = DataPart (s +* (Initialized J)) by Th9;
hence ( I is_closed_on s iff I is_closed_on s +* (Initialized J) ) by Th36; :: thesis: verum