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 holds not IC S in dom (ProgramPart p)
let S be non empty stored-program IC-Ins-separated definite realistic COM-Struct of N; :: thesis: for p being PartState of S holds not IC S in dom (ProgramPart p)
let p be PartState of S; :: thesis: not IC S in dom (ProgramPart p)
assume A1: IC S in dom (ProgramPart p) ; :: thesis: contradiction
dom (ProgramPart p) c= NAT by RELAT_1:87;
then reconsider l = IC S as Element of NAT by A1;
not l in dom (ProgramPart p) by Def21;
hence contradiction by Def21; :: thesis: verum