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 the carrier of S = (dom (NPP s)) \/ (dom (ProgramPart s))
let S be non empty stored-program IC-Ins-separated definite realistic COM-Struct of N; :: thesis: for s being State of S holds the carrier of S = (dom (NPP s)) \/ (dom (ProgramPart s))
let s be State of S; :: thesis: the carrier of S = (dom (NPP s)) \/ (dom (ProgramPart s))
thus the carrier of S = dom s by PARTFUN1:def 4
.= dom ((NPP s) \/ (ProgramPart s)) by Th43
.= (dom (NPP s)) \/ (dom (ProgramPart s)) by RELAT_1:13 ; :: thesis: verum