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 s being State of S holds NPP s = s | ((dom s) \ NAT)
let S be non empty stored-program IC-Ins-separated definite realistic COM-Struct of N; :: thesis: for s being State of S holds NPP s = s | ((dom s) \ NAT)
let s be State of S; :: thesis: NPP s = s | ((dom s) \ NAT)
thus NPP s = s | ( the carrier of S \ NAT) by Th65
.= s | ((dom s) \ NAT) by PARTFUN1:def 4 ; :: thesis: verum