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 NPP p = p | (the carrier of S \ NAT )
let S be non empty stored-program IC-Ins-separated definite realistic COM-Struct of N; :: thesis: for p being PartState of S holds NPP p = p | (the carrier of S \ NAT )
let p be PartState of S; :: thesis: NPP p = p | (the carrier of S \ NAT )
dom p c= the carrier of S by RELAT_1:def 18;
hence NPP p = p | (the carrier of S \ NAT ) by RELAT_1:211; :: thesis: verum