let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty COM-Struct of N
for p being data-only PartState of S holds NPP p = p
let S be non empty COM-Struct of N; :: thesis: for p being data-only PartState of S holds NPP p = p
let p be data-only PartState of S; :: thesis: NPP p = p
A1: dom p misses NAT by Th40;
dom p c= the carrier of S by RELAT_1:def 18;
then A2: dom p c= the carrier of S \ NAT by A1, XBOOLE_1:86;
thus NPP p = p | ( the carrier of S \ NAT) by Th65
.= p by A2, RELAT_1:97 ; :: thesis: verum