let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty stored-program IC-Ins-separated definite realistic COM-Struct of N
for p being PartState of S st IC in dom p holds
IC in dom (NPP p)
let S be non empty stored-program IC-Ins-separated definite realistic COM-Struct of N; :: thesis: for p being PartState of S st IC in dom p holds
IC in dom (NPP p)
let p be PartState of S; :: thesis: ( IC in dom p implies IC in dom (NPP p) )
assume IC in dom p ; :: thesis: IC in dom (NPP p)
then A1: dom (NPP p) = {(IC )} \/ (dom (DataPart p)) by Th70;
IC in {(IC )} by TARSKI:def 1;
hence IC in dom (NPP p) by A1, XBOOLE_0:def 3; :: thesis: verum