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, q being PartState of S st p c= q holds
NPP p c= NPP q
let S be non empty stored-program IC-Ins-separated definite realistic COM-Struct of N; :: thesis: for p, q being PartState of S st p c= q holds
NPP p c= NPP q
let p, q be PartState of S; :: thesis: ( p c= q implies NPP p c= NPP q )
( NPP p = p | ( the carrier of S \ NAT) & NPP q = q | ( the carrier of S \ NAT) ) by Th65;
hence ( p c= q implies NPP p c= NPP q ) by RELAT_1:105; :: thesis: verum