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
for d being program-free PartState of S holds ProgramPart (p +* d) = ProgramPart p
let S be non empty stored-program IC-Ins-separated definite realistic COM-Struct of N; :: thesis: for p being PartState of S
for d being program-free PartState of S holds ProgramPart (p +* d) = ProgramPart p
let p be PartState of S; :: thesis: for d being program-free PartState of S holds ProgramPart (p +* d) = ProgramPart p
let d be program-free PartState of S; :: thesis: ProgramPart (p +* d) = ProgramPart p
thus ProgramPart (p +* d) = (ProgramPart p) +* (d | NAT) by FUNCT_4:75
.= (ProgramPart p) +* {} by Def29
.= ProgramPart p by FUNCT_4:22 ; :: thesis: verum