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 S in dom p holds
not p is NAT -defined
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 S in dom p holds
not p is NAT -defined
let p be PartState of S; :: thesis: ( IC S in dom p implies not p is NAT -defined )
assume A1: IC S in dom p ; :: thesis: not p is NAT -defined
assume p is NAT -defined ; :: thesis: contradiction
then dom p = dom (ProgramPart p) by RELAT_1:209;
hence contradiction by A1, Th12; :: thesis: verum